%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWW470+2 : TPTP v8.1.2. Released v5.3.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n014.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 3.42s 3.66s
% Output   : Proof 3.42s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.21  % Problem    : SWW470+2 : TPTP v8.1.2. Released v5.3.0.
% 0.11/0.23  % Command    : do_cvc5 %s %d
% 0.23/0.44  % Computer : n014.cluster.edu
% 0.23/0.44  % Model    : x86_64 x86_64
% 0.23/0.44  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.44  % Memory   : 8042.1875MB
% 0.23/0.44  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.23/0.44  % CPULimit   : 300
% 0.23/0.44  % WCLimit    : 300
% 0.23/0.44  % DateTime   : Sun Aug 27 20:38:46 EDT 2023
% 0.23/0.44  % CPUTime    : 
% 0.29/0.66  %----Proving TF0_NAR, FOF, or CNF
% 3.42/3.66  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.BE405oF5vK/cvc5---1.0.5_5162.p...
% 3.42/3.66  ------- get file name : TPTP file name is SWW470+2
% 3.42/3.66  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_5162.smt2...
% 3.42/3.66  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 3.42/3.66  % SZS status Theorem for SWW470+2
% 3.42/3.66  % SZS output start Proof for SWW470+2
% 3.42/3.66  (
% 3.42/3.66  (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_606018542rivs_a tptp.g))) (let ((_let_5 (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_4 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a (tptp.hoare_1760757500iple_a _let_3 tptp.c _let_1)) tptp.bot_bo1181479936a_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_nat_bool (tptp.hAPP_b1013836512t_bool tptp.cOMBK_bool_nat P) Q) P))))) (let ((_let_10 (forall ((Pa $$unsorted)) (= (tptp.collect_nat Pa) Pa)))) (let ((_let_11 (forall ((X_2 $$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 ((_let_12 (tptp.hAPP_b1013836512t_bool tptp.cOMBK_bool_nat tptp.fFalse))) (let ((_let_13 (tptp.collect_nat _let_12))) (let ((_let_14 (= tptp.bot_bot_fun_nat_bool _let_13))) (let ((_let_15 (forall ((A_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_1) tptp.bot_bot_fun_nat_bool)))))) (let ((_let_16 (forall ((Ga $$unsorted) (Ca $$unsorted) (Q_1 $$unsorted) (Pa $$unsorted)) (=> (forall ((Z_7 $$unsorted) (S_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_a2036067514e_bool Pa Z_7) S_2)) (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hoare_606018542rivs_a Ga) (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a (tptp.hoare_1760757500iple_a (tptp.hAPP_f762886889e_bool tptp.cOMBK_1458035955bool_a (tptp.hAPP_s1806633685e_bool (tptp.hAPP_f817621513e_bool tptp.cOMBC_2027030106e_bool tptp.fequal_state) S_2)) Ca (tptp.hAPP_f762886889e_bool tptp.cOMBK_1458035955bool_a (tptp.hAPP_a2036067514e_bool Q_1 Z_7)))) tptp.bot_bo1181479936a_bool))))) (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hoare_606018542rivs_a Ga) (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a (tptp.hoare_1760757500iple_a Pa Ca Q_1)) tptp.bot_bo1181479936a_bool))))))) (let ((_let_17 (tptp.is_bool tptp.fFalse))) (let ((_let_18 (= _let_12 _let_13))) (let ((_let_19 (tptp.hAPP_f22106695ol_nat (tptp.finite_fold1_nat tptp.times_times_nat) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_20 (tptp.hBOOL (tptp.hAPP_nat_bool tptp.bot_bot_fun_nat_bool _let_19)))) (let ((_let_21 (tptp.hAPP_a2036067514e_bool _let_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_61))) (let ((_let_22 (tptp.hBOOL (tptp.hAPP_state_bool _let_21 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_62)))) (let ((_let_23 (= _let_2 _let_21))) (let ((_let_24 (= tptp.fFalse (tptp.hAPP_nat_bool _let_12 _let_19)))) (let ((_let_25 (= tptp.fFalse (tptp.hAPP_state_bool _let_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_62)))) (let ((_let_26 (ASSUME :args (_let_14)))) (let ((_let_27 (forall ((Pa $$unsorted)) (= Pa (tptp.collect_nat Pa))))) (let ((_let_28 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_29 (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat _let_19) tptp.bot_bot_fun_nat_bool)))) (let ((_let_30 (= _let_29 _let_20))) (let ((_let_31 (not _let_20))) (let ((_let_32 (_let_11))) (let ((_let_33 (ASSUME :args _let_32))) (let ((_let_34 (_let_15))) (let ((_let_35 (ASSUME :args _let_34))) (let ((_let_36 (not _let_22))) (let ((_let_37 (or _let_36 (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_4 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a (tptp.hoare_1760757500iple_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_62)) tptp.c (tptp.hAPP_f762886889e_bool tptp.cOMBK_1458035955bool_a (tptp.hAPP_a2036067514e_bool _let_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_61)))) tptp.bot_bo1181479936a_bool)))))) (let ((_let_38 (forall ((Z_7 $$unsorted) (S_2 $$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_7) S_2))) (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hoare_606018542rivs_a tptp.g) (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a (tptp.hoare_1760757500iple_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_7)))) tptp.bot_bo1181479936a_bool))))))) (let ((_let_39 (not _let_37))) (let ((_let_40 (not _let_38))) (let ((_let_41 (or _let_40 _let_5))) (let ((_let_42 (forall ((Ga $$unsorted) (Ca $$unsorted) (Q_1 $$unsorted) (Pa $$unsorted)) (or (not (forall ((Z_7 $$unsorted) (S_2 $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_a2036067514e_bool Pa Z_7) S_2))) (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hoare_606018542rivs_a Ga) (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a (tptp.hoare_1760757500iple_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_7)))) tptp.bot_bo1181479936a_bool)))))) (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hoare_606018542rivs_a Ga) (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a (tptp.hoare_1760757500iple_a Pa Ca Q_1)) tptp.bot_bo1181479936a_bool))))))) (let ((_let_43 (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_44 (or))) (let ((_let_45 (_let_40))) (let ((_let_46 (forall ((P $$unsorted) (Q $$unsorted)) (= P (tptp.hAPP_a2036067514e_bool (tptp.hAPP_f762886889e_bool tptp.cOMBK_1458035955bool_a P) Q))))) (let ((_let_47 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_48 (not _let_17))) (let ((_let_49 (or _let_48 _let_24))) (let ((_let_50 (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.is_bool P)) (= P (tptp.hAPP_nat_bool (tptp.hAPP_b1013836512t_bool tptp.cOMBK_bool_nat P) Q)))))) (let ((_let_51 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_52 (ASSUME :args (_let_17)))) (let ((_let_53 (or _let_48 _let_25))) (let ((_let_54 (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_55 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_56 (not _let_25))) (let ((_let_57 (not _let_23))) (let ((_let_58 (not _let_24))) (let ((_let_59 (not _let_18))) (let ((_let_60 (not _let_14))) (let ((_let_61 (ASSUME :args (_let_31)))) (let ((_let_62 (ASSUME :args (_let_18)))) (let ((_let_63 (ASSUME :args (_let_24)))) (let ((_let_64 (ASSUME :args (_let_25)))) (let ((_let_65 (ASSUME :args (_let_23)))) (let ((_let_66 (ASSUME :args (_let_22)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_61 _let_26 _let_62 _let_63 _let_64 _let_65 _let_66) :args (_let_14 _let_18 _let_31 _let_22 _let_24 _let_23 _let_25)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_66)) (CONG (TRANS (CONG (SYMM _let_65) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_62)) :args (APPLY_UF tptp.hAPP_state_bool)) (SYMM _let_64) (SYMM (SYMM _let_63)) (CONG (TRANS (SYMM (SYMM _let_62)) (SYMM _let_26)) (REFL :args (_let_19)) :args (APPLY_UF tptp.hAPP_nat_bool))) :args (APPLY_UF tptp.hBOOL)) (FALSE_INTRO _let_61))) :args (_let_31 _let_14 _let_18 _let_24 _let_25 _let_23 _let_22)) :args ((not (and _let_14 _let_18 _let_31 _let_22 _let_24 _let_23 _let_25)) SB_LITERAL))) (CONG (REFL :args (_let_60)) (REFL :args (_let_59)) (MACRO_SR_PRED_INTRO :args ((= (not _let_31) _let_20))) (REFL :args (_let_36)) (REFL :args (_let_58)) (REFL :args (_let_57)) (REFL :args (_let_56)) :args _let_44)) :args ((or _let_60 _let_20 _let_59 _let_36 _let_58 _let_57 _let_56))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_53)) :args ((or _let_48 _let_25 (not _let_53)))) _let_52 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_55 :args (tptp.fFalse SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_62 QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP_state_bool (tptp.hAPP_b2019457360e_bool tptp.cOMBK_bool_state P) Q)))) :args (_let_54))) _let_55 :args (_let_53 false _let_54)) :args (_let_25 false _let_17 false _let_53)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_49)) :args ((or _let_48 _let_24 (not _let_49)))) _let_52 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_51 :args (tptp.fFalse _let_19 QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP_nat_bool (tptp.hAPP_b1013836512t_bool tptp.cOMBK_bool_nat P) Q)))) :args (_let_50))) _let_51 :args (_let_49 false _let_50)) :args (_let_24 false _let_17 false _let_49)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_47 :args (_let_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_61 QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP_a2036067514e_bool (tptp.hAPP_f762886889e_bool tptp.cOMBK_1458035955bool_a P) Q)))) :args (_let_46))) _let_47 :args (_let_23 false _let_46)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_37 0)) (CONG (REFL :args (_let_37)) (MACRO_SR_PRED_INTRO :args ((= (not _let_36) _let_22))) :args _let_44)) :args ((or _let_22 _let_37))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_45)) :args _let_45)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_40) _let_38))) (REFL :args (_let_39)) :args _let_44)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_41)) :args ((or _let_5 _let_40 (not _let_41)))) (ASSUME :args (_let_6)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_43 :args (tptp.g tptp.c _let_1 _let_3 QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP_f540970102l_bool (tptp.hoare_606018542rivs_a Ga) (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a (tptp.hoare_1760757500iple_a Pa Ca Q_1)) tptp.bot_bo1181479936a_bool))))) :args (_let_42))) _let_43 :args (_let_41 false _let_42)) :args (_let_40 true _let_5 false _let_41)) :args (_let_39 true _let_38)) :args (_let_22 true _let_37)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_30)) :args ((or _let_29 _let_31 (not _let_30)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_35 :args (_let_19 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.hAPP_n215258509l_bool tptp.member_nat A_1)))) :args _let_34)) _let_35 :args ((not _let_29) false _let_15)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_33 :args (_let_19 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.hAPP_n215258509l_bool tptp.member_nat X_2)))) :args _let_32))) _let_33 :args (_let_30 false _let_11)) :args (_let_31 true _let_29 false _let_30)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_28 :args (_let_12 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.collect_nat Pa)))) :args (_let_27))) _let_28 :args (_let_18 false _let_27)) _let_26 :args (false false _let_25 false _let_24 false _let_23 false _let_22 true _let_20 false _let_18 false _let_14)) :args ((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 $$unsorted)) (=> (tptp.is_glb B_1_1) (tptp.is_vname (tptp.glb B_1_1)))) (forall ((B_1_1 $$unsorted)) (=> (tptp.is_loc B_1_1) (tptp.is_vname (tptp.loc B_1_1)))) (forall ((B_1_1 $$unsorted)) (tptp.is_bool (tptp.finite1200705745iple_a B_1_1))) (forall ((B_1_1 $$unsorted)) (tptp.is_bool (tptp.finite419198954a_bool B_1_1))) (forall ((B_1_1 $$unsorted)) (tptp.is_bool (tptp.finite1317819144e_bool B_1_1))) (forall ((B_1_1 $$unsorted)) (tptp.is_bool (tptp.finite1956789438t_bool B_1_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.finite1669978781iple_a B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.finite774711482_state 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.finite950012314iple_a B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.finite506823037_state 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_glb (tptp.undefined_glb tptp.glb_1)) (tptp.is_loc (tptp.undefined_loc tptp.loc_1)) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted) (B_3_1 $$unsorted) (B_4_1 $$unsorted)) (tptp.is_bool (tptp.evaln B_1_1 B_2_1 B_3_1 B_4_1))) (tptp.is_bool tptp.bot_bot_bool) _let_17 (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_H1421470952a_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.hAPP_H513860823e_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_f540970102l_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.hAPP_f1760790145l_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_f1637334154l_bool B_1_1 B_2_1))) (forall ((Ga $$unsorted)) (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hoare_606018542rivs_a Ga) tptp.bot_bo1181479936a_bool))) (forall ((Ga $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hoare_659004819_state Ga) tptp.bot_bo1055319631e_bool))) (forall ((Fun1_2 $$unsorted) (Com_1 $$unsorted) (Fun2_2 $$unsorted) (Fun1_1 $$unsorted) (Com $$unsorted) (Fun2_1 $$unsorted)) (= (= (tptp.hoare_1575745797_state Fun1_2 Com_1 Fun2_2) (tptp.hoare_1575745797_state Fun1_1 Com Fun2_1)) (and (= Fun1_2 Fun1_1) (= Com_1 Com) (= Fun2_2 Fun2_1)))) (forall ((Fun1_2 $$unsorted) (Com_1 $$unsorted) (Fun2_2 $$unsorted) (Fun1_1 $$unsorted) (Com $$unsorted) (Fun2_1 $$unsorted)) (= (= (tptp.hoare_1760757500iple_a Fun1_2 Com_1 Fun2_2) (tptp.hoare_1760757500iple_a Fun1_1 Com Fun2_1)) (and (= Fun1_2 Fun1_1) (= Com_1 Com) (= Fun2_2 Fun2_1)))) (forall ((Ga $$unsorted) (G_1 $$unsorted) (Ts $$unsorted)) (let ((_let_1 (tptp.hoare_606018542rivs_a Ga))) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hoare_606018542rivs_a G_1) Ts)) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 G_1)) (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 Ts)))))) (forall ((Ga $$unsorted) (G_1 $$unsorted) (Ts $$unsorted)) (let ((_let_1 (tptp.hoare_659004819_state Ga))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hoare_659004819_state G_1) Ts)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 G_1)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 Ts)))))) (forall ((Ts $$unsorted) (Ga $$unsorted) (T_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a T_1))) (let ((_let_2 (tptp.hoare_606018542rivs_a Ga))) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_2 (tptp.hAPP_f1591852335a_bool _let_1 tptp.bot_bo1181479936a_bool))) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_2 Ts)) (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_2 (tptp.hAPP_f1591852335a_bool _let_1 Ts)))))))) (forall ((Ts $$unsorted) (Ga $$unsorted) (T_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state T_1))) (let ((_let_2 (tptp.hoare_659004819_state Ga))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_2 (tptp.hAPP_f921536533e_bool _let_1 tptp.bot_bo1055319631e_bool))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_2 Ts)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_2 (tptp.hAPP_f921536533e_bool _let_1 Ts)))))))) (forall ((Ga $$unsorted) (Pa $$unsorted) (Ca $$unsorted) (Q_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.hoare_606018542rivs_a Ga))) (=> (=> (tptp.hBOOL C) (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a (tptp.hoare_1760757500iple_a Pa Ca Q_1)) tptp.bot_bo1181479936a_bool)))) (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a (tptp.hoare_1760757500iple_a (tptp.hAPP_b540892988e_bool (tptp.hAPP_f1824947087e_bool tptp.cOMBC_41962815e_bool (tptp.hAPP_f340725611e_bool (tptp.hAPP_f1006724181e_bool tptp.cOMBB_1348041619bool_a tptp.cOMBC_231445413l_bool) (tptp.hAPP_f1509969235l_bool (tptp.hAPP_f1178339559l_bool tptp.cOMBB_1355796797bool_a (tptp.hAPP_f1561913689l_bool tptp.cOMBB_188601460_state tptp.fconj)) Pa))) C) Ca Q_1)) tptp.bot_bo1181479936a_bool)))))) (forall ((Ga $$unsorted) (Pa $$unsorted) (Ca $$unsorted) (Q_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.hoare_659004819_state Ga))) (=> (=> (tptp.hBOOL C) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state (tptp.hoare_1575745797_state Pa Ca Q_1)) tptp.bot_bo1055319631e_bool)))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state (tptp.hoare_1575745797_state (tptp.hAPP_b1095269219e_bool (tptp.hAPP_f701449317e_bool tptp.cOMBC_471052088e_bool (tptp.hAPP_f873506917e_bool (tptp.hAPP_f1398071125e_bool tptp.cOMBB_1757942702_state tptp.cOMBC_231445413l_bool) (tptp.hAPP_f1283379615l_bool (tptp.hAPP_f1345202233l_bool tptp.cOMBB_1759179140_state (tptp.hAPP_f1561913689l_bool tptp.cOMBB_188601460_state tptp.fconj)) Pa))) C) Ca Q_1)) tptp.bot_bo1055319631e_bool)))))) _let_16 (forall ((Ga $$unsorted) (Ca $$unsorted) (Q_1 $$unsorted) (Pa $$unsorted)) (=> (forall ((Z_7 $$unsorted) (S_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool Pa Z_7) S_2)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hoare_659004819_state Ga) (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state (tptp.hoare_1575745797_state (tptp.hAPP_f1863945078e_bool tptp.cOMBK_631994958_state (tptp.hAPP_s1806633685e_bool (tptp.hAPP_f817621513e_bool tptp.cOMBC_2027030106e_bool tptp.fequal_state) S_2)) Ca (tptp.hAPP_f1863945078e_bool tptp.cOMBK_631994958_state (tptp.hAPP_s1806633685e_bool Q_1 Z_7)))) tptp.bot_bo1055319631e_bool))))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hoare_659004819_state Ga) (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state (tptp.hoare_1575745797_state Pa Ca Q_1)) tptp.bot_bo1055319631e_bool))))) (forall ((Q_1 $$unsorted) (Ga $$unsorted) (Pa $$unsorted) (Ca $$unsorted) (Q_3 $$unsorted)) (let ((_let_1 (tptp.hoare_606018542rivs_a Ga))) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a (tptp.hoare_1760757500iple_a Pa Ca Q_3)) tptp.bot_bo1181479936a_bool))) (=> (forall ((Z_7 $$unsorted) (S_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_a2036067514e_bool Q_3 Z_7) S_2)) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_a2036067514e_bool Q_1 Z_7) S_2)))) (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a (tptp.hoare_1760757500iple_a Pa Ca Q_1)) tptp.bot_bo1181479936a_bool))))))) (forall ((Q_1 $$unsorted) (Ga $$unsorted) (Pa $$unsorted) (Ca $$unsorted) (Q_3 $$unsorted)) (let ((_let_1 (tptp.hoare_659004819_state Ga))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state (tptp.hoare_1575745797_state Pa Ca Q_3)) tptp.bot_bo1055319631e_bool))) (=> (forall ((Z_7 $$unsorted) (S_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool Q_3 Z_7) S_2)) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool Q_1 Z_7) S_2)))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state (tptp.hoare_1575745797_state Pa Ca Q_1)) tptp.bot_bo1055319631e_bool))))))) (forall ((Pa $$unsorted) (Ga $$unsorted) (P_2 $$unsorted) (Ca $$unsorted) (Q_1 $$unsorted)) (let ((_let_1 (tptp.hoare_606018542rivs_a Ga))) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a (tptp.hoare_1760757500iple_a P_2 Ca Q_1)) tptp.bot_bo1181479936a_bool))) (=> (forall ((Z_7 $$unsorted) (S_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_a2036067514e_bool Pa Z_7) S_2)) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_a2036067514e_bool P_2 Z_7) S_2)))) (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a (tptp.hoare_1760757500iple_a Pa Ca Q_1)) tptp.bot_bo1181479936a_bool))))))) (forall ((Pa $$unsorted) (Ga $$unsorted) (P_2 $$unsorted) (Ca $$unsorted) (Q_1 $$unsorted)) (let ((_let_1 (tptp.hoare_659004819_state Ga))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state (tptp.hoare_1575745797_state P_2 Ca Q_1)) tptp.bot_bo1055319631e_bool))) (=> (forall ((Z_7 $$unsorted) (S_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool Pa Z_7) S_2)) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool P_2 Z_7) S_2)))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state (tptp.hoare_1575745797_state Pa Ca Q_1)) tptp.bot_bo1055319631e_bool))))))) (forall ((Q_1 $$unsorted) (Pa $$unsorted) (Ga $$unsorted) (P_2 $$unsorted) (Ca $$unsorted) (Q_3 $$unsorted)) (let ((_let_1 (tptp.hoare_606018542rivs_a Ga))) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a (tptp.hoare_1760757500iple_a P_2 Ca Q_3)) tptp.bot_bo1181479936a_bool))) (=> (forall ((Z_7 $$unsorted) (S_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_a2036067514e_bool Pa Z_7) S_2)) (forall ((S_3 $$unsorted)) (=> (forall ((Z_8 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_a2036067514e_bool P_2 Z_8) S_2)) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_a2036067514e_bool Q_3 Z_8) S_3)))) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_a2036067514e_bool Q_1 