TSTP Solution File: SWW470+3 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% 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 : n026.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 6.71s 6.89s
% Output : Proof 6.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.28 % Problem : SWW470+3 : TPTP v8.1.2. Released v5.3.0.
% 0.30/0.29 % Command : do_cvc5 %s %d
% 0.30/0.51 % Computer : n026.cluster.edu
% 0.30/0.51 % Model : x86_64 x86_64
% 0.30/0.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.30/0.51 % Memory : 8042.1875MB
% 0.30/0.51 % OS : Linux 3.10.0-693.el7.x86_64
% 0.30/0.51 % CPULimit : 300
% 0.30/0.51 % WCLimit : 300
% 0.30/0.51 % DateTime : Sun Aug 27 19:40:19 EDT 2023
% 0.30/0.51 % CPUTime :
% 0.62/0.80 %----Proving TF0_NAR, FOF, or CNF
% 6.71/6.89 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.epPxbTRxTq/cvc5---1.0.5_26047.p...
% 6.71/6.89 ------- get file name : TPTP file name is SWW470+3
% 6.71/6.89 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_26047.smt2...
% 6.71/6.89 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 6.71/6.89 % SZS status Theorem for SWW470+3
% 6.71/6.89 % SZS output start Proof for SWW470+3
% 6.71/6.89 (
% 6.71/6.89 (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_2102800559rivs_a tptp.g))) (let ((_let_5 (tptp.hBOOL (tptp.hAPP_f1695230391l_bool _let_4 (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a (tptp.hoare_1916936827iple_a _let_3 tptp.c _let_1)) tptp.bot_bo797238721a_bool))))) (let ((_let_6 (not _let_5))) (let ((_let_7 (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.hAPP_a2036067514e_bool (tptp.hAPP_f762886889e_bool tptp.cOMBK_1458035955bool_a P) Q) P)))) (let ((_let_8 (forall ((P $$unsorted) (Q $$unsorted)) (=> (tptp.is_bool P) (= (tptp.hAPP_state_bool (tptp.hAPP_b2019457360e_bool tptp.cOMBK_bool_state P) Q) P))))) (let ((_let_9 (forall ((P $$unsorted) (Q $$unsorted)) (=> (tptp.is_bool P) (= (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 $$unsorted)) (= (tptp.hAPP_f1805168059t_bool tptp.collect_int Pa) Pa)))) (let ((_let_13 (forall ((X_2 $$unsorted)) (= (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 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int A_13) tptp.bot_bot_fun_int_bool)))))) (let ((_let_18 (forall ((Ga $$unsorted) (Ca $$unsorted) (Q_1 $$unsorted) (Pa $$unsorted)) (=> (forall ((Z_11 $$unsorted) (S_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_a2036067514e_bool Pa Z_11) S_2)) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hoare_2102800559rivs_a Ga) (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a (tptp.hoare_1916936827iple_a (tptp.hAPP_f762886889e_bool tptp.cOMBK_1458035955bool_a (tptp.hAPP_s1806633685e_bool (tptp.hAPP_f817621513e_bool tptp.cOMBC_2027030106e_bool tptp.fequal_state) S_2)) Ca (tptp.hAPP_f762886889e_bool tptp.cOMBK_1458035955bool_a (tptp.hAPP_a2036067514e_bool Q_1 Z_11)))) tptp.bot_bo797238721a_bool))))) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hoare_2102800559rivs_a Ga) (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a (tptp.hoare_1916936827iple_a Pa Ca Q_1)) tptp.bot_bo797238721a_bool))))))) (let ((_let_19 (tptp.is_bool tptp.fFalse))) (let ((_let_20 (= _let_14 _let_15))) (let ((_let_21 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_22 (tptp.hBOOL (tptp.hAPP_int_bool tptp.bot_bot_fun_int_bool _let_21)))) (let ((_let_23 (tptp.hAPP_a2036067514e_bool _let_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_90))) (let ((_let_24 (tptp.hBOOL (tptp.hAPP_state_bool _let_23 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_91)))) (let ((_let_25 (= _let_2 _let_23))) (let ((_let_26 (= tptp.fFalse (tptp.hAPP_int_bool _let_14 _let_21)))) (let ((_let_27 (= tptp.fFalse (tptp.hAPP_state_bool _let_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_91)))) (let ((_let_28 (ASSUME :args (_let_16)))) (let ((_let_29 (forall ((Pa $$unsorted)) (= Pa (tptp.hAPP_f1805168059t_bool tptp.collect_int Pa))))) (let ((_let_30 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_31 (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int _let_21) tptp.bot_bot_fun_int_bool)))) (let ((_let_32 (= _let_31 _let_22))) (let ((_let_33 (not _let_22))) (let ((_let_34 (_let_13))) (let ((_let_35 (ASSUME :args _let_34))) (let ((_let_36 (_let_17))) (let ((_let_37 (ASSUME :args _let_36))) (let ((_let_38 (not _let_24))) (let ((_let_39 (or _let_38 (tptp.hBOOL (tptp.hAPP_f1695230391l_bool _let_4 (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a (tptp.hoare_1916936827iple_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_bo797238721a_bool)))))) (let ((_let_40 (forall ((Z_11 $$unsorted) (S_2 $$unsorted)) (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_f1695230391l_bool (tptp.hoare_2102800559rivs_a tptp.g) (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a (tptp.hoare_1916936827iple_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_bo797238721a_bool))))))) (let ((_let_41 (not _let_39))) (let ((_let_42 (not _let_40))) (let ((_let_43 (or _let_42 _let_5))) (let ((_let_44 (forall ((Ga $$unsorted) (Ca $$unsorted) (Q_1 $$unsorted) (Pa $$unsorted)) (or (not (forall ((Z_11 $$unsorted) (S_2 $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_a2036067514e_bool Pa Z_11) S_2))) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hoare_2102800559rivs_a Ga) (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a (tptp.hoare_1916936827iple_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_bo797238721a_bool)))))) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hoare_2102800559rivs_a Ga) (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a (tptp.hoare_1916936827iple_a Pa Ca Q_1)) tptp.bot_bo797238721a_bool))))))) (let ((_let_45 (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_46 (or))) (let ((_let_47 (_let_42))) (let ((_let_48 (forall ((P $$unsorted) (Q $$unsorted)) (= P (tptp.hAPP_a2036067514e_bool (tptp.hAPP_f762886889e_bool tptp.cOMBK_1458035955bool_a P) Q))))) (let ((_let_49 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_50 (not _let_19))) (let ((_let_51 (or _let_50 _let_26))) (let ((_let_52 (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.is_bool P)) (= P (tptp.hAPP_int_bool (tptp.hAPP_b396694332t_bool tptp.cOMBK_bool_int P) Q)))))) (let ((_let_53 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_54 (ASSUME :args (_let_19)))) (let ((_let_55 (or _let_50 _let_27))) (let ((_let_56 (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.is_bool P)) (= P (tptp.hAPP_state_bool (tptp.hAPP_b2019457360e_bool tptp.cOMBK_bool_state P) Q)))))) (let ((_let_57 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_58 (not _let_27))) (let ((_let_59 (not _let_25))) (let ((_let_60 (not _let_26))) (let ((_let_61 (not _let_20))) (let ((_let_62 (not _let_16))) (let ((_let_63 (ASSUME :args (_let_33)))) (let ((_let_64 (ASSUME :args (_let_20)))) (let ((_let_65 (ASSUME :args (_let_26)))) (let ((_let_66 (ASSUME :args (_let_27)))) (let ((_let_67 (ASSUME :args (_let_25)))) (let ((_let_68 (ASSUME :args (_let_24)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_63 _let_28 _let_64 _let_65 _let_66 _let_67 _let_68) :args (_let_16 _let_20 _let_33 _let_24 _let_26 _let_25 _let_27)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_68)) (CONG (TRANS (CONG (SYMM _let_67) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_91)) :args (APPLY_UF tptp.hAPP_state_bool)) (SYMM _let_66) (SYMM (SYMM _let_65)) (CONG (TRANS (SYMM (SYMM _let_64)) (SYMM _let_28)) (REFL :args (_let_21)) :args (APPLY_UF tptp.hAPP_int_bool))) :args (APPLY_UF tptp.hBOOL)) (FALSE_INTRO _let_63))) :args (_let_33 _let_16 _let_20 _let_26 _let_27 _let_25 _let_24)) :args ((not (and _let_16 _let_20 _let_33 _let_24 _let_26 _let_25 _let_27)) SB_LITERAL))) (CONG (REFL :args (_let_62)) (REFL :args (_let_61)) (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_22))) (REFL :args (_let_38)) (REFL :args (_let_60)) (REFL :args (_let_59)) (REFL :args (_let_58)) :args _let_46)) :args ((or _let_62 _let_22 _let_61 _let_38 _let_60 _let_59 _let_58))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_55)) :args ((or _let_50 _let_27 (not _let_55)))) _let_54 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_57 :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_56))) _let_57 :args (_let_55 false _let_56)) :args (_let_27 false _let_19 false _let_55)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_51)) :args ((or _let_50 _let_26 (not _let_51)))) _let_54 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_53 :args (tptp.fFalse _let_21 QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP_int_bool (tptp.hAPP_b396694332t_bool tptp.cOMBK_bool_int P) Q)))) :args (_let_52))) _let_53 :args (_let_51 false _let_52)) :args (_let_26 false _let_19 false _let_51)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_49 :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_48))) _let_49 :args (_let_25 false _let_48)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_39 0)) (CONG (REFL :args (_let_39)) (MACRO_SR_PRED_INTRO :args ((= (not _let_38) _let_24))) :args _let_46)) :args ((or _let_24 _let_39))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_47)) :args _let_47)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_42) _let_40))) (REFL :args (_let_41)) :args _let_46)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_43)) :args ((or _let_5 _let_42 (not _let_43)))) (ASSUME :args (_let_6)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_45 :args (tptp.g tptp.c _let_1 _let_3 QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP_f1695230391l_bool (tptp.hoare_2102800559rivs_a Ga) (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a (tptp.hoare_1916936827iple_a Pa Ca Q_1)) tptp.bot_bo797238721a_bool))))) :args (_let_44))) _let_45 :args (_let_43 false _let_44)) :args (_let_42 true _let_5 false _let_43)) :args (_let_41 true _let_40)) :args (_let_24 true _let_39)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_32)) :args ((or _let_31 _let_33 (not _let_32)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_37 :args (_let_21 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.hAPP_i2112223885l_bool tptp.member_int A_13)))) :args _let_36)) _let_37 :args ((not _let_31) false _let_17)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_35 :args (_let_21 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.hAPP_i2112223885l_bool tptp.member_int X_2)))) :args _let_34))) _let_35 :args (_let_32 false _let_13)) :args (_let_33 true _let_31 false _let_32)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_30 :args (_let_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.hAPP_f1805168059t_bool tptp.collect_int Pa)))) :args (_let_29))) _let_30 :args (_let_20 false _let_29)) _let_28 :args (false false _let_27 false _let_26 false _let_25 false _let_24 true _let_22 false _let_20 false _let_16)) :args ((forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.big_se1603268663iple_a B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.big_se913005884ig_int B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.big_se275732192ig_nat B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted)) (tptp.is_bool (tptp.finite1428139793iple_a B_1_1))) (forall ((B_1_1 $$unsorted)) (tptp.is_bool (tptp.finite2114894759a_bool B_1_1))) (forall ((B_1_1 $$unsorted)) (tptp.is_bool (tptp.finite1973466193nt_int B_1_1))) (forall ((B_1_1 $$unsorted)) (tptp.is_bool (tptp.finite1321096241t_bool B_1_1))) (forall ((B_1_1 $$unsorted)) (tptp.is_bool (tptp.finite2130160977at_nat B_1_1))) (forall ((B_1_1 $$unsorted)) (tptp.is_bool (tptp.finite1071749497t_bool B_1_1))) (forall ((B_1_1 $$unsorted)) (tptp.is_bool (tptp.finite648855052iple_a B_1_1))) (forall ((B_1_1 $$unsorted)) (tptp.is_bool (tptp.finite1803123436a_bool B_1_1))) (forall ((B_1_1 $$unsorted)) (tptp.is_bool (tptp.finite1704255308nt_int B_1_1))) (forall ((B_1_1 $$unsorted)) (tptp.is_bool (tptp.finite58652534t_bool B_1_1))) (forall ((B_1_1 $$unsorted)) (tptp.is_bool (tptp.finite1860950092at_nat B_1_1))) (forall ((B_1_1 $$unsorted)) (tptp.is_bool (tptp.finite1956789438t_bool B_1_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.finite1753440478iple_a B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.finite1626084323ne_int B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.finite988810631ne_nat B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.finite1033474011iple_a B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.finite1432773856em_int B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.finite795500164em_nat B_1_1 B_2_1))) (tptp.is_bool tptp.bot_bot_bool) _let_19 (tptp.is_bool tptp.fTrue) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.hAPP_state_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_bool B_2_1) (tptp.is_bool (tptp.hAPP_bool_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.hAPP_H1037229737a_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.hAPP_int_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.hAPP_nat_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.hAPP_f1695230391l_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.hAPP_f448129468l_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.hAPP_f54304608l_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.hAPP_f2110825313l_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.hAPP_f215623910l_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.hAPP_f1637334154l_bool B_1_1 B_2_1))) (forall ((Ga $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hoare_2102800559rivs_a Ga) tptp.bot_bo797238721a_bool))) (forall ((Fun1_2 $$unsorted) (Com_2 $$unsorted) (Fun2_2 $$unsorted) (Fun1_1 $$unsorted) (Com_1 $$unsorted) (Fun2_1 $$unsorted)) (= (= (tptp.hoare_1916936827iple_a Fun1_2 Com_2 Fun2_2) (tptp.hoare_1916936827iple_a Fun1_1 Com_1 Fun2_1)) (and (= Fun1_2 Fun1_1) (= Com_2 Com_1) (= Fun2_2 Fun2_1)))) (forall ((Ga $$unsorted) (G_1 $$unsorted) (Ts $$unsorted)) (let ((_let_1 (tptp.hoare_2102800559rivs_a Ga))) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hoare_2102800559rivs_a G_1) Ts)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool _let_1 G_1)) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool _let_1 Ts)))))) (forall ((Ts $$unsorted) (Ga $$unsorted) (T_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a T_2))) (let ((_let_2 (tptp.hoare_2102800559rivs_a Ga))) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool _let_2 (tptp.hAPP_f20753329a_bool _let_1 tptp.bot_bo797238721a_bool))) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool _let_2 Ts)) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool _let_2 (tptp.hAPP_f20753329a_bool _let_1 Ts)))))))) (forall ((Ga $$unsorted) (Pa $$unsorted) (Ca $$unsorted) (Q_1 $$unsorted) (C_5 $$unsorted)) (let ((_let_1 (tptp.hoare_2102800559rivs_a Ga))) (=> (=> (tptp.hBOOL C_5) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool _let_1 (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a (tptp.hoare_1916936827iple_a Pa Ca Q_1)) tptp.bot_bo797238721a_bool)))) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool _let_1 (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a (tptp.hoare_1916936827iple_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_bo797238721a_bool)))))) _let_18 (forall ((Q_1 $$unsorted) (Ga $$unsorted) (Pa $$unsorted) (Ca $$unsorted) (Q_3 $$unsorted)) (let ((_let_1 (tptp.hoare_2102800559rivs_a Ga))) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool _let_1 (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a (tptp.hoare_1916936827iple_a Pa Ca Q_3)) tptp.bot_bo797238721a_bool))) (=> (forall ((Z_11 $$unsorted) (S_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_a2036067514e_bool Q_3 Z_11) S_2)) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_a2036067514e_bool Q_1 Z_11) S_2)))) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool _let_1 (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a (tptp.hoare_1916936827iple_a Pa Ca Q_1)) tptp.bot_bo797238721a_bool))))))) (forall ((Pa $$unsorted) (Ga $$unsorted) (P_2 $$unsorted) (Ca $$unsorted) (Q_1 $$unsorted)) (let ((_let_1 (tptp.hoare_2102800559rivs_a Ga))) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool _let_1 (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a (tptp.hoare_1916936827iple_a P_2 Ca Q_1)) tptp.bot_bo797238721a_bool))) (=> (forall ((Z_11 $$unsorted) (S_2 $$unsorted)) (=> (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_f1695230391l_bool _let_1 (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a (tptp.hoare_1916936827iple_a Pa Ca Q_1)) tptp.bot_bo797238721a_bool))))))) (forall ((Q_1 $$unsorted) (Pa $$unsorted) (Ga $$unsorted) (P_2 $$unsorted) (Ca $$unsorted) (Q_3 $$unsorted)) (let ((_let_1 (tptp.hoare_2102800559rivs_a Ga))) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool _let_1 (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a (tptp.hoare_1916936827iple_a P_2 Ca Q_3)) tptp.bot_bo797238721a_bool))) (=> (forall ((Z_11 $$unsorted) (S_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_a2036067514e_bool Pa Z_11) S_2)) (forall ((S_3 $$unsorted)) (=> (forall ((Z_12 $$unsorted)) (=> (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_f1695230391l_bool _let_1 (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a (tptp.hoare_1916936827iple_a Pa Ca Q_1)) tptp.bot_bo797238721a_bool))))))) (forall ((A_13 $$unsorted) (Ba $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat A_13))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat Ba) A))) (=> (not (= A_13 Ba)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 A)))))) (forall ((A_13 $$unsorted) (Ba $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a A_13))) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool _let_1 (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a Ba) A))) (=> (not (= A_13 Ba)) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool _let_1 A)))))) (forall ((A_13 $$unsorted) (Ba $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_i2112223885l_bool tptp.member_int A_13))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int Ba) A))) (=> (not (= A_13 Ba)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 A)))))) (forall ((Ba $$unsorted) (A_13 $$unsorted) (B $$unsorted)) (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 $$unsorted) (A_13 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a A_13))) (=> (=> (not (tptp.hBOOL (tptp.hAPP_f1695230391l_bool _let_1 B))) (= A_13 Ba)) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool _let_1 (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a Ba) B)))))) (forall ((Ba $$unsorted) (A_13 $$unsorted) (B $$unsorted)) (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 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a A_13) tptp.bot_bo797238721a_bool)))) (forall ((A_13 $$unsorted)) (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 $$unsorted)) (= (tptp.hAPP_f800510211t_bool tptp.collect_nat (tptp.hAPP_n1699378549t_bool tptp.fequal_nat A_13)) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13) tptp.bot_bot_fun_nat_bool))) (forall ((A_13 $$unsorted)) (= (tptp.hAPP_f20753329a_bool tptp.collec351493750iple_a (tptp.hAPP_H426895267a_bool tptp.fequal963300192iple_a A_13)) (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a A_13) tptp.bot_bo797238721a_bool))) (forall ((A_13 $$unsorted)) (= (tptp.hAPP_f1805168059t_bool tptp.collect_int (tptp.hAPP_i1948725293t_bool tptp.fequal_int A_13)) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_13) tptp.bot_bot_fun_int_bool))) (forall ((A_13 $$unsorted)) (= (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 $$unsorted)) (= (tptp.hAPP_f20753329a_bool tptp.collec351493750iple_a (tptp.hAPP_H426895267a_bool (tptp.hAPP_f920293029a_bool tptp.cOMBC_1940896922a_bool tptp.fequal963300192iple_a) A_13)) (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a A_13) tptp.bot_bo797238721a_bool))) (forall ((A_13 $$unsorted)) (= (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 $$unsorted) (A_13 $$unsorted)) (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 $$unsorted) (A_13 $$unsorted)) (let ((_let_1 (tptp.hAPP_f20753329a_bool tptp.collec351493750iple_a (tptp.hAPP_f20753329a_bool (tptp.hAPP_f607497069a_bool tptp.cOMBS_154988028l_bool (tptp.hAPP_f146754017l_bool (tptp.hAPP_f239971723l_bool tptp.cOMBB_1866391387iple_a tptp.fconj) (tptp.hAPP_H426895267a_bool tptp.fequal963300192iple_a A_13))) Pa)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_H1037229737a_bool Pa A_13)))) (and (=> _let_2 (= _let_1 (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a A_13) tptp.bot_bo797238721a_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bo797238721a_bool)))))) (forall ((Pa $$unsorted) (A_13 $$unsorted)) (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 $$unsorted) (A_13 $$unsorted)) (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 $$unsorted) (A_13 $$unsorted)) (let ((_let_1 (tptp.hAPP_f20753329a_bool tptp.collec351493750iple_a (tptp.hAPP_f20753329a_bool (tptp.hAPP_f607497069a_bool tptp.cOMBS_154988028l_bool (tptp.hAPP_f146754017l_bool (tptp.hAPP_f239971723l_bool tptp.cOMBB_1866391387iple_a tptp.fconj) (tptp.hAPP_H426895267a_bool (tptp.hAPP_f920293029a_bool tptp.cOMBC_1940896922a_bool tptp.fequal963300192iple_a) A_13))) Pa)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_H1037229737a_bool Pa A_13)))) (and (=> _let_2 (= _let_1 (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a A_13) tptp.bot_bo797238721a_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bo797238721a_bool)))))) (forall ((Pa $$unsorted) (A_13 $$unsorted)) (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 $$unsorted) (A $$unsorted)) (=> (= A tptp.bot_bo797238721a_bool) (not (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a A_13) A))))) (forall ((A_13 $$unsorted) (A $$unsorted)) (=> (= 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 $$unsorted) (A $$unsorted)) (=> (= 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 $$unsorted)) (= (= (tptp.hAPP_f20753329a_bool tptp.collec351493750iple_a Pa) tptp.bot_bo797238721a_bool) (forall ((X_2 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_H1037229737a_bool Pa X_2)))))) (forall ((Pa $$unsorted)) (= (= (tptp.hAPP_f1805168059t_bool tptp.collect_int Pa) tptp.bot_bot_fun_int_bool) (forall ((X_2 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_int_bool Pa X_2)))))) (forall ((Pa $$unsorted)) (= (= (tptp.hAPP_f800510211t_bool tptp.collect_nat Pa) tptp.bot_bot_fun_nat_bool) (forall ((X_2 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_nat_bool Pa X_2)))))) (forall ((Ca $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a Ca) tptp.bot_bo797238721a_bool)))) (forall ((Ca $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat Ca) tptp.bot_bot_fun_nat_bool)))) (forall ((Ca $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Ca) tptp.bot_bot_fun_int_bool)))) (forall ((Pa $$unsorted)) (= (= tptp.bot_bo797238721a_bool (tptp.hAPP_f20753329a_bool tptp.collec351493750iple_a Pa)) (forall ((X_2 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_H1037229737a_bool Pa X_2)))))) (forall ((Pa $$unsorted)) (= (= tptp.bot_bot_fun_int_bool (tptp.hAPP_f1805168059t_bool tptp.collect_int Pa)) (forall ((X_2 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_int_bool Pa X_2)))))) (forall ((Pa $$unsorted)) (= (= tptp.bot_bot_fun_nat_bool (tptp.hAPP_f800510211t_bool tptp.collect_nat Pa)) (forall ((X_2 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_nat_bool Pa X_2)))))) (forall ((A $$unsorted)) (= (exists ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_2) A))) (not (= A tptp.bot_bo797238721a_bool)))) (forall ((A $$unsorted)) (= (exists ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) A))) (not (= A tptp.bot_bot_fun_nat_bool)))) (forall ((A $$unsorted)) (= (exists ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_2) A))) (not (= A tptp.bot_bot_fun_int_bool)))) (forall ((A $$unsorted)) (= (forall ((X_2 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_2) A)))) (= A tptp.bot_bo797238721a_bool))) (forall ((A $$unsorted)) (= (forall ((X_2 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) A)))) (= A tptp.bot_bot_fun_nat_bool))) (forall ((A $$unsorted)) (= (forall ((X_2 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_2) A)))) (= A tptp.bot_bot_fun_int_bool))) (= tptp.bot_bo797238721a_bool (tptp.hAPP_f20753329a_bool tptp.collec351493750iple_a (tptp.hAPP_b1882817719a_bool tptp.cOMBK_235286536iple_a tptp.fFalse))) _let_16 (= tptp.bot_bot_fun_nat_bool (tptp.hAPP_f800510211t_bool tptp.collect_nat (tptp.hAPP_b1013836512t_bool tptp.cOMBK_bool_nat tptp.fFalse))) (forall ((A_13 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_13) A)) (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13) A) A))) (forall ((A_13 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a A_13) A)) (= (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a A_13) A) A))) (forall ((A_13 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int A_13) A)) (= (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_13) A) A))) (forall ((Ba $$unsorted) (A_13 $$unsorted) (B $$unsorted)) (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 $$unsorted) (A_13 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a A_13))) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool _let_1 B)) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool _let_1 (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a Ba) B)))))) (forall ((Ba $$unsorted) (A_13 $$unsorted) (B $$unsorted)) (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 $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1))) (let ((_let_2 (tptp.hAPP_n215258509l_bool tptp.member_nat X_1))) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_2 A))) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_2 B))) (= (= (tptp.hAPP_f800510211t_bool _let_1 A) (tptp.hAPP_f800510211t_bool _let_1 B)) (= A B))))))) (forall ((B $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a X_1))) (let ((_let_2 (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_1))) (=> (not (tptp.hBOOL (tptp.hAPP_f1695230391l_bool _let_2 A))) (=> (not (tptp.hBOOL (tptp.hAPP_f1695230391l_bool _let_2 B))) (= (= (tptp.hAPP_f20753329a_bool _let_1 A) (tptp.hAPP_f20753329a_bool _let_1 B)) (= A B))))))) (forall ((B $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1))) (let ((_let_2 (tptp.hAPP_i2112223885l_bool tptp.member_int X_1))) (=> (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_2 A))) (=> (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_2 B))) (= (= (tptp.hAPP_f1805168059t_bool _let_1 A) (tptp.hAPP_f1805168059t_bool _let_1 B)) (= A B))))))) (forall ((Y_1 $$unsorted) (A $$unsorted) (X_1 $$unsorted)) (= (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 $$unsorted) (A $$unsorted) (X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_H1037229737a_bool (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a Y_1) A) X_1)) (or (= Y_1 X_1) (tptp.hBOOL (tptp.hAPP_H1037229737a_bool A X_1))))) (forall ((Y_1 $$unsorted) (A $$unsorted) (X_1 $$unsorted)) (= (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 $$unsorted) (Ba $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat A_13))) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat Ba) A))) (or (= A_13 Ba) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 A)))))) (forall ((A_13 $$unsorted) (Ba $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a A_13))) (= (tptp.hBOOL (tptp.hAPP_f1695230391l_bool _let_1 (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a Ba) A))) (or (= A_13 Ba) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool _let_1 A)))))) (forall ((A_13 $$unsorted) (Ba $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_i2112223885l_bool tptp.member_int A_13))) (= (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int Ba) A))) (or (= A_13 Ba) (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 A)))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (A $$unsorted)) (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 $$unsorted) (Y_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a X_1))) (let ((_let_2 (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a Y_1))) (= (tptp.hAPP_f20753329a_bool _let_1 (tptp.hAPP_f20753329a_bool _let_2 A)) (tptp.hAPP_f20753329a_bool _let_2 (tptp.hAPP_f20753329a_bool _let_1 A)))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (A $$unsorted)) (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 $$unsorted) (A $$unsorted)) (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 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a X_1))) (let ((_let_2 (tptp.hAPP_f20753329a_bool _let_1 A))) (= (tptp.hAPP_f20753329a_bool _let_1 _let_2) _let_2)))) (forall ((X_1 $$unsorted) (A $$unsorted)) (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 $$unsorted) (Pa $$unsorted)) (= (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 $$unsorted) (Pa $$unsorted)) (= (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a A_13) (tptp.hAPP_f20753329a_bool tptp.collec351493750iple_a Pa)) (tptp.hAPP_f20753329a_bool tptp.collec351493750iple_a (tptp.hAPP_f20753329a_bool (tptp.hAPP_f607497069a_bool tptp.cOMBS_154988028l_bool (tptp.hAPP_f146754017l_bool (tptp.hAPP_f239971723l_bool tptp.cOMBB_1866391387iple_a tptp.fimplies) (tptp.hAPP_f20753329a_bool (tptp.hAPP_f604201481a_bool tptp.cOMBB_1882975613iple_a tptp.fNot) (tptp.hAPP_H426895267a_bool (tptp.hAPP_f920293029a_bool tptp.cOMBC_1940896922a_bool tptp.fequal963300192iple_a) A_13)))) Pa)))) (forall ((A_13 $$unsorted) (Pa $$unsorted)) (= (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 $$unsorted) (B $$unsorted)) (= (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 $$unsorted) (B $$unsorted)) (= (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a A_13) B) (tptp.hAPP_f20753329a_bool tptp.collec351493750iple_a (tptp.hAPP_f20753329a_bool (tptp.hAPP_f607497069a_bool tptp.cOMBS_154988028l_bool (tptp.hAPP_f146754017l_bool (tptp.hAPP_f239971723l_bool tptp.cOMBB_1866391387iple_a tptp.fdisj) (tptp.hAPP_H426895267a_bool (tptp.hAPP_f920293029a_bool tptp.cOMBC_1940896922a_bool tptp.fequal963300192iple_a) A_13))) (tptp.hAPP_f20753329a_bool (tptp.hAPP_f247708275a_bool tptp.cOMBC_1519416966l_bool tptp.member1797258804iple_a) B))))) (forall ((A_13 $$unsorted) (B $$unsorted)) (= (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 $$unsorted) (B $$unsorted)) (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 $$unsorted) (B $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a A_13) (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a A_13) B)))) (forall ((A_13 $$unsorted) (B $$unsorted)) (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 $$unsorted) (Xa $$unsorted)) (= (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 $$unsorted) (Xa $$unsorted)) (= (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a X_2) Xa) (tptp.hAPP_f20753329a_bool tptp.collec351493750iple_a (tptp.hAPP_f20753329a_bool (tptp.hAPP_f607497069a_bool tptp.cOMBS_154988028l_bool (tptp.hAPP_f146754017l_bool (tptp.hAPP_f239971723l_bool tptp.cOMBB_1866391387iple_a tptp.fdisj) (tptp.hAPP_H426895267a_bool (tptp.hAPP_f920293029a_bool tptp.cOMBC_1940896922a_bool tptp.fequal963300192iple_a) X_2))) (tptp.hAPP_f20753329a_bool (tptp.hAPP_f247708275a_bool tptp.cOMBC_1519416966l_bool tptp.member1797258804iple_a) Xa))))) (forall ((X_2 $$unsorted) (Xa $$unsorted)) (= (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 $$unsorted) (Ba $$unsorted)) (=> (= (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 $$unsorted) (Ba $$unsorted)) (=> (= (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a A_13) tptp.bot_bo797238721a_bool) (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a Ba) tptp.bot_bo797238721a_bool)) (= A_13 Ba))) (forall ((A_13 $$unsorted) (Ba $$unsorted)) (=> (= (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 $$unsorted) (A_13 $$unsorted)) (=> (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 $$unsorted) (A_13 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a Ba) (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a A_13) tptp.bot_bo797238721a_bool))) (= Ba A_13))) (forall ((Ba $$unsorted) (A_13 $$unsorted)) (=> (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 $$unsorted) (Ba $$unsorted) (Ca $$unsorted) (D_1 $$unsorted)) (= (= (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 $$unsorted) (Ba $$unsorted) (Ca $$unsorted) (D_1 $$unsorted)) (= (= (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a A_13) (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a Ba) tptp.bot_bo797238721a_bool)) (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a Ca) (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a D_1) tptp.bot_bo797238721a_bool))) (or (and (= A_13 Ca) (= Ba D_1)) (and (= A_13 D_1) (= Ba Ca))))) (forall ((A_13 $$unsorted) (Ba $$unsorted) (Ca $$unsorted) (D_1 $$unsorted)) (= (= (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 $$unsorted) (A_13 $$unsorted)) (= (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 $$unsorted) (A_13 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a Ba) (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a A_13) tptp.bot_bo797238721a_bool))) (= Ba A_13))) (forall ((Ba $$unsorted) (A_13 $$unsorted)) (= (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 $$unsorted) (A $$unsorted)) (not (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13) A) tptp.bot_bot_fun_nat_bool))) (forall ((A_13 $$unsorted) (A $$unsorted)) (not (= (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a A_13) A) tptp.bot_bo797238721a_bool))) (forall ((A_13 $$unsorted) (A $$unsorted)) (not (= (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_13) A) tptp.bot_bot_fun_int_bool))) (forall ((A_13 $$unsorted) (A $$unsorted)) (not (= tptp.bot_bot_fun_nat_bool (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13) A)))) (forall ((A_13 $$unsorted) (A $$unsorted)) (not (= tptp.bot_bo797238721a_bool (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a A_13) A)))) (forall ((A_13 $$unsorted) (A $$unsorted)) (not (= tptp.bot_bot_fun_int_bool (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_13) A)))) (forall ((X_1 $$unsorted)) (= (tptp.hAPP_f22106695ol_nat tptp.the_elem_nat (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) tptp.bot_bot_fun_nat_bool)) X_1)) (forall ((X_1 $$unsorted)) (= (tptp.hAPP_f1693662087iple_a tptp.the_el1519802624iple_a (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a X_1) tptp.bot_bo797238721a_bool)) X_1)) (forall ((X_1 $$unsorted)) (= (tptp.hAPP_f1594865479ol_int tptp.the_elem_int (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1) tptp.bot_bot_fun_int_bool)) X_1)) (forall ((X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_H1037229737a_bool tptp.bot_bo797238721a_bool X_1)) (tptp.hBOOL tptp.bot_bot_bool))) (forall ((X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_int_bool tptp.bot_bot_fun_int_bool X_1)) (tptp.hBOOL tptp.bot_bot_bool))) (forall ((X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_nat_bool tptp.bot_bot_fun_nat_bool X_1)) (tptp.hBOOL tptp.bot_bot_bool))) (forall ((X_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_H1037229737a_bool tptp.bot_bo797238721a_bool X_2)) (tptp.hBOOL tptp.bot_bot_bool))) (forall ((X_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_int_bool tptp.bot_bot_fun_int_bool X_2)) (tptp.hBOOL tptp.bot_bot_bool))) (forall ((X_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_nat_bool tptp.bot_bot_fun_nat_bool X_2)) (tptp.hBOOL tptp.bot_bot_bool))) (forall ((Ga $$unsorted) (Pa $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hoare_2102800559rivs_a Ga) (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a (tptp.hoare_1916936827iple_a Pa tptp.skip Pa)) tptp.bot_bo797238721a_bool)))) (forall ((D_1 $$unsorted) (R_1 $$unsorted) (Ga $$unsorted) (Pa $$unsorted) (Ca $$unsorted) (Q_1 $$unsorted)) (let ((_let_1 (tptp.hoare_2102800559rivs_a Ga))) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool _let_1 (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a (tptp.hoare_1916936827iple_a Pa Ca Q_1)) tptp.bot_bo797238721a_bool))) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool _let_1 (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a (tptp.hoare_1916936827iple_a Q_1 D_1 R_1)) tptp.bot_bo797238721a_bool))) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool _let_1 (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a (tptp.hoare_1916936827iple_a Pa (tptp.semi Ca D_1) R_1)) tptp.bot_bo797238721a_bool))))))) (forall ((Y_1 $$unsorted)) (not (forall ((Fun1 $$unsorted) (Com $$unsorted) (Fun2 $$unsorted)) (not (= Y_1 (tptp.hoare_1916936827iple_a Fun1 Com Fun2)))))) (forall ((X_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)) (not (forall ((B_35 $$unsorted)) (=> (= 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 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_1) A)) (not (forall ((B_35 $$unsorted)) (=> (= A (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a X_1) B_35)) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_1) B_35))))))) (forall ((X_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A)) (not (forall ((B_35 $$unsorted)) (=> (= 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 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_13) A)) (exists ((B_35 $$unsorted)) (and (= A (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13) B_35)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_13) B_35))))))) (forall ((A_13 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a A_13) A)) (exists ((B_35 $$unsorted)) (and (= A (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a A_13) B_35)) (not (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a A_13) B_35))))))) (forall ((A_13 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int A_13) A)) (exists ((B_35 $$unsorted)) (and (= A (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_13) B_35)) (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int A_13) B_35))))))) (forall ((A $$unsorted)) (=> (forall ((Y_21 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a Y_21) A)))) (= A tptp.bot_bo797238721a_bool))) (forall ((A $$unsorted)) (=> (forall ((Y_21 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat Y_21) A)))) (= A tptp.bot_bot_fun_nat_bool))) (forall ((A $$unsorted)) (=> (forall ((Y_21 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Y_21) A)))) (= A tptp.bot_bot_fun_int_bool))) (forall ((Q_1 $$unsorted) (Ga $$unsorted) (Ca $$unsorted) (Pa $$unsorted)) (=> (forall ((Z_11 $$unsorted) (S_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_a2036067514e_bool Pa Z_11) S_2)) (exists ((P_1 $$unsorted) (Q_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hoare_2102800559rivs_a Ga) (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a (tptp.hoare_1916936827iple_a P_1 Ca Q_2)) tptp.bot_bo797238721a_bool))) (forall ((S_3 $$unsorted)) (=> (forall ((Z_12 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_a2036067514e_bool P_1 Z_12) S_2)) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_a2036067514e_bool Q_2 Z_12) S_3)))) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_a2036067514e_bool Q_1 Z_11) S_3)))))))) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hoare_2102800559rivs_a Ga) (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a (tptp.hoare_1916936827iple_a Pa Ca Q_1)) tptp.bot_bo797238721a_bool))))) (forall ((A $$unsorted)) (= (not (= A tptp.bot_bot_fun_nat_bool)) (exists ((X_2 $$unsorted) (B_35 $$unsorted)) (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 $$unsorted)) (= (not (= A tptp.bot_bo797238721a_bool)) (exists ((X_2 $$unsorted) (B_35 $$unsorted)) (and (= A (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a X_2) B_35)) (not (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_2) B_35))))))) (forall ((A $$unsorted)) (= (not (= A tptp.bot_bot_fun_int_bool)) (exists ((X_2 $$unsorted) (B_35 $$unsorted)) (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 $$unsorted) (Com2_2 $$unsorted)) (not (= (tptp.semi Com1_2 Com2_2) tptp.skip))) (forall ((Com1_2 $$unsorted) (Com2_2 $$unsorted)) (not (= tptp.skip (tptp.semi Com1_2 Com2_2)))) (forall ((X_28 $$unsorted)) (= (tptp.hAPP_f22106695ol_nat tptp.the_elem_nat X_28) (tptp.hAPP_f22106695ol_nat tptp.the_nat (tptp.hAPP_f158894502t_bool (tptp.hAPP_f1777703707t_bool tptp.cOMBB_955900739ol_nat (tptp.hAPP_f103356543l_bool tptp.fequal_fun_nat_bool X_28)) (tptp.hAPP_f1570313510t_bool (tptp.hAPP_f688831301t_bool tptp.cOMBC_178881787t_bool tptp.insert_nat) tptp.bot_bot_fun_nat_bool))))) (forall ((X_28 $$unsorted)) (= (tptp.hAPP_f1693662087iple_a tptp.the_el1519802624iple_a X_28) (tptp.hAPP_f1693662087iple_a tptp.the_Ho830102290iple_a (tptp.hAPP_f1194757675a_bool (tptp.hAPP_f1697223433a_bool tptp.cOMBB_1610959875iple_a (tptp.hAPP_f1767618879l_bool tptp.fequal874423448a_bool X_28)) (tptp.hAPP_f1181346091a_bool (tptp.hAPP_f571476211a_bool tptp.cOMBC_1570214144a_bool tptp.insert956547291iple_a) tptp.bot_bo797238721a_bool))))) (forall ((X_28 $$unsorted)) (= (tptp.hAPP_f1594865479ol_int tptp.the_elem_int X_28) (tptp.hAPP_f1594865479ol_int tptp.the_int (tptp.hAPP_f2119767738t_bool (tptp.hAPP_f423804115t_bool tptp.cOMBB_1418110531ol_int (tptp.hAPP_f284875647l_bool tptp.fequal_fun_int_bool X_28)) (tptp.hAPP_f1048215610t_bool (tptp.hAPP_f472159229t_bool tptp.cOMBC_1683390479t_bool tptp.insert_int) tptp.bot_bot_fun_int_bool))))) (forall ((Com1_1 $$unsorted) (Com2_1 $$unsorted) (Com1 $$unsorted) (Com2 $$unsorted)) (= (= (tptp.semi Com1_1 Com2_1) (tptp.semi Com1 Com2)) (and (= Com1_1 Com1) (= Com2_1 Com2)))) (forall ((F $$unsorted) (A_13 $$unsorted) (Ba $$unsorted)) (= (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 $$unsorted) (A_13 $$unsorted) (Ba $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_H1037229737a_bool (tptp.finite1621280049iple_a F (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a A_13) tptp.bot_bo797238721a_bool)) Ba)) (= A_13 Ba))) (forall ((F $$unsorted) (A_13 $$unsorted) (Ba $$unsorted)) (= (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 $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (=> (tptp.hBOOL (tptp.finite988810631ne_nat F F_1)) (= (tptp.hAPP_f22106695ol_nat F_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) tptp.bot_bot_fun_nat_bool)) X_1))) (forall ((X_1 $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (=> (tptp.hBOOL (tptp.finite1753440478iple_a F F_1)) (= (tptp.hAPP_f1693662087iple_a F_1 (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a X_1) tptp.bot_bo797238721a_bool)) X_1))) (forall ((X_1 $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (=> (tptp.hBOOL (tptp.finite1626084323ne_int F F_1)) (= (tptp.hAPP_f1594865479ol_int F_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1) tptp.bot_bot_fun_int_bool)) X_1))) (forall ((X_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_H1037229737a_bool tptp.bot_bo797238721a_bool X_2)) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_2) tptp.bot_bo797238721a_bool)))) (forall ((X_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_nat_bool tptp.bot_bot_fun_nat_bool X_2)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) tptp.bot_bot_fun_nat_bool)))) _let_13 (forall ((Ga $$unsorted) (Pa $$unsorted) (X_28 $$unsorted) (A_13 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hoare_2102800559rivs_a Ga) (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a (tptp.hoare_1916936827iple_a (tptp.hAPP_f100967412e_bool (tptp.hAPP_f1460451647e_bool tptp.cOMBC_524597097e_bool (tptp.hAPP_f1406200875e_bool (tptp.hAPP_f635443597e_bool tptp.cOMBB_2139825703bool_a tptp.cOMBB_844853809_state) Pa)) (tptp.hAPP_f871651461_state (tptp.hAPP_f851239890_state tptp.cOMBS_777315357_state (tptp.hAPP_v365393659_state (tptp.hAPP_f1542232213_state tptp.cOMBC_1193272608_state tptp.update) X_28)) A_13)) (tptp.ass X_28 A_13) Pa)) tptp.bot_bo797238721a_bool)))) (forall ((F $$unsorted) (A_13 $$unsorted)) (= (tptp.hAPP_f22106695ol_nat (tptp.finite_fold1_nat F) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13) tptp.bot_bot_fun_nat_bool)) A_13)) (forall ((F $$unsorted) (A_13 $$unsorted)) (= (tptp.hAPP_f1693662087iple_a (tptp.finite1465856449iple_a F) (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a A_13) tptp.bot_bo797238721a_bool)) A_13)) (forall ((F $$unsorted) (A_13 $$unsorted)) (= (tptp.hAPP_f1594865479ol_int (tptp.finite_fold1_int F) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_13) tptp.bot_bot_fun_int_bool)) A_13)) (forall ((A_13 $$unsorted) (G $$unsorted) (F $$unsorted)) (=> (= 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 $$unsorted) (G $$unsorted) (F $$unsorted)) (=> (= G (tptp.finite1465856449iple_a F)) (= (tptp.hAPP_f1693662087iple_a G (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a A_13) tptp.bot_bo797238721a_bool)) A_13))) (forall ((A_13 $$unsorted) (G $$unsorted) (F $$unsorted)) (=> (= 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 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.image_48635758_a_nat (tptp.hAPP_n1653940209_a_nat tptp.cOMBK_1028443109iple_a Ca) A))) (let ((_let_2 (= A tptp.bot_bo797238721a_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 $$unsorted) (A $$unsorted)) (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 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.image_533441733iple_a (tptp.hAPP_H2085992369iple_a tptp.cOMBK_2052406350iple_a Ca) A))) (let ((_let_2 (= A tptp.bot_bo797238721a_bool))) (and (=> _let_2 (= _let_1 tptp.bot_bo797238721a_bool)) (=> (not _let_2) (= _let_1 (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a Ca) tptp.bot_bo797238721a_bool))))))) (forall ((Ca $$unsorted) (A $$unsorted)) (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 $$unsorted) (A $$unsorted)) (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 $$unsorted) (A $$unsorted)) (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 $$unsorted) (Ba $$unsorted) (F $$unsorted) (X_1 $$unsorted)) (=> (= Ba (tptp.hAPP_H905846293iple_a F X_1)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_1) A)) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a Ba) (tptp.image_533441733iple_a F A)))))) (forall ((A $$unsorted) (Ba $$unsorted) (F $$unsorted) (X_1 $$unsorted)) (=> (= Ba (tptp.hAPP_n261501868iple_a F X_1)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a Ba) (tptp.image_1865589340iple_a F A)))))) (forall ((A $$unsorted) (Ba $$unsorted) (F $$unsorted) (X_1 $$unsorted)) (=> (= Ba (tptp.hAPP_i240634960iple_a F X_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A)) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a Ba) (tptp.image_1844722432iple_a F A)))))) (forall ((A $$unsorted) (Ba $$unsorted) (F $$unsorted) (X_1 $$unsorted)) (=> (= Ba (tptp.hAPP_H592031934_a_nat F X_1)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_1) A)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat Ba) (tptp.image_48635758_a_nat F A)))))) (forall ((A $$unsorted) (Ba $$unsorted) (F $$unsorted) (X_1 $$unsorted)) (=> (= 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 $$unsorted) (Ba $$unsorted) (F $$unsorted) (X_1 $$unsorted)) (=> (= Ba (tptp.hAPP_H1229305626_a_int F X_1)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_1) A)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Ba) (tptp.image_685909450_a_int F A)))))) (forall ((A $$unsorted) (Ba $$unsorted) (F $$unsorted) (X_1 $$unsorted)) (=> (= 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 $$unsorted) (Ba $$unsorted) (F $$unsorted) (X_1 $$unsorted)) (=> (= 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 $$unsorted) (A $$unsorted)) (= (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 $$unsorted) (A $$unsorted)) (= (tptp.hAPP_f1693662087iple_a (tptp.finite1465856449iple_a F) A) (tptp.hAPP_f1693662087iple_a tptp.the_Ho830102290iple_a (tptp.finite1621280049iple_a F A)))) (forall ((F $$unsorted) (A $$unsorted)) (= (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 $$unsorted) (Fun_1 $$unsorted) (Vname $$unsorted) (Fun $$unsorted)) (=> (and (tptp.is_vname Vname_1) (tptp.is_vname Vname)) (= (= (tptp.ass Vname_1 Fun_1) (tptp.ass Vname Fun)) (and (= Vname_1 Vname) (= Fun_1 Fun))))) (forall ((Ba $$unsorted) (F $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_1) A)) (=> (= Ba (tptp.hAPP_H905846293iple_a F X_1)) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a Ba) (tptp.image_533441733iple_a F A)))))) (forall ((Ba $$unsorted) (F $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)) (=> (= Ba (tptp.hAPP_n261501868iple_a F X_1)) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a Ba) (tptp.image_1865589340iple_a F A)))))) (forall ((Ba $$unsorted) (F $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A)) (=> (= Ba (tptp.hAPP_i240634960iple_a F X_1)) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a Ba) (tptp.image_1844722432iple_a F A)))))) (forall ((Ba $$unsorted) (F $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_1) A)) (=> (= Ba (tptp.hAPP_H592031934_a_nat F X_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat Ba) (tptp.image_48635758_a_nat F A)))))) (forall ((Ba $$unsorted) (F $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (=> (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 $$unsorted) (F $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_1) A)) (=> (= Ba (tptp.hAPP_H1229305626_a_int F X_1)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Ba) (tptp.image_685909450_a_int F A)))))) (forall ((Ba $$unsorted) (F $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (=> (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 $$unsorted) (F $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (=> (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 $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_1) A)) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a (tptp.hAPP_H905846293iple_a F X_1)) (tptp.image_533441733iple_a F A))))) (forall ((F $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a (tptp.hAPP_n261501868iple_a F X_1)) (tptp.image_1865589340iple_a F A))))) (forall ((F $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A)) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a (tptp.hAPP_i240634960iple_a F X_1)) (tptp.image_1844722432iple_a F A))))) (forall ((F $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_1) A)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat (tptp.hAPP_H592031934_a_nat F X_1)) (tptp.image_48635758_a_nat F A))))) (forall ((F $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int (tptp.hAPP_int_int F X_1)) (tptp.image_int_int F A))))) (forall ((F $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_1) A)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int (tptp.hAPP_H1229305626_a_int F X_1)) (tptp.image_685909450_a_int F A))))) (forall ((F $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat (tptp.hAPP_nat_nat F X_1)) (tptp.image_nat_nat F A))))) (forall ((F $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (=> (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 $$unsorted) (F $$unsorted) (A $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a Z_1) (tptp.image_533441733iple_a F A))) (exists ((X_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_2) A)) (= Z_1 (tptp.hAPP_H905846293iple_a F X_2)))))) (forall ((Z_1 $$unsorted) (F $$unsorted) (A $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Z_1) (tptp.image_int_int F A))) (exists ((X_2 $$unsorted)) (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 $$unsorted) (F $$unsorted) (A $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat Z_1) (tptp.image_nat_nat F A))) (exists ((X_2 $$unsorted)) (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 $$unsorted) (F $$unsorted) (A $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Z_1) (tptp.image_nat_int F A))) (exists ((X_2 $$unsorted)) (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 $$unsorted) (G $$unsorted) (A $$unsorted)) (= (tptp.image_nat_int F (tptp.image_int_nat G A)) (tptp.image_int_int (tptp.hAPP_f147134065nt_int (tptp.hAPP_f1673907925nt_int tptp.cOMBB_nat_int_int F) G) A))) (forall ((F $$unsorted) (G $$unsorted) (A $$unsorted)) (= (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 $$unsorted)) (= (tptp.image_int_int tptp.cOMBI_int Y_23) Y_23)) (forall ((Y_23 $$unsorted)) (= (tptp.image_533441733iple_a tptp.cOMBI_1301683934iple_a Y_23) Y_23)) (forall ((Y_23 $$unsorted)) (= (tptp.image_nat_nat tptp.cOMBI_nat Y_23) Y_23)) (forall ((Vname_1 $$unsorted) (Fun_1 $$unsorted) (Com1 $$unsorted) (Com2 $$unsorted)) (not (= (tptp.ass Vname_1 Fun_1) (tptp.semi Com1 Com2)))) (forall ((Com1 $$unsorted) (Com2 $$unsorted) (Vname_1 $$unsorted) (Fun_1 $$unsorted)) (not (= (tptp.semi Com1 Com2) (tptp.ass Vname_1 Fun_1)))) (forall ((Vname $$unsorted) (Fun $$unsorted)) (not (= tptp.skip (tptp.ass Vname Fun)))) (forall ((X_1 $$unsorted) (A $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_1) A)) (tptp.hBOOL (tptp.hAPP_H1037229737a_bool A X_1)))) (forall ((X_1 $$unsorted) (A $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)) (tptp.hBOOL (tptp.hAPP_nat_bool A X_1)))) (forall ((X_1 $$unsorted) (A $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A)) (tptp.hBOOL (tptp.hAPP_int_bool A X_1)))) _let_12 (forall ((Pa $$unsorted)) (= (tptp.hAPP_f20753329a_bool tptp.collec351493750iple_a Pa) Pa)) (forall ((Pa $$unsorted)) (= (tptp.hAPP_f800510211t_bool tptp.collect_nat Pa) Pa)) (forall ((Vname $$unsorted) (Fun $$unsorted)) (not (= (tptp.ass Vname Fun) tptp.skip))) (forall ((F $$unsorted) (A $$unsorted)) (= (= (tptp.image_533441733iple_a F A) tptp.bot_bo797238721a_bool) (= A tptp.bot_bo797238721a_bool))) (forall ((F $$unsorted) (A $$unsorted)) (= (= (tptp.image_int_int F A) tptp.bot_bot_fun_int_bool) (= A tptp.bot_bot_fun_int_bool))) (forall ((F $$unsorted) (A $$unsorted)) (= (= (tptp.image_nat_nat F A) tptp.bot_bot_fun_nat_bool) (= A tptp.bot_bot_fun_nat_bool))) (forall ((F $$unsorted) (A $$unsorted)) (= (= (tptp.image_nat_int F A) tptp.bot_bot_fun_int_bool) (= A tptp.bot_bot_fun_nat_bool))) (forall ((F $$unsorted)) (= (tptp.image_533441733iple_a F tptp.bot_bo797238721a_bool) tptp.bot_bo797238721a_bool)) (forall ((F $$unsorted)) (= (tptp.image_int_int F tptp.bot_bot_fun_int_bool) tptp.bot_bot_fun_int_bool)) (forall ((F $$unsorted)) (= (tptp.image_nat_nat F tptp.bot_bot_fun_nat_bool) tptp.bot_bot_fun_nat_bool)) (forall ((F $$unsorted)) (= (tptp.image_nat_int F tptp.bot_bot_fun_nat_bool) tptp.bot_bot_fun_int_bool)) (forall ((F $$unsorted) (A $$unsorted)) (= (= tptp.bot_bo797238721a_bool (tptp.image_533441733iple_a F A)) (= A tptp.bot_bo797238721a_bool))) (forall ((F $$unsorted) (A $$unsorted)) (= (= tptp.bot_bot_fun_int_bool (tptp.image_int_int F A)) (= A tptp.bot_bot_fun_int_bool))) (forall ((F $$unsorted) (A $$unsorted)) (= (= tptp.bot_bot_fun_nat_bool (tptp.image_nat_nat F A)) (= A tptp.bot_bot_fun_nat_bool))) (forall ((F $$unsorted) (A $$unsorted)) (= (= tptp.bot_bot_fun_int_bool (tptp.image_nat_int F A)) (= A tptp.bot_bot_fun_nat_bool))) (forall ((F $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (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 $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.image_533441733iple_a F A))) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_1) A)) (= (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a (tptp.hAPP_H905846293iple_a F X_1)) _let_1) _let_1)))) (forall ((F $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (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 $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.image_685909450_a_int F A))) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_1) A)) (= (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int (tptp.hAPP_H1229305626_a_int F X_1)) _let_1) _let_1)))) (forall ((F $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (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 $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.image_nat_int F A))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)) (= (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int (tptp.hAPP_nat_int F X_1)) _let_1) _let_1)))) (forall ((F $$unsorted) (A_13 $$unsorted) (B $$unsorted)) (= (tptp.image_48635758_a_nat F (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a A_13) B)) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat (tptp.hAPP_H592031934_a_nat F A_13)) (tptp.image_48635758_a_nat F B)))) (forall ((F $$unsorted) (A_13 $$unsorted) (B $$unsorted)) (= (tptp.image_int_nat F (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_13) B)) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat (tptp.hAPP_int_nat F A_13)) (tptp.image_int_nat F B)))) (forall ((F $$unsorted) (A_13 $$unsorted) (B $$unsorted)) (= (tptp.image_533441733iple_a F (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a A_13) B)) (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a (tptp.hAPP_H905846293iple_a F A_13)) (tptp.image_533441733iple_a F B)))) (forall ((F $$unsorted) (A_13 $$unsorted) (B $$unsorted)) (= (tptp.image_1865589340iple_a F (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13) B)) (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a (tptp.hAPP_n261501868iple_a F A_13)) (tptp.image_1865589340iple_a F B)))) (forall ((F $$unsorted) (A_13 $$unsorted) (B $$unsorted)) (= (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 $$unsorted) (A_13 $$unsorted) (B $$unsorted)) (= (tptp.image_nat_nat F (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13) B)) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat (tptp.hAPP_nat_nat F A_13)) (tptp.image_nat_nat F B)))) (forall ((F $$unsorted) (A_13 $$unsorted) (B $$unsorted)) (= (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 $$unsorted) (A $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_H1037229737a_bool (tptp.finite1621280049iple_a F A) X_1)) (not (= A tptp.bot_bo797238721a_bool)))) (forall ((F $$unsorted) (A $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.finite_fold1Set_int F A) X_1)) (not (= A tptp.bot_bot_fun_int_bool)))) (forall ((F $$unsorted) (A $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.finite_fold1Set_nat F A) X_1)) (not (= A tptp.bot_bot_fun_nat_bool)))) (forall ((F $$unsorted) (X_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_H1037229737a_bool (tptp.finite1621280049iple_a F tptp.bot_bo797238721a_bool) X_1)))) (forall ((F $$unsorted) (X_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.finite_fold1Set_int F tptp.bot_bot_fun_int_bool) X_1)))) (forall ((F $$unsorted) (X_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.finite_fold1Set_nat F tptp.bot_bot_fun_nat_bool) X_1)))) (forall ((Ca $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_1) A)) (= (tptp.image_48635758_a_nat (tptp.hAPP_n1653940209_a_nat tptp.cOMBK_1028443109iple_a Ca) A) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat Ca) tptp.bot_bot_fun_nat_bool)))) (forall ((Ca $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A)) (= (tptp.image_int_nat (tptp.hAPP_nat_fun_int_nat tptp.cOMBK_nat_int Ca) A) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat Ca) tptp.bot_bot_fun_nat_bool)))) (forall ((Ca $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_1) A)) (= (tptp.image_533441733iple_a (tptp.hAPP_H2085992369iple_a tptp.cOMBK_2052406350iple_a Ca) A) (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a Ca) tptp.bot_bo797238721a_bool)))) (forall ((Ca $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A)) (= (tptp.image_int_int (tptp.hAPP_int_fun_int_int tptp.cOMBK_int_int Ca) A) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int Ca) tptp.bot_bot_fun_int_bool)))) (forall ((Ca $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_1) A)) (= (tptp.image_685909450_a_int (tptp.hAPP_i1475897073_a_int tptp.cOMBK_1007576201iple_a Ca) A) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int Ca) tptp.bot_bot_fun_int_bool)))) (forall ((Ca $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)) (= (tptp.image_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.cOMBK_nat_nat Ca) A) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat Ca) tptp.bot_bot_fun_nat_bool)))) (forall ((Ca $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (=> (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 $$unsorted) (F $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a Ba) (tptp.image_533441733iple_a F A))) (not (forall ((X_2 $$unsorted)) (=> (= Ba (tptp.hAPP_H905846293iple_a F X_2)) (not (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_2) A)))))))) (forall ((Ba $$unsorted) (F $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat Ba) (tptp.image_48635758_a_nat F A))) (not (forall ((X_2 $$unsorted)) (=> (= Ba (tptp.hAPP_H592031934_a_nat F X_2)) (not (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_2) A)))))))) (forall ((Ba $$unsorted) (F $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Ba) (tptp.image_685909450_a_int F A))) (not (forall ((X_2 $$unsorted)) (=> (= Ba (tptp.hAPP_H1229305626_a_int F X_2)) (not (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_2) A)))))))) (forall ((Ba $$unsorted) (F $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a Ba) (tptp.image_1865589340iple_a F A))) (not (forall ((X_2 $$unsorted)) (=> (= Ba (tptp.hAPP_n261501868iple_a F X_2)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) A)))))))) (forall ((Ba $$unsorted) (F $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Ba) (tptp.image_int_int F A))) (not (forall ((X_2 $$unsorted)) (=> (= 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 $$unsorted) (F $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a Ba) (tptp.image_1844722432iple_a F A))) (not (forall ((X_2 $$unsorted)) (=> (= Ba (tptp.hAPP_i240634960iple_a F X_2)) (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_2) A)))))))) (forall ((Ba $$unsorted) (F $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat Ba) (tptp.image_nat_nat F A))) (not (forall ((X_2 $$unsorted)) (=> (= 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 $$unsorted) (F $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Ba) (tptp.image_nat_int F A))) (not (forall ((X_2 $$unsorted)) (=> (= 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 $$unsorted)) (= (tptp.hAPP_f1594865479ol_int tptp.the_int (tptp.hAPP_i1948725293t_bool tptp.fequal_int X_1)) X_1)) (forall ((X_1 $$unsorted)) (= (tptp.hAPP_f1693662087iple_a tptp.the_Ho830102290iple_a (tptp.hAPP_H426895267a_bool tptp.fequal963300192iple_a X_1)) X_1)) (forall ((X_1 $$unsorted)) (= (tptp.hAPP_f22106695ol_nat tptp.the_nat (tptp.hAPP_n1699378549t_bool tptp.fequal_nat X_1)) X_1)) (forall ((A_13 $$unsorted)) (= (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 $$unsorted)) (= (tptp.hAPP_f1693662087iple_a tptp.the_Ho830102290iple_a (tptp.hAPP_H426895267a_bool (tptp.hAPP_f920293029a_bool tptp.cOMBC_1940896922a_bool tptp.fequal963300192iple_a) A_13)) A_13)) (forall ((A_13 $$unsorted)) (= (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 $$unsorted) (Y_1 $$unsorted) (Pa $$unsorted)) (let ((_let_1 (tptp.hAPP_f428220345t_bool tptp.cOMBC_int_int_bool tptp.fequal_int))) (let ((_let_2 (tptp.hAPP_f1594865479ol_int tptp.the_int (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f727283836t_bool tptp.cOMBS_int_bool_bool (tptp.hAPP_f2144054103l_bool (tptp.hAPP_f1734373249l_bool tptp.cOMBB_1652995168ol_int tptp.fconj) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f627970963t_bool tptp.cOMBB_bool_bool_int (tptp.hAPP_b589554111l_bool tptp.fimplies Pa)) (tptp.hAPP_i1948725293t_bool _let_1 X_1)))) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f627970963t_bool tptp.cOMBB_bool_bool_int (tptp.hAPP_b589554111l_bool tptp.fimplies (tptp.hAPP_bool_bool tptp.fNot Pa))) (tptp.hAPP_i1948725293t_bool _let_1 Y_1)))))) (let ((_let_3 (tptp.hBOOL Pa))) (and (=> _let_3 (= X_1 _let_2)) (=> (not _let_3) (= Y_1 _let_2))))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (Pa $$unsorted)) (let ((_let_1 (tptp.hAPP_f920293029a_bool tptp.cOMBC_1940896922a_bool tptp.fequal963300192iple_a))) (let ((_let_2 (tptp.hAPP_f1693662087iple_a tptp.the_Ho830102290iple_a (tptp.hAPP_f20753329a_bool (tptp.hAPP_f607497069a_bool tptp.cOMBS_154988028l_bool (tptp.hAPP_f146754017l_bool (tptp.hAPP_f239971723l_bool tptp.cOMBB_1866391387iple_a tptp.fconj) (tptp.hAPP_f20753329a_bool (tptp.hAPP_f604201481a_bool tptp.cOMBB_1882975613iple_a (tptp.hAPP_b589554111l_bool tptp.fimplies Pa)) (tptp.hAPP_H426895267a_bool _let_1 X_1)))) (tptp.hAPP_f20753329a_bool (tptp.hAPP_f604201481a_bool tptp.cOMBB_1882975613iple_a (tptp.hAPP_b589554111l_bool tptp.fimplies (tptp.hAPP_bool_bool tptp.fNot Pa))) (tptp.hAPP_H426895267a_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 $$unsorted) (Y_1 $$unsorted) (Pa $$unsorted)) (let ((_let_1 (tptp.hAPP_f229349961t_bool tptp.cOMBC_nat_nat_bool tptp.fequal_nat))) (let ((_let_2 (tptp.hAPP_f22106695ol_nat tptp.the_nat (tptp.hAPP_f800510211t_bool (tptp.hAPP_f561022312t_bool tptp.cOMBS_nat_bool_bool (tptp.hAPP_f1146629647l_bool (tptp.hAPP_f1080886329l_bool tptp.cOMBB_1015721476ol_nat tptp.fconj) (tptp.hAPP_f800510211t_bool (tptp.hAPP_f894608603t_bool tptp.cOMBB_bool_bool_nat (tptp.hAPP_b589554111l_bool tptp.fimplies Pa)) (tptp.hAPP_n1699378549t_bool _let_1 X_1)))) (tptp.hAPP_f800510211t_bool (tptp.hAPP_f894608603t_bool tptp.cOMBB_bool_bool_nat (tptp.hAPP_b589554111l_bool tptp.fimplies (tptp.hAPP_bool_bool tptp.fNot Pa))) (tptp.hAPP_n1699378549t_bool _let_1 Y_1)))))) (let ((_let_3 (tptp.hBOOL Pa))) (and (=> _let_3 (= X_1 _let_2)) (=> (not _let_3) (= Y_1 _let_2))))))) (forall ((F $$unsorted) (G $$unsorted) (M_3 $$unsorted) (N_3 $$unsorted)) (=> (= M_3 N_3) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_2) N_3)) (= (tptp.hAPP_H905846293iple_a F X_2) (tptp.hAPP_H905846293iple_a G X_2)))) (= (tptp.image_533441733iple_a F M_3) (tptp.image_533441733iple_a G N_3))))) (forall ((F $$unsorted) (G $$unsorted) (M_3 $$unsorted) (N_3 $$unsorted)) (=> (= M_3 N_3) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_2) N_3)) (= (tptp.hAPP_int_int F X_2) (tptp.hAPP_int_int G X_2)))) (= (tptp.image_int_int F M_3) (tptp.image_int_int G N_3))))) (forall ((F $$unsorted) (G $$unsorted) (M_3 $$unsorted) (N_3 $$unsorted)) (=> (= M_3 N_3) (=> (forall ((X_2 $$unsorted)) (=> (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 $$unsorted) (G $$unsorted) (M_3 $$unsorted) (N_3 $$unsorted)) (=> (= M_3 N_3) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) N_3)) (= (tptp.hAPP_nat_int F X_2) (tptp.hAPP_nat_int G X_2)))) (= (tptp.image_nat_int F M_3) (tptp.image_nat_int G N_3))))) (forall ((F $$unsorted) (A_13 $$unsorted) (A $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool (tptp.finite929467206at_nat F) A_13) A) X_1)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_13) A))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.finite_fold1Set_nat F (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13) A)) X_1))))) (forall ((F $$unsorted) (A_13 $$unsorted) (A $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_H1037229737a_bool (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool (tptp.finite90892550iple_a F) A_13) A) X_1)) (=> (not (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a A_13) A))) (tptp.hBOOL (tptp.hAPP_H1037229737a_bool (tptp.finite1621280049iple_a F (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a A_13) A)) X_1))))) (forall ((F $$unsorted) (A_13 $$unsorted) (A $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool (tptp.finite772772422nt_int F) A_13) A) X_1)) (=> (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int A_13) A))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.finite_fold1Set_int F (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_13) A)) X_1))))) (forall ((Pa $$unsorted) (A_13 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_int_bool Pa A_13)) (=> (forall ((X_2 $$unsorted)) (=> (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 $$unsorted) (A_13 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_H1037229737a_bool Pa A_13)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_H1037229737a_bool Pa X_2)) (= X_2 A_13))) (= (tptp.hAPP_f1693662087iple_a tptp.the_Ho830102290iple_a Pa) A_13)))) (forall ((Pa $$unsorted) (A_13 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool Pa A_13)) (=> (forall ((X_2 $$unsorted)) (=> (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 $$unsorted) (A $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (=> (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 $$unsorted) (A $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (=> (tptp.hBOOL (tptp.finite1753440478iple_a F F_1)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A)) (=> (not (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_1) A))) (=> (not (= A tptp.bot_bo797238721a_bool)) (= (tptp.hAPP_f1693662087iple_a F_1 (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a X_1) A)) (tptp.hAPP_H905846293iple_a (tptp.hAPP_H2085992369iple_a F X_1) (tptp.hAPP_f1693662087iple_a F_1 A)))))))) (forall ((X_1 $$unsorted) (A $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (=> (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 $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (=> (tptp.hBOOL (tptp.finite1753440478iple_a F F_1)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A)) (= (tptp.hAPP_f1693662087iple_a F_1 A) (tptp.hAPP_f1693662087iple_a (tptp.finite1465856449iple_a F) A))))) (forall ((A $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (=> (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 $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (=> (tptp.hBOOL (tptp.finite1626084323ne_int F F_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (= (tptp.hAPP_f1594865479ol_int F_1 A) (tptp.hAPP_f1594865479ol_int (tptp.finite_fold1_int F) A))))) (forall ((A $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (=> (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 $$unsorted) (Y_21 $$unsorted)) (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 $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (=> (tptp.hBOOL (tptp.finite1753440478iple_a F F_1)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A)) (=> (not (= A tptp.bot_bo797238721a_bool)) (=> (forall ((X_2 $$unsorted) (Y_21 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a (tptp.hAPP_H905846293iple_a (tptp.hAPP_H2085992369iple_a F X_2) Y_21)) (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a X_2) (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a Y_21) tptp.bot_bo797238721a_bool))))) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a (tptp.hAPP_f1693662087iple_a F_1 A)) A))))))) (forall ((A $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (=> (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 $$unsorted) (Y_21 $$unsorted)) (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 $$unsorted) (Pa $$unsorted)) (=> (or (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a (tptp.hAPP_f20753329a_bool tptp.collec351493750iple_a Pa))) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a (tptp.hAPP_f20753329a_bool tptp.collec351493750iple_a Q_1)))) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a (tptp.hAPP_f20753329a_bool tptp.collec351493750iple_a (tptp.hAPP_f20753329a_bool (tptp.hAPP_f607497069a_bool tptp.cOMBS_154988028l_bool (tptp.hAPP_f146754017l_bool (tptp.hAPP_f239971723l_bool tptp.cOMBB_1866391387iple_a tptp.fconj) Pa)) Q_1)))))) (forall ((Q_1 $$unsorted) (Pa $$unsorted)) (=> (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 $$unsorted) (Pa $$unsorted)) (=> (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_f1695230391l_bool tptp.finite1738664244iple_a tptp.bot_bo797238721a_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 $$unsorted) (A $$unsorted)) (=> (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 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A)) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a A_13) A))))) (forall ((A_13 $$unsorted) (A $$unsorted)) (=> (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 $$unsorted) (F_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a F_1)) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a (tptp.image_533441733iple_a H F_1))))) (forall ((H $$unsorted) (F_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat F_1)) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a (tptp.image_1865589340iple_a H F_1))))) (forall ((H $$unsorted) (F_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int F_1)) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a (tptp.image_1844722432iple_a H F_1))))) (forall ((H $$unsorted) (F_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a F_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.image_48635758_a_nat H F_1))))) (forall ((H $$unsorted) (F_1 $$unsorted)) (=> (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 $$unsorted) (F_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a F_1)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.image_685909450_a_int H F_1))))) (forall ((H $$unsorted) (F_1 $$unsorted)) (=> (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 $$unsorted) (F_1 $$unsorted)) (=> (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 $$unsorted) (Q_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a (tptp.hAPP_f20753329a_bool tptp.collec351493750iple_a (tptp.hAPP_f20753329a_bool (tptp.hAPP_f607497069a_bool tptp.cOMBS_154988028l_bool (tptp.hAPP_f146754017l_bool (tptp.hAPP_f239971723l_bool tptp.cOMBB_1866391387iple_a tptp.fdisj) Pa)) Q_1)))) (and (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a (tptp.hAPP_f20753329a_bool tptp.collec351493750iple_a Pa))) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a (tptp.hAPP_f20753329a_bool tptp.collec351493750iple_a Q_1)))))) (forall ((Pa $$unsorted) (Q_1 $$unsorted)) (= (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 $$unsorted) (Q_1 $$unsorted)) (= (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 $$unsorted) (A $$unsorted)) (= (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 $$unsorted) (A $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a A_13) A))) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A)))) (forall ((A_13 $$unsorted) (A $$unsorted)) (= (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 $$unsorted) (Z_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_H1037229737a_bool (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool (tptp.finite90892550iple_a F) Z_1) tptp.bot_bo797238721a_bool) Z_1))) (forall ((F $$unsorted) (Z_1 $$unsorted)) (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 $$unsorted) (Z_1 $$unsorted)) (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 $$unsorted) (Z_1 $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_H1037229737a_bool (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool (tptp.finite90892550iple_a F) Z_1) tptp.bot_bo797238721a_bool) X_1)) (= X_1 Z_1))) (forall ((F $$unsorted) (Z_1 $$unsorted) (X_1 $$unsorted)) (=> (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 $$unsorted) (Z_1 $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool (tptp.finite929467206at_nat F) Z_1) tptp.bot_bot_fun_nat_bool) X_1)) (= X_1 Z_1))) (forall ((F $$unsorted) (Z_1 $$unsorted) (Y_1 $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (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 $$unsorted) (Z_1 $$unsorted) (Y_1 $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_H1743777351a_bool (tptp.finite90892550iple_a F) Z_1))) (=> (not (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_1) A))) (=> (tptp.hBOOL (tptp.hAPP_H1037229737a_bool (tptp.hAPP_f20753329a_bool _let_1 A) Y_1)) (tptp.hBOOL (tptp.hAPP_H1037229737a_bool (tptp.hAPP_f20753329a_bool _let_1 (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a X_1) A)) (tptp.hAPP_H905846293iple_a (tptp.hAPP_H2085992369iple_a F X_1) Y_1))))))) (forall ((F $$unsorted) (Z_1 $$unsorted) (Y_1 $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (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 $$unsorted) (A_13 $$unsorted) (X_28 $$unsorted) (X_1 $$unsorted)) (=> (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 $$unsorted) (A_43 $$unsorted)) (=> (= (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 $$unsorted) (A_13 $$unsorted) (X_28 $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_H1037229737a_bool (tptp.finite1621280049iple_a F (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a A_13) X_28)) X_1)) (not (forall ((A_12 $$unsorted) (A_43 $$unsorted)) (=> (= (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a A_13) X_28) (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a A_12) A_43)) (=> (tptp.hBOOL (tptp.hAPP_H1037229737a_bool (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool (tptp.finite90892550iple_a F) A_12) A_43) X_1)) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a A_12) A_43)))))))) (forall ((F $$unsorted) (A_13 $$unsorted) (X_28 $$unsorted) (X_1 $$unsorted)) (=> (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 $$unsorted) (A_43 $$unsorted)) (=> (= (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 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A)) (=> (not (= A tptp.bot_bo797238721a_bool)) (exists ((X1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_H1037229737a_bool (tptp.finite1621280049iple_a F A) X1)))))) (forall ((F $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (not (= A tptp.bot_bot_fun_nat_bool)) (exists ((X1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.finite_fold1Set_nat F A) X1)))))) (forall ((F $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (=> (not (= A tptp.bot_bot_fun_int_bool)) (exists ((X1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.finite_fold1Set_int F A) X1)))))) (forall ((A_13 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A_13)) (or (= A_13 tptp.bot_bot_fun_nat_bool) (exists ((A_43 $$unsorted) (A_12 $$unsorted)) (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 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A_13)) (or (= A_13 tptp.bot_bo797238721a_bool) (exists ((A_43 $$unsorted) (A_12 $$unsorted)) (and (= A_13 (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a A_12) A_43)) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A_43))))))) (forall ((A_13 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A_13)) (or (= A_13 tptp.bot_bot_fun_int_bool) (exists ((A_43 $$unsorted) (A_12 $$unsorted)) (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 $$unsorted) (F_1 $$unsorted)) (=> (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 $$unsorted) (F_2 $$unsorted)) (=> (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 $$unsorted) (F_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a F_1)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool Pa tptp.bot_bo797238721a_bool)) (=> (forall ((X_2 $$unsorted) (F_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a F_2)) (=> (not (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_2) F_2))) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool Pa F_2)) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool Pa (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a X_2) F_2))))))) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool Pa F_1)))))) (forall ((Pa $$unsorted) (F_1 $$unsorted)) (=> (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 $$unsorted) (F_2 $$unsorted)) (=> (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 $$unsorted) (A $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A))) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a (tptp.image_533441733iple_a F A))) (exists ((X_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_2) A)) (not (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a (tptp.hAPP_f20753329a_bool tptp.collec351493750iple_a (tptp.hAPP_f20753329a_bool (tptp.hAPP_f607497069a_bool tptp.cOMBS_154988028l_bool (tptp.hAPP_f146754017l_bool (tptp.hAPP_f239971723l_bool tptp.cOMBB_1866391387iple_a tptp.fconj) (tptp.hAPP_f20753329a_bool (tptp.hAPP_f247708275a_bool tptp.cOMBC_1519416966l_bool tptp.member1797258804iple_a) A))) (tptp.hAPP_H426895267a_bool (tptp.hAPP_f920293029a_bool tptp.cOMBC_1940896922a_bool (tptp.hAPP_f960023481a_bool (tptp.hAPP_f1786170683a_bool tptp.cOMBB_683172471iple_a tptp.fequal963300192iple_a) F)) (tptp.hAPP_H905846293iple_a F X_2)))))))))))) (forall ((F $$unsorted) (A $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.image_48635758_a_nat F A))) (exists ((X_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_2) A)) (not (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a (tptp.hAPP_f20753329a_bool tptp.collec351493750iple_a (tptp.hAPP_f20753329a_bool (tptp.hAPP_f607497069a_bool tptp.cOMBS_154988028l_bool (tptp.hAPP_f146754017l_bool (tptp.hAPP_f239971723l_bool tptp.cOMBB_1866391387iple_a tptp.fconj) (tptp.hAPP_f20753329a_bool (tptp.hAPP_f247708275a_bool tptp.cOMBC_1519416966l_bool tptp.member1797258804iple_a) A))) (tptp.hAPP_n1919155532a_bool (tptp.hAPP_f228417655a_bool tptp.cOMBC_364739t_bool (tptp.hAPP_f1872860171t_bool (tptp.hAPP_f1981448543t_bool tptp.cOMBB_1391527205iple_a tptp.fequal_nat) F)) (tptp.hAPP_H592031934_a_nat F X_2)))))))))))) (forall ((F $$unsorted) (A $$unsorted)) (=> (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 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_2) A)) (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.hAPP_f1805168059t_bool tptp.collect_int (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f727283836t_bool tptp.cOMBS_int_bool_bool (tptp.hAPP_f2144054103l_bool (tptp.hAPP_f1734373249l_bool tptp.cOMBB_1652995168ol_int tptp.fconj) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f202917053t_bool tptp.cOMBC_94739984l_bool tptp.member_int) A))) (tptp.hAPP_n1082236369t_bool (tptp.hAPP_f175561985t_bool tptp.cOMBC_int_nat_bool (tptp.hAPP_f876579787t_bool (tptp.hAPP_f2026117279t_bool tptp.cOMBB_1437810218ol_int tptp.fequal_nat) F)) (tptp.hAPP_int_nat F X_2)))))))))))) (forall ((F $$unsorted) (A $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.image_685909450_a_int F A))) (exists ((X_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_2) A)) (not (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a (tptp.hAPP_f20753329a_bool