Z_7) S_3)))))) (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a (tptp.hoare_1760757500iple_a Pa Ca Q_1)) tptp.bot_bo1181479936a_bool))))))) (forall ((Q_1 $$unsorted) (Pa $$unsorted) (Ga $$unsorted) (P_2 $$unsorted) (Ca $$unsorted) (Q_3 $$unsorted)) (let ((_let_1 (tptp.hoare_659004819_state Ga))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state (tptp.hoare_1575745797_state P_2 Ca Q_3)) tptp.bot_bo1055319631e_bool))) (=> (forall ((Z_7 $$unsorted) (S_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool Pa Z_7) S_2)) (forall ((S_3 $$unsorted)) (=> (forall ((Z_8 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool P_2 Z_8) S_2)) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool Q_3 Z_8) S_3)))) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool Q_1 Z_7) S_3)))))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state (tptp.hoare_1575745797_state Pa Ca Q_1)) tptp.bot_bo1055319631e_bool))))))) (forall ((A_1 $$unsorted) (Ba $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a A_1))) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a Ba) A))) (=> (not (= A_1 Ba)) (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 A)))))) (forall ((A_1 $$unsorted) (Ba $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat A_1))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat Ba) A))) (=> (not (= A_1 Ba)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 A)))))) (forall ((A_1 $$unsorted) (Ba $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_H248360617l_bool tptp.member1758697444_state A_1))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state Ba) A))) (=> (not (= A_1 Ba)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 A)))))) (forall ((Ba $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a A_1))) (=> (=> (not (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 B))) (= A_1 Ba)) (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a Ba) B)))))) (forall ((Ba $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat A_1))) (=> (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B))) (= A_1 Ba)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat Ba) B)))))) (forall ((Ba $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H248360617l_bool tptp.member1758697444_state A_1))) (=> (=> (not (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 B))) (= A_1 Ba)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state Ba) B)))))) (forall ((A_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a A_1) tptp.bot_bo1181479936a_bool)))) (forall ((A_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state A_1) tptp.bot_bo1055319631e_bool)))) _let_15 (forall ((A_1 $$unsorted)) (= (tptp.collec268032053iple_a (tptp.hAPP_H1190454433a_bool tptp.fequal879838495iple_a A_1)) (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a A_1) tptp.bot_bo1181479936a_bool))) (forall ((A_1 $$unsorted)) (= (tptp.collect_nat (tptp.hAPP_n1699378549t_bool tptp.fequal_nat A_1)) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_1) tptp.bot_bot_fun_nat_bool))) (forall ((A_1 $$unsorted)) (= (tptp.collect_fun_nat_bool (tptp.hAPP_f103356543l_bool tptp.fequal_fun_nat_bool A_1)) (tptp.hAPP_f1246832597l_bool (tptp.hAPP_f633452666l_bool tptp.insert_fun_nat_bool A_1) tptp.bot_bo1701429464l_bool))) (forall ((A_1 $$unsorted)) (= (tptp.collec727977250_state (tptp.hAPP_H1645666623e_bool tptp.fequal1531560888_state A_1)) (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A_1) tptp.bot_bo1055319631e_bool))) (forall ((A_1 $$unsorted)) (= (tptp.collec268032053iple_a (tptp.hAPP_H1190454433a_bool (tptp.hAPP_f1371755681a_bool tptp.cOMBC_839220826a_bool tptp.fequal879838495iple_a) A_1)) (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a A_1) tptp.bot_bo1181479936a_bool))) (forall ((A_1 $$unsorted)) (= (tptp.collect_nat (tptp.hAPP_n1699378549t_bool (tptp.hAPP_f229349961t_bool tptp.cOMBC_nat_nat_bool tptp.fequal_nat) A_1)) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_1) tptp.bot_bot_fun_nat_bool))) (forall ((A_1 $$unsorted)) (= (tptp.collect_fun_nat_bool (tptp.hAPP_f103356543l_bool (tptp.hAPP_f643944041l_bool tptp.cOMBC_1693257480l_bool