tptp.collec351493750iple_a (tptp.hAPP_f20753329a_bool (tptp.hAPP_f607497069a_bool tptp.cOMBS_154988028l_bool (tptp.hAPP_f146754017l_bool (tptp.hAPP_f239971723l_bool tptp.cOMBB_1866391387iple_a tptp.fconj) (tptp.hAPP_f20753329a_bool (tptp.hAPP_f247708275a_bool tptp.cOMBC_1519416966l_bool tptp.member1797258804iple_a) A))) (tptp.hAPP_i611776424a_bool (tptp.hAPP_f920351535a_bool tptp.cOMBC_1530706207t_bool (tptp.hAPP_f2142913731t_bool (tptp.hAPP_f1329415375t_bool tptp.cOMBB_1505691757iple_a tptp.fequal_int) F)) (tptp.hAPP_H1229305626_a_int F X_2)))))))))))) (forall ((F $$unsorted) (A $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A))) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a (tptp.image_1865589340iple_a F A))) (exists ((X_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) A)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.hAPP_f800510211t_bool tptp.collect_nat (tptp.hAPP_f800510211t_bool (tptp.hAPP_f561022312t_bool tptp.cOMBS_nat_bool_bool (tptp.hAPP_f1146629647l_bool (tptp.hAPP_f1080886329l_bool tptp.cOMBB_1015721476ol_nat tptp.fconj) (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1722879237t_bool tptp.cOMBC_226598744l_bool tptp.member_nat) A))) (tptp.hAPP_H144868812t_bool (tptp.hAPP_f1886543991t_bool tptp.cOMBC_533513393a_bool (tptp.hAPP_f260875897a_bool (tptp.hAPP_f1930382715a_bool tptp.cOMBB_1063143712ol_nat tptp.fequal963300192iple_a) F)) (tptp.hAPP_n261501868iple_a F X_2)))))))))))) (forall ((F $$unsorted) (A $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.image_int_int F A))) (exists ((X_2 $$unsorted)) (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 $$unsorted) (A $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A))) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a (tptp.image_1844722432iple_a F A))) (exists ((X_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_2) A)) (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.hAPP_f1805168059t_bool tptp.collect_int (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f727283836t_bool tptp.cOMBS_int_bool_bool (tptp.hAPP_f2144054103l_bool (tptp.hAPP_f1734373249l_bool tptp.cOMBB_1652995168ol_int tptp.fconj) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f202917053t_bool tptp.cOMBC_94739984l_bool tptp.member_int) A))) (tptp.hAPP_H1675210280t_bool (tptp.hAPP_f936407855t_bool tptp.cOMBC_1719122773a_bool (tptp.hAPP_f298605433a_bool (tptp.hAPP_f1421841531a_bool tptp.cOMBB_1700417404ol_int tptp.fequal963300192iple_a) F)) (tptp.hAPP_i240634960iple_a F X_2)))))))))))) (forall ((F $$unsorted) (A $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.image_nat_nat F A))) (exists ((X_2 $$unsorted)) (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 $$unsorted) (A $$unsorted)) (=> (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 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) A)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.hAPP_f800510211t_bool tptp.collect_nat (tptp.hAPP_f800510211t_bool (tptp.hAPP_f561022312t_bool tptp.cOMBS_nat_bool_bool (tptp.hAPP_f1146629647l_bool (tptp.hAPP_f1080886329l_bool tptp.cOMBB_1015721476ol_nat tptp.fconj) (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1722879237t_bool tptp.cOMBC_226598744l_bool tptp.member_nat) A))) (tptp.hAPP_i418383825t_bool (tptp.hAPP_f482008321t_bool tptp.cOMBC_nat_int_bool (tptp.hAPP_f1533130627t_bool (tptp.hAPP_f879109391t_bool tptp.cOMBB_1628441366ol_nat tptp.fequal_int) F)) (tptp.hAPP_nat_int F X_2)))))))))))) (forall ((F $$unsorted) (Z_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A)) (exists ((X1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_H1037229737a_bool (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool (tptp.finite90892550iple_a F) Z_1) A) X1))))) (forall ((F $$unsorted) (Z_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (exists ((X1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool (tptp.finite929467206at_nat F) Z_1) A) X1))))) (forall ((F $$unsorted) (Z_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (exists ((X1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool (tptp.finite772772422nt_int F) Z_1) A) X1))))) (forall ((F $$unsorted) (A1 $$unsorted) (A2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.finite_fold1Set_nat F A1) A2)) (exists ((A_12 $$unsorted) (A_43 $$unsorted) (X_2 $$unsorted)) (and (= A1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_12) A_43)) (= A2 X_2) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool (tptp.finite929467206at_nat F) A_12) A_43) X_2)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_12) A_43))))))) (forall ((F $$unsorted) (A1 $$unsorted) (A2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_H1037229737a_bool (tptp.finite1621280049iple_a F A1) A2)) (exists ((A_12 $$unsorted) (A_43 $$unsorted) (X_2 $$unsorted)) (and (= A1 (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a A_12) A_43)) (= A2 X_2) (tptp.hBOOL (tptp.hAPP_H1037229737a_bool (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool (tptp.finite90892550iple_a F) A_12) A_43) X_2)) (not (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a A_12) A_43))))))) (forall ((F $$unsorted) (A1 $$unsorted) (A2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.finite_fold1Set_int F A1) A2)) (exists ((A_12 $$unsorted) (A_43 $$unsorted) (X_2 $$unsorted)) (and (= A1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_12) A_43)) (= A2 X_2) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool (tptp.finite772772422nt_int F) A_12) A_43) X_2)) (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int A_12) A_43))))))) (forall ((Pa $$unsorted) (A_13 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_int_bool Pa A_13)) (=> (forall ((X_2 $$unsorted)) (=> (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 $$unsorted) (A_13 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_H1037229737a_bool Pa A_13)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_H1037229737a_bool Pa X_2)) (= X_2 A_13))) (tptp.hBOOL (tptp.hAPP_H1037229737a_bool Pa (tptp.hAPP_f1693662087iple_a tptp.the_Ho830102290iple_a Pa)))))) (forall ((Pa $$unsorted) (A_13 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool Pa A_13)) (=> (forall ((X_2 $$unsorted)) (=> (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 $$unsorted) (Pa $$unsorted)) (=> (exists ((X_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_int_bool Pa X_2)) (forall ((Y_21 $$unsorted)) (=> (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 $$unsorted) (Pa $$unsorted)) (=> (exists ((X_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_H1037229737a_bool Pa X_2)) (forall ((Y_21 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_H1037229737a_bool Pa Y_21)) (= Y_21 X_2))))) (=> (tptp.hBOOL (tptp.hAPP_H1037229737a_bool Pa A_13)) (= (tptp.hAPP_f1693662087iple_a tptp.the_Ho830102290iple_a Pa) A_13)))) (forall ((A_13 $$unsorted) (Pa $$unsorted)) (=> (exists ((X_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_nat_bool Pa X_2)) (forall ((Y_21 $$unsorted)) (=> (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 $$unsorted)) (=> (exists ((X_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_int_bool Pa X_2)) (forall ((Y_21 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_int_bool Pa Y_21)) (= Y_21 X_2))))) (tptp.hBOOL (tptp.hAPP_int_bool Pa (tptp.hAPP_f1594865479ol_int tptp.the_int Pa))))) (forall ((Pa $$unsorted)) (=> (exists ((X_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_H1037229737a_bool Pa X_2)) (forall ((Y_21 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_H1037229737a_bool Pa Y_21)) (= Y_21 X_2))))) (tptp.hBOOL (tptp.hAPP_H1037229737a_bool Pa (tptp.hAPP_f1693662087iple_a tptp.the_Ho830102290iple_a Pa))))) (forall ((Pa $$unsorted)) (=> (exists ((X_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_nat_bool Pa X_2)) (forall ((Y_21 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool Pa Y_21)) (= Y_21 X_2))))) (tptp.hBOOL (tptp.hAPP_nat_bool Pa (tptp.hAPP_f22106695ol_nat tptp.the_nat Pa))))) (forall ((F $$unsorted) (Z_1 $$unsorted) (A1 $$unsorted) (A2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool (tptp.finite929467206at_nat F) Z_1) A1) A2)) (or (and (= A1 tptp.bot_bot_fun_nat_bool) (= A2 Z_1)) (exists ((X_2 $$unsorted) (A_43 $$unsorted) (Y_21 $$unsorted)) (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 $$unsorted) (Z_1 $$unsorted) (A1 $$unsorted) (A2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_H1037229737a_bool (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool (tptp.finite90892550iple_a F) Z_1) A1) A2)) (or (and (= A1 tptp.bot_bo797238721a_bool) (= A2 Z_1)) (exists ((X_2 $$unsorted) (A_43 $$unsorted) (Y_21 $$unsorted)) (and (= A1 (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a X_2) A_43)) (= A2 (tptp.hAPP_H905846293iple_a (tptp.hAPP_H2085992369iple_a F X_2) Y_21)) (not (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_2) A_43))) (tptp.hBOOL (tptp.hAPP_H1037229737a_bool (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool (tptp.finite90892550iple_a F) Z_1) A_43) Y_21))))))) (forall ((F $$unsorted) (Z_1 $$unsorted) (A1 $$unsorted) (A2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool (tptp.finite772772422nt_int F) Z_1) A1) A2)) (or (and (= A1 tptp.bot_bot_fun_int_bool) (= A2 Z_1)) (exists ((X_2 $$unsorted) (A_43 $$unsorted) (Y_21 $$unsorted)) (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 $$unsorted) (A $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (=> (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 $$unsorted) (A $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (=> (tptp.hBOOL (tptp.finite1033474011iple_a F F_1)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A)) (=> (not (= A tptp.bot_bo797238721a_bool)) (= (tptp.hAPP_f1693662087iple_a F_1 (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a X_1) A)) (tptp.hAPP_H905846293iple_a (tptp.hAPP_H2085992369iple_a F X_1) (tptp.hAPP_f1693662087iple_a F_1 A))))))) (forall ((X_1 $$unsorted) (A $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (=> (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 $$unsorted) (F_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat F_1)) (=> (not (= F_1 tptp.bot_bot_fun_nat_bool)) (=> (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool Pa (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_2) tptp.bot_bot_fun_nat_bool)))) (=> (forall ((X_2 $$unsorted) (F_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat F_2)) (=> (not (= F_2 tptp.bot_bot_fun_nat_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) F_2))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool Pa F_2)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool Pa (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_2) F_2)))))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool Pa F_1))))))) (forall ((Pa $$unsorted) (F_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a F_1)) (=> (not (= F_1 tptp.bot_bo797238721a_bool)) (=> (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool Pa (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a X_2) tptp.bot_bo797238721a_bool)))) (=> (forall ((X_2 $$unsorted) (F_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a F_2)) (=> (not (= F_2 tptp.bot_bo797238721a_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_2) F_2))) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool Pa F_2)) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool Pa (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a X_2) F_2)))))))) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool Pa F_1))))))) (forall ((Pa $$unsorted) (F_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int F_1)) (=> (not (= F_1 tptp.bot_bot_fun_int_bool)) (=> (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool Pa (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_2) tptp.bot_bot_fun_int_bool)))) (=> (forall ((X_2 $$unsorted) (F_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int F_2)) (=> (not (= F_2 tptp.bot_bot_fun_int_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_2) F_2))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool Pa F_2)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool Pa (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_2) F_2)))))))) (tptp.hBOOL (tptp.hAPP_f448129468l_bool Pa F_1))))))) (forall ((A $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (=> (tptp.hBOOL (tptp.big_se1603268663iple_a F F_1)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A)) (= (tptp.hAPP_f1693662087iple_a F_1 A) (tptp.hAPP_f1693662087iple_a (tptp.finite1465856449iple_a F) A))))) (forall ((A $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (=> (tptp.hBOOL (tptp.big_se275732192ig_nat F F_1)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (= (tptp.hAPP_f22106695ol_nat F_1 A) (tptp.hAPP_f22106695ol_nat (tptp.finite_fold1_nat F) A))))) (forall ((A $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (=> (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 $$unsorted) (A $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (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 $$unsorted) (A $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f20753329a_bool (tptp.hAPP_f1706700729a_bool tptp.minus_85316870a_bool A) (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a X_1) tptp.bot_bo797238721a_bool)))) (let ((_let_2 (tptp.hAPP_f1693662087iple_a F_1 A))) (let ((_let_3 (= _let_1 tptp.bot_bo797238721a_bool))) (=> (tptp.hBOOL (tptp.finite1753440478iple_a F F_1)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_1) A)) (and (=> _let_3 (= _let_2 X_1)) (=> (not _let_3) (= _let_2 (tptp.hAPP_H905846293iple_a (tptp.hAPP_H2085992369iple_a F X_1) (tptp.hAPP_f1693662087iple_a F_1 _let_1)))))))))))) (forall ((X_1 $$unsorted) (A $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (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 $$unsorted) (A $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (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 $$unsorted) (A $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a X_1))) (let ((_let_2 (tptp.hAPP_f20753329a_bool (tptp.hAPP_f1706700729a_bool tptp.minus_85316870a_bool A) (tptp.hAPP_f20753329a_bool _let_1 tptp.bot_bo797238721a_bool)))) (let ((_let_3 (tptp.hAPP_f1693662087iple_a F_1 (tptp.hAPP_f20753329a_bool _let_1 A)))) (let ((_let_4 (= _let_2 tptp.bot_bo797238721a_bool))) (=> (tptp.hBOOL (tptp.finite1753440478iple_a F F_1)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A)) (and (=> _let_4 (= _let_3 X_1)) (=> (not _let_4) (= _let_3 (tptp.hAPP_H905846293iple_a (tptp.hAPP_H2085992369iple_a F X_1) (tptp.hAPP_f1693662087iple_a F_1 _let_2)))))))))))) (forall ((X_1 $$unsorted) (A $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (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 $$unsorted) (A $$unsorted)) (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 $$unsorted) (A $$unsorted)) (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 $$unsorted) (Ca $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a Ca))) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool _let_1 A)) (=> (not (tptp.hBOOL (tptp.hAPP_f1695230391l_bool _let_1 B))) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool _let_1 (tptp.hAPP_f20753329a_bool (tptp.hAPP_f1706700729a_bool tptp.minus_85316870a_bool A) B))))))) (forall ((B $$unsorted) (Ca $$unsorted) (A $$unsorted)) (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 $$unsorted) (Ca $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_i2112223885l_bool tptp.member_int Ca))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 A)) (=> (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 B))) (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) B))))))) (forall ((Ca $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a Ca))) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool _let_1 (tptp.hAPP_f20753329a_bool (tptp.hAPP_f1706700729a_bool tptp.minus_85316870a_bool A) B))) (not (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool _let_1 B))))))) (forall ((Ca $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat Ca))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) B))) (not (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B))))))) (forall ((Ca $$unsorted) (A $$unsorted) (B $$unsorted)) (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 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A)) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a (tptp.hAPP_f20753329a_bool (tptp.hAPP_f1706700729a_bool tptp.minus_85316870a_bool A) B))))) (forall ((B $$unsorted) (A $$unsorted)) (=> (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 $$unsorted) (A $$unsorted)) (=> (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 $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (=> (tptp.hBOOL (tptp.finite1432773856em_int F F_1)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int F X_1) X_1) X_1))) (forall ((X_1 $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (=> (tptp.hBOOL (tptp.finite1033474011iple_a F F_1)) (= (tptp.hAPP_H905846293iple_a (tptp.hAPP_H2085992369iple_a F X_1) X_1) X_1))) (forall ((X_1 $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (=> (tptp.hBOOL (tptp.finite795500164em_nat F F_1)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat F X_1) X_1) X_1))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f247708275a_bool tptp.cOMBC_1519416966l_bool tptp.member1797258804iple_a))) (= (tptp.hAPP_f20753329a_bool (tptp.hAPP_f1706700729a_bool tptp.minus_85316870a_bool A) B) (tptp.hAPP_f20753329a_bool tptp.collec351493750iple_a (tptp.hAPP_f20753329a_bool (tptp.hAPP_f607497069a_bool tptp.cOMBS_154988028l_bool (tptp.hAPP_f146754017l_bool (tptp.hAPP_f239971723l_bool tptp.cOMBB_1866391387iple_a tptp.fconj) (tptp.hAPP_f20753329a_bool _let_1 A))) (tptp.hAPP_f20753329a_bool (tptp.hAPP_f604201481a_bool tptp.cOMBB_1882975613iple_a tptp.fNot) (tptp.hAPP_f20753329a_bool _let_1 B))))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f1722879237t_bool tptp.cOMBC_226598744l_bool tptp.member_nat))) (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) B) (tptp.hAPP_f800510211t_bool tptp.collect_nat (tptp.hAPP_f800510211t_bool (tptp.hAPP_f561022312t_bool tptp.cOMBS_nat_bool_bool (tptp.hAPP_f1146629647l_bool (tptp.hAPP_f1080886329l_bool tptp.cOMBB_1015721476ol_nat tptp.fconj) (tptp.hAPP_f800510211t_bool _let_1 A))) (tptp.hAPP_f800510211t_bool (tptp.hAPP_f894608603t_bool tptp.cOMBB_bool_bool_nat tptp.fNot) (tptp.hAPP_f800510211t_bool _let_1 B))))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f202917053t_bool tptp.cOMBC_94739984l_bool tptp.member_int))) (= (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) B) (tptp.hAPP_f1805168059t_bool tptp.collect_int (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f727283836t_bool tptp.cOMBS_int_bool_bool (tptp.hAPP_f2144054103l_bool (tptp.hAPP_f1734373249l_bool tptp.cOMBB_1652995168ol_int tptp.fconj) (tptp.hAPP_f1805168059t_bool _let_1 A))) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f627970963t_bool tptp.cOMBB_bool_bool_int tptp.fNot) (tptp.hAPP_f1805168059t_bool _let_1 B))))))) (forall ((Ca $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a Ca))) (= (tptp.hBOOL (tptp.hAPP_f1695230391l_bool _let_1 (tptp.hAPP_f20753329a_bool (tptp.hAPP_f1706700729a_bool tptp.minus_85316870a_bool A) B))) (and (tptp.hBOOL (tptp.hAPP_f1695230391l_bool _let_1 A)) (not (tptp.hBOOL (tptp.hAPP_f1695230391l_bool _let_1 B))))))) (forall ((Ca $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat Ca))) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) B))) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 A)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B))))))) (forall ((Ca $$unsorted) (A $$unsorted) (B $$unsorted)) (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 $$unsorted) (B $$unsorted)) (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 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f20753329a_bool (tptp.hAPP_f1706700729a_bool tptp.minus_85316870a_bool A) B))) (= (tptp.hAPP_f20753329a_bool (tptp.hAPP_f1706700729a_bool tptp.minus_85316870a_bool _let_1) B) _let_1))) (forall ((A $$unsorted) (B $$unsorted)) (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 $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a Ca))) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool _let_1 (tptp.hAPP_f20753329a_bool (tptp.hAPP_f1706700729a_bool tptp.minus_85316870a_bool A) B))) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool _let_1 A))))) (forall ((Ca $$unsorted) (A $$unsorted) (B $$unsorted)) (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 $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_i2112223885l_bool tptp.member_int Ca))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) B))) (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 A))))) (forall ((Ca $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a Ca))) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool _let_1 (tptp.hAPP_f20753329a_bool (tptp.hAPP_f1706700729a_bool tptp.minus_85316870a_bool A) B))) (not (tptp.hBOOL (tptp.hAPP_f1695230391l_bool _let_1 B)))))) (forall ((Ca $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat Ca))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) B))) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B)))))) (forall ((Ca $$unsorted) (A $$unsorted) (B $$unsorted)) (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 $$unsorted)) (= (tptp.hAPP_f20753329a_bool (tptp.hAPP_f1706700729a_bool tptp.minus_85316870a_bool tptp.bot_bo797238721a_bool) A) tptp.bot_bo797238721a_bool)) (forall ((A $$unsorted)) (= (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 $$unsorted)) (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool tptp.bot_bot_fun_nat_bool) A) tptp.bot_bot_fun_nat_bool)) (forall ((A $$unsorted)) (= (tptp.hAPP_f20753329a_bool (tptp.hAPP_f1706700729a_bool tptp.minus_85316870a_bool A) tptp.bot_bo797238721a_bool) A)) (forall ((A $$unsorted)) (= (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) tptp.bot_bot_fun_int_bool) A)) (forall ((A $$unsorted)) (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) tptp.bot_bot_fun_nat_bool) A)) (forall ((A $$unsorted)) (= (tptp.hAPP_f20753329a_bool (tptp.hAPP_f1706700729a_bool tptp.minus_85316870a_bool A) A) tptp.bot_bo797238721a_bool)) (forall ((A $$unsorted)) (= (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) A) tptp.bot_bot_fun_int_bool)) (forall ((A $$unsorted)) (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) A) tptp.bot_bot_fun_nat_bool)) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a B)) (= (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a (tptp.hAPP_f20753329a_bool (tptp.hAPP_f1706700729a_bool tptp.minus_85316870a_bool A) B))) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat B)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) B))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int B)) (= (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) B))) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A))))) (forall ((A $$unsorted) (X_1 $$unsorted) (B $$unsorted)) (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 $$unsorted) (X_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f20753329a_bool (tptp.hAPP_f1706700729a_bool tptp.minus_85316870a_bool A) B))) (let ((_let_2 (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a X_1))) (let ((_let_3 (tptp.hAPP_f20753329a_bool (tptp.hAPP_f1706700729a_bool tptp.minus_85316870a_bool (tptp.hAPP_f20753329a_bool _let_2 A)) B))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_1) B)))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (tptp.hAPP_f20753329a_bool _let_2 _let_1))))))))) (forall ((A $$unsorted) (X_1 $$unsorted) (B $$unsorted)) (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 $$unsorted) (X_1 $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) B)) (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) A)) B) (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) B)))) (forall ((A $$unsorted) (X_1 $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_1) B)) (= (tptp.hAPP_f20753329a_bool (tptp.hAPP_f1706700729a_bool tptp.minus_85316870a_bool (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a X_1) A)) B) (tptp.hAPP_f20753329a_bool (tptp.hAPP_f1706700729a_bool tptp.minus_85316870a_bool A) B)))) (forall ((A $$unsorted) (X_1 $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) B)) (= (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1) A)) B) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) B)))) (forall ((A_13 $$unsorted) (Ba $$unsorted) (A $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.finite929467206at_nat tptp.times_times_nat))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool _let_1 Ba) A) X_1)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_13) A)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat Ba) A))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool _let_1 A_13) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat Ba) (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13) tptp.bot_bot_fun_nat_bool)))) X_1))))))) (forall ((A_13 $$unsorted) (Ba $$unsorted) (A $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.finite772772422nt_int tptp.times_times_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool _let_1 Ba) A) X_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int A_13) A)) (=> (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Ba) A))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool _let_1 A_13) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int Ba) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_13) tptp.bot_bot_fun_int_bool)))) X_1))))))) (forall ((A $$unsorted) (A_13 $$unsorted) (B $$unsorted)) (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 $$unsorted) (A_13 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a A_13))) (let ((_let_2 (tptp.hAPP_f1706700729a_bool tptp.minus_85316870a_bool A))) (= (tptp.hAPP_f20753329a_bool _let_2 (tptp.hAPP_f20753329a_bool _let_1 B)) (tptp.hAPP_f20753329a_bool (tptp.hAPP_f1706700729a_bool tptp.minus_85316870a_bool (tptp.hAPP_f20753329a_bool _let_2 B)) (tptp.hAPP_f20753329a_bool _let_1 tptp.bot_bo797238721a_bool)))))) (forall ((A $$unsorted) (A_13 $$unsorted) (B $$unsorted)) (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 $$unsorted) (A_13 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13))) (let ((_let_2 (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A))) (= (tptp.hAPP_f800510211t_bool _let_2 (tptp.hAPP_f800510211t_bool _let_1 B)) (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool (tptp.hAPP_f800510211t_bool _let_2 (tptp.hAPP_f800510211t_bool _let_1 tptp.bot_bot_fun_nat_bool))) B))))) (forall ((A $$unsorted) (A_13 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a A_13))) (let ((_let_2 (tptp.hAPP_f1706700729a_bool tptp.minus_85316870a_bool A))) (= (tptp.hAPP_f20753329a_bool _let_2 (tptp.hAPP_f20753329a_bool _let_1 B)) (tptp.hAPP_f20753329a_bool (tptp.hAPP_f1706700729a_bool tptp.minus_85316870a_bool (tptp.hAPP_f20753329a_bool _let_2 (tptp.hAPP_f20753329a_bool _let_1 tptp.bot_bo797238721a_bool))) B))))) (forall ((A $$unsorted) (A_13 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_i1529485324t_bool tptp.insert_int A_13))) (let ((_let_2 (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A))) (= (tptp.hAPP_f1805168059t_bool _let_2 (tptp.hAPP_f1805168059t_bool _let_1 B)) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool (tptp.hAPP_f1805168059t_bool _let_2 (tptp.hAPP_f1805168059t_bool _let_1 tptp.bot_bot_fun_int_bool))) B))))) (forall ((A_13 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13))) (= (tptp.hAPP_f800510211t_bool _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) (tptp.hAPP_f800510211t_bool _let_1 tptp.bot_bot_fun_nat_bool))) (tptp.hAPP_f800510211t_bool _let_1 A)))) (forall ((A_13 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a A_13))) (= (tptp.hAPP_f20753329a_bool _let_1 (tptp.hAPP_f20753329a_bool (tptp.hAPP_f1706700729a_bool tptp.minus_85316870a_bool A) (tptp.hAPP_f20753329a_bool _let_1 tptp.bot_bo797238721a_bool))) (tptp.hAPP_f20753329a_bool _let_1 A)))) (forall ((A_13 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_i1529485324t_bool tptp.insert_int A_13))) (= (tptp.hAPP_f1805168059t_bool _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) (tptp.hAPP_f1805168059t_bool _let_1 tptp.bot_bot_fun_int_bool))) (tptp.hAPP_f1805168059t_bool _let_1 A)))) (forall ((X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1))) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A))) (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool (tptp.hAPP_f800510211t_bool _let_1 A)) (tptp.hAPP_f800510211t_bool _let_1 tptp.bot_bot_fun_nat_bool)) A)))) (forall ((X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a X_1))) (=> (not (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_1) A))) (= (tptp.hAPP_f20753329a_bool (tptp.hAPP_f1706700729a_bool tptp.minus_85316870a_bool (tptp.hAPP_f20753329a_bool _let_1 A)) (tptp.hAPP_f20753329a_bool _let_1 tptp.bot_bo797238721a_bool)) A)))) (forall ((X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1))) (=> (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A))) (= (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool (tptp.hAPP_f1805168059t_bool _let_1 A)) (tptp.hAPP_f1805168059t_bool _let_1 tptp.bot_bot_fun_int_bool)) A)))) (forall ((A_13 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_13) A)) (= (tptp.hAPP_f800510211t_bool _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) (tptp.hAPP_f800510211t_bool _let_1 tptp.bot_bot_fun_nat_bool))) A)))) (forall ((A_13 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a A_13))) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a A_13) A)) (= (tptp.hAPP_f20753329a_bool _let_1 (tptp.hAPP_f20753329a_bool (tptp.hAPP_f1706700729a_bool tptp.minus_85316870a_bool A) (tptp.hAPP_f20753329a_bool _let_1 tptp.bot_bo797238721a_bool))) A)))) (forall ((A_13 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_i1529485324t_bool tptp.insert_int A_13))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int A_13) A)) (= (tptp.hAPP_f1805168059t_bool _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) (tptp.hAPP_f1805168059t_bool _let_1 tptp.bot_bot_fun_int_bool))) A)))) (forall ((A $$unsorted) (A_13 $$unsorted) (B $$unsorted)) (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 $$unsorted) (A_13 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f1706700729a_bool tptp.minus_85316870a_bool A))) (= (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a (tptp.hAPP_f20753329a_bool _let_1 (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a A_13) B)))) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a (tptp.hAPP_f20753329a_bool _let_1 B)))))) (forall ((A $$unsorted) (A_13 $$unsorted) (B $$unsorted)) (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 $$unsorted) (Ba $$unsorted) (A $$unsorted) (Y_1 $$unsorted)) (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 $$unsorted) (Ba $$unsorted) (A $$unsorted) (Y_1 $$unsorted)) (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 $$unsorted) (A $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1693662087iple_a F_1 A))) (=> (tptp.hBOOL (tptp.finite1033474011iple_a F F_1)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_1) A)) (= (tptp.hAPP_H905846293iple_a (tptp.hAPP_H2085992369iple_a F X_1) _let_1) _let_1)))))) (forall ((X_1 $$unsorted) (A $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (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 $$unsorted) (A $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (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 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (not (= A tptp.bot_bot_fun_nat_bool)) (=> (forall ((X_2 $$unsorted) (Y_21 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat X_2) Y_21)) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_2) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat Y_21) tptp.bot_bot_fun_nat_bool))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat (tptp.hAPP_f22106695ol_nat (tptp.finite_fold1_nat tptp.times_times_nat) A)) A)))))) (forall ((A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (=> (not (= A tptp.bot_bot_fun_int_bool)) (=> (forall ((X_2 $$unsorted) (Y_21 $$unsorted)) (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 $$unsorted) (H $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (=> (tptp.hBOOL (tptp.finite1033474011iple_a F F_1)) (=> (forall ((X_2 $$unsorted) (Y_21 $$unsorted)) (= (tptp.hAPP_H905846293iple_a H (tptp.hAPP_H905846293iple_a (tptp.hAPP_H2085992369iple_a F X_2) Y_21)) (tptp.hAPP_H905846293iple_a (tptp.hAPP_H2085992369iple_a F (tptp.hAPP_H905846293iple_a H X_2)) (tptp.hAPP_H905846293iple_a H Y_21)))) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a N_3)) (=> (not (= N_3 tptp.bot_bo797238721a_bool)) (= (tptp.hAPP_H905846293iple_a H (tptp.hAPP_f1693662087iple_a F_1 N_3)) (tptp.hAPP_f1693662087iple_a F_1 (tptp.image_533441733iple_a H N_3)))))))) (forall ((N_3 $$unsorted) (H $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (=> (tptp.hBOOL (tptp.finite1432773856em_int F F_1)) (=> (forall ((X_2 $$unsorted) (Y_21 $$unsorted)) (= (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 $$unsorted) (H $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (=> (tptp.hBOOL (tptp.finite795500164em_nat F F_1)) (=> (forall ((X_2 $$unsorted) (Y_21 $$unsorted)) (= (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 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool Pa A)) (=> (forall ((A_12 $$unsorted) (A_43 $$unsorted)) (=> (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 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool Pa A)) (=> (forall ((A_12 $$unsorted) (A_43 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A_43)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a A_12) A_43)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool Pa A_43)) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool Pa (tptp.hAPP_f20753329a_bool (tptp.hAPP_f1706700729a_bool tptp.minus_85316870a_bool A_43) (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a A_12) tptp.bot_bo797238721a_bool)))))))) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool Pa tptp.bot_bo797238721a_bool)))))) (forall ((Pa $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool Pa A)) (=> (forall ((A_12 $$unsorted) (A_43 $$unsorted)) (=> (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 $$unsorted) (B $$unsorted) (X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) B) X_1)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.minus_minus_bool (tptp.hAPP_int_bool A X_1)) (tptp.hAPP_int_bool B X_1))))) (forall ((A $$unsorted) (B $$unsorted) (X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_H1037229737a_bool (tptp.hAPP_f20753329a_bool (tptp.hAPP_f1706700729a_bool tptp.minus_85316870a_bool A) B) X_1)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.minus_minus_bool (tptp.hAPP_H1037229737a_bool A X_1)) (tptp.hAPP_H1037229737a_bool B X_1))))) (forall ((A $$unsorted) (B $$unsorted) (X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) B) X_1)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.minus_minus_bool (tptp.hAPP_nat_bool A X_1)) (tptp.hAPP_nat_bool B X_1))))) (forall ((A $$unsorted) (B $$unsorted) (X_2 $$unsorted)) (= (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 $$unsorted) (B $$unsorted) (X_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_H1037229737a_bool (tptp.hAPP_f20753329a_bool (tptp.hAPP_f1706700729a_bool tptp.minus_85316870a_bool A) B) X_2)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.minus_minus_bool (tptp.hAPP_H1037229737a_bool A X_2)) (tptp.hAPP_H1037229737a_bool B X_2))))) (forall ((A $$unsorted) (B $$unsorted) (X_2 $$unsorted)) (= (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.finite1803123436a_bool (tptp.hAPP_f550111323a_bool (tptp.hAPP_f615286271a_bool tptp.cOMBB_1176122337iple_a (tptp.hAPP_f957014749a_bool tptp.cOMBC_288844080a_bool tptp.minus_85316870a_bool)) (tptp.hAPP_f1181346091a_bool (tptp.hAPP_f571476211a_bool tptp.cOMBC_1570214144a_bool tptp.insert956547291iple_a) tptp.bot_bo797238721a_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 $$unsorted) (Z_1 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.hAPP_i1529485324t_bool F X_1))) (let ((_let_2 (tptp.hAPP_f1805168059t_bool _let_1 Z_1))) (=> (tptp.hBOOL (tptp.finite58652534t_bool F)) (= (tptp.hAPP_f1805168059t_bool _let_1 _let_2) _let_2))))) (forall ((X_1 $$unsorted) (Z_1 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.hAPP_H1743777351a_bool F X_1))) (let ((_let_2 (tptp.hAPP_f20753329a_bool _let_1 Z_1))) (=> (tptp.hBOOL (tptp.finite1803123436a_bool F)) (= (tptp.hAPP_f20753329a_bool _let_1 _let_2) _let_2))))) (forall ((X_1 $$unsorted) (Z_1 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.hAPP_n1512601776t_bool F X_1))) (let ((_let_2 (tptp.hAPP_f800510211t_bool _let_1 Z_1))) (=> (tptp.hBOOL (tptp.finite1956789438t_bool F)) (= (tptp.hAPP_f800510211t_bool _let_1 _let_2) _let_2))))) (tptp.hBOOL (tptp.finite1956789438t_bool tptp.insert_nat)) (tptp.hBOOL (tptp.finite1803123436a_bool tptp.insert956547291iple_a)) (tptp.hBOOL (tptp.finite58652534t_bool tptp.insert_int)) (forall ((A_13 $$unsorted) (Z_1 $$unsorted) (A $$unsorted) (Y_1 $$unsorted) (F $$unsorted)) (=> (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 $$unsorted)) (and (= Y_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat F A_13) Y_22)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool (tptp.finite929467206at_nat F) Z_1) (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13) tptp.bot_bot_fun_nat_bool))) Y_22)))))))) (forall ((A_13 $$unsorted) (Z_1 $$unsorted) (A $$unsorted) (Y_1 $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.finite1428139793iple_a F)) (=> (tptp.hBOOL (tptp.hAPP_H1037229737a_bool (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool (tptp.finite90892550iple_a F) Z_1) A) Y_1)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a A_13) A)) (exists ((Y_22 $$unsorted)) (and (= Y_1 (tptp.hAPP_H905846293iple_a (tptp.hAPP_H2085992369iple_a F A_13) Y_22)) (tptp.hBOOL (tptp.hAPP_H1037229737a_bool (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool (tptp.finite90892550iple_a F) Z_1) (tptp.hAPP_f20753329a_bool (tptp.hAPP_f1706700729a_bool tptp.minus_85316870a_bool A) (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a A_13) tptp.bot_bo797238721a_bool))) Y_22)))))))) (forall ((A_13 $$unsorted) (Z_1 $$unsorted) (A $$unsorted) (Y_1 $$unsorted) (F $$unsorted)) (=> (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 $$unsorted)) (and (= Y_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int F A_13) Y_22)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool (tptp.finite772772422nt_int F) Z_1) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_13) tptp.bot_bot_fun_int_bool))) Y_22)))))))) (forall ((F $$unsorted) (A_13 $$unsorted) (A $$unsorted)) (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 $$unsorted) (A_13 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f1544320301ol_int tptp.big_co1977834938_a_int F))) (let ((_let_2 (tptp.hAPP_f587450508ol_int _let_1 A))) (let ((_let_3 (tptp.hAPP_f587450508ol_int _let_1 (tptp.hAPP_f20753329a_bool (tptp.hAPP_f1706700729a_bool tptp.minus_85316870a_bool A) (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a A_13) tptp.bot_bo797238721a_bool))))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a A_13) A)))) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A)) (and (=> _let_4 (= _let_3 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int _let_2) (tptp.hAPP_H1229305626_a_int F A_13)))) (=> (not _let_4) (= _let_3 _let_2))))))))) (forall ((F $$unsorted) (A_13 $$unsorted) (A $$unsorted)) (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 $$unsorted) (A_13 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f1599440987ol_int tptp.big_co1024481617at_int F))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_13) A)) (= (tptp.hAPP_f659380387ol_int _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13) tptp.bot_bot_fun_nat_bool))) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_f659380387ol_int _let_1 A)) (tptp.hAPP_nat_int F A_13))))))) (forall ((F $$unsorted) (A_13 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f1544320301ol_int tptp.big_co1977834938_a_int F))) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a A_13) A)) (= (tptp.hAPP_f587450508ol_int _let_1 (tptp.hAPP_f20753329a_bool (tptp.hAPP_f1706700729a_bool tptp.minus_85316870a_bool A) (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a A_13) tptp.bot_bo797238721a_bool))) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_f587450508ol_int _let_1 A)) (tptp.hAPP_H1229305626_a_int F A_13))))))) (forall ((F $$unsorted) (A_13 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f1926459811ol_int tptp.big_co230513141nt_int F))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int A_13) A)) (= (tptp.hAPP_f1594865479ol_int _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_13) tptp.bot_bot_fun_int_bool))) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_f1594865479ol_int _let_1 A)) (tptp.hAPP_int_int F A_13))))))) (forall ((G $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (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 $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a X_1))) (let ((_let_2 (tptp.big_co1815942735_a_nat G))) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A)) (= (tptp.hAPP_f2097660464ol_nat _let_2 (tptp.hAPP_f20753329a_bool _let_1 A)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_H592031934_a_nat G X_1)) (tptp.hAPP_f2097660464ol_nat _let_2 (tptp.hAPP_f20753329a_bool (tptp.hAPP_f1706700729a_bool tptp.minus_85316870a_bool A) (tptp.hAPP_f20753329a_bool _let_1 tptp.bot_bo797238721a_bool))))))))) (forall ((G $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (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 $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1))) (let ((_let_2 (tptp.big_co195215938at_int G))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (= (tptp.hAPP_f659380387ol_int _let_2 (tptp.hAPP_f800510211t_bool _let_1 A)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_nat_int G X_1)) (tptp.hAPP_f659380387ol_int _let_2 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) (tptp.hAPP_f800510211t_bool _let_1 tptp.bot_bot_fun_nat_bool))))))))) (forall ((G $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a X_1))) (let ((_let_2 (tptp.big_co305732779_a_int G))) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A)) (= (tptp.hAPP_f587450508ol_int _let_2 (tptp.hAPP_f20753329a_bool _let_1 A)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_H1229305626_a_int G X_1)) (tptp.hAPP_f587450508ol_int _let_2 (tptp.hAPP_f20753329a_bool (tptp.hAPP_f1706700729a_bool tptp.minus_85316870a_bool A) (tptp.hAPP_f20753329a_bool _let_1 tptp.bot_bo797238721a_bool))))))))) (forall ((G $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1))) (let ((_let_2 (tptp.big_co1548731110nt_int G))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (= (tptp.hAPP_f1594865479ol_int _let_2 (tptp.hAPP_f1805168059t_bool _let_1 A)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int G X_1)) (tptp.hAPP_f1594865479ol_int _let_2 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) (tptp.hAPP_f1805168059t_bool _let_1 tptp.bot_bot_fun_int_bool))))))))) (forall ((G $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (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 $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.big_co1815942735_a_nat G))) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_1) A)) (= (tptp.hAPP_f2097660464ol_nat _let_1 A) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_H592031934_a_nat G X_1)) (tptp.hAPP_f2097660464ol_nat _let_1 (tptp.hAPP_f20753329a_bool (tptp.hAPP_f1706700729a_bool tptp.minus_85316870a_bool A) (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a X_1) tptp.bot_bo797238721a_bool))))))))) (forall ((G $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (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 $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.big_co195215938at_int G))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)) (= (tptp.hAPP_f659380387ol_int _let_1 A) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_nat_int G X_1)) (tptp.hAPP_f659380387ol_int _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) tptp.bot_bot_fun_nat_bool))))))))) (forall ((G $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.big_co305732779_a_int G))) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_1) A)) (= (tptp.hAPP_f587450508ol_int _let_1 A) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_H1229305626_a_int G X_1)) (tptp.hAPP_f587450508ol_int _let_1 (tptp.hAPP_f20753329a_bool (tptp.hAPP_f1706700729a_bool tptp.minus_85316870a_bool A) (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a X_1) tptp.bot_bo797238721a_bool))))))))) (forall ((G $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.big_co1548731110nt_int G))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A)) (= (tptp.hAPP_f1594865479ol_int _let_1 A) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int G X_1)) (tptp.hAPP_f1594865479ol_int _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1) tptp.bot_bot_fun_int_bool))))))))) (forall ((B $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool B) A) (tptp.hAPP_f800510211t_bool (tptp.finite1578363458t_bool (tptp.hAPP_f10625010t_bool (tptp.hAPP_f1115950719t_bool tptp.cOMBB_1654519265ol_nat (tptp.hAPP_f1311642927t_bool tptp.cOMBC_646315179t_bool tptp.minus_2067140911t_bool)) (tptp.hAPP_f1570313510t_bool (tptp.hAPP_f688831301t_bool tptp.cOMBC_178881787t_bool tptp.insert_nat) tptp.bot_bot_fun_nat_bool)) B) A)))) (forall ((B $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A)) (= (tptp.hAPP_f20753329a_bool (tptp.hAPP_f1706700729a_bool tptp.minus_85316870a_bool B) A) (tptp.hAPP_f20753329a_bool (tptp.finite1215486064a_bool (tptp.hAPP_f550111323a_bool (tptp.hAPP_f615286271a_bool tptp.cOMBB_1176122337iple_a (tptp.hAPP_f957014749a_bool tptp.cOMBC_288844080a_bool tptp.minus_85316870a_bool)) (tptp.hAPP_f1181346091a_bool (tptp.hAPP_f571476211a_bool tptp.cOMBC_1570214144a_bool tptp.insert956547291iple_a) tptp.bot_bo797238721a_bool)) B) A)))) (forall ((B $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (= (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool B) A) (tptp.hAPP_f1805168059t_bool (tptp.finite1827710202t_bool (tptp.hAPP_f1468280982t_bool (tptp.hAPP_f1596157055t_bool tptp.cOMBB_765314529ol_int (tptp.hAPP_f194616807t_bool tptp.cOMBC_922884543t_bool tptp.minus_1449998731t_bool)) (tptp.hAPP_f1048215610t_bool (tptp.hAPP_f472159229t_bool tptp.cOMBC_1683390479t_bool tptp.insert_int) tptp.bot_bot_fun_int_bool)) B) A)))) (forall ((X_1 $$unsorted) (Z_1 $$unsorted) (A $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.hAPP_H2085992369iple_a F X_1))) (=> (tptp.hBOOL (tptp.finite1428139793iple_a F)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A)) (= (tptp.hAPP_H905846293iple_a _let_1 (tptp.hAPP_f1693662087iple_a (tptp.finite1205970312iple_a F Z_1) A)) (tptp.hAPP_f1693662087iple_a (tptp.finite1205970312iple_a F (tptp.hAPP_H905846293iple_a _let_1 Z_1)) A)))))) (forall ((X_1 $$unsorted) (Z_1 $$unsorted) (A $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.hAPP_H1743777351a_bool F X_1))) (=> (tptp.hBOOL (tptp.finite2114894759a_bool F)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A)) (= (tptp.hAPP_f20753329a_bool _let_1 (tptp.hAPP_f20753329a_bool (tptp.finite1215486064a_bool F Z_1) A)) (tptp.hAPP_f20753329a_bool (tptp.finite1215486064a_bool F (tptp.hAPP_f20753329a_bool _let_1 Z_1)) A)))))) (forall ((X_1 $$unsorted) (Z_1 $$unsorted) (A $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat F X_1))) (=> (tptp.hBOOL (tptp.finite2130160977at_nat F)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_f22106695ol_nat (tptp.finite_fold_nat_nat F Z_1) A)) (tptp.hAPP_f22106695ol_nat (tptp.finite_fold_nat_nat F (tptp.hAPP_nat_nat _let_1 Z_1)) A)))))) (forall ((X_1 $$unsorted) (Z_1 $$unsorted) (A $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.hAPP_n1512601776t_bool F X_1))) (=> (tptp.hBOOL (tptp.finite1071749497t_bool F)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (= (tptp.hAPP_f800510211t_bool _let_1 (tptp.hAPP_f800510211t_bool (tptp.finite1578363458t_bool F Z_1) A)) (tptp.hAPP_f800510211t_bool (tptp.finite1578363458t_bool F (tptp.hAPP_f800510211t_bool _let_1 Z_1)) A)))))) (forall ((X_1 $$unsorted) (Z_1 $$unsorted) (A $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.hAPP_int_fun_int_int F X_1))) (=> (tptp.hBOOL (tptp.finite1973466193nt_int F)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_f1594865479ol_int (tptp.finite_fold_int_int F Z_1) A)) (tptp.hAPP_f1594865479ol_int (tptp.finite_fold_int_int F (tptp.hAPP_int_int _let_1 Z_1)) A)))))) (forall ((X_1 $$unsorted) (Z_1 $$unsorted) (A $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.hAPP_i1529485324t_bool F X_1))) (=> (tptp.hBOOL (tptp.finite1321096241t_bool F)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (= (tptp.hAPP_f1805168059t_bool _let_1 (tptp.hAPP_f1805168059t_bool (tptp.finite1827710202t_bool F Z_1) A)) (tptp.hAPP_f1805168059t_bool (tptp.finite1827710202t_bool F (tptp.hAPP_f1805168059t_bool _let_1 Z_1)) A)))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (Z_1 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.hAPP_int_fun_int_int F X_1))) (let ((_let_2 (tptp.hAPP_int_fun_int_int F Y_1))) (=> (tptp.hBOOL (tptp.finite1973466193nt_int F)) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int _let_2 Z_1)) (tptp.hAPP_int_int _let_2 (tptp.hAPP_int_int _let_1 Z_1))))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (Z_1 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat F X_1))) (let ((_let_2 (tptp.hAPP_nat_fun_nat_nat F Y_1))) (=> (tptp.hBOOL (tptp.finite2130160977at_nat F)) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat _let_2 Z_1)) (tptp.hAPP_nat_nat _let_2 (tptp.hAPP_nat_nat _let_1 Z_1))))))) (forall ((F $$unsorted) (B $$unsorted) (A $$unsorted)) (= (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 $$unsorted) (B $$unsorted) (A $$unsorted)) (= (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat (tptp.hAPP_f2122367971at_nat (tptp.hAPP_f870149665at_nat tptp.cOMBC_2036134968ol_nat (tptp.hAPP_f883871819ol_nat (tptp.hAPP_f424754463ol_nat tptp.cOMBB_1716606670at_nat tptp.big_co1340561246_a_nat) F)) B)) A) (tptp.hAPP_f2097660464ol_nat (tptp.hAPP_f1371399797ol_nat tptp.big_co1340561246_a_nat (tptp.hAPP_f1464798435_a_nat (tptp.hAPP_f1012303887_a_nat tptp.cOMBC_1159891896ol_nat (tptp.hAPP_f1669765561ol_nat (tptp.hAPP_f1073041467ol_nat tptp.cOMBB_10565751iple_a tptp.big_co387207925at_nat) (tptp.hAPP_f2146713109at_nat tptp.cOMBC_441305270_a_nat F))) A)) B))) (forall ((F $$unsorted) (B $$unsorted) (A $$unsorted)) (= (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 $$unsorted) (B $$unsorted) (A $$unsorted)) (= (tptp.hAPP_f2097660464ol_nat (tptp.hAPP_f1371399797ol_nat tptp.big_co1340561246_a_nat (tptp.hAPP_f1464798435_a_nat (tptp.hAPP_f1012303887_a_nat tptp.cOMBC_1159891896ol_nat (tptp.hAPP_f1669765561ol_nat (tptp.hAPP_f1073041467ol_nat tptp.cOMBB_10565751iple_a tptp.big_co387207925at_nat) F)) B)) A) (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat (tptp.hAPP_f2122367971at_nat (tptp.hAPP_f870149665at_nat tptp.cOMBC_2036134968ol_nat (tptp.hAPP_f883871819ol_nat (tptp.hAPP_f424754463ol_nat tptp.cOMBB_1716606670at_nat tptp.big_co1340561246_a_nat) (tptp.hAPP_f1903462933_a_nat tptp.cOMBC_667342884at_nat F))) A)) B))) (forall ((Z_1 $$unsorted) (A $$unsorted) (Y_1 $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.finite1973466193nt_int F)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool (tptp.finite772772422nt_int F) Z_1) A) Y_1)) (= (tptp.hAPP_f1594865479ol_int (tptp.finite_fold_int_int F Z_1) A) Y_1)))) (forall ((Z_1 $$unsorted) (A $$unsorted) (Y_1 $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.finite2130160977at_nat F)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool (tptp.finite929467206at_nat F) Z_1) A) Y_1)) (= (tptp.hAPP_f22106695ol_nat (tptp.finite_fold_nat_nat F Z_1) A) Y_1)))) (forall ((Z_1 $$unsorted) (A $$unsorted) (Y_1 $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.finite1428139793iple_a F)) (=> (tptp.hBOOL (tptp.hAPP_H1037229737a_bool (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool (tptp.finite90892550iple_a F) Z_1) A) Y_1)) (= (tptp.hAPP_f1693662087iple_a (tptp.finite1205970312iple_a F Z_1) A) Y_1)))) (forall ((Z_1 $$unsorted) (A $$unsorted) (Y_1 $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.finite1321096241t_bool F)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool (tptp.hAPP_f1634429330l_bool (tptp.finite1008073724t_bool F) Z_1) A) Y_1)) (= (tptp.hAPP_f1805168059t_bool (tptp.finite1827710202t_bool F Z_1) A) Y_1)))) (forall ((Z_1 $$unsorted) (A $$unsorted) (Y_1 $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.finite2114894759a_bool F)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_f1767618879l_bool (tptp.hAPP_f1577095245l_bool (tptp.finite1152845682a_bool F) Z_1) A) Y_1)) (= (tptp.hAPP_f20753329a_bool (tptp.finite1215486064a_bool F Z_1) A) Y_1)))) (forall ((Z_1 $$unsorted) (A $$unsorted) (Y_1 $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.finite1071749497t_bool F)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool (tptp.hAPP_f1266913334l_bool (tptp.finite758726980t_bool F) Z_1) A) Y_1)) (= (tptp.hAPP_f800510211t_bool (tptp.finite1578363458t_bool F Z_1) A) Y_1)))) (forall ((F $$unsorted) (Z_1 $$unsorted)) (= (tptp.hAPP_f1693662087iple_a (tptp.finite1205970312iple_a F Z_1) tptp.bot_bo797238721a_bool) Z_1)) (forall ((F $$unsorted) (Z_1 $$unsorted)) (= (tptp.hAPP_f20753329a_bool (tptp.finite1215486064a_bool F Z_1) tptp.bot_bo797238721a_bool) Z_1)) (forall ((F $$unsorted) (Z_1 $$unsorted)) (= (tptp.hAPP_f1594865479ol_int (tptp.finite_fold_int_int F Z_1) tptp.bot_bot_fun_int_bool) Z_1)) (forall ((F $$unsorted) (Z_1 $$unsorted)) (= (tptp.hAPP_f1805168059t_bool (tptp.finite1827710202t_bool F Z_1) tptp.bot_bot_fun_int_bool) Z_1)) (forall ((F $$unsorted) (Z_1 $$unsorted)) (= (tptp.hAPP_f22106695ol_nat (tptp.finite_fold_nat_nat F Z_1) tptp.bot_bot_fun_nat_bool) Z_1)) (forall ((F $$unsorted) (Z_1 $$unsorted)) (= (tptp.hAPP_f800510211t_bool (tptp.finite1578363458t_bool F Z_1) tptp.bot_bot_fun_nat_bool) Z_1)) (forall ((Z_1 $$unsorted) (X_1 $$unsorted) (A $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.finite2130160977at_nat F)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A))) (= (tptp.hAPP_f22106695ol_nat (tptp.finite_fold_nat_nat F Z_1) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) A)) (tptp.hAPP_f22106695ol_nat (tptp.finite_fold_nat_nat F (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat F X_1) Z_1)) A)))))) (forall ((Z_1 $$unsorted) (X_1 $$unsorted) (A $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.finite1071749497t_bool F)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A))) (= (tptp.hAPP_f800510211t_bool (tptp.finite1578363458t_bool F Z_1) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) A)) (tptp.hAPP_f800510211t_bool (tptp.finite1578363458t_bool F (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool F X_1) Z_1)) A)))))) (forall ((Z_1 $$unsorted) (X_1 $$unsorted) (A $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.finite1428139793iple_a F)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A)) (=> (not (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_1) A))) (= (tptp.hAPP_f1693662087iple_a (tptp.finite1205970312iple_a F Z_1) (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a X_1) A)) (tptp.hAPP_f1693662087iple_a (tptp.finite1205970312iple_a F (tptp.hAPP_H905846293iple_a (tptp.hAPP_H2085992369iple_a F X_1) Z_1)) A)))))) (forall ((Z_1 $$unsorted) (X_1 $$unsorted) (A $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.finite2114894759a_bool F)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A)) (=> (not (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_1) A))) (= (tptp.hAPP_f20753329a_bool (tptp.finite1215486064a_bool F Z_1) (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a X_1) A)) (tptp.hAPP_f20753329a_bool (tptp.finite1215486064a_bool F (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool F X_1) Z_1)) A)))))) (forall ((Z_1 $$unsorted) (X_1 $$unsorted) (A $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.finite1973466193nt_int F)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (=> (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A))) (= (tptp.hAPP_f1594865479ol_int (tptp.finite_fold_int_int F Z_1) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1) A)) (tptp.hAPP_f1594865479ol_int (tptp.finite_fold_int_int F (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int F X_1) Z_1)) A)))))) (forall ((Z_1 $$unsorted) (X_1 $$unsorted) (A $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.finite1321096241t_bool F)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (=> (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A))) (= (tptp.hAPP_f1805168059t_bool (tptp.finite1827710202t_bool F Z_1) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1) A)) (tptp.hAPP_f1805168059t_bool (tptp.finite1827710202t_bool F (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool F X_1) Z_1)) A)))))) (forall ((Z_1 $$unsorted) (X_1 $$unsorted) (A $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.finite_fold_nat_nat F Z_1))) (=> (tptp.hBOOL (tptp.finite2130160977at_nat F)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A))) (= (tptp.hAPP_f22106695ol_nat _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) A)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat F X_1) (tptp.hAPP_f22106695ol_nat _let_1 A)))))))) (forall ((Z_1 $$unsorted) (X_1 $$unsorted) (A $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.finite1578363458t_bool F Z_1))) (=> (tptp.hBOOL (tptp.finite1071749497t_bool F)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A))) (= (tptp.hAPP_f800510211t_bool _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) A)) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool F X_1) (tptp.hAPP_f800510211t_bool _let_1 A)))))))) (forall ((Z_1 $$unsorted) (X_1 $$unsorted) (A $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.finite1205970312iple_a F Z_1))) (=> (tptp.hBOOL (tptp.finite1428139793iple_a F)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A)) (=> (not (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_1) A))) (= (tptp.hAPP_f1693662087iple_a _let_1 (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a X_1) A)) (tptp.hAPP_H905846293iple_a (tptp.hAPP_H2085992369iple_a F X_1) (tptp.hAPP_f1693662087iple_a _let_1 A)))))))) (forall ((Z_1 $$unsorted) (X_1 $$unsorted) (A $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.finite1215486064a_bool F Z_1))) (=> (tptp.hBOOL (tptp.finite2114894759a_bool F)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A)) (=> (not (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_1) A))) (= (tptp.hAPP_f20753329a_bool _let_1 (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a X_1) A)) (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool F X_1) (tptp.hAPP_f20753329a_bool _let_1 A)))))))) (forall ((Z_1 $$unsorted) (X_1 $$unsorted) (A $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.finite_fold_int_int F Z_1))) (=> (tptp.hBOOL (tptp.finite1973466193nt_int F)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (=> (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A))) (= (tptp.hAPP_f1594865479ol_int _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1) A)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int F X_1) (tptp.hAPP_f1594865479ol_int _let_1 A)))))))) (forall ((Z_1 $$unsorted) (X_1 $$unsorted) (A $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.finite1827710202t_bool F Z_1))) (=> (tptp.hBOOL (tptp.finite1321096241t_bool F)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (=> (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A))) (= (tptp.hAPP_f1805168059t_bool _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1) A)) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool F X_1) (tptp.hAPP_f1805168059t_bool _let_1 A)))))))) (forall ((Z_1 $$unsorted) (A $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.finite1428139793iple_a F)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A)) (tptp.hBOOL (tptp.hAPP_H1037229737a_bool (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool (tptp.finite90892550iple_a F) Z_1) A) (tptp.hAPP_f1693662087iple_a (tptp.finite1205970312iple_a F Z_1) A)))))) (forall ((Z_1 $$unsorted) (A $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.finite2114894759a_bool F)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A)) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_f1767618879l_bool (tptp.hAPP_f1577095245l_bool (tptp.finite1152845682a_bool F) Z_1) A) (tptp.hAPP_f20753329a_bool (tptp.finite1215486064a_bool F Z_1) A)))))) (forall ((Z_1 $$unsorted) (A $$unsorted) (F $$unsorted)) (=> (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 $$unsorted) (A $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.finite1071749497t_bool F)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool (tptp.hAPP_f1266913334l_bool (tptp.finite758726980t_bool F) Z_1) A) (tptp.hAPP_f800510211t_bool (tptp.finite1578363458t_bool F Z_1) A)))))) (forall ((Z_1 $$unsorted) (A $$unsorted) (F $$unsorted)) (=> (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 $$unsorted) (A $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.finite1321096241t_bool F)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool (tptp.hAPP_f1634429330l_bool (tptp.finite1008073724t_bool F) Z_1) A) (tptp.hAPP_f1805168059t_bool (tptp.finite1827710202t_bool F Z_1) A)))))) (forall ((F $$unsorted) (A $$unsorted) (G $$unsorted) (B $$unsorted)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat F) A)) (tptp.hAPP_f957591787ol_nat (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat G) B)) (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat (tptp.hAPP_f1473602334at_nat (tptp.hAPP_f630508183at_nat tptp.cOMBC_1505178355ol_nat (tptp.hAPP_f299305025ol_nat (tptp.hAPP_f1632710027ol_nat tptp.cOMBB_1453893592at_nat tptp.big_co1740723097nt_nat) (tptp.hAPP_f237327688nt_nat (tptp.hAPP_f1633513941nt_nat tptp.cOMBC_1218031117nt_nat (tptp.hAPP_f2080483477nt_nat (tptp.hAPP_f1701814485nt_nat tptp.cOMBB_737513486at_nat tptp.cOMBB_nat_nat_int) (tptp.hAPP_f1639111240at_nat (tptp.hAPP_f1731313045at_nat tptp.cOMBB_963856155at_nat tptp.times_times_nat) F))) G))) B)) A))) (forall ((F $$unsorted) (A $$unsorted) (G $$unsorted) (B $$unsorted)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat F) A)) (tptp.hAPP_f2097660464ol_nat (tptp.hAPP_f1371399797ol_nat tptp.big_co1340561246_a_nat G) B)) (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat (tptp.hAPP_f2122367971at_nat (tptp.hAPP_f870149665at_nat tptp.cOMBC_2036134968ol_nat (tptp.hAPP_f883871819ol_nat (tptp.hAPP_f424754463ol_nat tptp.cOMBB_1716606670at_nat tptp.big_co1340561246_a_nat) (tptp.hAPP_f1393576712_a_nat (tptp.hAPP_f145529813_a_nat tptp.cOMBC_309106125_a_nat (tptp.hAPP_f1485673429_a_nat (tptp.hAPP_f2006236373_a_nat tptp.cOMBB_2005430478at_nat tptp.cOMBB_1250632933iple_a) (tptp.hAPP_f1639111240at_nat (tptp.hAPP_f1731313045at_nat tptp.cOMBB_963856155at_nat tptp.times_times_nat) F))) G))) B)) A))) (forall ((F $$unsorted) (A $$unsorted) (G $$unsorted) (B $$unsorted)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_f957591787ol_nat (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat F) A)) (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat G) B)) (tptp.hAPP_f957591787ol_nat (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat (tptp.hAPP_f787214110nt_nat (tptp.hAPP_f261731407nt_nat tptp.cOMBC_462113011ol_nat (tptp.hAPP_f1501159417ol_nat (tptp.hAPP_f1029311995ol_nat tptp.cOMBB_1562322300at_int tptp.big_co387207925at_nat) (tptp.hAPP_f1169617132at_nat (tptp.hAPP_f701299925at_nat tptp.cOMBC_1294079849at_nat (tptp.hAPP_f1033905301at_nat (tptp.hAPP_f1315855317at_nat tptp.cOMBB_891709290at_int tptp.cOMBB_nat_nat_nat) (tptp.hAPP_f1463450952at_nat (tptp.hAPP_f1087393429at_nat tptp.cOMBB_1601129847at_int tptp.times_times_nat) F))) G))) B)) A))) (forall ((F $$unsorted) (A $$unsorted) (G $$unsorted) (B $$unsorted)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_f2097660464ol_nat (tptp.hAPP_f1371399797ol_nat tptp.big_co1340561246_a_nat F) A)) (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat G) B)) (tptp.hAPP_f2097660464ol_nat (tptp.hAPP_f1371399797ol_nat tptp.big_co1340561246_a_nat (tptp.hAPP_f1464798435_a_nat (tptp.hAPP_f1012303887_a_nat tptp.cOMBC_1159891896ol_nat (tptp.hAPP_f1669765561ol_nat (tptp.hAPP_f1073041467ol_nat tptp.cOMBB_10565751iple_a tptp.big_co387207925at_nat) (tptp.hAPP_f221335601at_nat (tptp.hAPP_f388255893at_nat tptp.cOMBC_1038836708at_nat (tptp.hAPP_f1879857877at_nat (tptp.hAPP_f481016213at_nat tptp.cOMBB_1672982117iple_a tptp.cOMBB_nat_nat_nat) (tptp.hAPP_f429024520at_nat (tptp.hAPP_f703420885at_nat tptp.cOMBB_789959282iple_a tptp.times_times_nat) F))) G))) B)) A))) (forall ((F $$unsorted) (A $$unsorted) (R_2 $$unsorted)) (= (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 $$unsorted) (A $$unsorted) (R_2 $$unsorted)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_f957591787ol_nat (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat F) A)) R_2) (tptp.hAPP_f957591787ol_nat (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat (tptp.hAPP_nat_fun_int_nat (tptp.hAPP_f879494613nt_nat tptp.cOMBC_int_nat_nat (tptp.hAPP_f1463450952at_nat (tptp.hAPP_f1087393429at_nat tptp.cOMBB_1601129847at_int tptp.times_times_nat) F)) R_2)) A))) (forall ((F $$unsorted) (A $$unsorted) (R_2 $$unsorted)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_f2097660464ol_nat (tptp.hAPP_f1371399797ol_nat tptp.big_co1340561246_a_nat F) A)) R_2) (tptp.hAPP_f2097660464ol_nat (tptp.hAPP_f1371399797ol_nat tptp.big_co1340561246_a_nat (tptp.hAPP_n1653940209_a_nat (tptp.hAPP_f1903462933_a_nat tptp.cOMBC_667342884at_nat (tptp.hAPP_f429024520at_nat (tptp.hAPP_f703420885at_nat tptp.cOMBB_789959282iple_a tptp.times_times_nat) F)) R_2)) A))) (forall ((R_2 $$unsorted) (F $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat R_2))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat F) A)) (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat (tptp.hAPP_f1914919701at_nat (tptp.hAPP_f1585078997at_nat tptp.cOMBB_nat_nat_nat _let_1) F)) A)))) (forall ((R_2 $$unsorted) (F $$unsorted) (A $$unsorted)) (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 $$unsorted) (F $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat R_2))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_f2097660464ol_nat (tptp.hAPP_f1371399797ol_nat tptp.big_co1340561246_a_nat F) A)) (tptp.hAPP_f2097660464ol_nat (tptp.hAPP_f1371399797ol_nat tptp.big_co1340561246_a_nat (tptp.hAPP_f106743253_a_nat (tptp.hAPP_f500900629_a_nat tptp.cOMBB_1250632933iple_a _let_1) F)) A)))) (tptp.hBOOL (tptp.finite2130160977at_nat tptp.times_times_nat)) (tptp.hBOOL (tptp.finite1973466193nt_int tptp.times_times_int)) (forall ((Y_1 $$unsorted) (Z_1 $$unsorted) (A $$unsorted) (X_1 $$unsorted) (F $$unsorted)) (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 $$unsorted) (Z_1 $$unsorted) (A $$unsorted) (X_1 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool (tptp.finite929467206at_nat F) Z_1) A))) (=> (tptp.hBOOL (tptp.finite2130160977at_nat F)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 X_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Y_1)) (= Y_1 X_1)))))) (forall ((Y_1 $$unsorted) (Z_1 $$unsorted) (A $$unsorted) (X_1 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool (tptp.finite90892550iple_a F) Z_1) A))) (=> (tptp.hBOOL (tptp.finite1428139793iple_a F)) (=> (tptp.hBOOL (tptp.hAPP_H1037229737a_bool _let_1 X_1)) (=> (tptp.hBOOL (tptp.hAPP_H1037229737a_bool _let_1 Y_1)) (= Y_1 X_1)))))) (forall ((G $$unsorted) (H $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A)) (= (tptp.hAPP_f2097660464ol_nat (tptp.big_co1815942735_a_nat (tptp.hAPP_f106743253_a_nat (tptp.hAPP_f1418102009_a_nat tptp.cOMBS_1756972052at_nat (tptp.hAPP_f429024520at_nat (tptp.hAPP_f703420885at_nat tptp.cOMBB_789959282iple_a tptp.times_times_nat) G)) H)) A) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_f2097660464ol_nat (tptp.big_co1815942735_a_nat G) A)) (tptp.hAPP_f2097660464ol_nat (tptp.big_co1815942735_a_nat H) A))))) (forall ((G $$unsorted) (H $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A)) (= (tptp.hAPP_f587450508ol_int (tptp.big_co305732779_a_int (tptp.hAPP_f1561000661_a_int (tptp.hAPP_f789902073_a_int tptp.cOMBS_1600277268nt_int (tptp.hAPP_f231878828nt_int (tptp.hAPP_f1621780181nt_int tptp.cOMBB_1885471694iple_a tptp.times_times_int) G)) H)) A) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_f587450508ol_int (tptp.big_co305732779_a_int G) A)) (tptp.hAPP_f587450508ol_int (tptp.big_co305732779_a_int H) A))))) (forall ((Z_1 $$unsorted) (X_1 $$unsorted) (A $$unsorted) (F $$unsorted)) (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 $$unsorted) (X_1 $$unsorted) (A $$unsorted) (F $$unsorted)) (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 $$unsorted) (X_1 $$unsorted) (A $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.finite1205970312iple_a F Z_1))) (=> (tptp.hBOOL (tptp.finite1428139793iple_a F)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_1) A)) (= (tptp.hAPP_f1693662087iple_a _let_1 A) (tptp.hAPP_H905846293iple_a (tptp.hAPP_H2085992369iple_a F X_1) (tptp.hAPP_f1693662087iple_a _let_1 (tptp.hAPP_f20753329a_bool (tptp.hAPP_f1706700729a_bool tptp.minus_85316870a_bool A) (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a X_1) tptp.bot_bo797238721a_bool)))))))))) (forall ((Z_1 $$unsorted) (X_1 $$unsorted) (A $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.finite1215486064a_bool F Z_1))) (=> (tptp.hBOOL (tptp.finite2114894759a_bool F)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_1) A)) (= (tptp.hAPP_f20753329a_bool _let_1 A) (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool F X_1) (tptp.hAPP_f20753329a_bool _let_1 (tptp.hAPP_f20753329a_bool (tptp.hAPP_f1706700729a_bool tptp.minus_85316870a_bool A) (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a X_1) tptp.bot_bo797238721a_bool)))))))))) (forall ((Z_1 $$unsorted) (X_1 $$unsorted) (A $$unsorted) (F $$unsorted)) (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 $$unsorted) (X_1 $$unsorted) (A $$unsorted) (F $$unsorted)) (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 $$unsorted) (X_1 $$unsorted) (A $$unsorted) (F $$unsorted)) (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 $$unsorted) (X_1 $$unsorted) (A $$unsorted) (F $$unsorted)) (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 $$unsorted) (X_1 $$unsorted) (A $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a X_1))) (let ((_let_2 (tptp.finite1205970312iple_a F Z_1))) (=> (tptp.hBOOL (tptp.finite1428139793iple_a F)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A)) (= (tptp.hAPP_f1693662087iple_a _let_2 (tptp.hAPP_f20753329a_bool _let_1 A)) (tptp.hAPP_H905846293iple_a (tptp.hAPP_H2085992369iple_a F X_1) (tptp.hAPP_f1693662087iple_a _let_2 (tptp.hAPP_f20753329a_bool (tptp.hAPP_f1706700729a_bool tptp.minus_85316870a_bool A) (tptp.hAPP_f20753329a_bool _let_1 tptp.bot_bo797238721a_bool)))))))))) (forall ((Z_1 $$unsorted) (X_1 $$unsorted) (A $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a X_1))) (let ((_let_2 (tptp.finite1215486064a_bool F Z_1))) (=> (tptp.hBOOL (tptp.finite2114894759a_bool F)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A)) (= (tptp.hAPP_f20753329a_bool _let_2 (tptp.hAPP_f20753329a_bool _let_1 A)) (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool F X_1) (tptp.hAPP_f20753329a_bool _let_2 (tptp.hAPP_f20753329a_bool (tptp.hAPP_f1706700729a_bool tptp.minus_85316870a_bool A) (tptp.hAPP_f20753329a_bool _let_1 tptp.bot_bo797238721a_bool)))))))))) (forall ((Z_1 $$unsorted) (X_1 $$unsorted) (A $$unsorted) (F $$unsorted)) (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 $$unsorted) (X_1 $$unsorted) (A $$unsorted) (F $$unsorted)) (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 $$unsorted) (A_13 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.big_co1705425894at_nat F))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_13) A))) (= (tptp.hAPP_f22106695ol_nat _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13) A)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat F A_13)) (tptp.hAPP_f22106695ol_nat _let_1 A))))))) (forall ((F $$unsorted) (A_13 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.big_co1815942735_a_nat F))) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A)) (=> (not (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a A_13) A))) (= (tptp.hAPP_f2097660464ol_nat _let_1 (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a A_13) A)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_H592031934_a_nat F A_13)) (tptp.hAPP_f2097660464ol_nat _let_1 A))))))) (forall ((F $$unsorted) (A_13 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.big_co195215938at_int F))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_13) A))) (= (tptp.hAPP_f659380387ol_int _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13) A)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_nat_int F A_13)) (tptp.hAPP_f659380387ol_int _let_1 A))))))) (forall ((F $$unsorted) (A_13 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.big_co305732779_a_int F))) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A)) (=> (not (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a A_13) A))) (= (tptp.hAPP_f587450508ol_int _let_1 (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a A_13) A)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_H1229305626_a_int F A_13)) (tptp.hAPP_f587450508ol_int _let_1 A))))))) (forall ((G $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.big_co1705425894at_nat G))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A))) (= (tptp.hAPP_f22106695ol_nat _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) A)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat G X_1)) (tptp.hAPP_f22106695ol_nat _let_1 A))))))) (forall ((G $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.big_co1815942735_a_nat G))) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A)) (=> (not (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_1) A))) (= (tptp.hAPP_f2097660464ol_nat _let_1 (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a X_1) A)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_H592031934_a_nat G X_1)) (tptp.hAPP_f2097660464ol_nat _let_1 A))))))) (forall ((G $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.big_co195215938at_int G))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A))) (= (tptp.hAPP_f659380387ol_int _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) A)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_nat_int G X_1)) (tptp.hAPP_f659380387ol_int _let_1 A))))))) (forall ((G $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.big_co305732779_a_int G))) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A)) (=> (not (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_1) A))) (= (tptp.hAPP_f587450508ol_int _let_1 (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a X_1) A)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_H1229305626_a_int G X_1)) (tptp.hAPP_f587450508ol_int _let_1 A))))))) (forall ((F $$unsorted) (A_13 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat F))) (let ((_let_2 (tptp.hAPP_f22106695ol_nat _let_1 A))) (let ((_let_3 (tptp.hAPP_f22106695ol_nat _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13) tptp.bot_bot_fun_nat_bool))))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_13) A)))) (and (=> _let_4 (= _let_3 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat _let_2) (tptp.hAPP_nat_nat F A_13)))) (=> (not _let_4) (= _let_3 _let_2)))))))) (forall ((F $$unsorted) (A_13 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f1371399797ol_nat tptp.big_co1340561246_a_nat F))) (let ((_let_2 (tptp.hAPP_f2097660464ol_nat _let_1 A))) (let ((_let_3 (tptp.hAPP_f2097660464ol_nat _let_1 (tptp.hAPP_f20753329a_bool (tptp.hAPP_f1706700729a_bool tptp.minus_85316870a_bool A) (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a A_13) tptp.bot_bo797238721a_bool))))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_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_H592031934_a_nat F A_13)))) (=> (not _let_4) (= _let_3 _let_2)))))))) (forall ((F $$unsorted) (A_13 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat F))) (let ((_let_2 (tptp.hAPP_f957591787ol_nat _let_1 A))) (let ((_let_3 (tptp.hAPP_f957591787ol_nat _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_13) tptp.bot_bot_fun_int_bool))))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int A_13) A)))) (and (=> _let_4 (= _let_3 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat _let_2) (tptp.hAPP_int_nat F A_13)))) (=> (not _let_4) (= _let_3 _let_2)))))))) (forall ((F $$unsorted) (Z_1 $$unsorted) (A $$unsorted)) (= (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 $$unsorted) (Z_1 $$unsorted) (A $$unsorted)) (= (tptp.hAPP_f22106695ol_nat (tptp.finite_fold_nat_nat F Z_1) A) (tptp.hAPP_f22106695ol_nat tptp.the_nat (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool (tptp.finite929467206at_nat F) Z_1) A)))) (forall ((F $$unsorted) (Z_1 $$unsorted) (A $$unsorted)) (= (tptp.hAPP_f1693662087iple_a (tptp.finite1205970312iple_a F Z_1) A) (tptp.hAPP_f1693662087iple_a tptp.the_Ho830102290iple_a (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool (tptp.finite90892550iple_a F) Z_1) A)))) (forall ((F $$unsorted) (Z_1 $$unsorted) (A $$unsorted)) (= (tptp.hAPP_f1805168059t_bool (tptp.finite1827710202t_bool F Z_1) A) (tptp.hAPP_f631471077t_bool tptp.the_fun_int_bool (tptp.hAPP_f284875647l_bool (tptp.hAPP_f1634429330l_bool (tptp.finite1008073724t_bool F) Z_1) A)))) (forall ((F $$unsorted) (Z_1 $$unsorted) (A $$unsorted)) (= (tptp.hAPP_f20753329a_bool (tptp.finite1215486064a_bool F Z_1) A) (tptp.hAPP_f258822235a_bool tptp.the_fu1555441254a_bool (tptp.hAPP_f1767618879l_bool (tptp.hAPP_f1577095245l_bool (tptp.finite1152845682a_bool F) Z_1) A)))) (forall ((F $$unsorted) (Z_1 $$unsorted) (A $$unsorted)) (= (tptp.hAPP_f800510211t_bool (tptp.finite1578363458t_bool F Z_1) A) (tptp.hAPP_f582319405t_bool tptp.the_fun_nat_bool (tptp.hAPP_f103356543l_bool (tptp.hAPP_f1266913334l_bool (tptp.finite758726980t_bool F) Z_1) A)))) (forall ((Z_1 $$unsorted) (X_1 $$unsorted) (A $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.finite1860950092at_nat F)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (= (tptp.hAPP_f22106695ol_nat (tptp.finite_fold_nat_nat F Z_1) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) A)) (tptp.hAPP_f22106695ol_nat (tptp.finite_fold_nat_nat F (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat F X_1) Z_1)) A))))) (forall ((Z_1 $$unsorted) (X_1 $$unsorted) (A $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.finite1956789438t_bool F)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (= (tptp.hAPP_f800510211t_bool (tptp.finite1578363458t_bool F Z_1) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) A)) (tptp.hAPP_f800510211t_bool (tptp.finite1578363458t_bool F (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool F X_1) Z_1)) A))))) (forall ((Z_1 $$unsorted) (X_1 $$unsorted) (A $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.finite648855052iple_a F)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A)) (= (tptp.hAPP_f1693662087iple_a (tptp.finite1205970312iple_a F Z_1) (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a X_1) A)) (tptp.hAPP_f1693662087iple_a (tptp.finite1205970312iple_a F (tptp.hAPP_H905846293iple_a (tptp.hAPP_H2085992369iple_a F X_1) Z_1)) A))))) (forall ((Z_1 $$unsorted) (X_1 $$unsorted) (A $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.finite1803123436a_bool F)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A)) (= (tptp.hAPP_f20753329a_bool (tptp.finite1215486064a_bool F Z_1) (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a X_1) A)) (tptp.hAPP_f20753329a_bool (tptp.finite1215486064a_bool F (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool F X_1) Z_1)) A))))) (forall ((Z_1 $$unsorted) (X_1 $$unsorted) (A $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.finite1704255308nt_int F)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (= (tptp.hAPP_f1594865479ol_int (tptp.finite_fold_int_int F Z_1) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1) A)) (tptp.hAPP_f1594865479ol_int (tptp.finite_fold_int_int F (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int F X_1) Z_1)) A))))) (forall ((Z_1 $$unsorted) (X_1 $$unsorted) (A $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.finite58652534t_bool F)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (= (tptp.hAPP_f1805168059t_bool (tptp.finite1827710202t_bool F Z_1) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1) A)) (tptp.hAPP_f1805168059t_bool (tptp.finite1827710202t_bool F (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool F X_1) Z_1)) A))))) (forall ((Z_1 $$unsorted) (X_1 $$unsorted) (A $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.finite_fold_nat_nat F Z_1))) (=> (tptp.hBOOL (tptp.finite1860950092at_nat F)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (= (tptp.hAPP_f22106695ol_nat _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) A)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat F X_1) (tptp.hAPP_f22106695ol_nat _let_1 A))))))) (forall ((Z_1 $$unsorted) (X_1 $$unsorted) (A $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.finite1578363458t_bool F Z_1))) (=> (tptp.hBOOL (tptp.finite1956789438t_bool