tptp.fequal_fun_nat_bool) A_1)) (tptp.hAPP_f1246832597l_bool (tptp.hAPP_f633452666l_bool tptp.insert_fun_nat_bool A_1) tptp.bot_bo1701429464l_bool))) (forall ((A_1 $$unsorted)) (= (tptp.collec727977250_state (tptp.hAPP_H1645666623e_bool (tptp.hAPP_f262880489e_bool tptp.cOMBC_1424981238e_bool tptp.fequal1531560888_state) A_1)) (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A_1) tptp.bot_bo1055319631e_bool))) (forall ((Pa $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.collec268032053iple_a (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1203760810a_bool tptp.cOMBS_1148211387l_bool (tptp.hAPP_f997599971l_bool (tptp.hAPP_f439164429l_bool tptp.cOMBB_1782929690iple_a tptp.fconj) (tptp.hAPP_H1190454433a_bool tptp.fequal879838495iple_a A_1))) Pa)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_H1421470952a_bool Pa A_1)))) (and (=> _let_2 (= _let_1 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a A_1) tptp.bot_bo1181479936a_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bo1181479936a_bool)))))) (forall ((Pa $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (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_1))) Pa)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_nat_bool Pa A_1)))) (and (=> _let_2 (= _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_1) tptp.bot_bot_fun_nat_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bot_fun_nat_bool)))))) (forall ((Pa $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.collect_fun_nat_bool (tptp.hAPP_f1246832597l_bool (tptp.hAPP_f1743029098l_bool tptp.cOMBS_1187019125l_bool (tptp.hAPP_f1974927549l_bool (tptp.hAPP_f857404385l_bool tptp.cOMBB_444170502t_bool tptp.fconj) (tptp.hAPP_f103356543l_bool tptp.fequal_fun_nat_bool A_1))) Pa)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_f54304608l_bool Pa A_1)))) (and (=> _let_2 (= _let_1 (tptp.hAPP_f1246832597l_bool (tptp.hAPP_f633452666l_bool tptp.insert_fun_nat_bool A_1) tptp.bot_bo1701429464l_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bo1701429464l_bool)))))) (forall ((Pa $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.collec727977250_state (tptp.hAPP_f921536533e_bool (tptp.hAPP_f760664097e_bool tptp.cOMBS_1248383340l_bool (tptp.hAPP_f1558728829l_bool (tptp.hAPP_f1442918689l_bool tptp.cOMBB_1382207997_state tptp.fconj) (tptp.hAPP_H1645666623e_bool tptp.fequal1531560888_state A_1))) Pa)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_H513860823e_bool Pa A_1)))) (and (=> _let_2 (= _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A_1) tptp.bot_bo1055319631e_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bo1055319631e_bool)))))) (forall ((Pa $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.collec268032053iple_a (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1203760810a_bool tptp.cOMBS_1148211387l_bool (tptp.hAPP_f997599971l_bool (tptp.hAPP_f439164429l_bool tptp.cOMBB_1782929690iple_a tptp.fconj) (tptp.hAPP_H1190454433a_bool (tptp.hAPP_f1371755681a_bool tptp.cOMBC_839220826a_bool tptp.fequal879838495iple_a) A_1))) Pa)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_H1421470952a_bool Pa A_1)))) (and (=> _let_2 (= _let_1 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a A_1) tptp.bot_bo1181479936a_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bo1181479936a_bool)))))) (forall ((Pa $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (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_1))) Pa)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_nat_bool Pa A_1)))) (and (=> _let_2 (= _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_1) tptp.bot_bot_fun_nat_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bot_fun_nat_bool)))))) (forall ((Pa $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.collect_fun_nat_bool (tptp.hAPP_f1246832597l_bool (tptp.hAPP_f1743029098l_bool tptp.cOMBS_1187019125l_bool (tptp.hAPP_f1974927549l_bool (tptp.hAPP_f857404385l_bool tptp.cOMBB_444170502t_bool tptp.fconj) (tptp.hAPP_f103356543l_bool (tptp.hAPP_f643944041l_bool tptp.cOMBC_1693257480l_bool