F)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (= (tptp.hAPP_f800510211t_bool _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) A)) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool F X_1) (tptp.hAPP_f800510211t_bool _let_1 A))))))) (forall ((Z_1 $$unsorted) (X_1 $$unsorted) (A $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.finite1205970312iple_a F Z_1))) (=> (tptp.hBOOL (tptp.finite648855052iple_a F)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A)) (= (tptp.hAPP_f1693662087iple_a _let_1 (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a X_1) A)) (tptp.hAPP_H905846293iple_a (tptp.hAPP_H2085992369iple_a F X_1) (tptp.hAPP_f1693662087iple_a _let_1 A))))))) (forall ((Z_1 $$unsorted) (X_1 $$unsorted) (A $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.finite1215486064a_bool F Z_1))) (=> (tptp.hBOOL (tptp.finite1803123436a_bool F)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A)) (= (tptp.hAPP_f20753329a_bool _let_1 (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a X_1) A)) (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool F X_1) (tptp.hAPP_f20753329a_bool _let_1 A))))))) (forall ((Z_1 $$unsorted) (X_1 $$unsorted) (A $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.finite_fold_int_int F Z_1))) (=> (tptp.hBOOL (tptp.finite1704255308nt_int F)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (= (tptp.hAPP_f1594865479ol_int _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1) A)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int F X_1) (tptp.hAPP_f1594865479ol_int _let_1 A))))))) (forall ((Z_1 $$unsorted) (X_1 $$unsorted) (A $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.finite1827710202t_bool F Z_1))) (=> (tptp.hBOOL (tptp.finite58652534t_bool F)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (= (tptp.hAPP_f1805168059t_bool _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1) A)) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool F X_1) (tptp.hAPP_f1805168059t_bool _let_1 A))))))) (forall ((X_1 $$unsorted) (A $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (=> (tptp.hBOOL (tptp.finite988810631ne_nat F F_1)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A))) (= (tptp.hAPP_f22106695ol_nat F_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) A)) (tptp.hAPP_f22106695ol_nat (tptp.finite_fold_nat_nat F X_1) A)))))) (forall ((X_1 $$unsorted) (A $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (=> (tptp.hBOOL (tptp.finite1753440478iple_a F F_1)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A)) (=> (not (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_1) A))) (= (tptp.hAPP_f1693662087iple_a F_1 (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a X_1) A)) (tptp.hAPP_f1693662087iple_a (tptp.finite1205970312iple_a F X_1) A)))))) (forall ((X_1 $$unsorted) (A $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (=> (tptp.hBOOL (tptp.finite1626084323ne_int F F_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (=> (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A))) (= (tptp.hAPP_f1594865479ol_int F_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1) A)) (tptp.hAPP_f1594865479ol_int (tptp.finite_fold_int_int F X_1) A)))))) (forall ((A_13 $$unsorted) (A $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (=> (tptp.hBOOL (tptp.finite795500164em_nat F F_1)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (= (tptp.hAPP_f22106695ol_nat F_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13) A)) (tptp.hAPP_f22106695ol_nat (tptp.finite_fold_nat_nat F A_13) A))))) (forall ((A_13 $$unsorted) (A $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (=> (tptp.hBOOL (tptp.finite1033474011iple_a F F_1)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A)) (= (tptp.hAPP_f1693662087iple_a F_1 (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a A_13) A)) (tptp.hAPP_f1693662087iple_a (tptp.finite1205970312iple_a F A_13) A))))) (forall ((A_13 $$unsorted) (A $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (=> (tptp.hBOOL (tptp.finite1432773856em_int F F_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (= (tptp.hAPP_f1594865479ol_int F_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_13) A)) (tptp.hAPP_f1594865479ol_int (tptp.finite_fold_int_int F A_13) A))))) (forall ((A_13 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_13) A))) (= (tptp.hAPP_f22106695ol_nat (tptp.finite_fold1_nat tptp.times_times_nat) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13) A)) (tptp.hAPP_f22106695ol_nat (tptp.finite_fold_nat_nat tptp.times_times_nat A_13) A))))) (forall ((A_13 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (=> (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int A_13) A))) (= (tptp.hAPP_f1594865479ol_int (tptp.finite_fold1_int tptp.times_times_int) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_13) A)) (tptp.hAPP_f1594865479ol_int (tptp.finite_fold_int_int tptp.times_times_int A_13) A))))) (forall ((Z_1 $$unsorted) (X_1 $$unsorted) (A $$unsorted) (V $$unsorted) (F $$unsorted)) (=> (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 $$unsorted)) (=> (= V (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat F X_1) Y_21)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool (tptp.finite929467206at_nat F) Z_1) A) Y_21)))))))))) (forall ((Z_1 $$unsorted) (X_1 $$unsorted) (A $$unsorted) (V $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.finite1428139793iple_a F)) (=> (tptp.hBOOL (tptp.hAPP_H1037229737a_bool (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool (tptp.finite90892550iple_a F) Z_1) (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a X_1) A)) V)) (=> (not (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_1) A))) (not (forall ((Y_21 $$unsorted)) (=> (= V (tptp.hAPP_H905846293iple_a (tptp.hAPP_H2085992369iple_a F X_1) Y_21)) (not (tptp.hBOOL (tptp.hAPP_H1037229737a_bool (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool (tptp.finite90892550iple_a F) Z_1) A) Y_21)))))))))) (forall ((Z_1 $$unsorted) (X_1 $$unsorted) (A $$unsorted) (V $$unsorted) (F $$unsorted)) (=> (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 $$unsorted)) (=> (= V (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int F X_1) Y_21)) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool (tptp.finite772772422nt_int F) Z_1) A) Y_21)))))))))) (forall ((G $$unsorted) (F $$unsorted) (S_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1371399797ol_nat tptp.big_co1340561246_a_nat G))) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a S_1)) (= (tptp.hAPP_f2097660464ol_nat _let_1 S_1) (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat (tptp.hAPP_f966999552at_nat (tptp.hAPP_f724467227at_nat tptp.cOMBB_161916371at_nat _let_1) (tptp.hAPP_f2087582327a_bool (tptp.hAPP_f1396758363a_bool tptp.cOMBB_391046962ol_nat tptp.collec351493750iple_a) (tptp.hAPP_f2087582327a_bool (tptp.hAPP_f1396758363a_bool tptp.cOMBB_391046962ol_nat (tptp.hAPP_f607497069a_bool tptp.cOMBS_154988028l_bool (tptp.hAPP_f146754017l_bool (tptp.hAPP_f239971723l_bool tptp.cOMBB_1866391387iple_a tptp.fconj) (tptp.hAPP_f20753329a_bool (tptp.hAPP_f247708275a_bool tptp.cOMBC_1519416966l_bool tptp.member1797258804iple_a) S_1)))) (tptp.hAPP_f228417655a_bool tptp.cOMBC_364739t_bool (tptp.hAPP_f1872860171t_bool (tptp.hAPP_f1981448543t_bool tptp.cOMBB_1391527205iple_a tptp.fequal_nat) F)))))) (tptp.image_48635758_a_nat F S_1)))))) (forall ((G $$unsorted) (F $$unsorted) (S_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat G))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int S_1)) (= (tptp.hAPP_f957591787ol_nat _let_1 S_1) (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat (tptp.hAPP_f389300155at_nat (tptp.hAPP_f109563153at_nat tptp.cOMBB_1381347800at_nat _let_1) (tptp.hAPP_f2022049025t_bool (tptp.hAPP_f1986088027t_bool tptp.cOMBB_2101530536ol_nat tptp.collect_int) (tptp.hAPP_f2022049025t_bool (tptp.hAPP_f1986088027t_bool tptp.cOMBB_2101530536ol_nat (tptp.hAPP_f727283836t_bool tptp.cOMBS_int_bool_bool (tptp.hAPP_f2144054103l_bool (tptp.hAPP_f1734373249l_bool tptp.cOMBB_1652995168ol_int tptp.fconj) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f202917053t_bool tptp.cOMBC_94739984l_bool tptp.member_int) S_1)))) (tptp.hAPP_f175561985t_bool tptp.cOMBC_int_nat_bool (tptp.hAPP_f876579787t_bool (tptp.hAPP_f2026117279t_bool tptp.cOMBB_1437810218ol_int tptp.fequal_nat) F)))))) (tptp.image_int_nat F S_1)))))) (forall ((G $$unsorted) (F $$unsorted) (S_1 $$unsorted)) (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_f2097660464ol_nat (tptp.hAPP_f1371399797ol_nat tptp.big_co1340561246_a_nat (tptp.hAPP_f2085403241_a_nat (tptp.hAPP_f734830747_a_nat tptp.cOMBB_1107515603iple_a _let_1) (tptp.hAPP_f27379319t_bool (tptp.hAPP_f196067081t_bool tptp.cOMBB_437532599iple_a tptp.collect_nat) (tptp.hAPP_f27379319t_bool (tptp.hAPP_f196067081t_bool tptp.cOMBB_437532599iple_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_f1886543991t_bool tptp.cOMBC_533513393a_bool (tptp.hAPP_f260875897a_bool (tptp.hAPP_f1930382715a_bool tptp.cOMBB_1063143712ol_nat tptp.fequal963300192iple_a) F)))))) (tptp.image_1865589340iple_a F S_1)))))) (forall ((G $$unsorted) (F $$unsorted) (S_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat G))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int S_1)) (= (tptp.hAPP_f957591787ol_nat _let_1 S_1) (tptp.hAPP_f957591787ol_nat (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat (tptp.hAPP_f1134349059nt_nat (tptp.hAPP_f2100446809nt_nat tptp.cOMBB_2018621492at_int _let_1) (tptp.hAPP_f428220345t_bool (tptp.hAPP_f654702867t_bool tptp.cOMBB_591320580ol_int tptp.collect_int) (tptp.hAPP_f428220345t_bool (tptp.hAPP_f654702867t_bool tptp.cOMBB_591320580ol_int (tptp.hAPP_f727283836t_bool tptp.cOMBS_int_bool_bool (tptp.hAPP_f2144054103l_bool (tptp.hAPP_f1734373249l_bool tptp.cOMBB_1652995168ol_int tptp.fconj) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f202917053t_bool tptp.cOMBC_94739984l_bool tptp.member_int) S_1)))) (tptp.hAPP_f428220345t_bool tptp.cOMBC_int_int_bool (tptp.hAPP_f1791153283t_bool (tptp.hAPP_f1399575567t_bool tptp.cOMBB_118231410ol_int tptp.fequal_int) F)))))) (tptp.image_int_int F S_1)))))) (forall ((G $$unsorted) (F $$unsorted) (S_1 $$unsorted)) (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_f2097660464ol_nat (tptp.hAPP_f1371399797ol_nat tptp.big_co1340561246_a_nat (tptp.hAPP_f342603021_a_nat (tptp.hAPP_f575660003_a_nat tptp.cOMBB_1357028143iple_a _let_1) (tptp.hAPP_f138254639t_bool (tptp.hAPP_f1998609161t_bool tptp.cOMBB_1870764287iple_a tptp.collect_int) (tptp.hAPP_f138254639t_bool (tptp.hAPP_f1998609161t_bool tptp.cOMBB_1870764287iple_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_f936407855t_bool tptp.cOMBC_1719122773a_bool (tptp.hAPP_f298605433a_bool (tptp.hAPP_f1421841531a_bool tptp.cOMBB_1700417404ol_int tptp.fequal963300192iple_a) F)))))) (tptp.image_1844722432iple_a F S_1)))))) (forall ((G $$unsorted) (F $$unsorted) (S_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat G))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat S_1)) (= (tptp.hAPP_f22106695ol_nat _let_1 S_1) (tptp.hAPP_f957591787ol_nat (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat (tptp.hAPP_f1161717855nt_nat (tptp.hAPP_f1964560145nt_nat tptp.cOMBB_1125113304at_int _let_1) (tptp.hAPP_f783004929t_bool (tptp.hAPP_f1410409747t_bool tptp.cOMBB_1746576572ol_int tptp.collect_nat) (tptp.hAPP_f783004929t_bool (tptp.hAPP_f1410409747t_bool tptp.cOMBB_1746576572ol_int (tptp.hAPP_f561022312t_bool tptp.cOMBS_nat_bool_bool (tptp.hAPP_f1146629647l_bool (tptp.hAPP_f1080886329l_bool tptp.cOMBB_1015721476ol_nat tptp.fconj) (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1722879237t_bool tptp.cOMBC_226598744l_bool tptp.member_nat) S_1)))) (tptp.hAPP_f482008321t_bool tptp.cOMBC_nat_int_bool (tptp.hAPP_f1533130627t_bool (tptp.hAPP_f879109391t_bool tptp.cOMBB_1628441366ol_nat tptp.fequal_int) F)))))) (tptp.image_nat_int F S_1)))))) (forall ((G $$unsorted) (H $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_2) A)) (= (tptp.hAPP_H592031934_a_nat G X_2) (tptp.hAPP_H592031934_a_nat H X_2)))) (= (tptp.hAPP_f2097660464ol_nat (tptp.hAPP_f1371399797ol_nat tptp.big_co1340561246_a_nat G) A) (tptp.hAPP_f2097660464ol_nat (tptp.hAPP_f1371399797ol_nat tptp.big_co1340561246_a_nat H) A))))) (forall ((G $$unsorted) (H $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) A)) (= (tptp.hAPP_nat_nat G X_2) (tptp.hAPP_nat_nat H X_2)))) (= (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat G) A) (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat H) A))))) (forall ((G $$unsorted) (H $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_2) A)) (= (tptp.hAPP_int_nat G X_2) (tptp.hAPP_int_nat H X_2)))) (= (tptp.hAPP_f957591787ol_nat (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat G) A) (tptp.hAPP_f957591787ol_nat (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat H) A))))) (forall ((F $$unsorted) (R_1 $$unsorted) (T_1 $$unsorted) (S_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int S_1)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat T_1)) (= (tptp.hAPP_f957591787ol_nat (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat (tptp.hAPP_f1161717855nt_nat (tptp.hAPP_f369809936nt_nat tptp.cOMBS_1063588099ol_nat (tptp.hAPP_f1501159417ol_nat (tptp.hAPP_f1029311995ol_nat tptp.cOMBB_1562322300at_int tptp.big_co387207925at_nat) F)) (tptp.hAPP_f783004929t_bool (tptp.hAPP_f1410409747t_bool tptp.cOMBB_1746576572ol_int tptp.collect_nat) (tptp.hAPP_f783004929t_bool (tptp.hAPP_f1410409747t_bool tptp.cOMBB_1746576572ol_int (tptp.hAPP_f561022312t_bool tptp.cOMBS_nat_bool_bool (tptp.hAPP_f1146629647l_bool (tptp.hAPP_f1080886329l_bool tptp.cOMBB_1015721476ol_nat tptp.fconj) (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1722879237t_bool tptp.cOMBC_226598744l_bool tptp.member_nat) T_1)))) R_1)))) S_1) (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat (tptp.hAPP_f389300155at_nat (tptp.hAPP_f1750007732at_nat tptp.cOMBS_2106653443ol_nat (tptp.hAPP_f299305025ol_nat (tptp.hAPP_f1632710027ol_nat tptp.cOMBB_1453893592at_nat tptp.big_co1740723097nt_nat) (tptp.hAPP_f879494613nt_nat tptp.cOMBC_int_nat_nat F))) (tptp.hAPP_f2022049025t_bool (tptp.hAPP_f1986088027t_bool tptp.cOMBB_2101530536ol_nat tptp.collect_int) (tptp.hAPP_f2022049025t_bool (tptp.hAPP_f1986088027t_bool tptp.cOMBB_2101530536ol_nat (tptp.hAPP_f727283836t_bool tptp.cOMBS_int_bool_bool (tptp.hAPP_f2144054103l_bool (tptp.hAPP_f1734373249l_bool tptp.cOMBB_1652995168ol_int tptp.fconj) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f202917053t_bool tptp.cOMBC_94739984l_bool tptp.member_int) S_1)))) (tptp.hAPP_f175561985t_bool tptp.cOMBC_int_nat_bool R_1))))) T_1))))) (forall ((F $$unsorted) (R_1 $$unsorted) (T_1 $$unsorted) (S_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a S_1)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat T_1)) (= (tptp.hAPP_f2097660464ol_nat (tptp.hAPP_f1371399797ol_nat tptp.big_co1340561246_a_nat (tptp.hAPP_f2085403241_a_nat (tptp.hAPP_f1052116629_a_nat tptp.cOMBS_397915080ol_nat (tptp.hAPP_f1669765561ol_nat (tptp.hAPP_f1073041467ol_nat tptp.cOMBB_10565751iple_a tptp.big_co387207925at_nat) F)) (tptp.hAPP_f27379319t_bool (tptp.hAPP_f196067081t_bool tptp.cOMBB_437532599iple_a tptp.collect_nat) (tptp.hAPP_f27379319t_bool (tptp.hAPP_f196067081t_bool tptp.cOMBB_437532599iple_a (tptp.hAPP_f561022312t_bool tptp.cOMBS_nat_bool_bool (tptp.hAPP_f1146629647l_bool (tptp.hAPP_f1080886329l_bool tptp.cOMBB_1015721476ol_nat tptp.fconj) (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1722879237t_bool tptp.cOMBC_226598744l_bool tptp.member_nat) T_1)))) R_1)))) S_1) (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat (tptp.hAPP_f966999552at_nat (tptp.hAPP_f264818750at_nat tptp.cOMBS_1274158152ol_nat (tptp.hAPP_f883871819ol_nat (tptp.hAPP_f424754463ol_nat tptp.cOMBB_1716606670at_nat tptp.big_co1340561246_a_nat) (tptp.hAPP_f1903462933_a_nat tptp.cOMBC_667342884at_nat F))) (tptp.hAPP_f2087582327a_bool (tptp.hAPP_f1396758363a_bool tptp.cOMBB_391046962ol_nat tptp.collec351493750iple_a) (tptp.hAPP_f2087582327a_bool (tptp.hAPP_f1396758363a_bool tptp.cOMBB_391046962ol_nat (tptp.hAPP_f607497069a_bool tptp.cOMBS_154988028l_bool (tptp.hAPP_f146754017l_bool (tptp.hAPP_f239971723l_bool tptp.cOMBB_1866391387iple_a tptp.fconj) (tptp.hAPP_f20753329a_bool (tptp.hAPP_f247708275a_bool tptp.cOMBC_1519416966l_bool tptp.member1797258804iple_a) S_1)))) (tptp.hAPP_f228417655a_bool tptp.cOMBC_364739t_bool R_1))))) T_1))))) (forall ((F $$unsorted) (R_1 $$unsorted) (T_1 $$unsorted) (S_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a S_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int T_1)) (= (tptp.hAPP_f2097660464ol_nat (tptp.hAPP_f1371399797ol_nat tptp.big_co1340561246_a_nat (tptp.hAPP_f342603021_a_nat (tptp.hAPP_f270087133_a_nat tptp.cOMBS_1333400172ol_nat (tptp.hAPP_f224922881ol_nat (tptp.hAPP_f543861963ol_nat tptp.cOMBB_1075417391iple_a tptp.big_co1740723097nt_nat) F)) (tptp.hAPP_f138254639t_bool (tptp.hAPP_f1998609161t_bool tptp.cOMBB_1870764287iple_a tptp.collect_int) (tptp.hAPP_f138254639t_bool (tptp.hAPP_f1998609161t_bool tptp.cOMBB_1870764287iple_a (tptp.hAPP_f727283836t_bool tptp.cOMBS_int_bool_bool (tptp.hAPP_f2144054103l_bool (tptp.hAPP_f1734373249l_bool tptp.cOMBB_1652995168ol_int tptp.fconj) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f202917053t_bool tptp.cOMBC_94739984l_bool tptp.member_int) T_1)))) R_1)))) S_1) (tptp.hAPP_f957591787ol_nat (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat (tptp.hAPP_f2050777416nt_nat (tptp.hAPP_f1895921634nt_nat tptp.cOMBS_202713324ol_nat (tptp.hAPP_f1442126667ol_nat (tptp.hAPP_f1072896543ol_nat tptp.cOMBB_206396714at_int tptp.big_co1340561246_a_nat) (tptp.hAPP_f183615253_a_nat tptp.cOMBC_2020858056nt_nat F))) (tptp.hAPP_f1718504751a_bool (tptp.hAPP_f481410067a_bool tptp.cOMBB_1028320654ol_int tptp.collec351493750iple_a) (tptp.hAPP_f1718504751a_bool (tptp.hAPP_f481410067a_bool tptp.cOMBB_1028320654ol_int (tptp.hAPP_f607497069a_bool tptp.cOMBS_154988028l_bool (tptp.hAPP_f146754017l_bool (tptp.hAPP_f239971723l_bool tptp.cOMBB_1866391387iple_a tptp.fconj) (tptp.hAPP_f20753329a_bool (tptp.hAPP_f247708275a_bool tptp.cOMBC_1519416966l_bool tptp.member1797258804iple_a) S_1)))) (tptp.hAPP_f920351535a_bool tptp.cOMBC_1530706207t_bool R_1))))) T_1))))) (forall ((F $$unsorted) (R_1 $$unsorted) (T_1 $$unsorted) (S_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat S_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int T_1)) (= (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat (tptp.hAPP_f389300155at_nat (tptp.hAPP_f1750007732at_nat tptp.cOMBS_2106653443ol_nat (tptp.hAPP_f299305025ol_nat (tptp.hAPP_f1632710027ol_nat tptp.cOMBB_1453893592at_nat tptp.big_co1740723097nt_nat) F)) (tptp.hAPP_f2022049025t_bool (tptp.hAPP_f1986088027t_bool tptp.cOMBB_2101530536ol_nat tptp.collect_int) (tptp.hAPP_f2022049025t_bool (tptp.hAPP_f1986088027t_bool tptp.cOMBB_2101530536ol_nat (tptp.hAPP_f727283836t_bool tptp.cOMBS_int_bool_bool (tptp.hAPP_f2144054103l_bool (tptp.hAPP_f1734373249l_bool tptp.cOMBB_1652995168ol_int tptp.fconj) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f202917053t_bool tptp.cOMBC_94739984l_bool tptp.member_int) T_1)))) R_1)))) S_1) (tptp.hAPP_f957591787ol_nat (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat (tptp.hAPP_f1161717855nt_nat (tptp.hAPP_f369809936nt_nat tptp.cOMBS_1063588099ol_nat (tptp.hAPP_f1501159417ol_nat (tptp.hAPP_f1029311995ol_nat tptp.cOMBB_1562322300at_int tptp.big_co387207925at_nat) (tptp.hAPP_f446977493at_nat tptp.cOMBC_nat_int_nat F))) (tptp.hAPP_f783004929t_bool (tptp.hAPP_f1410409747t_bool tptp.cOMBB_1746576572ol_int tptp.collect_nat) (tptp.hAPP_f783004929t_bool (tptp.hAPP_f1410409747t_bool tptp.cOMBB_1746576572ol_int (tptp.hAPP_f561022312t_bool tptp.cOMBS_nat_bool_bool (tptp.hAPP_f1146629647l_bool (tptp.hAPP_f1080886329l_bool tptp.cOMBB_1015721476ol_nat tptp.fconj) (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1722879237t_bool tptp.cOMBC_226598744l_bool tptp.member_nat) S_1)))) (tptp.hAPP_f482008321t_bool tptp.cOMBC_nat_int_bool R_1))))) T_1))))) (forall ((F $$unsorted) (R_1 $$unsorted) (T_1 $$unsorted) (S_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat S_1)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a T_1)) (= (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat (tptp.hAPP_f966999552at_nat (tptp.hAPP_f264818750at_nat tptp.cOMBS_1274158152ol_nat (tptp.hAPP_f883871819ol_nat (tptp.hAPP_f424754463ol_nat tptp.cOMBB_1716606670at_nat tptp.big_co1340561246_a_nat) F)) (tptp.hAPP_f2087582327a_bool (tptp.hAPP_f1396758363a_bool tptp.cOMBB_391046962ol_nat tptp.collec351493750iple_a) (tptp.hAPP_f2087582327a_bool (tptp.hAPP_f1396758363a_bool tptp.cOMBB_391046962ol_nat (tptp.hAPP_f607497069a_bool tptp.cOMBS_154988028l_bool (tptp.hAPP_f146754017l_bool (tptp.hAPP_f239971723l_bool tptp.cOMBB_1866391387iple_a tptp.fconj) (tptp.hAPP_f20753329a_bool (tptp.hAPP_f247708275a_bool tptp.cOMBC_1519416966l_bool tptp.member1797258804iple_a) T_1)))) R_1)))) S_1) (tptp.hAPP_f2097660464ol_nat (tptp.hAPP_f1371399797ol_nat tptp.big_co1340561246_a_nat (tptp.hAPP_f2085403241_a_nat (tptp.hAPP_f1052116629_a_nat tptp.cOMBS_397915080ol_nat (tptp.hAPP_f1669765561ol_nat (tptp.hAPP_f1073041467ol_nat tptp.cOMBB_10565751iple_a tptp.big_co387207925at_nat) (tptp.hAPP_f2146713109at_nat tptp.cOMBC_441305270_a_nat F))) (tptp.hAPP_f27379319t_bool (tptp.hAPP_f196067081t_bool tptp.cOMBB_437532599iple_a tptp.collect_nat) (tptp.hAPP_f27379319t_bool (tptp.hAPP_f196067081t_bool tptp.cOMBB_437532599iple_a (tptp.hAPP_f561022312t_bool tptp.cOMBS_nat_bool_bool (tptp.hAPP_f1146629647l_bool (tptp.hAPP_f1080886329l_bool tptp.cOMBB_1015721476ol_nat tptp.fconj) (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1722879237t_bool tptp.cOMBC_226598744l_bool tptp.member_nat) S_1)))) (tptp.hAPP_f1886543991t_bool tptp.cOMBC_533513393a_bool R_1))))) T_1))))) (forall ((F $$unsorted) (R_1 $$unsorted) (T_1 $$unsorted) (S_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f202917053t_bool tptp.cOMBC_94739984l_bool tptp.member_int))) (let ((_let_2 (tptp.hAPP_f1734373249l_bool tptp.cOMBB_1652995168ol_int tptp.fconj))) (let ((_let_3 (tptp.hAPP_f654702867t_bool tptp.cOMBB_591320580ol_int tptp.collect_int))) (let ((_let_4 (tptp.hAPP_f1331458699ol_nat tptp.cOMBB_2091167284at_int tptp.big_co1740723097nt_nat))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int S_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int T_1)) (= (tptp.hAPP_f957591787ol_nat (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat (tptp.hAPP_f1134349059nt_nat (tptp.hAPP_f446447448nt_nat tptp.cOMBS_1999073191ol_nat (tptp.hAPP_f1548925761ol_nat _let_4 F)) (tptp.hAPP_f428220345t_bool _let_3 (tptp.hAPP_f428220345t_bool (tptp.hAPP_f654702867t_bool tptp.cOMBB_591320580ol_int (tptp.hAPP_f727283836t_bool tptp.cOMBS_int_bool_bool (tptp.hAPP_f2144054103l_bool _let_2 (tptp.hAPP_f1805168059t_bool _let_1 T_1)))) R_1)))) S_1) (tptp.hAPP_f957591787ol_nat (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat (tptp.hAPP_f1134349059nt_nat (tptp.hAPP_f446447448nt_nat tptp.cOMBS_1999073191ol_nat (tptp.hAPP_f1548925761ol_nat _let_4 (tptp.hAPP_f909851349nt_nat tptp.cOMBC_int_int_nat F))) (tptp.hAPP_f428220345t_bool _let_3 (tptp.hAPP_f428220345t_bool (tptp.hAPP_f654702867t_bool tptp.cOMBB_591320580ol_int (tptp.hAPP_f727283836t_bool tptp.cOMBS_int_bool_bool (tptp.hAPP_f2144054103l_bool _let_2 (tptp.hAPP_f1805168059t_bool _let_1 S_1)))) (tptp.hAPP_f428220345t_bool tptp.cOMBC_int_int_bool R_1))))) T_1))))))))) (forall ((F $$unsorted) (R_1 $$unsorted) (T_1 $$unsorted) (S_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int S_1)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a T_1)) (= (tptp.hAPP_f957591787ol_nat (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat (tptp.hAPP_f2050777416nt_nat (tptp.hAPP_f1895921634nt_nat tptp.cOMBS_202713324ol_nat (tptp.hAPP_f1442126667ol_nat (tptp.hAPP_f1072896543ol_nat tptp.cOMBB_206396714at_int tptp.big_co1340561246_a_nat) F)) (tptp.hAPP_f1718504751a_bool (tptp.hAPP_f481410067a_bool tptp.cOMBB_1028320654ol_int tptp.collec351493750iple_a) (tptp.hAPP_f1718504751a_bool (tptp.hAPP_f481410067a_bool tptp.cOMBB_1028320654ol_int (tptp.hAPP_f607497069a_bool tptp.cOMBS_154988028l_bool (tptp.hAPP_f146754017l_bool (tptp.hAPP_f239971723l_bool tptp.cOMBB_1866391387iple_a tptp.fconj) (tptp.hAPP_f20753329a_bool (tptp.hAPP_f247708275a_bool tptp.cOMBC_1519416966l_bool tptp.member1797258804iple_a) T_1)))) R_1)))) S_1) (tptp.hAPP_f2097660464ol_nat (tptp.hAPP_f1371399797ol_nat tptp.big_co1340561246_a_nat (tptp.hAPP_f342603021_a_nat (tptp.hAPP_f270087133_a_nat tptp.cOMBS_1333400172ol_nat (tptp.hAPP_f224922881ol_nat (tptp.hAPP_f543861963ol_nat tptp.cOMBB_1075417391iple_a tptp.big_co1740723097nt_nat) (tptp.hAPP_f1451619093nt_nat tptp.cOMBC_1917249810_a_nat F))) (tptp.hAPP_f138254639t_bool (tptp.hAPP_f1998609161t_bool tptp.cOMBB_1870764287iple_a tptp.collect_int) (tptp.hAPP_f138254639t_bool (tptp.hAPP_f1998609161t_bool tptp.cOMBB_1870764287iple_a (tptp.hAPP_f727283836t_bool tptp.cOMBS_int_bool_bool (tptp.hAPP_f2144054103l_bool (tptp.hAPP_f1734373249l_bool tptp.cOMBB_1652995168ol_int tptp.fconj) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f202917053t_bool tptp.cOMBC_94739984l_bool tptp.member_int) S_1)))) (tptp.hAPP_f936407855t_bool tptp.cOMBC_1719122773a_bool R_1))))) T_1))))) (forall ((G $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (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 $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f1599440987ol_int tptp.big_co1024481617at_int G))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)) (= (tptp.hAPP_f659380387ol_int _let_1 A) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_nat_int G X_1)) (tptp.hAPP_f659380387ol_int _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) tptp.bot_bot_fun_nat_bool))))))))) (forall ((G $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f1544320301ol_int tptp.big_co1977834938_a_int G))) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_1) A)) (= (tptp.hAPP_f587450508ol_int _let_1 A) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_H1229305626_a_int G X_1)) (tptp.hAPP_f587450508ol_int _let_1 (tptp.hAPP_f20753329a_bool (tptp.hAPP_f1706700729a_bool tptp.minus_85316870a_bool A) (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a X_1) tptp.bot_bo797238721a_bool))))))))) (forall ((G $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f1926459811ol_int tptp.big_co230513141nt_int G))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A)) (= (tptp.hAPP_f1594865479ol_int _let_1 A) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int G X_1)) (tptp.hAPP_f1594865479ol_int _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1) tptp.bot_bot_fun_int_bool))))))))) (forall ((G $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f1371399797ol_nat tptp.big_co1340561246_a_nat G))) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_1) A)) (= (tptp.hAPP_f2097660464ol_nat _let_1 A) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_H592031934_a_nat G X_1)) (tptp.hAPP_f2097660464ol_nat _let_1 (tptp.hAPP_f20753329a_bool (tptp.hAPP_f1706700729a_bool tptp.minus_85316870a_bool A) (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a X_1) tptp.bot_bo797238721a_bool))))))))) (forall ((G $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat G))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A)) (= (tptp.hAPP_f957591787ol_nat _let_1 A) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_int_nat G X_1)) (tptp.hAPP_f957591787ol_nat _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1) tptp.bot_bot_fun_int_bool))))))))) (forall ((F $$unsorted) (A_13 $$unsorted) (A $$unsorted)) (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 $$unsorted) (A_13 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f1599440987ol_int tptp.big_co1024481617at_int F))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_13) A)) (= (tptp.hAPP_f659380387ol_int _let_1 A) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_nat_int F A_13)) (tptp.hAPP_f659380387ol_int _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13) tptp.bot_bot_fun_nat_bool))))))))) (forall ((F $$unsorted) (A_13 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f1544320301ol_int tptp.big_co1977834938_a_int F))) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a A_13) A)) (= (tptp.hAPP_f587450508ol_int _let_1 A) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_H1229305626_a_int F A_13)) (tptp.hAPP_f587450508ol_int _let_1 (tptp.hAPP_f20753329a_bool (tptp.hAPP_f1706700729a_bool tptp.minus_85316870a_bool A) (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a A_13) tptp.bot_bo797238721a_bool))))))))) (forall ((F $$unsorted) (A_13 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f1926459811ol_int tptp.big_co230513141nt_int F))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int A_13) A)) (= (tptp.hAPP_f1594865479ol_int _let_1 A) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int F A_13)) (tptp.hAPP_f1594865479ol_int _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_13) tptp.bot_bot_fun_int_bool))))))))) (forall ((F $$unsorted) (A_13 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f1371399797ol_nat tptp.big_co1340561246_a_nat F))) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a A_13) A)) (= (tptp.hAPP_f2097660464ol_nat _let_1 A) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_H592031934_a_nat F A_13)) (tptp.hAPP_f2097660464ol_nat _let_1 (tptp.hAPP_f20753329a_bool (tptp.hAPP_f1706700729a_bool tptp.minus_85316870a_bool A) (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a A_13) tptp.bot_bo797238721a_bool))))))))) (forall ((F $$unsorted) (A_13 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat F))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int A_13) A)) (= (tptp.hAPP_f957591787ol_nat _let_1 A) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_int_nat F A_13)) (tptp.hAPP_f957591787ol_nat _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_13) tptp.bot_bot_fun_int_bool))))))))) (forall ((G $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (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 $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1))) (let ((_let_2 (tptp.hAPP_f1599440987ol_int tptp.big_co1024481617at_int G))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (= (tptp.hAPP_f659380387ol_int _let_2 (tptp.hAPP_f800510211t_bool _let_1 A)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_nat_int G X_1)) (tptp.hAPP_f659380387ol_int _let_2 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) (tptp.hAPP_f800510211t_bool _let_1 tptp.bot_bot_fun_nat_bool))))))))) (forall ((G $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a X_1))) (let ((_let_2 (tptp.hAPP_f1544320301ol_int tptp.big_co1977834938_a_int G))) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A)) (= (tptp.hAPP_f587450508ol_int _let_2 (tptp.hAPP_f20753329a_bool _let_1 A)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_H1229305626_a_int G X_1)) (tptp.hAPP_f587450508ol_int _let_2 (tptp.hAPP_f20753329a_bool (tptp.hAPP_f1706700729a_bool tptp.minus_85316870a_bool A) (tptp.hAPP_f20753329a_bool _let_1 tptp.bot_bo797238721a_bool))))))))) (forall ((G $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1))) (let ((_let_2 (tptp.hAPP_f1926459811ol_int tptp.big_co230513141nt_int G))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (= (tptp.hAPP_f1594865479ol_int _let_2 (tptp.hAPP_f1805168059t_bool _let_1 A)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int G X_1)) (tptp.hAPP_f1594865479ol_int _let_2 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) (tptp.hAPP_f1805168059t_bool _let_1 tptp.bot_bot_fun_int_bool))))))))) (forall ((G $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a X_1))) (let ((_let_2 (tptp.hAPP_f1371399797ol_nat tptp.big_co1340561246_a_nat G))) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A)) (= (tptp.hAPP_f2097660464ol_nat _let_2 (tptp.hAPP_f20753329a_bool _let_1 A)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_H592031934_a_nat G X_1)) (tptp.hAPP_f2097660464ol_nat _let_2 (tptp.hAPP_f20753329a_bool (tptp.hAPP_f1706700729a_bool tptp.minus_85316870a_bool A) (tptp.hAPP_f20753329a_bool _let_1 tptp.bot_bo797238721a_bool))))))))) (forall ((G $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1))) (let ((_let_2 (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat G))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (= (tptp.hAPP_f957591787ol_nat _let_2 (tptp.hAPP_f1805168059t_bool _let_1 A)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_int_nat G X_1)) (tptp.hAPP_f957591787ol_nat _let_2 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) (tptp.hAPP_f1805168059t_bool _let_1 tptp.bot_bot_fun_int_bool))))))))) (forall ((F $$unsorted) (G $$unsorted) (A $$unsorted)) (= (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 $$unsorted) (G $$unsorted) (A $$unsorted)) (= (tptp.hAPP_f957591787ol_nat (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat (tptp.hAPP_f2132704789nt_nat (tptp.hAPP_f1399363134nt_nat tptp.cOMBS_int_nat_nat (tptp.hAPP_f1463450952at_nat (tptp.hAPP_f1087393429at_nat tptp.cOMBB_1601129847at_int tptp.plus_plus_nat) F)) G)) A) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_f957591787ol_nat (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat F) A)) (tptp.hAPP_f957591787ol_nat (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat G) A)))) (forall ((F $$unsorted) (G $$unsorted) (A $$unsorted)) (= (tptp.hAPP_f2097660464ol_nat (tptp.hAPP_f1371399797ol_nat tptp.big_co1340561246_a_nat (tptp.hAPP_f106743253_a_nat (tptp.hAPP_f1418102009_a_nat tptp.cOMBS_1756972052at_nat (tptp.hAPP_f429024520at_nat (tptp.hAPP_f703420885at_nat tptp.cOMBB_789959282iple_a tptp.plus_plus_nat) F)) G)) A) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_f2097660464ol_nat (tptp.hAPP_f1371399797ol_nat tptp.big_co1340561246_a_nat F) A)) (tptp.hAPP_f2097660464ol_nat (tptp.hAPP_f1371399797ol_nat tptp.big_co1340561246_a_nat G) A)))) (forall ((G $$unsorted) (H $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (= (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat (tptp.hAPP_f1914919701at_nat (tptp.hAPP_f1408247010at_nat tptp.cOMBS_nat_nat_nat (tptp.hAPP_f1639111240at_nat (tptp.hAPP_f1731313045at_nat tptp.cOMBB_963856155at_nat tptp.plus_plus_nat) G)) H)) A) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat G) A)) (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat H) A))))) (forall ((G $$unsorted) (H $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A)) (= (tptp.hAPP_f2097660464ol_nat (tptp.hAPP_f1371399797ol_nat tptp.big_co1340561246_a_nat (tptp.hAPP_f106743253_a_nat (tptp.hAPP_f1418102009_a_nat tptp.cOMBS_1756972052at_nat (tptp.hAPP_f429024520at_nat (tptp.hAPP_f703420885at_nat tptp.cOMBB_789959282iple_a tptp.plus_plus_nat) G)) H)) A) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_f2097660464ol_nat (tptp.hAPP_f1371399797ol_nat tptp.big_co1340561246_a_nat G) A)) (tptp.hAPP_f2097660464ol_nat (tptp.hAPP_f1371399797ol_nat tptp.big_co1340561246_a_nat H) A))))) (forall ((G $$unsorted) (H $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A)) (= (tptp.hAPP_f587450508ol_int (tptp.hAPP_f1544320301ol_int tptp.big_co1977834938_a_int (tptp.hAPP_f1561000661_a_int (tptp.hAPP_f789902073_a_int tptp.cOMBS_1600277268nt_int (tptp.hAPP_f231878828nt_int (tptp.hAPP_f1621780181nt_int tptp.cOMBB_1885471694iple_a tptp.plus_plus_int) G)) H)) A) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_f587450508ol_int (tptp.hAPP_f1544320301ol_int tptp.big_co1977834938_a_int G) A)) (tptp.hAPP_f587450508ol_int (tptp.hAPP_f1544320301ol_int tptp.big_co1977834938_a_int H) A))))) (forall ((G $$unsorted) (H $$unsorted) (A $$unsorted)) (=> (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 $$unsorted) (A_13 $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat F))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat F_1)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_13) F_1))) (= (tptp.hAPP_f22106695ol_nat _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13) F_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat F A_13)) (tptp.hAPP_f22106695ol_nat _let_1 F_1))))))) (forall ((F $$unsorted) (A_13 $$unsorted) (F_1 $$unsorted)) (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 $$unsorted) (A_13 $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1544320301ol_int tptp.big_co1977834938_a_int F))) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a F_1)) (=> (not (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a A_13) F_1))) (= (tptp.hAPP_f587450508ol_int _let_1 (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a A_13) F_1)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_H1229305626_a_int F A_13)) (tptp.hAPP_f587450508ol_int _let_1 F_1))))))) (forall ((F $$unsorted) (A_13 $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1371399797ol_nat tptp.big_co1340561246_a_nat F))) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a F_1)) (=> (not (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a A_13) F_1))) (= (tptp.hAPP_f2097660464ol_nat _let_1 (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a A_13) F_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_H592031934_a_nat F A_13)) (tptp.hAPP_f2097660464ol_nat _let_1 F_1))))))) (forall ((F $$unsorted) (A_13 $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat F))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int F_1)) (=> (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int A_13) F_1))) (= (tptp.hAPP_f957591787ol_nat _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_13) F_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_int_nat F A_13)) (tptp.hAPP_f957591787ol_nat _let_1 F_1))))))) (forall ((G $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (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 $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f1599440987ol_int tptp.big_co1024481617at_int G))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A))) (= (tptp.hAPP_f659380387ol_int _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) A)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_nat_int G X_1)) (tptp.hAPP_f659380387ol_int _let_1 A))))))) (forall ((G $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f1544320301ol_int tptp.big_co1977834938_a_int G))) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A)) (=> (not (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_1) A))) (= (tptp.hAPP_f587450508ol_int _let_1 (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a X_1) A)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_H1229305626_a_int G X_1)) (tptp.hAPP_f587450508ol_int _let_1 A))))))) (forall ((G $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f1371399797ol_nat tptp.big_co1340561246_a_nat G))) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A)) (=> (not (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_1) A))) (= (tptp.hAPP_f2097660464ol_nat _let_1 (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a X_1) A)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_H592031934_a_nat G X_1)) (tptp.hAPP_f2097660464ol_nat _let_1 A))))))) (forall ((G $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (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 $$unsorted) (E $$unsorted) (Ca $$unsorted) (Ba $$unsorted) (D_1 $$unsorted)) (= (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_13) E)) Ca) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Ba) E)) D_1)) (= Ca (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int Ba) A_13)) E)) D_1)))) (forall ((A_13 $$unsorted) (E $$unsorted) (Ca $$unsorted) (Ba $$unsorted) (D_1 $$unsorted)) (= (= (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 $$unsorted) (B_34 $$unsorted)) (= (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 $$unsorted) (B_33 $$unsorted)) (= (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 $$unsorted) (Y_1 $$unsorted) (X_1 $$unsorted) (Z_1 $$unsorted)) (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 $$unsorted) (Y_1 $$unsorted) (X_1 $$unsorted) (Z_1 $$unsorted)) (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 $$unsorted) (E_1 $$unsorted) (B_32 $$unsorted) (C_28 $$unsorted)) (= (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 $$unsorted) (E_1 $$unsorted) (B_32 $$unsorted) (C_28 $$unsorted)) (= (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 $$unsorted) (M_4 $$unsorted) (B_31 $$unsorted)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_39) M_4)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat B_31) M_4)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_39) B_31)) M_4))) (forall ((A_39 $$unsorted) (M_4 $$unsorted) (B_31 $$unsorted)) (= (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 $$unsorted) (A_38 $$unsorted) (C_27 $$unsorted)) (=> (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat B_30) A_38) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat C_27) A_38)) (= B_30 C_27))) (forall ((B_30 $$unsorted) (A_38 $$unsorted) (C_27 $$unsorted)) (=> (= (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 $$unsorted) (B_29 $$unsorted) (C_26 $$unsorted)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_37))) (=> (= (tptp.hAPP_nat_nat _let_1 B_29) (tptp.hAPP_nat_nat _let_1 C_26)) (= B_29 C_26)))) (forall ((A_37 $$unsorted) (B_29 $$unsorted) (C_26 $$unsorted)) (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 $$unsorted) (B_28 $$unsorted) (C_25 $$unsorted)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_36))) (=> (= (tptp.hAPP_nat_nat _let_1 B_28) (tptp.hAPP_nat_nat _let_1 C_25)) (= B_28 C_25)))) (forall ((A_36 $$unsorted) (B_28 $$unsorted) (C_25 $$unsorted)) (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 $$unsorted) (B_27 $$unsorted) (C_24 $$unsorted) (D_6 $$unsorted)) (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 $$unsorted) (B_27 $$unsorted) (C_24 $$unsorted) (D_6 $$unsorted)) (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 $$unsorted) (A_13 $$unsorted) (Ca $$unsorted)) (= (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Ba) A_13) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Ca) A_13)) (= Ba Ca))) (forall ((Ba $$unsorted) (A_13 $$unsorted) (Ca $$unsorted)) (= (= (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 $$unsorted) (Ba $$unsorted) (Ca $$unsorted)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_13))) (= (= (tptp.hAPP_nat_nat _let_1 Ba) (tptp.hAPP_nat_nat _let_1 Ca)) (= Ba Ca)))) (forall ((A_13 $$unsorted) (Ba $$unsorted) (Ca $$unsorted)) (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 $$unsorted) (B_26 $$unsorted) (C_23 $$unsorted)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_34))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 B_26)) C_23) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 C_23)) B_26)))) (forall ((A_34 $$unsorted) (B_26 $$unsorted) (C_23 $$unsorted)) (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 $$unsorted) (B_25 $$unsorted) (C_22 $$unsorted)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_33))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 B_25)) C_22) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat B_25) C_22))))) (forall ((A_33 $$unsorted) (B_25 $$unsorted) (C_22 $$unsorted)) (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 $$unsorted) (B_24 $$unsorted) (C_21 $$unsorted)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_32))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 B_24)) C_21) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat B_24) C_21))))) (forall ((A_32 $$unsorted) (B_24 $$unsorted) (C_21 $$unsorted)) (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 $$unsorted) (C_20 $$unsorted) (D_5 $$unsorted)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_31))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat C_20) D_5)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 C_20)) D_5)))) (forall ((A_31 $$unsorted) (C_20 $$unsorted) (D_5 $$unsorted)) (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 $$unsorted) (C_19 $$unsorted) (D_4 $$unsorted)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_30))) (let ((_let_2 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat C_19))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat _let_2 D_4)) (tptp.hAPP_nat_nat _let_2 (tptp.hAPP_nat_nat _let_1 D_4)))))) (forall ((A_30 $$unsorted) (C_19 $$unsorted) (D_4 $$unsorted)) (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 $$unsorted) (C_18 $$unsorted)) (= (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 $$unsorted) (C_18 $$unsorted)) (= (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 $$unsorted) (Ly_4 $$unsorted) (Rx_6 $$unsorted) (Ry_4 $$unsorted)) (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 $$unsorted) (Ly_4 $$unsorted) (Rx_6 $$unsorted) (Ry_4 $$unsorted)) (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 $$unsorted) (Ly_3 $$unsorted) (Rx_5 $$unsorted) (Ry_3 $$unsorted)) (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 $$unsorted) (Ly_3 $$unsorted) (Rx_5 $$unsorted) (Ry_3 $$unsorted)) (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 $$unsorted) (Ly_2 $$unsorted) (Rx_4 $$unsorted) (Ry_2 $$unsorted)) (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 $$unsorted) (Ly_2 $$unsorted) (Rx_4 $$unsorted) (Ry_2 $$unsorted)) (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 $$unsorted) (Ly_1 $$unsorted) (Rx_3 $$unsorted)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat Lx_3))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat _let_1 Ly_1)) Rx_3) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat _let_1 Rx_3)) Ly_1)))) (forall ((Lx_3 $$unsorted) (Ly_1 $$unsorted) (Rx_3 $$unsorted)) (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 $$unsorted) (Ly $$unsorted) (Rx_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat Lx_2))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat _let_1 Ly)) Rx_2) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat Ly) Rx_2))))) (forall ((Lx_2 $$unsorted) (Ly $$unsorted) (Rx_2 $$unsorted)) (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 $$unsorted) (B_23 $$unsorted) (C_17 $$unsorted)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_28))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat _let_1 B_23)) C_17) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat B_23) C_17))))) (forall ((A_28 $$unsorted) (B_23 $$unsorted) (C_17 $$unsorted)) (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 $$unsorted) (Rx_1 $$unsorted) (Ry_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat Lx_1))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat Rx_1) Ry_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat _let_1 Rx_1)) Ry_1)))) (forall ((Lx_1 $$unsorted) (Rx_1 $$unsorted) (Ry_1 $$unsorted)) (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 $$unsorted) (Rx $$unsorted) (Ry $$unsorted)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat Lx))) (let ((_let_2 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat Rx))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat _let_2 Ry)) (tptp.hAPP_nat_nat _let_2 (tptp.hAPP_nat_nat _let_1 Ry)))))) (forall ((Lx $$unsorted) (Rx $$unsorted) (Ry $$unsorted)) (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 $$unsorted) (B_22 $$unsorted)) (= (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 $$unsorted) (B_22 $$unsorted)) (= (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 $$unsorted) (Ba $$unsorted) (Ca $$unsorted) (D_1 $$unsorted)) (=> (= (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 $$unsorted) (Y_20 $$unsorted) (Z_10 $$unsorted)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat X_27))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Y_20) Z_10)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 Y_20)) (tptp.hAPP_nat_nat _let_1 Z_10))))) (forall ((X_27 $$unsorted) (Y_20 $$unsorted) (Z_10 $$unsorted)) (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 $$unsorted) (D_1 $$unsorted) (A_13 $$unsorted) (Ba $$unsorted)) (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 $$unsorted) (D_1 $$unsorted) (A_13 $$unsorted) (Ba $$unsorted)) (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 $$unsorted) (B_21 $$unsorted) (C_16 $$unsorted)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_26) B_21)) C_16) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_26) C_16)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_21) C_16)))) (forall ((A_26 $$unsorted) (B_21 $$unsorted) (C_16 $$unsorted)) (= (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 $$unsorted) (B_20 $$unsorted) (C_15 $$unsorted)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_25) B_20)) C_15) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_25) C_15)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_20) C_15)))) (forall ((A_25 $$unsorted) (B_20 $$unsorted) (C_15 $$unsorted)) (= (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 $$unsorted) (G $$unsorted) (A $$unsorted)) (=> (forall ((X_2 $$unsorted)) (=> (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 $$unsorted) (G $$unsorted) (A $$unsorted)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_2) A)) (= (tptp.hAPP_H592031934_a_nat F X_2) (tptp.hAPP_H592031934_a_nat G X_2)))) (= (tptp.hAPP_f2097660464ol_nat (tptp.hAPP_f1371399797ol_nat tptp.big_co1340561246_a_nat F) A) (tptp.hAPP_f2097660464ol_nat (tptp.hAPP_f1371399797ol_nat tptp.big_co1340561246_a_nat G) A)))) (forall ((F $$unsorted) (G $$unsorted) (A $$unsorted)) (=> (forall ((X_2 $$unsorted)) (=> (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 $$unsorted) (G $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (= A B) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_2) B)) (= (tptp.hAPP_int_nat F X_2) (tptp.hAPP_int_nat G X_2)))) (= (tptp.hAPP_f957591787ol_nat (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat F) A) (tptp.hAPP_f957591787ol_nat (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat G) B))))) (forall ((F $$unsorted) (G $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (= A B) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_2) B)) (= (tptp.hAPP_H592031934_a_nat F X_2) (tptp.hAPP_H592031934_a_nat G X_2)))) (= (tptp.hAPP_f2097660464ol_nat (tptp.hAPP_f1371399797ol_nat tptp.big_co1340561246_a_nat F) A) (tptp.hAPP_f2097660464ol_nat (tptp.hAPP_f1371399797ol_nat tptp.big_co1340561246_a_nat G) B))))) (forall ((F $$unsorted) (G $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (= A B) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) B)) (= (tptp.hAPP_nat_nat F X_2) (tptp.hAPP_nat_nat G X_2)))) (= (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat F) A) (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat G) B))))) (forall ((H $$unsorted) (G $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (= A B) (=> (forall ((X_2 $$unsorted)) (=> (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 $$unsorted) (G $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (= A B) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_2) B)) (= (tptp.hAPP_H592031934_a_nat H X_2) (tptp.hAPP_H592031934_a_nat G X_2)))) (= (tptp.hAPP_f2097660464ol_nat (tptp.hAPP_f1371399797ol_nat tptp.big_co1340561246_a_nat H) A) (tptp.hAPP_f2097660464ol_nat (tptp.hAPP_f1371399797ol_nat tptp.big_co1340561246_a_nat G) B))))) (forall ((H $$unsorted) (G $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (= A B) (=> (forall ((X_2 $$unsorted)) (=> (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 $$unsorted)) (let ((_let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat K_1) tptp.bot_bot_fun_nat_bool))) (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool _let_1) (tptp.hAPP_n1699378549t_bool tptp.ord_lessThan_nat K_1)) _let_1))) (forall ((K_1 $$unsorted)) (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 $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f1371399797ol_nat tptp.big_co1340561246_a_nat F))) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a B)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_f1767618879l_bool tptp.ord_le1523781517a_bool B) A)) (= (tptp.hAPP_f2097660464ol_nat _let_1 (tptp.hAPP_f20753329a_bool (tptp.hAPP_f1706700729a_bool tptp.minus_85316870a_bool A) B)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_f2097660464ol_nat _let_1 A)) (tptp.hAPP_f2097660464ol_nat _let_1 B))))))) (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (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 $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat F))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat B)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool B) A)) (= (tptp.hAPP_f22106695ol_nat _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) B)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_f22106695ol_nat _let_1 A)) (tptp.hAPP_f22106695ol_nat _let_1 B))))))) (forall ((X_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool X_1) X_1))) (forall ((X_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool X_1) X_1))) (forall ((X_26 $$unsorted)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_26) X_26))) (forall ((X_26 $$unsorted)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_26) X_26))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool B) A)) (= A B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool B) A)) (= A B)))) (forall ((Ca $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a Ca))) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_f1767618879l_bool tptp.ord_le1523781517a_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool _let_1 B)))))) (forall ((Ca $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_i2112223885l_bool tptp.member_int Ca))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 B)))))) (forall ((Ca $$unsorted) (A $$unsorted) (B $$unsorted)) (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 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool tptp.bot_bot_fun_nat_bool) A))) (forall ((A $$unsorted)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool tptp.bot_bot_fun_int_bool) A))) (forall ((A $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_f1767618879l_bool tptp.ord_le1523781517a_bool tptp.bot_bo797238721a_bool) A))) (forall ((A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A)) (tptp.hBOOL (tptp.hAPP_f2110825313l_bool tptp.finite268574148a_bool (tptp.hAPP_f396832789l_bool tptp.collec999179778a_bool (tptp.hAPP_f1767618879l_bool (tptp.hAPP_f2100528361l_bool tptp.cOMBC_627599030l_bool tptp.ord_le1523781517a_bool) A)))))) (forall ((A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (tptp.hBOOL (tptp.hAPP_f215623910l_bool tptp.finite1395289673t_bool (tptp.hAPP_f1948010709l_bool tptp.collect_fun_int_bool (tptp.hAPP_f284875647l_bool (tptp.hAPP_f1399552105l_bool tptp.cOMBC_605892544l_bool tptp.ord_le951220754t_bool) A)))))) (forall ((A $$unsorted)) (=> (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 $$unsorted) (S_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f247708275a_bool tptp.cOMBC_1519416966l_bool tptp.member1797258804iple_a))) (= (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_f1767618879l_bool tptp.ord_le1523781517a_bool (tptp.hAPP_f20753329a_bool _let_1 R_1)) (tptp.hAPP_f20753329a_bool _let_1 S_1))) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_f1767618879l_bool tptp.ord_le1523781517a_bool R_1) S_1))))) (forall ((R_1 $$unsorted) (S_1 $$unsorted)) (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 $$unsorted) (S_1 $$unsorted)) (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 $$unsorted) (Y_19 $$unsorted)) (=> (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 $$unsorted) (Y_19 $$unsorted)) (=> (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 $$unsorted) (F $$unsorted) (G $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool F) G)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_int_bool F X_1)) (tptp.hAPP_int_bool G X_1))))) (forall ((X_1 $$unsorted) (F $$unsorted) (G $$unsorted)) (=> (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 $$unsorted) (Y_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool Z_1))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool Y_1) X_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 Y_1)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 X_1)))))) (forall ((Z_1 $$unsorted) (Y_1 $$unsorted) (X_1 $$unsorted)) (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 $$unsorted) (Y_18 $$unsorted) (X_24 $$unsorted)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Z_9))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Y_18) X_24)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Y_18)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 X_24)))))) (forall ((Z_9 $$unsorted) (Y_18 $$unsorted) (X_24 $$unsorted)) (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 $$unsorted) (X_1 $$unsorted)) (=> (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 $$unsorted) (X_1 $$unsorted)) (=> (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 $$unsorted) (X_23 $$unsorted)) (=> (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 $$unsorted) (X_23 $$unsorted)) (=> (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 $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool X_1))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 Y_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool Y_1) Z_1)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 Z_1)))))) (forall ((Z_1 $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted)) (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 $$unsorted) (X_22 $$unsorted) (Y_16 $$unsorted)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_22))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Y_16)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Y_16) Z_8)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Z_8)))))) (forall ((Z_8 $$unsorted) (X_22 $$unsorted) (Y_16 $$unsorted)) (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 $$unsorted) (Y_1 $$unsorted)) (=> (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 $$unsorted) (Y_1 $$unsorted)) (=> (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 $$unsorted) (Y_15 $$unsorted)) (=> (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 $$unsorted) (Y_15 $$unsorted)) (=> (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 $$unsorted) (Ba $$unsorted) (A_13 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool Ba) A_13)) (=> (= Ba Ca) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool Ca) A_13))))) (forall ((Ca $$unsorted) (Ba $$unsorted) (A_13 $$unsorted)) (=> (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 $$unsorted) (B_19 $$unsorted) (A_24 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_19) A_24)) (=> (= B_19 C_14) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int C_14) A_24))))) (forall ((C_14 $$unsorted) (B_19 $$unsorted) (A_24 $$unsorted)) (=> (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 $$unsorted) (A_13 $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A_13))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 Ba)) (=> (= Ba Ca) (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 Ca)))))) (forall ((Ca $$unsorted) (A_13 $$unsorted) (Ba $$unsorted)) (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 $$unsorted) (A_23 $$unsorted) (B_18 $$unsorted)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_23))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_18)) (=> (= B_18 C_13) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 C_13)))))) (forall ((C_13 $$unsorted) (A_23 $$unsorted) (B_18 $$unsorted)) (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 $$unsorted) (A_13 $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool Ca))) (=> (= A_13 Ba) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 Ba)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 A_13)))))) (forall ((Ca $$unsorted) (A_13 $$unsorted) (Ba $$unsorted)) (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 $$unsorted) (A_22 $$unsorted) (B_17 $$unsorted)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int C_12))) (=> (= A_22 B_17) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_17)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A_22)))))) (forall ((C_12 $$unsorted) (A_22 $$unsorted) (B_17 $$unsorted)) (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 $$unsorted) (A_13 $$unsorted) (Ba $$unsorted)) (=> (= A_13 Ba) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool Ba) Ca)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A_13) Ca))))) (forall ((Ca $$unsorted) (A_13 $$unsorted) (Ba $$unsorted)) (=> (= 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 $$unsorted) (A_21 $$unsorted) (B_16 $$unsorted)) (=> (= A_21 B_16) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_16) C_11)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_21) C_11))))) (forall ((C_11 $$unsorted) (A_21 $$unsorted) (B_16 $$unsorted)) (=> (= 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 $$unsorted) (X_1 $$unsorted)) (=> (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 $$unsorted) (X_1 $$unsorted)) (=> (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 $$unsorted) (X_1 $$unsorted)) (=> (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 $$unsorted) (X_1 $$unsorted)) (=> (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 $$unsorted) (F $$unsorted) (G $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool F) G)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_int_bool F X_1)) (tptp.hAPP_int_bool G X_1))))) (forall ((X_1 $$unsorted) (F $$unsorted) (G $$unsorted)) (=> (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 $$unsorted) (Y_1 $$unsorted)) (=> (= 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 $$unsorted) (Y_1 $$unsorted)) (=> (= 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 $$unsorted) (Y_14 $$unsorted)) (=> (= 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 $$unsorted) (Y_14 $$unsorted)) (=> (= 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 $$unsorted) (Y_1 $$unsorted)) (= (= 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 $$unsorted) (Y_1 $$unsorted)) (= (= 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 $$unsorted) (Y_1 $$unsorted)) (= (= 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 $$unsorted) (Y_1 $$unsorted)) (= (= 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 $$unsorted) (Y_13 $$unsorted)) (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 $$unsorted) (Y_13 $$unsorted)) (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 $$unsorted) (G $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool F) G)) (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_int_bool F X_2)) (tptp.hAPP_int_bool G X_2)))))) (forall ((F $$unsorted) (G $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool F) G)) (forall ((X_2 $$unsorted)) (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 $$unsorted) (B $$unsorted)) (=> (= 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 $$unsorted) (B $$unsorted)) (=> (= 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 $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 B)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool B) C_5)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 C_5)))))) (forall ((C_5 $$unsorted) (A $$unsorted) (B $$unsorted)) (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 $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_1))) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_f1767618879l_bool tptp.ord_le1523781517a_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool _let_1 B)))))) (forall ((X_1 $$unsorted) (A $$unsorted) (B $$unsorted)) (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 $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat X_1))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B)))))) (forall ((B $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_1))) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool _let_1 A)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_f1767618879l_bool tptp.ord_le1523781517a_bool A) B)) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool _let_1 B)))))) (forall ((B $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_i2112223885l_bool tptp.member_int X_1))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 A)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A) B)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 B)))))) (forall ((B $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (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 $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_1))) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_f1767618879l_bool tptp.ord_le1523781517a_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool _let_1 B)))))) (forall ((X_1 $$unsorted) (A $$unsorted) (B $$unsorted)) (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 $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat X_1))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool B) A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool B) A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A) B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) B)))) (forall ((A $$unsorted) (B $$unsorted)) (= (= A B) (and (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A) B)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool B) A))))) (forall ((A $$unsorted) (B $$unsorted)) (= (= A B) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) B)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool B) A))))) (forall ((A $$unsorted)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A) A))) (forall ((A $$unsorted)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) A))) (forall ((X_1 $$unsorted) (Pa $$unsorted) (Q_1 $$unsorted)) (=> (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 $$unsorted) (Pa $$unsorted) (Q_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Pa) Q_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool Pa X_1)) (tptp.hBOOL (tptp.hAPP_nat_bool Q_1 X_1))))) (forall ((Q_1 $$unsorted) (Pa $$unsorted) (X_1 $$unsorted)) (=> (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 $$unsorted) (Pa $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool Pa X_1)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Pa) Q_1)) (tptp.hBOOL (tptp.hAPP_nat_bool Q_1 X_1))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool (tptp.hAPP_i1948725293t_bool tptp.ord_lessThan_int X_1)) (tptp.hAPP_i1948725293t_bool tptp.ord_lessThan_int Y_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_1) Y_1)))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_n1699378549t_bool tptp.ord_lessThan_nat X_1)) (tptp.hAPP_n1699378549t_bool tptp.ord_lessThan_nat Y_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_1) Y_1)))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (= (= (tptp.hAPP_n1699378549t_bool tptp.ord_lessThan_nat X_1) (tptp.hAPP_n1699378549t_bool tptp.ord_lessThan_nat Y_1)) (= X_1 Y_1))) (forall ((C_10 $$unsorted) (A_20 $$unsorted) (B_15 $$unsorted)) (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 $$unsorted) (A_20 $$unsorted) (B_15 $$unsorted)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat C_10))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 A_20)) (tptp.hAPP_nat_nat _let_1 B_15))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_20) B_15))))) (forall ((A_19 $$unsorted) (C_9 $$unsorted) (B_14 $$unsorted)) (=> (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 $$unsorted) (C_9 $$unsorted) (B_14 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_19) C_9)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat B_14) C_9))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_19) B_14)))) (forall ((C_8 $$unsorted) (D_3 $$unsorted) (A_18 $$unsorted) (B_13 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_18) B_13)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int C_8) D_3)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_18) C_8)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int B_13) D_3)))))) (forall ((C_8 $$unsorted) (D_3 $$unsorted) (A_18 $$unsorted) (B_13 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_18) B_13)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat C_8) D_3)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_18) C_8)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat B_13) D_3)))))) (forall ((C_7 $$unsorted) (A_17 $$unsorted) (B_12 $$unsorted)) (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 $$unsorted) (A_17 $$unsorted) (B_12 $$unsorted)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat C_7))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_17) B_12)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 A_17)) (tptp.hAPP_nat_nat _let_1 B_12)))))) (forall ((C_6 $$unsorted) (A_16 $$unsorted) (B_11 $$unsorted)) (=> (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 $$unsorted) (A_16 $$unsorted) (B_11 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_16) B_11)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_16) C_6)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat B_11) C_6))))) (forall ((Ca $$unsorted) (A_13 $$unsorted) (Ba $$unsorted)) (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 $$unsorted) (A_13 $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Ca))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 A_13)) (tptp.hAPP_nat_nat _let_1 Ba))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_13) Ba))))) (forall ((A_13 $$unsorted) (Ca $$unsorted) (Ba $$unsorted)) (= (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 $$unsorted) (Ca $$unsorted) (Ba $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_13) Ca)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Ba) Ca))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_13) Ba)))) (forall ((A_13 $$unsorted)) (=> (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 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A_13) tptp.bot_bot_fun_nat_bool)) (= A_13 tptp.bot_bot_fun_nat_bool))) (forall ((A_13 $$unsorted)) (=> (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 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_f1767618879l_bool tptp.ord_le1523781517a_bool A_13) tptp.bot_bo797238721a_bool)) (= A_13 tptp.bot_bo797238721a_bool))) (forall ((A_15 $$unsorted)) (=> (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 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool A_13) tptp.bot_bot_bool)) (= (tptp.hBOOL A_13) (tptp.hBOOL tptp.bot_bot_bool)))) (forall ((A_13 $$unsorted)) (= (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 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A_13) tptp.bot_bot_fun_int_bool)) (= A_13 tptp.bot_bot_fun_int_bool))) (forall ((A_13 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_f1767618879l_bool tptp.ord_le1523781517a_bool A_13) tptp.bot_bo797238721a_bool)) (= A_13 tptp.bot_bo797238721a_bool))) (forall ((A_13 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_13) tptp.bot_bot_nat)) (= A_13 tptp.bot_bot_nat))) (forall ((A_13 $$unsorted)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool tptp.bot_bot_bool) A_13))) (forall ((A_13 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool tptp.bot_bot_fun_nat_bool) A_13))) (forall ((A_13 $$unsorted)) (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 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_f1767618879l_bool tptp.ord_le1523781517a_bool tptp.bot_bo797238721a_bool) A_13))) (forall ((A_14 $$unsorted)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.bot_bot_nat) A_14))) (forall ((A_13 $$unsorted) (Ba $$unsorted) (Ca $$unsorted) (D_1 $$unsorted)) (=> (= (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 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) tptp.bot_bot_fun_nat_bool)) (= A tptp.bot_bot_fun_nat_bool))) (forall ((A $$unsorted)) (= (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 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_f1767618879l_bool tptp.ord_le1523781517a_bool A) tptp.bot_bo797238721a_bool)) (= A tptp.bot_bo797238721a_bool))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_f1767618879l_bool tptp.ord_le1523781517a_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a B)) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int B)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat B)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a B)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_f1767618879l_bool tptp.ord_le1523781517a_bool A) B)) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int B)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A) B)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat B)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) B)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A))))) (forall ((A_13 $$unsorted) (C_5 $$unsorted) (D_2 $$unsorted)) (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 $$unsorted) (C_5 $$unsorted) (D_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_i1529485324t_bool tptp.insert_int A_13))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool C_5) D_2)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool (tptp.hAPP_f1805168059t_bool _let_1 C_5)) (tptp.hAPP_f1805168059t_bool _let_1 D_2)))))) (forall ((A_13 $$unsorted) (C_5 $$unsorted) (D_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a A_13))) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_f1767618879l_bool tptp.ord_le1523781517a_bool C_5) D_2)) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_f1767618879l_bool tptp.ord_le1523781517a_bool (tptp.hAPP_f20753329a_bool _let_1 C_5)) (tptp.hAPP_f20753329a_bool _let_1 D_2)))))) (forall ((Ba $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat Ba) B)))))) (forall ((Ba $$unsorted) (A $$unsorted) (B $$unsorted)) (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 $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f1767618879l_bool tptp.ord_le1523781517a_bool A))) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool _let_1 B)) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool _let_1 (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a Ba) B)))))) (forall ((B $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (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 $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A))) (=> (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A))) (= (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1) B))) (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 B)))))) (forall ((B $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f1767618879l_bool tptp.ord_le1523781517a_bool A))) (=> (not (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_1) A))) (= (tptp.hBOOL (tptp.hAPP_f1695230391l_bool _let_1 (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a X_1) B))) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool _let_1 B)))))) (forall ((X_1 $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) A)) B)) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) B)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) B))))) (forall ((X_1 $$unsorted) (A $$unsorted) (B $$unsorted)) (= (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 $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_f1767618879l_bool tptp.ord_le1523781517a_bool (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a X_1) A)) B)) (and (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_1) B)) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_f1767618879l_bool tptp.ord_le1523781517a_bool A) B))))) (forall ((B $$unsorted) (A_13 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool B) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13) B)))) (forall ((B $$unsorted) (A_13 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool B) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_13) B)))) (forall ((B $$unsorted) (A_13 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_f1767618879l_bool tptp.ord_le1523781517a_bool B) (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a A_13) B)))) (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (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 $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_f1767618879l_bool tptp.ord_le1523781517a_bool A) B)) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_f1767618879l_bool tptp.ord_le1523781517a_bool (tptp.image_533441733iple_a F A)) (tptp.image_533441733iple_a F B))))) (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (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 $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) B)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.image_nat_nat F A)) (tptp.image_nat_nat F B))))) (forall ((B $$unsorted) (F $$unsorted) (A $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool B) (tptp.image_int_int F A))) (exists ((AA $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool AA) A)) (= B (tptp.image_int_int F AA)))))) (forall ((B $$unsorted) (F $$unsorted) (A $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_f1767618879l_bool tptp.ord_le1523781517a_bool B) (tptp.image_533441733iple_a F A))) (exists ((AA $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_f1767618879l_bool tptp.ord_le1523781517a_bool AA) A)) (= B (tptp.image_533441733iple_a F AA)))))) (forall ((B $$unsorted) (F $$unsorted) (A $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool B) (tptp.image_nat_int F A))) (exists ((AA $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool AA) A)) (= B (tptp.image_nat_int F AA)))))) (forall ((B $$unsorted) (F $$unsorted) (A $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool B) (tptp.image_nat_nat F A))) (exists ((AA $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool AA) A)) (= B (tptp.image_nat_nat F AA)))))) (forall ((C_5 $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (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 $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_f1767618879l_bool tptp.ord_le1523781517a_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_f1767618879l_bool tptp.ord_le1523781517a_bool B) C_5)) (= (tptp.hAPP_f20753329a_bool (tptp.hAPP_f1706700729a_bool tptp.minus_85316870a_bool B) (tptp.hAPP_f20753329a_bool (tptp.hAPP_f1706700729a_bool tptp.minus_85316870a_bool C_5) A)) A)))) (forall ((C_5 $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (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 $$unsorted) (B $$unsorted) (A $$unsorted) (C_5 $$unsorted)) (=> (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 $$unsorted) (B $$unsorted) (A $$unsorted) (C_5 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_f1767618879l_bool tptp.ord_le1523781517a_bool A) C_5)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_f1767618879l_bool tptp.ord_le1523781517a_bool D_2) B)) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_f1767618879l_bool tptp.ord_le1523781517a_bool (tptp.hAPP_f20753329a_bool (tptp.hAPP_f1706700729a_bool tptp.minus_85316870a_bool A) B)) (tptp.hAPP_f20753329a_bool (tptp.hAPP_f1706700729a_bool tptp.minus_85316870a_bool C_5) D_2)))))) (forall ((D_2 $$unsorted) (B $$unsorted) (A $$unsorted) (C_5 $$unsorted)) (=> (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 $$unsorted) (B $$unsorted)) (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 $$unsorted) (B $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_f1767618879l_bool tptp.ord_le1523781517a_bool (tptp.hAPP_f20753329a_bool (tptp.hAPP_f1706700729a_bool tptp.minus_85316870a_bool A) B)) A))) (forall ((A $$unsorted) (B $$unsorted)) (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 $$unsorted) (Ga $$unsorted) (Ts_1 $$unsorted)) (let ((_let_1 (tptp.hoare_2102800559rivs_a Ga))) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool _let_1 Ts_1)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_f1767618879l_bool tptp.ord_le1523781517a_bool Ts) Ts_1)) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool _let_1 Ts)))))) (forall ((Ts $$unsorted) (Ga $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_f1767618879l_bool tptp.ord_le1523781517a_bool Ts) Ga)) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hoare_2102800559rivs_a Ga) Ts)))) (forall ((A $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) tptp.bot_bot_fun_nat_bool))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) _let_1)) (or (= A tptp.bot_bot_fun_nat_bool) (= A _let_1))))) (forall ((A $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1) tptp.bot_bot_fun_int_bool))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A) _let_1)) (or (= A tptp.bot_bot_fun_int_bool) (= A _let_1))))) (forall ((A $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a X_1) tptp.bot_bo797238721a_bool))) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_f1767618879l_bool tptp.ord_le1523781517a_bool A) _let_1)) (or (= A tptp.bot_bo797238721a_bool) (= A _let_1))))) (forall ((B $$unsorted) (F $$unsorted) (A $$unsorted)) (=> (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 $$unsorted) (F $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_f1767618879l_bool tptp.ord_le1523781517a_bool B) (tptp.image_533441733iple_a F A))) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a B))))) (forall ((B $$unsorted) (F $$unsorted) (A $$unsorted)) (=> (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 $$unsorted) (F $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool B) (tptp.image_nat_nat F A))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat B))))) (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (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 $$unsorted) (A $$unsorted) (B $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_f1767618879l_bool tptp.ord_le1523781517a_bool (tptp.hAPP_f20753329a_bool (tptp.hAPP_f1706700729a_bool tptp.minus_85316870a_bool (tptp.image_533441733iple_a F A)) (tptp.image_533441733iple_a F B))) (tptp.image_533441733iple_a F (tptp.hAPP_f20753329a_bool (tptp.hAPP_f1706700729a_bool tptp.minus_85316870a_bool A) B))))) (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (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 $$unsorted) (A $$unsorted) (B $$unsorted)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool (tptp.image_nat_nat F A)) (tptp.image_nat_nat F B))) (tptp.image_nat_nat F (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) B))))) (forall ((A_13 $$unsorted) (E $$unsorted) (Ca $$unsorted) (Ba $$unsorted) (D_1 $$unsorted)) (= (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 $$unsorted) (E $$unsorted) (Ca $$unsorted) (Ba $$unsorted) (D_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_13) E)) Ca)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Ba) E)) D_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Ca) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int Ba) A_13)) E)) D_1))))) (forall ((A $$unsorted) (X_1 $$unsorted) (B $$unsorted)) (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 $$unsorted) (X_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) (tptp.hAPP_f1805168059t_bool _let_1 tptp.bot_bot_fun_int_bool))) B)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A) (tptp.hAPP_f1805168059t_bool _let_1 B))))))) (forall ((A $$unsorted) (X_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a X_1))) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_f1767618879l_bool tptp.ord_le1523781517a_bool (tptp.hAPP_f20753329a_bool (tptp.hAPP_f1706700729a_bool tptp.minus_85316870a_bool A) (tptp.hAPP_f20753329a_bool _let_1 tptp.bot_bo797238721a_bool))) B)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_1) A)) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_f1767618879l_bool tptp.ord_le1523781517a_bool A) (tptp.hAPP_f20753329a_bool _let_1 B))))))) (forall ((A $$unsorted) (X_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)))) (let ((_let_3 (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1))) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f800510211t_bool _let_3 B))) (and (=> _let_2 (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) (tptp.hAPP_f800510211t_bool _let_3 tptp.bot_bot_fun_nat_bool))) B))) (=> (not _let_2) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B))))))))) (forall ((A $$unsorted) (X_1 $$unsorted) (B $$unsorted)) (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 $$unsorted) (X_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f1767618879l_bool tptp.ord_le1523781517a_bool A))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_1) A)))) (let ((_let_3 (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a X_1))) (= (tptp.hBOOL (tptp.hAPP_f1695230391l_bool _let_1 (tptp.hAPP_f20753329a_bool _let_3 B))) (and (=> _let_2 (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_f1767618879l_bool tptp.ord_le1523781517a_bool (tptp.hAPP_f20753329a_bool (tptp.hAPP_f1706700729a_bool tptp.minus_85316870a_bool A) (tptp.hAPP_f20753329a_bool _let_3 tptp.bot_bo797238721a_bool))) B))) (=> (not _let_2) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool _let_1 B))))))))) (forall ((B $$unsorted) (A $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1693662087iple_a F_1 A))) (=> (tptp.hBOOL (tptp.finite1033474011iple_a F F_1)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a A)) (=> (not (= B tptp.bot_bo797238721a_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_f1767618879l_bool tptp.ord_le1523781517a_bool B) A)) (= (tptp.hAPP_H905846293iple_a (tptp.hAPP_H2085992369iple_a F (tptp.hAPP_f1693662087iple_a F_1 B)) _let_1) _let_1))))))) (forall ((B $$unsorted) (A $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1594865479ol_int F_1 A))) (=> (tptp.hBOOL (tptp.finite1432773856em_int F F_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (=> (not (= B tptp.bot_bot_fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool B) A)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int F (tptp.hAPP_f1594865479ol_int F_1 B)) _let_1) _let_1))))))) (forall ((B $$unsorted) (A $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f22106695ol_nat F_1 A))) (=> (tptp.hBOOL (tptp.finite795500164em_nat F F_1)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (not (= B tptp.bot_bot_fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool B) A)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat F (tptp.hAPP_f22106695ol_nat F_1 B)) _let_1) _let_1))))))) (forall ((Pa $$unsorted) (A $$unsorted) (F_1 $$unsorted)) (=> (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 $$unsorted) (F_2 $$unsorted)) (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 $$unsorted) (A $$unsorted) (F_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int F_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool F_1) A)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool Pa tptp.bot_bot_fun_int_bool)) (=> (forall ((A_12 $$unsorted) (F_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_i2112223885l_bool tptp.member_int A_12))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int F_2)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 A)) (=> (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 F_2))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool Pa F_2)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool Pa (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_12) F_2))))))))) (tptp.hBOOL (tptp.hAPP_f448129468l_bool Pa F_1))))))) (forall ((Pa $$unsorted) (A $$unsorted) (F_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a F_1)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_f1767618879l_bool tptp.ord_le1523781517a_bool F_1) A)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool Pa tptp.bot_bo797238721a_bool)) (=> (forall ((A_12 $$unsorted) (F_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a A_12))) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a F_2)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool _let_1 A)) (=> (not (tptp.hBOOL (tptp.hAPP_f1695230391l_bool _let_1 F_2))) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool Pa F_2)) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool Pa (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a A_12) F_2))))))))) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool Pa F_1))))))) (forall ((B $$unsorted) (A $$unsorted)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_2))) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool _let_1 B))))) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_f1767618879l_bool tptp.ord_le1523781517a_bool A) B)))) (forall ((B $$unsorted) (A $$unsorted)) (=> (forall ((X_2 $$unsorted)) (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 $$unsorted) (A $$unsorted)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat X_2))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) B)))) (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (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 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool C_4) A)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int C_4)) (= B (tptp.image_int_int F C_4))))))) (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a B)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_f1767618879l_bool tptp.ord_le1523781517a_bool B) (tptp.image_533441733iple_a F A))) (exists ((C_4 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_f1767618879l_bool tptp.ord_le1523781517a_bool C_4) A)) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool tptp.finite1738664244iple_a C_4)) (= B (tptp.image_533441733iple_a F C_4))))))) (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (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 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool C_4) A)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat C_4)) (= B (tptp.image_nat_int F C_4))))))) (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (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 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool C_4) A)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat C_4)) (= B (tptp.image_nat_nat F C_4))))))) (forall ((F $$unsorted) (G $$unsorted) (K_3 $$unsorted)) (=> (forall ((I_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int I_2) K_3)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_int_nat F I_2)) (tptp.hAPP_int_nat G I_2))))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f957591787ol_nat (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat F) K_3)) (tptp.hAPP_f957591787ol_nat (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat G) K_3))))) (forall ((F $$unsorted) (G $$unsorted) (K_3 $$unsorted)) (=> (forall ((I_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a I_2) K_3)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_H592031934_a_nat F I_2)) (tptp.hAPP_H592031934_a_nat G I_2))))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f2097660464ol_nat (tptp.hAPP_f1371399797ol_nat tptp.big_co1340561246_a_nat F) K_3)) (tptp.hAPP_f2097660464ol_nat (tptp.hAPP_f1371399797ol_nat tptp.big_co1340561246_a_nat G) K_3))))) (forall ((F $$unsorted) (G $$unsorted) (K_3 $$unsorted)) (=> (forall ((I_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat I_2) K_3)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat F I_2)) (tptp.hAPP_nat_nat G I_2))))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat F) K_3)) (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat G) K_3))))) (forall ((F $$unsorted) (B $$unsorted) (A $$unsorted)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_2) A)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int (tptp.hAPP_int_int F X_2)) B)))) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool (tptp.image_int_int F A)) B)))) (forall ((F $$unsorted) (B $$unsorted) (A $$unsorted)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a X_2) A)) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool tptp.member1797258804iple_a (tptp.hAPP_H905846293iple_a F X_2)) B)))) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_f1767618879l_bool tptp.ord_le1523781517a_bool (tptp.image_533441733iple_a F A)) B)))) (forall ((F $$unsorted) (B $$unsorted) (A $$unsorted)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) A)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int (tptp.hAPP_nat_int F X_2)) B)))) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool (tptp.image_nat_int F A)) B)))) (forall ((F $$unsorted) (B $$unsorted) (A $$unsorted)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) A)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat (tptp.hAPP_nat_nat F X_2)) B)))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.image_nat_nat F A)) B)))) (forall ((F $$unsorted) (G $$unsorted)) (=> (forall ((X_2 $$unsorted)) (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 $$unsorted) (G $$unsorted)) (=> (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_nat_bool F X_2)) (tptp.hAPP_nat_bool G X_2)))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool F) G)))) (forall ((A $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int Ba) tptp.bot_bot_fun_int_bool))) (let ((_let_2 (tptp.hAPP_f1594865479ol_int (tptp.partial_flat_lub_int Ba) A))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A) _let_1)))) (and (=> _let_3 (= _let_2 Ba)) (=> (not _let_3) (= _let_2 (tptp.hAPP_f1594865479ol_int tptp.the_int (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f202917053t_bool tptp.cOMBC_94739984l_bool tptp.member_int) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) _let_1)))))))))) (forall ((A $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool tptp.insert956547291iple_a Ba) tptp.bot_bo797238721a_bool))) (let ((_let_2 (tptp.hAPP_f1693662087iple_a (tptp.partia1949573335iple_a Ba) A))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_f1767618879l_bool tptp.ord_le1523781517a_bool A) _let_1)))) (and (=> _let_3 (= _let_2 Ba)) (=> (not _let_3) (= _let_2 (tptp.hAPP_f1693662087iple_a tptp.the_Ho830102290iple_a (tptp.hAPP_f20753329a_bool (tptp.hAPP_f247708275a_bool tptp.cOMBC_1519416966l_bool tptp.member1797258804iple_a) (tptp.hAPP_f20753329a_bool (tptp.hAPP_f1706700729a_bool tptp.minus_85316870a_bool A) _let_1)))))))))) (forall ((A $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat Ba) tptp.bot_bot_fun_nat_bool))) (let ((_let_2 (tptp.hAPP_f22106695ol_nat (tptp.partial_flat_lub_nat Ba) A))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) _let_1)))) (and (=> _let_3 (= _let_2 Ba)) (=> (not _let_3) (= _let_2 (tptp.hAPP_f22106695ol_nat tptp.the_nat (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1722879237t_bool tptp.cOMBC_226598744l_bool tptp.member_nat) (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) _let_1)))))))))) (forall ((N_1 $$unsorted) (Q_1 $$unsorted) (Pa $$unsorted)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_lessThan_nat N_1))) (=> (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat Q_1 X_2)) (tptp.hAPP_nat_nat Pa X_2)))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat Pa) _let_1)) (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat Q_1) _let_1)) (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat (tptp.hAPP_f1914919701at_nat (tptp.hAPP_f1408247010at_nat tptp.cOMBS_nat_nat_nat (tptp.hAPP_f1639111240at_nat (tptp.hAPP_f1731313045at_nat tptp.cOMBB_963856155at_nat tptp.minus_minus_nat) Pa)) Q_1)) _let_1))))) (forall ((B $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.finite_fold1_int tptp.ord_min_int))) (=> (not (= A tptp.bot_bot_fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int B)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_f1594865479ol_int _let_1 B)) (tptp.hAPP_f1594865479ol_int _let_1 A)))))))) (forall ((B $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.finite_fold1_nat tptp.ord_min_nat))) (=> (not (= A tptp.bot_bot_fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat B)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f22106695ol_nat _let_1 B)) (tptp.hAPP_f22106695ol_nat _let_1 A)))))))) (forall ((Q_1 $$unsorted) (Pa $$unsorted)) (=> (forall ((X_2 $$unsorted)) (=> (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 $$unsorted) (Pa $$unsorted)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool Pa X_2)) (tptp.hBOOL (tptp.hAPP_nat_bool Q_1 X_2)))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Pa) Q_1)))) (forall ((Q_1 $$unsorted) (Pa $$unsorted)) (=> (forall ((X_2 $$unsorted)) (=> (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 $$unsorted) (Pa $$unsorted)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_H1037229737a_bool Pa X_2)) (tptp.hBOOL (tptp.hAPP_H1037229737a_bool Q_1 X_2)))) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_f1767618879l_bool tptp.ord_le1523781517a_bool (tptp.hAPP_f20753329a_bool tptp.collec351493750iple_a Pa)) (tptp.hAPP_f20753329a_bool tptp.collec351493750iple_a Q_1))))) (forall ((Q_1 $$unsorted) (Pa $$unsorted)) (=> (forall ((X_2 $$unsorted)) (=> (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 $$unsorted) (N_3 $$unsorted)) (=> (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 $$unsorted) (N_3 $$unsorted)) (=> (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 $$unsorted) (N_3 $$unsorted)) (=> (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 $$unsorted) (N_3 $$unsorted)) (=> (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 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.hAPP_n1699378549t_bool tptp.ord_lessThan_nat K_1)))) (forall ((K_1 $$unsorted)) (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 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat N_3)) (exists ((M_1 $$unsorted)) (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) N_3)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_2) M_1))))))) (forall ((X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f1594865479ol_int tptp.big_linorder_Min_int A))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.ord_min_int X_1) _let_1) _let_1))))) (forall ((X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f22106695ol_nat tptp.big_linorder_Min_nat A))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat X_1) _let_1) _let_1))))) (forall ((X_18 $$unsorted)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat X_18) X_18) X_18)) (forall ((X_17 $$unsorted) (Y_12 $$unsorted) (Z_7 $$unsorted)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat X_17))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat (tptp.hAPP_nat_nat _let_1 Y_12)) Z_7) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat Y_12) Z_7))))) (forall ((A_11 $$unsorted) (B_10 $$unsorted) (C_3 $$unsorted)) (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 $$unsorted) (Y_11 $$unsorted) (Z_6 $$unsorted)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat X_16))) (let ((_let_2 (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat Y_11))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat _let_2 Z_6)) (tptp.hAPP_nat_nat _let_2 (tptp.hAPP_nat_nat _let_1 Z_6)))))) (forall ((B_9 $$unsorted) (A_10 $$unsorted) (C_2 $$unsorted)) (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 $$unsorted) (Y_10 $$unsorted)) (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 $$unsorted) (B_8 $$unsorted)) (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 $$unsorted) (Y_9 $$unsorted)) (= (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 $$unsorted) (B_7 $$unsorted)) (= (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 $$unsorted)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat A_7) A_7) A_7)) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (Z_1 $$unsorted)) (= (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 $$unsorted) (Y_1 $$unsorted) (Z_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.ord_min_int X_1) Y_1)) Z_1)) (or (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_1) Z_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Y_1) Z_1))))) (forall ((X_13 $$unsorted) (A_6 $$unsorted) (B_6 $$unsorted)) (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 $$unsorted) (A_6 $$unsorted) (B_6 $$unsorted)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_13))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.ord_min_int A_6) B_6))) (not (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A_6)) (not (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_6)))))))) (forall ((B_5 $$unsorted) (D $$unsorted) (A_5 $$unsorted) (C_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_5) C_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat B_5) D)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat A_5) B_5)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat C_1) D)))))) (forall ((B_5 $$unsorted) (D $$unsorted) (A_5 $$unsorted) (C_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_5) C_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_5) D)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.ord_min_int A_5) B_5)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.ord_min_int C_1) D)))))) (forall ((Z_5 $$unsorted) (X_12 $$unsorted) (Y_8 $$unsorted)) (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 $$unsorted) (X_12 $$unsorted) (Y_8 $$unsorted)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_12))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Y_8)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Z_5)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.ord_min_int Y_8) Z_5))))))) (forall ((B_4 $$unsorted) (X_11 $$unsorted) (A_4 $$unsorted)) (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 $$unsorted) (X_11 $$unsorted) (A_4 $$unsorted)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_11))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A_4)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_4)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.ord_min_int A_4) B_4))))))) (forall ((Y_7 $$unsorted) (X_10 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_7) X_10)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat X_10) Y_7) Y_7))) (forall ((Y_7 $$unsorted) (X_10 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Y_7) X_10)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.ord_min_int X_10) Y_7) Y_7))) (forall ((X_9 $$unsorted) (Y_6 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_9) Y_6)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat X_9) Y_6) X_9))) (forall ((X_9 $$unsorted) (Y_6 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_9) Y_6)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.ord_min_int X_9) Y_6) X_9))) (forall ((A_3 $$unsorted) (B_3 $$unsorted) (X_8 $$unsorted)) (=> (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 $$unsorted) (B_3 $$unsorted) (X_8 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_3) X_8)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.ord_min_int A_3) B_3)) X_8)))) (forall ((B_2 $$unsorted) (A_2 $$unsorted) (X_7 $$unsorted)) (=> (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 $$unsorted) (A_2 $$unsorted) (X_7 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_2) X_7)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.ord_min_int A_2) B_2)) X_7)))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (Z_1 $$unsorted)) (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 $$unsorted) (Y_1 $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_1))) (= (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.ord_min_int Y_1) Z_1))) (and (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Y_1)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Z_1)))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_1) Y_1)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat X_1) Y_1) X_1))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_1) Y_1)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.ord_min_int X_1) Y_1) X_1))) (forall ((X_6 $$unsorted) (Y_5 $$unsorted)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat X_6) Y_5)) Y_5))) (forall ((X_6 $$unsorted) (Y_5 $$unsorted)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.ord_min_int X_6) Y_5)) Y_5))) (forall ((X_5 $$unsorted) (Y_4 $$unsorted)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat X_5) Y_4)) X_5))) (forall ((X_5 $$unsorted) (Y_4 $$unsorted)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.ord_min_int X_5) Y_4)) X_5))) (forall ((X_4 $$unsorted) (Y_3 $$unsorted) (Z_4 $$unsorted)) (= (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 $$unsorted) (Y_3 $$unsorted) (Z_4 $$unsorted)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat X_4) Y_3)) Z_4) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat X_4) Z_4)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Y_3) Z_4)))) (forall ((X_3 $$unsorted) (Y_2 $$unsorted) (Z_3 $$unsorted)) (= (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 $$unsorted) (F $$unsorted)) (=> (forall ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_2) (tptp.hAPP_nat_nat F N_2)))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.hAPP_f800510211t_bool tptp.collect_nat (tptp.hAPP_n1699378549t_bool (tptp.hAPP_f229349961t_bool tptp.cOMBC_nat_nat_bool (tptp.hAPP_f618557131t_bool (tptp.hAPP_f1505651103t_bool tptp.cOMBB_800536526ol_nat tptp.ord_less_eq_nat) F)) U)))))) (forall ((N_1 $$unsorted) (K_1 $$unsorted) (M_2 $$unsorted)) (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 $$unsorted) (L_1 $$unsorted) (I $$unsorted) (J $$unsorted)) (=> (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 $$unsorted) (I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat K))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I) J)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 I)) (tptp.hAPP_nat_nat _let_1 J)))))) (forall ((K $$unsorted) (I $$unsorted) (J $$unsorted)) (=> (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 $$unsorted)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat _let_1 M)))))) (forall ((M $$unsorted)) (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 $$unsorted)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N) N))) (forall ((M $$unsorted) (N $$unsorted)) (or (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N) M)))) (forall ((M $$unsorted) (N $$unsorted)) (=> (= M N) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N)))) (forall ((K $$unsorted) (I $$unsorted) (J $$unsorted)) (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 $$unsorted) (N $$unsorted)) (=> (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 $$unsorted) (K $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M) K)) N)) (not (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K) N))))))) (forall ((M $$unsorted) (K $$unsorted) (N $$unsorted)) (=> (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 $$unsorted) (K $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M) K)) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K) N)))) (forall ((K $$unsorted) (L_1 $$unsorted) (I $$unsorted) (J $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I) J)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K) L_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I) K)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat J) L_1)))))) (forall ((K $$unsorted) (I $$unsorted) (J $$unsorted)) (=> (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 $$unsorted) (I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 J)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M) J)))))) (forall ((M $$unsorted) (I $$unsorted) (J $$unsorted)) (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 $$unsorted) (M_2 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat K_1))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 M_2)) (tptp.hAPP_nat_nat _let_1 N_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_2) N_1))))) (forall ((M_2 $$unsorted) (N_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_2) N_1)) (exists ((K_2 $$unsorted)) (= N_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_2) K_2))))) (forall ((N $$unsorted) (M $$unsorted)) (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 $$unsorted) (M $$unsorted)) (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 $$unsorted) (I $$unsorted) (N $$unsorted)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M) I)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N) I)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat M) N)) I))) (forall ((K $$unsorted) (M $$unsorted) (N $$unsorted)) (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 $$unsorted) (N $$unsorted)) (= (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 $$unsorted) (M $$unsorted)) (= (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 $$unsorted) (J $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat I))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat _let_1 J)) K) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat J) K))))) (forall ((I $$unsorted) (J $$unsorted) (K $$unsorted)) (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 $$unsorted) (N $$unsorted) (K $$unsorted)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M) N)) K) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M) K)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat N) K)))) (forall ((K $$unsorted) (M $$unsorted) (N $$unsorted)) (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 $$unsorted) (K $$unsorted) (N $$unsorted)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M) K)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat N) K)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M) N))) (forall ((M $$unsorted) (N $$unsorted)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M) N)) M))) (forall ((I $$unsorted) (K $$unsorted) (J $$unsorted)) (=> (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 $$unsorted) (K_1 $$unsorted) (I_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat J_1) K_1)) I_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat J_1) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I_1) K_1))))) (forall ((M $$unsorted) (K $$unsorted) (N $$unsorted)) (=> (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 $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat L_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 N)) (tptp.hAPP_nat_nat _let_1 M)))))) (forall ((L_1 $$unsorted) (M $$unsorted) (N $$unsorted)) (=> (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 $$unsorted) (N $$unsorted)) (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 $$unsorted) (M $$unsorted)) (=> (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 $$unsorted) (K $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K) J)) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat J) K)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat _let_1 J)) K))))) (forall ((I_1 $$unsorted) (K_1 $$unsorted) (J_1 $$unsorted)) (=> (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 $$unsorted) (M $$unsorted)) (=> (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 $$unsorted) (I_1 $$unsorted) (J_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_1) J_1)) (= (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat J_1) I_1) K_1) (= J_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat K_1) I_1))))) (forall ((I $$unsorted) (K $$unsorted) (J $$unsorted)) (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 $$unsorted) (K $$unsorted) (J $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K) J)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat J) K)) I) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat J) I)) K)))) (forall ((I $$unsorted) (K $$unsorted) (J $$unsorted)) (=> (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 $$unsorted) (K_1 $$unsorted) (M_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M_2)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N_1)) (= (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M_2) K_1) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N_1) K_1)) (= M_2 N_1)))))) (forall ((N $$unsorted) (K $$unsorted) (M $$unsorted)) (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 $$unsorted) (M_2 $$unsorted) (N_1 $$unsorted) (I_1 $$unsorted) (J_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_1) J_1)) (= (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat I_1) U)) M_2) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat J_1) U)) N_1)) (= M_2 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat J_1) I_1)) U)) N_1))))) (forall ((U_1 $$unsorted) (M $$unsorted) (N $$unsorted) (I $$unsorted) (J $$unsorted)) (=> (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 $$unsorted) (M_2 $$unsorted) (N_1 $$unsorted) (I_1 $$unsorted) (J_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_1) J_1)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat I_1) U)) M_2)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat J_1) U)) N_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_2) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat J_1) I_1)) U)) N_1)))))) (forall ((U $$unsorted) (M_2 $$unsorted) (N_1 $$unsorted) (J_1 $$unsorted) (I_1 $$unsorted)) (=> (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 $$unsorted) (M $$unsorted) (N $$unsorted) (J $$unsorted) (I $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat J) I)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat I) U_1)) M)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat J) U_1)) N)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat I) J)) U_1)) M)) N)))) (forall ((M $$unsorted) (N $$unsorted) (K $$unsorted)) (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 $$unsorted) (N $$unsorted)) (= (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 $$unsorted) (K_1 $$unsorted) (N_1 $$unsorted)) (= (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_2) K_1) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat N_1) K_1)) (= M_2 N_1))) (forall ((K_1 $$unsorted) (M_2 $$unsorted) (N_1 $$unsorted)) (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 $$unsorted) (N $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 N)) K) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat N) K))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (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 $$unsorted) (N $$unsorted)) (= (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 $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat K))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M) N)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 M)) (tptp.hAPP_nat_nat _let_1 N))))) (forall ((M $$unsorted) (N $$unsorted) (K $$unsorted)) (= (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 $$unsorted) (U_1 $$unsorted) (J $$unsorted) (K $$unsorted)) (= (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 $$unsorted) (M_2 $$unsorted) (N_1 $$unsorted) (J_1 $$unsorted) (I_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat J_1) I_1)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat I_1) U)) M_2)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat J_1) U)) N_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat I_1) J_1)) U)) M_2)) N_1))))) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (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 $$unsorted) (X $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Z)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Y) Z)))))) (forall ((N $$unsorted) (M $$unsorted)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N) M)) M) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_max_nat N) M))) (forall ((U $$unsorted)) (= (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat (tptp.hAPP_n1699378549t_bool tptp.ord_lessThan_nat U)) U)) (forall ((M_2 $$unsorted) (N_1 $$unsorted)) (= (= (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 $$unsorted)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat N) tptp.one_one_nat) N)) (forall ((M_2 $$unsorted) (N_1 $$unsorted)) (= (= tptp.one_one_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M_2) N_1)) (and (= M_2 tptp.one_one_nat) (= N_1 tptp.one_one_nat)))) (forall ((N $$unsorted)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat tptp.one_one_nat) N) N)) (forall ((M $$unsorted) (N $$unsorted) (Z $$unsorted)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int M)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int N)) Z)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M) N))) Z))) (forall ((M $$unsorted) (N $$unsorted)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int M)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int N)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M) N)))) (forall ((M_2 $$unsorted) (N_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int M_2)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_2) N_1)))) (forall ((M $$unsorted) (N $$unsorted)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int M)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int N)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M) N)))) (forall ((M $$unsorted) (N $$unsorted)) (= (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M) N)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int M)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int N)))) (= _let_11 tptp.one_one_int) (forall ((N $$unsorted) (M $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N) M)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int M)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int N)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M) N))))) (forall ((N $$unsorted) (M $$unsorted)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int tptp.uminus_uminus_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int N))) (tptp.hAPP_nat_int tptp.semiri1621563631at_int M)))) (forall ((L $$unsorted) (U $$unsorted)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.hAPP_n1699378549t_bool (tptp.ord_at238088361st_nat L) U)))) (forall ((K_1 $$unsorted)) (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 $$unsorted) (Z_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int W) Z_1)) (exists ((N_2 $$unsorted)) (= Z_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int W) (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_2)))))) (forall ((M $$unsorted) (N $$unsorted)) (= (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat M) N)) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int M)) N))) (forall ((M $$unsorted) (N $$unsorted)) (= (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int M)) N) (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat M) N)))) (forall ((M_2 $$unsorted) (N_1 $$unsorted)) (= (= (tptp.hAPP_nat_int tptp.semiri1621563631at_int M_2) (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_1)) (= M_2 N_1))) (forall ((Z $$unsorted) (W_1 $$unsorted)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.uminus_uminus_int Z)) W_1) (tptp.hAPP_int_int tptp.uminus_uminus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Z) W_1)))) (forall ((Z $$unsorted) (W_1 $$unsorted)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int Z) (tptp.hAPP_int_int tptp.uminus_uminus_int W_1)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int Z) W_1))) (forall ((Z $$unsorted) (W_1 $$unsorted)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int Z) W_1) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int Z) (tptp.hAPP_int_int tptp.uminus_uminus_int W_1)))) (forall ((Z $$unsorted) (W_1 $$unsorted)) (= (tptp.hAPP_int_int tptp.uminus_uminus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int Z) W_1)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int tptp.uminus_uminus_int Z)) (tptp.hAPP_int_int tptp.uminus_uminus_int W_1)))) (forall ((W_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int W_1) W_1))) (forall ((Z $$unsorted) (W_1 $$unsorted)) (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 $$unsorted) (I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int I))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 J)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int J) K)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 K)))))) (forall ((Z $$unsorted) (W_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Z) W_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int W_1) Z)) (= Z W_1)))) (forall ((Z1 $$unsorted) (Z2 $$unsorted) (Z3 $$unsorted)) (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 $$unsorted) (Y $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.hAPP_int_fun_nat_int tptp.power_power_int X))) (= (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int (tptp.hAPP_nat_int _let_1 Y)) Z) (tptp.hAPP_nat_int _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat Y) Z))))) (forall ((Z $$unsorted) (W_1 $$unsorted)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Z) W_1) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int W_1) Z))) (forall ((Z1 $$unsorted) (Z2 $$unsorted) (W_1 $$unsorted)) (= (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 $$unsorted) (Z1 $$unsorted) (Z2 $$unsorted)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int W_1))) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int Z1) Z2)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_int_int _let_1 Z1)) (tptp.hAPP_int_int _let_1 Z2))))) (forall ((Z1 $$unsorted) (Z2 $$unsorted) (Z3 $$unsorted)) (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 $$unsorted) (Y $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.plus_plus_int X))) (let ((_let_2 (tptp.hAPP_int_fun_int_int tptp.plus_plus_int Y))) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int _let_2 Z)) (tptp.hAPP_int_int _let_2 (tptp.hAPP_int_int _let_1 Z)))))) (forall ((Z $$unsorted) (W_1 $$unsorted)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int Z) W_1) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int W_1) Z))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (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 $$unsorted) (Z1 $$unsorted) (Z2 $$unsorted)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int W_1))) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int Z1) Z2)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int _let_1 Z1)) (tptp.hAPP_int_int _let_1 Z2))))) (forall ((Z1 $$unsorted) (Z2 $$unsorted) (W_1 $$unsorted)) (= (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 $$unsorted) (I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.plus_plus_int K))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int I) J)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int _let_1 I)) (tptp.hAPP_int_int _let_1 J)))))) (forall ((Z $$unsorted)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Z) tptp.one_one_int) Z)) (forall ((Z $$unsorted)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int tptp.one_one_int) Z) Z)) (forall ((I $$unsorted) (J $$unsorted) (K $$unsorted)) (=> (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 $$unsorted) (N $$unsorted) (K $$unsorted) (L_1 $$unsorted)) (=> (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 $$unsorted) (L_1 $$unsorted) (I $$unsorted) (J $$unsorted)) (=> (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 $$unsorted) (I $$unsorted) (J $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I) J)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I) K)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat J) K))))) (forall ((M $$unsorted) (I $$unsorted) (J $$unsorted)) (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 $$unsorted) (I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 J)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat J) M)))))) (forall ((K_1 $$unsorted) (M_2 $$unsorted) (N_1 $$unsorted)) (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 $$unsorted) (I $$unsorted)) (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 $$unsorted) (J $$unsorted)) (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 $$unsorted) (N_1 $$unsorted)) (= (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 $$unsorted) (N_1 $$unsorted)) (= (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 $$unsorted) (N $$unsorted)) (=> (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 $$unsorted) (N $$unsorted)) (=> (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 $$unsorted) (N $$unsorted)) (=> (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 $$unsorted) (J $$unsorted) (K $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat J) K)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat J) N)) K)))) (forall ((L_1 $$unsorted) (M $$unsorted) (N $$unsorted)) (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 $$unsorted) (M_2 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool Pa N_1) M_2)))) (=> (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_2) N_1)) _let_1) (=> (=> (= M_2 N_1) _let_1) (=> (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N_1) M_2)) _let_1) _let_1))))) (forall ((S $$unsorted) (T $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat S) T)) (not (= S T)))) (forall ((N $$unsorted) (M $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N) M)) (not (= M N)))) (forall ((N $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N) N)))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (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 $$unsorted) (N_1 $$unsorted)) (= (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 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N) N)))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X) Y)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X) Y)))) (forall ((Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (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 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Y) Z)))))) (forall ((K_1 $$unsorted) (I_1 $$unsorted) (J_1 $$unsorted)) (= (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 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat N_3)) (exists ((M_1 $$unsorted)) (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) N_3)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_2) M_1))))))) (forall ((Pa $$unsorted) (I_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.hAPP_f800510211t_bool tptp.collect_nat (tptp.hAPP_f800510211t_bool (tptp.hAPP_f561022312t_bool tptp.cOMBS_nat_bool_bool (tptp.hAPP_f1146629647l_bool (tptp.hAPP_f1080886329l_bool tptp.cOMBB_1015721476ol_nat tptp.fconj) Pa)) (tptp.hAPP_n1699378549t_bool (tptp.hAPP_f229349961t_bool tptp.cOMBC_nat_nat_bool tptp.ord_less_nat) I_1)))))) (forall ((N_1 $$unsorted)) (= (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 $$unsorted) (N $$unsorted)) (=> (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 $$unsorted) (J_1 $$unsorted) (K_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_1) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat J_1) K_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I_1) K_1)) J_1)))) (forall ((N_1 $$unsorted) (K_1 $$unsorted) (M_2 $$unsorted)) (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 $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_1) B_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat C) A_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat A_1) C)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat B_1) C)))))) (forall ((U $$unsorted) (M_2 $$unsorted) (N_1 $$unsorted) (J_1 $$unsorted) (I_1 $$unsorted)) (=> (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 $$unsorted) (M_2 $$unsorted) (N_1 $$unsorted) (I_1 $$unsorted) (J_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_1) J_1)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat I_1) U)) M_2)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat J_1) U)) N_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_2) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat J_1) I_1)) U)) N_1)))))) (forall ((N $$unsorted) (M $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int N)) (tptp.hAPP_int_int tptp.uminus_uminus_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int M)))))) (forall ((Z_1 $$unsorted) (W $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Z_1) W)) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Z_1) W)) (not (= Z_1 W))))) (forall ((K $$unsorted) (I $$unsorted) (J $$unsorted)) (=> (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 $$unsorted)) (= (tptp.hAPP_int_int tptp.uminus_uminus_int (tptp.hAPP_int_int tptp.uminus_uminus_int Z)) Z)) (forall ((Z_2 $$unsorted) (Z $$unsorted) (W_2 $$unsorted) (W_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int W_2) W_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Z_2) Z)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int W_2) Z_2)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int W_1) Z)))))) (forall ((M_2 $$unsorted) (N_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int M_2)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_2) N_1)))) (forall ((W $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int W))) (= (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int Z_1) tptp.one_one_int))) (or (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Z_1)) (= W Z_1))))) (forall ((M_2 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.ord_at875362053st_int M_2))) (let ((_let_2 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) N_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int M_2) _let_2)) (= (tptp.hAPP_i1948725293t_bool _let_1 _let_2) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int _let_2) (tptp.hAPP_i1948725293t_bool _let_1 N_1))))))) (forall ((W_1 $$unsorted) (Z $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int W_1) Z)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int W_1) tptp.one_one_int)) Z)))) (forall ((W $$unsorted) (Z_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int W) tptp.one_one_int)) Z_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int W) Z_1)))) (forall ((W $$unsorted) (Z_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int W) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int Z_1) tptp.one_one_int))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int W) Z_1)))) (forall ((W $$unsorted) (Z_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int W) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int Z_1) tptp.one_one_int))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int W) Z_1)))) (forall ((Pa $$unsorted) (I_1 $$unsorted) (K_1 $$unsorted)) (=> (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 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int I_2) K_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool Pa I_2)) (tptp.hBOOL (tptp.hAPP_int_bool Pa (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int I_2) tptp.one_one_int)))))) (tptp.hBOOL (tptp.hAPP_int_bool Pa I_1)))))) (forall ((L $$unsorted) (U $$unsorted)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.hAPP_i1948725293t_bool (tptp.ord_at875362053st_int L) U)))) (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X) Y)) (= X Y) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Y) X)))) (forall ((J_1 $$unsorted) (I_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool (tptp.ord_at875362053st_int I_1) J_1))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int J_1) I_1)))) (and (=> _let_2 (= _let_1 tptp.bot_bot_fun_int_bool)) (=> (not _let_2) (= _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int I_1) (tptp.hAPP_i1948725293t_bool (tptp.ord_at875362053st_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int I_1) tptp.one_one_int)) J_1)))))))) (forall ((Pa $$unsorted) (I_1 $$unsorted) (K_1 $$unsorted)) (=> (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 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int I_2) K_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool Pa I_2)) (tptp.hBOOL (tptp.hAPP_int_bool Pa (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int I_2) tptp.one_one_int)))))) (tptp.hBOOL (tptp.hAPP_int_bool Pa I_1)))))) (forall ((A $$unsorted)) (= (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 $$unsorted) (B $$unsorted)) (= (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 $$unsorted) (A $$unsorted)) (= (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 $$unsorted) (B $$unsorted)) (= (= A B) (= (tptp.image_nat_int tptp.semiri1621563631at_int A) (tptp.image_nat_int tptp.semiri1621563631at_int B)))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (Pa $$unsorted)) (let ((_let_1 (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat (tptp.if_nat Pa) X_1) Y_1)))) (let ((_let_2 (tptp.hBOOL Pa))) (and (=> _let_2 (= (tptp.hAPP_nat_int tptp.semiri1621563631at_int X_1) _let_1)) (=> (not _let_2) (= (tptp.hAPP_nat_int tptp.semiri1621563631at_int Y_1) _let_1)))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (= (= (tptp.hAPP_nat_int tptp.semiri1621563631at_int X_1) (tptp.hAPP_nat_int tptp.semiri1621563631at_int Y_1)) (= X_1 Y_1))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool A) B)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le1912455174t_bool (tptp.image_nat_int tptp.semiri1621563631at_int A)) (tptp.image_nat_int tptp.semiri1621563631at_int B))))) (forall ((A $$unsorted)) (= (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 $$unsorted) (Y_1 $$unsorted)) (= (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 $$unsorted) (Y_1 $$unsorted)) (= (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 $$unsorted) (Y $$unsorted)) (= (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 $$unsorted) (Y $$unsorted)) (= (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 $$unsorted) (N $$unsorted)) (= (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 $$unsorted) (K_1 $$unsorted) (I_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K_1) I_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool Pa (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int K_1) tptp.one_one_int))) (=> (forall ((I_2 $$unsorted)) (=> (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 $$unsorted) (K_1 $$unsorted) (I_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K_1) I_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool Pa K_1)) (=> (forall ((I_2 $$unsorted)) (=> (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 $$unsorted) (K_1 $$unsorted) (F $$unsorted)) (=> (forall ((M_1 $$unsorted) (N_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_1) N_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat F M_1)) (tptp.hAPP_nat_nat F N_2))))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat F M_2)) K_1)) (tptp.hAPP_nat_nat F (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_2) K_1)))))) (forall ((N_1 $$unsorted) (N_3 $$unsorted)) (=> (forall ((X_2 $$unsorted)) (=> (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 $$unsorted)) (not (forall ((M_1 $$unsorted) (N_2 $$unsorted)) (not (= Z (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int M_1)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_2))))))) (forall ((I_1 $$unsorted) (J_1 $$unsorted) (F $$unsorted)) (=> (forall ((I_2 $$unsorted) (J_2 $$unsorted)) (=> (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 $$unsorted) (Pa $$unsorted) (K_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_int_bool Pa K_1)) (=> (forall ((I_2 $$unsorted)) (=> (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 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int I_2) K_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool Pa I_2)) (tptp.hBOOL (tptp.hAPP_int_bool Pa (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int I_2) tptp.one_one_int)))))) (tptp.hBOOL (tptp.hAPP_int_bool Pa I_1)))))) (forall ((N $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N) tptp.zero_zero_nat)))) (forall ((N $$unsorted)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) N))) (forall ((L $$unsorted) (U $$unsorted)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.hAPP_n1699378549t_bool (tptp.ord_gr375877188st_nat L) U)))) (forall ((N $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 X)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int X) N)))))) (forall ((Pa $$unsorted)) (= (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) X_2)) (tptp.hBOOL (tptp.hAPP_int_bool Pa X_2)))) (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_int_bool Pa (tptp.hAPP_nat_int tptp.semiri1621563631at_int X_2)))))) (forall ((Pa $$unsorted)) (= (exists ((X_2 $$unsorted)) (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 $$unsorted)) (tptp.hBOOL (tptp.hAPP_int_bool Pa (tptp.hAPP_nat_int tptp.semiri1621563631at_int X_2)))))) (forall ((Z $$unsorted)) (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 $$unsorted) (X $$unsorted)) (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 $$unsorted) (X $$unsorted)) (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 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int K)) tptp.zero_zero_int)))) (forall ((N_1 $$unsorted)) (= (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 $$unsorted) (L $$unsorted)) (= (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 $$unsorted) (I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int K))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int I) J)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) K)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int _let_1 I)) (tptp.hAPP_int_int _let_1 J))))))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) tptp.one_one_int)) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat))) (= (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat X_1) N_1))) (or (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 X_1)) (= N_1 tptp.zero_zero_nat))))) (forall ((M $$unsorted) (N $$unsorted) (I $$unsorted)) (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 $$unsorted)) (=> (not (= N tptp.zero_zero_nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N)))) (forall ((M $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N)) (not (= N tptp.zero_zero_nat)))) (forall ((N $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N) tptp.zero_zero_nat)))) (forall ((N_1 $$unsorted)) (= (not (= N_1 tptp.zero_zero_nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_1)))) (forall ((N $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N) tptp.zero_zero_nat)))) (forall ((P $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP_bool_bool tptp.fNot P))) (not (tptp.hBOOL P)))) (forall ((P $$unsorted)) (or (tptp.hBOOL P) (tptp.hBOOL (tptp.hAPP_bool_bool tptp.fNot P)))) (forall ((Q $$unsorted) (P $$unsorted)) (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 $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fconj P) Q))) (tptp.hBOOL P))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fconj P) Q))) (tptp.hBOOL Q))) (forall ((Q $$unsorted) (P $$unsorted)) (or (not (tptp.hBOOL P)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fdisj P) Q)))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL Q)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fdisj P) Q)))) (forall ((P $$unsorted) (Q $$unsorted)) (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 $$unsorted)) (=> (tptp.is_bool P) (or (= P tptp.fTrue) (= P tptp.fFalse)))) (forall ((Q $$unsorted) (P $$unsorted)) (or (tptp.hBOOL P) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fimplies P) Q)))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL Q)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fimplies P) Q)))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fimplies P) Q))) (not (tptp.hBOOL P)) (tptp.hBOOL Q))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat (tptp.if_nat tptp.fTrue) X) Y) X)) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat (tptp.if_nat tptp.fFalse) X) Y) Y)) (forall ((P $$unsorted)) (=> (tptp.is_bool P) (or (= P tptp.fTrue) (= P tptp.fFalse)))) (forall ((P $$unsorted)) (= (tptp.hAPP_int_int tptp.cOMBI_int P) P)) (forall ((P $$unsorted)) (= (tptp.hAPP_nat_nat tptp.cOMBI_nat P) P)) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.fequal_int X) Y))) (= X Y))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.fequal_int X) Y)))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.fequal_nat X) Y))) (= X Y))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.fequal_nat X) Y)))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool tptp.fequal_state X) Y))) (= X Y))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool tptp.fequal_state X) Y)))) (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.cOMBK_int_int P) Q) P)) (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.cOMBK_int_nat P) Q) P)) (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.hAPP_int_nat (tptp.hAPP_nat_fun_int_nat tptp.cOMBK_nat_int P) Q) P)) (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.cOMBK_nat_nat P) Q) P)) _let_9 (forall ((P $$unsorted) (Q $$unsorted)) (=> (tptp.is_bool P) (= (tptp.hAPP_nat_bool (tptp.hAPP_b1013836512t_bool tptp.cOMBK_bool_nat P) Q) P))) _let_8 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.fequal_fun_int_bool X) Y))) (= X Y))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.fequal_fun_int_bool X) Y)))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.fequal_fun_nat_bool X) Y))) (= X Y))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.fequal_fun_nat_bool X) Y)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_nat_int (tptp.hAPP_f1139079189at_int (tptp.hAPP_f1431025877at_int tptp.cOMBB_int_int_nat P) Q) R) (tptp.hAPP_int_int P (tptp.hAPP_nat_int Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (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 $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_int_nat (tptp.hAPP_f2132704789nt_nat (tptp.hAPP_f901215189nt_nat tptp.cOMBB_nat_nat_int P) Q) R) (tptp.hAPP_nat_nat P (tptp.hAPP_int_nat Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (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 $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_int_nat (tptp.hAPP_int_fun_int_nat (tptp.hAPP_f909851349nt_nat tptp.cOMBC_int_int_nat P) Q) R) (tptp.hAPP_int_nat (tptp.hAPP_int_fun_int_nat P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (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 $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_nat_nat (tptp.hAPP_int_fun_nat_nat (tptp.hAPP_f446977493at_nat tptp.cOMBC_nat_int_nat P) Q) R) (tptp.hAPP_int_nat (tptp.hAPP_nat_fun_int_nat P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (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 $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_int_nat (tptp.hAPP_f2132704789nt_nat (tptp.hAPP_f1399363134nt_nat tptp.cOMBS_int_nat_nat P) Q) R) (tptp.hAPP_nat_nat (tptp.hAPP_int_fun_nat_nat P R) (tptp.hAPP_int_nat Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (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 $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.hAPP_f428220345t_bool tptp.cOMBC_int_int_bool P) Q) R) (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (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 $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_nat_bool (tptp.hAPP_i418383825t_bool (tptp.hAPP_f482008321t_bool tptp.cOMBC_nat_int_bool P) Q) R) (tptp.hAPP_int_bool (tptp.hAPP_n1082236369t_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (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 $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_int_bool (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f627970963t_bool tptp.cOMBB_bool_bool_int P) Q) R) (tptp.hAPP_bool_bool P (tptp.hAPP_int_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (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 $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_int_bool (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f727283836t_bool tptp.cOMBS_int_bool_bool P) Q) R) (tptp.hAPP_bool_bool (tptp.hAPP_i68813070l_bool P R) (tptp.hAPP_int_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (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 $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_state_bool (tptp.hAPP_f1759915619e_bool (tptp.hAPP_f2073279419e_bool tptp.cOMBB_160679318_state P) Q) R) (tptp.hAPP_bool_bool P (tptp.hAPP_state_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (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 $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_state_bool (tptp.hAPP_f1759915619e_bool (tptp.hAPP_f644196280e_bool tptp.cOMBS_1378840469l_bool P) Q) R) (tptp.hAPP_bool_bool (tptp.hAPP_s58564346l_bool P R) (tptp.hAPP_state_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (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 $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_state_bool (tptp.hAPP_f746301080e_bool (tptp.hAPP_f162060345e_bool tptp.cOMBB_844853809_state P) Q) R) (tptp.hAPP_state_bool P (tptp.hAPP_state_state Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (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 $$unsorted)) (= (tptp.hAPP_H905846293iple_a tptp.cOMBI_1301683934iple_a P) P)) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP_H1037229737a_bool (tptp.hAPP_H426895267a_bool tptp.fequal963300192iple_a X) Y))) (= X Y))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_H1037229737a_bool (tptp.hAPP_H426895267a_bool tptp.fequal963300192iple_a X) Y)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (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 $$unsorted) (Q $$unsorted)) (= (tptp.hAPP_H1229305626_a_int (tptp.hAPP_i1475897073_a_int tptp.cOMBK_1007576201iple_a P) Q) P)) (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.hAPP_H592031934_a_nat (tptp.hAPP_n1653940209_a_nat tptp.cOMBK_1028443109iple_a P) Q) P)) (forall ((P $$unsorted) (Q $$unsorted)) (=> (tptp.is_bool P) (= (tptp.hAPP_H1037229737a_bool (tptp.hAPP_b1882817719a_bool tptp.cOMBK_235286536iple_a P) Q) P))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_int_fun_nat_nat (tptp.hAPP_f1463450952at_nat (tptp.hAPP_f1087393429at_nat tptp.cOMBB_1601129847at_int P) Q) R) (tptp.hAPP_nat_fun_nat_nat P (tptp.hAPP_int_nat Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (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 $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_i1948725293t_bool (tptp.hAPP_f1791153283t_bool (tptp.hAPP_f1399575567t_bool tptp.cOMBB_118231410ol_int P) Q) R) (tptp.hAPP_i1948725293t_bool P (tptp.hAPP_int_int Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (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 $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_i418383825t_bool (tptp.hAPP_f876579787t_bool (tptp.hAPP_f2026117279t_bool tptp.cOMBB_1437810218ol_int P) Q) R) (tptp.hAPP_n1699378549t_bool P (tptp.hAPP_int_nat Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (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 $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_int_nat (tptp.hAPP_f1134349059nt_nat (tptp.hAPP_f2100446809nt_nat tptp.cOMBB_2018621492at_int P) Q) R) (tptp.hAPP_f957591787ol_nat P (tptp.hAPP_i1948725293t_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (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 $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_int_nat (tptp.hAPP_f1161717855nt_nat (tptp.hAPP_f1964560145nt_nat tptp.cOMBB_1125113304at_int P) Q) R) (tptp.hAPP_f22106695ol_nat P (tptp.hAPP_i418383825t_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (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 $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_nat_nat (tptp.hAPP_f1473602334at_nat (tptp.hAPP_f630508183at_nat tptp.cOMBC_1505178355ol_nat P) Q) R) (tptp.hAPP_f957591787ol_nat (tptp.hAPP_n259507732ol_nat P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (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 $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_int_nat (tptp.hAPP_f1161717855nt_nat (tptp.hAPP_f369809936nt_nat tptp.cOMBS_1063588099ol_nat P) Q) R) (tptp.hAPP_f22106695ol_nat (tptp.hAPP_i1530422220ol_nat P R) (tptp.hAPP_i418383825t_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (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 $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_int_bool (tptp.hAPP_f2119767738t_bool (tptp.hAPP_f423804115t_bool tptp.cOMBB_1418110531ol_int P) Q) R) (tptp.hAPP_f448129468l_bool P (tptp.hAPP_i1948725293t_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (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 $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_int_bool (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f202917053t_bool tptp.cOMBC_94739984l_bool P) Q) R) (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (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 $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_i68813070l_bool (tptp.hAPP_f2144054103l_bool (tptp.hAPP_f1734373249l_bool tptp.cOMBB_1652995168ol_int P) Q) R) (tptp.hAPP_b589554111l_bool P (tptp.hAPP_int_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (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 $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_s58564346l_bool (tptp.hAPP_f1259673775l_bool (tptp.hAPP_f1561913689l_bool tptp.cOMBB_188601460_state P) Q) R) (tptp.hAPP_b589554111l_bool P (tptp.hAPP_state_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (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 $$unsorted) (Y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_f1767618879l_bool tptp.fequal874423448a_bool X) Y))) (= X Y))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_f1695230391l_bool (tptp.hAPP_f1767618879l_bool tptp.fequal874423448a_bool X) Y)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H592031934_a_nat (tptp.hAPP_f106743253_a_nat (tptp.hAPP_f500900629_a_nat tptp.cOMBB_1250632933iple_a P) Q) R) (tptp.hAPP_nat_nat P (tptp.hAPP_H592031934_a_nat Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H592031934_a_nat (tptp.hAPP_i1313984149_a_nat (tptp.hAPP_f183615253_a_nat tptp.cOMBC_2020858056nt_nat P) Q) R) (tptp.hAPP_int_nat (tptp.hAPP_H978941973nt_nat P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H592031934_a_nat (tptp.hAPP_n1653940209_a_nat (tptp.hAPP_f1903462933_a_nat tptp.cOMBC_667342884at_nat P) Q) R) (tptp.hAPP_nat_nat (tptp.hAPP_H1772910449at_nat P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_int_nat (tptp.hAPP_H978941973nt_nat (tptp.hAPP_f1451619093nt_nat tptp.cOMBC_1917249810_a_nat P) Q) R) (tptp.hAPP_H592031934_a_nat (tptp.hAPP_i1313984149_a_nat P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_nat_nat (tptp.hAPP_H1772910449at_nat (tptp.hAPP_f2146713109at_nat tptp.cOMBC_441305270_a_nat P) Q) R) (tptp.hAPP_H592031934_a_nat (tptp.hAPP_n1653940209_a_nat P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H1229305626_a_int (tptp.hAPP_f1561000661_a_int (tptp.hAPP_f789902073_a_int tptp.cOMBS_1600277268nt_int P) Q) R) (tptp.hAPP_int_int (tptp.hAPP_H1140854897nt_int P R) (tptp.hAPP_H1229305626_a_int Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H592031934_a_nat (tptp.hAPP_f106743253_a_nat (tptp.hAPP_f1418102009_a_nat tptp.cOMBS_1756972052at_nat P) Q) R) (tptp.hAPP_nat_nat (tptp.hAPP_H1772910449at_nat P R) (tptp.hAPP_H592031934_a_nat Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H1037229737a_bool (tptp.hAPP_i611776424a_bool (tptp.hAPP_f920351535a_bool tptp.cOMBC_1530706207t_bool P) Q) R) (tptp.hAPP_int_bool (tptp.hAPP_H1675210280t_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H1037229737a_bool (tptp.hAPP_n1919155532a_bool (tptp.hAPP_f228417655a_bool tptp.cOMBC_364739t_bool P) Q) R) (tptp.hAPP_nat_bool (tptp.hAPP_H144868812t_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_int_bool (tptp.hAPP_H1675210280t_bool (tptp.hAPP_f936407855t_bool tptp.cOMBC_1719122773a_bool P) Q) R) (tptp.hAPP_H1037229737a_bool (tptp.hAPP_i611776424a_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_nat_bool (tptp.hAPP_H144868812t_bool (tptp.hAPP_f1886543991t_bool tptp.cOMBC_533513393a_bool P) Q) R) (tptp.hAPP_H1037229737a_bool (tptp.hAPP_n1919155532a_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H1037229737a_bool (tptp.hAPP_f20753329a_bool (tptp.hAPP_f604201481a_bool tptp.cOMBB_1882975613iple_a P) Q) R) (tptp.hAPP_bool_bool P (tptp.hAPP_H1037229737a_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H1037229737a_bool (tptp.hAPP_f20753329a_bool (tptp.hAPP_f607497069a_bool tptp.cOMBS_154988028l_bool P) Q) R) (tptp.hAPP_bool_bool (tptp.hAPP_H2130837971l_bool P R) (tptp.hAPP_H1037229737a_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (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 $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_a2036067514e_bool (tptp.hAPP_f100967412e_bool (tptp.hAPP_f1460451647e_bool tptp.cOMBC_524597097e_bool P) Q) R) (tptp.hAPP_f746301080e_bool (tptp.hAPP_a1224971408e_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (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 $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_nat_fun_int_nat (tptp.hAPP_f237327688nt_nat (tptp.hAPP_f1633513941nt_nat tptp.cOMBC_1218031117nt_nat P) Q) R) (tptp.hAPP_f2132704789nt_nat (tptp.hAPP_n74706760nt_nat P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (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 $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_n1082236369t_bool (tptp.hAPP_f2022049025t_bool (tptp.hAPP_f1986088027t_bool tptp.cOMBB_2101530536ol_nat P) Q) R) (tptp.hAPP_f1805168059t_bool P (tptp.hAPP_n1082236369t_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (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 $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_i1948725293t_bool (tptp.hAPP_f1048215610t_bool (tptp.hAPP_f472159229t_bool tptp.cOMBC_1683390479t_bool P) Q) R) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (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 $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool (tptp.hAPP_f1399552105l_bool tptp.cOMBC_605892544l_bool P) Q) R) (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (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 $$unsorted) (Q $$unsorted)) (= (tptp.hAPP_H905846293iple_a (tptp.hAPP_H2085992369iple_a tptp.cOMBK_2052406350iple_a P) Q) P)) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H1140854897nt_int (tptp.hAPP_f231878828nt_int (tptp.hAPP_f1621780181nt_int tptp.cOMBB_1885471694iple_a P) Q) R) (tptp.hAPP_int_fun_int_int P (tptp.hAPP_H1229305626_a_int Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H1772910449at_nat (tptp.hAPP_f429024520at_nat (tptp.hAPP_f703420885at_nat tptp.cOMBB_789959282iple_a P) Q) R) (tptp.hAPP_nat_fun_nat_nat P (tptp.hAPP_H592031934_a_nat Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H1675210280t_bool (tptp.hAPP_f2142913731t_bool (tptp.hAPP_f1329415375t_bool tptp.cOMBB_1505691757iple_a P) Q) R) (tptp.hAPP_i1948725293t_bool P (tptp.hAPP_H1229305626_a_int Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H144868812t_bool (tptp.hAPP_f1872860171t_bool (tptp.hAPP_f1981448543t_bool tptp.cOMBB_1391527205iple_a P) Q) R) (tptp.hAPP_n1699378549t_bool P (tptp.hAPP_H592031934_a_nat Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_nat_nat (tptp.hAPP_f966999552at_nat (tptp.hAPP_f724467227at_nat tptp.cOMBB_161916371at_nat P) Q) R) (tptp.hAPP_f2097660464ol_nat P (tptp.hAPP_n1919155532a_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H592031934_a_nat (tptp.hAPP_f342603021_a_nat (tptp.hAPP_f575660003_a_nat tptp.cOMBB_1357028143iple_a P) Q) R) (tptp.hAPP_f957591787ol_nat P (tptp.hAPP_H1675210280t_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H592031934_a_nat (tptp.hAPP_f2085403241_a_nat (tptp.hAPP_f734830747_a_nat tptp.cOMBB_1107515603iple_a P) Q) R) (tptp.hAPP_f22106695ol_nat P (tptp.hAPP_H144868812t_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H592031934_a_nat (tptp.hAPP_f1464798435_a_nat (tptp.hAPP_f1012303887_a_nat tptp.cOMBC_1159891896ol_nat P) Q) R) (tptp.hAPP_f22106695ol_nat (tptp.hAPP_H1993634375ol_nat P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_nat_nat (tptp.hAPP_f2122367971at_nat (tptp.hAPP_f870149665at_nat tptp.cOMBC_2036134968ol_nat P) Q) R) (tptp.hAPP_f2097660464ol_nat (tptp.hAPP_n130255193ol_nat P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H592031934_a_nat (tptp.hAPP_f342603021_a_nat (tptp.hAPP_f270087133_a_nat tptp.cOMBS_1333400172ol_nat P) Q) R) (tptp.hAPP_f957591787ol_nat (tptp.hAPP_H781635819ol_nat P R) (tptp.hAPP_H1675210280t_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H592031934_a_nat (tptp.hAPP_f2085403241_a_nat (tptp.hAPP_f1052116629_a_nat tptp.cOMBS_397915080ol_nat P) Q) R) (tptp.hAPP_f22106695ol_nat (tptp.hAPP_H1993634375ol_nat P R) (tptp.hAPP_H144868812t_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_int_nat (tptp.hAPP_f2050777416nt_nat (tptp.hAPP_f1895921634nt_nat tptp.cOMBS_202713324ol_nat P) Q) R) (tptp.hAPP_f2097660464ol_nat (tptp.hAPP_i51375541ol_nat P R) (tptp.hAPP_i611776424a_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_nat_nat (tptp.hAPP_f966999552at_nat (tptp.hAPP_f264818750at_nat tptp.cOMBS_1274158152ol_nat P) Q) R) (tptp.hAPP_f2097660464ol_nat (tptp.hAPP_n130255193ol_nat P R) (tptp.hAPP_n1919155532a_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H2130837971l_bool (tptp.hAPP_f146754017l_bool (tptp.hAPP_f239971723l_bool tptp.cOMBB_1866391387iple_a P) Q) R) (tptp.hAPP_b589554111l_bool P (tptp.hAPP_H1037229737a_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_a849909144l_bool (tptp.hAPP_f1509969235l_bool (tptp.hAPP_f1178339559l_bool tptp.cOMBB_1355796797bool_a P) Q) R) (tptp.hAPP_f1259673775l_bool P (tptp.hAPP_a2036067514e_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (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 $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_n259507732ol_nat (tptp.hAPP_f299305025ol_nat (tptp.hAPP_f1632710027ol_nat tptp.cOMBB_1453893592at_nat P) Q) R) (tptp.hAPP_f1109019371ol_nat P (tptp.hAPP_nat_fun_int_nat Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (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 $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H1037229737a_bool (tptp.hAPP_H426895267a_bool (tptp.hAPP_f920293029a_bool tptp.cOMBC_1940896922a_bool P) Q) R) (tptp.hAPP_H1037229737a_bool (tptp.hAPP_H426895267a_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (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 $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool (tptp.hAPP_f1311642927t_bool tptp.cOMBC_646315179t_bool P) Q) R) (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H1772910449at_nat (tptp.hAPP_f221335601at_nat (tptp.hAPP_f388255893at_nat tptp.cOMBC_1038836708at_nat P) Q) R) (tptp.hAPP_f1914919701at_nat (tptp.hAPP_H1651200817at_nat P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H1675210280t_bool (tptp.hAPP_f138254639t_bool (tptp.hAPP_f1998609161t_bool tptp.cOMBB_1870764287iple_a P) Q) R) (tptp.hAPP_f1805168059t_bool P (tptp.hAPP_H1675210280t_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H144868812t_bool (tptp.hAPP_f27379319t_bool (tptp.hAPP_f196067081t_bool tptp.cOMBB_437532599iple_a P) Q) R) (tptp.hAPP_f800510211t_bool P (tptp.hAPP_H144868812t_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_a723219176e_bool (tptp.hAPP_f340725611e_bool (tptp.hAPP_f1006724181e_bool tptp.cOMBB_1348041619bool_a P) Q) R) (tptp.hAPP_f167292325e_bool P (tptp.hAPP_a849909144l_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (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 $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_i1876697324at_nat (tptp.hAPP_f1033905301at_nat (tptp.hAPP_f1315855317at_nat tptp.cOMBB_891709290at_int P) Q) R) (tptp.hAPP_f1585078997at_nat P (tptp.hAPP_int_fun_nat_nat Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (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 $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_i611776424a_bool (tptp.hAPP_f298605433a_bool (tptp.hAPP_f1421841531a_bool tptp.cOMBB_1700417404ol_int P) Q) R) (tptp.hAPP_H426895267a_bool P (tptp.hAPP_i240634960iple_a Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_n1919155532a_bool (tptp.hAPP_f260875897a_bool (tptp.hAPP_f1930382715a_bool tptp.cOMBB_1063143712ol_nat P) Q) R) (tptp.hAPP_H426895267a_bool P (tptp.hAPP_n261501868iple_a Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_i1529485324t_bool (tptp.hAPP_f1468280982t_bool (tptp.hAPP_f1596157055t_bool tptp.cOMBB_765314529ol_int P) Q) R) (tptp.hAPP_f1223193598t_bool P (tptp.hAPP_i1948725293t_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (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 $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H1037229737a_bool (tptp.hAPP_f1194757675a_bool (tptp.hAPP_f1697223433a_bool tptp.cOMBB_1610959875iple_a P) Q) R) (tptp.hAPP_f1695230391l_bool P (tptp.hAPP_H426895267a_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H1037229737a_bool (tptp.hAPP_f20753329a_bool (tptp.hAPP_f247708275a_bool tptp.cOMBC_1519416966l_bool P) Q) R) (tptp.hAPP_f1695230391l_bool (tptp.hAPP_H622608077l_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H781635819ol_nat (tptp.hAPP_f224922881ol_nat (tptp.hAPP_f543861963ol_nat tptp.cOMBB_1075417391iple_a P) Q) R) (tptp.hAPP_f1109019371ol_nat P (tptp.hAPP_H978941973nt_nat Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H1993634375ol_nat (tptp.hAPP_f1669765561ol_nat (tptp.hAPP_f1073041467ol_nat tptp.cOMBB_10565751iple_a P) Q) R) (tptp.hAPP_f782000547ol_nat P (tptp.hAPP_H1772910449at_nat Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_a1200519163e_bool (tptp.hAPP_f963367678e_bool (tptp.hAPP_f375255701e_bool tptp.cOMBB_145932198bool_a P) Q) R) (tptp.hAPP_f644196280e_bool P (tptp.hAPP_a849909144l_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_n1653940209_a_nat (tptp.hAPP_f1393576712_a_nat (tptp.hAPP_f145529813_a_nat tptp.cOMBC_309106125_a_nat P) Q) R) (tptp.hAPP_f106743253_a_nat (tptp.hAPP_n352002696_a_nat P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_i611776424a_bool (tptp.hAPP_f1718504751a_bool (tptp.hAPP_f481410067a_bool tptp.cOMBB_1028320654ol_int P) Q) R) (tptp.hAPP_f20753329a_bool P (tptp.hAPP_i611776424a_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_n1919155532a_bool (tptp.hAPP_f2087582327a_bool (tptp.hAPP_f1396758363a_bool tptp.cOMBB_391046962ol_nat P) Q) R) (tptp.hAPP_f20753329a_bool P (tptp.hAPP_n1919155532a_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f1695230391l_bool (tptp.hAPP_f1767618879l_bool (tptp.hAPP_f2100528361l_bool tptp.cOMBC_627599030l_bool P) Q) R) (tptp.hAPP_f1695230391l_bool (tptp.hAPP_f1767618879l_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H1651200817at_nat (tptp.hAPP_f1879857877at_nat (tptp.hAPP_f481016213at_nat tptp.cOMBB_1672982117iple_a P) Q) R) (tptp.hAPP_f1585078997at_nat P (tptp.hAPP_H1772910449at_nat Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H426895267a_bool (tptp.hAPP_f960023481a_bool (tptp.hAPP_f1786170683a_bool tptp.cOMBB_683172471iple_a P) Q) R) (tptp.hAPP_H426895267a_bool P (tptp.hAPP_H905846293iple_a Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_i51375541ol_nat (tptp.hAPP_f1442126667ol_nat (tptp.hAPP_f1072896543ol_nat tptp.cOMBB_206396714at_int P) Q) R) (tptp.hAPP_f1371399797ol_nat P (tptp.hAPP_i1313984149_a_nat Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_n130255193ol_nat (tptp.hAPP_f883871819ol_nat (tptp.hAPP_f424754463ol_nat tptp.cOMBB_1716606670at_nat P) Q) R) (tptp.hAPP_f1371399797ol_nat P (tptp.hAPP_n1653940209_a_nat Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H426895267a_bool (tptp.hAPP_f1181346091a_bool (tptp.hAPP_f571476211a_bool tptp.cOMBC_1570214144a_bool P) Q) R) (tptp.hAPP_f20753329a_bool (tptp.hAPP_H1743777351a_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_n352002696_a_nat (tptp.hAPP_f1485673429_a_nat (tptp.hAPP_f2006236373_a_nat tptp.cOMBB_2005430478at_nat P) Q) R) (tptp.hAPP_f500900629_a_nat P (tptp.hAPP_nat_fun_nat_nat Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f20753329a_bool (tptp.hAPP_f1706700729a_bool (tptp.hAPP_f957014749a_bool tptp.cOMBC_288844080a_bool P) Q) R) (tptp.hAPP_f20753329a_bool (tptp.hAPP_f1706700729a_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H1743777351a_bool (tptp.hAPP_f550111323a_bool (tptp.hAPP_f615286271a_bool tptp.cOMBB_1176122337iple_a P) Q) R) (tptp.hAPP_f1706700729a_bool P (tptp.hAPP_H426895267a_bool Q R)))) _let_6 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 6.71/6.91 )
% 6.71/6.91 % SZS output end Proof for SWW470+3
% 6.71/6.91 % cvc5---1.0.5 exiting
% 6.71/6.91 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------