tptp.fequal_fun_nat_bool) A_1))) Pa)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_f54304608l_bool Pa A_1)))) (and (=> _let_2 (= _let_1 (tptp.hAPP_f1246832597l_bool (tptp.hAPP_f633452666l_bool tptp.insert_fun_nat_bool A_1) tptp.bot_bo1701429464l_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bo1701429464l_bool)))))) (forall ((Pa $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.collec727977250_state (tptp.hAPP_f921536533e_bool (tptp.hAPP_f760664097e_bool tptp.cOMBS_1248383340l_bool (tptp.hAPP_f1558728829l_bool (tptp.hAPP_f1442918689l_bool tptp.cOMBB_1382207997_state tptp.fconj) (tptp.hAPP_H1645666623e_bool (tptp.hAPP_f262880489e_bool tptp.cOMBC_1424981238e_bool tptp.fequal1531560888_state) A_1))) Pa)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_H513860823e_bool Pa A_1)))) (and (=> _let_2 (= _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A_1) tptp.bot_bo1055319631e_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bo1055319631e_bool)))))) (forall ((A_1 $$unsorted) (A $$unsorted)) (=> (= A tptp.bot_bo1181479936a_bool) (not (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a A_1) A))))) (forall ((A_1 $$unsorted) (A $$unsorted)) (=> (= A tptp.bot_bo1055319631e_bool) (not (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state A_1) A))))) (forall ((A_1 $$unsorted) (A $$unsorted)) (=> (= A tptp.bot_bot_fun_nat_bool) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_1) A))))) (forall ((Pa $$unsorted)) (= (= (tptp.collect_nat Pa) tptp.bot_bot_fun_nat_bool) (forall ((X_2 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_nat_bool Pa X_2)))))) (forall ((Pa $$unsorted)) (= (= (tptp.collec268032053iple_a Pa) tptp.bot_bo1181479936a_bool) (forall ((X_2 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_H1421470952a_bool Pa X_2)))))) (forall ((Pa $$unsorted)) (= (= (tptp.collect_fun_nat_bool Pa) tptp.bot_bo1701429464l_bool) (forall ((X_2 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool Pa X_2)))))) (forall ((Pa $$unsorted)) (= (= (tptp.collec727977250_state Pa) tptp.bot_bo1055319631e_bool) (forall ((X_2 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_H513860823e_bool Pa X_2)))))) (forall ((Ca $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a Ca) tptp.bot_bo1181479936a_bool)))) (forall ((Ca $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state Ca) tptp.bot_bo1055319631e_bool)))) (forall ((Ca $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat Ca) tptp.bot_bot_fun_nat_bool)))) (forall ((Pa $$unsorted)) (= (= tptp.bot_bot_fun_nat_bool (tptp.collect_nat Pa)) (forall ((X_2 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_nat_bool Pa X_2)))))) (forall ((Pa $$unsorted)) (= (= tptp.bot_bo1181479936a_bool (tptp.collec268032053iple_a Pa)) (forall ((X_2 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_H1421470952a_bool Pa X_2)))))) (forall ((Pa $$unsorted)) (= (= tptp.bot_bo1701429464l_bool (tptp.collect_fun_nat_bool Pa)) (forall ((X_2 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool Pa X_2)))))) (forall ((Pa $$unsorted)) (= (= tptp.bot_bo1055319631e_bool (tptp.collec727977250_state Pa)) (forall ((X_2 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_H513860823e_bool Pa X_2)))))) (forall ((A $$unsorted)) (= (exists ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a X_2) A))) (not (= A tptp.bot_bo1181479936a_bool)))) (forall ((A $$unsorted)) (= (exists ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_2) A))) (not (= A tptp.bot_bo1055319631e_bool)))) (forall ((A $$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)) (= (forall ((X_2 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a X_2) A)))) (= A tptp.bot_bo1181479936a_bool))) (forall ((A $$unsorted)) (= (forall ((X_2 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_2) A)))) (= A tptp.bot_bo1055319631e_bool))) (forall ((A $$unsorted)) (= (forall ((X_2 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) A)))) (= A tptp.bot_bot_fun_nat_bool))) _let_14 (= tptp.bot_bo1181479936a_bool (tptp.collec268032053iple_a (tptp.hAPP_b119575286a_bool tptp.cOMBK_151824839iple_a tptp.fFalse))) (= tptp.bot_bo1701429464l_bool (tptp.collect_fun_nat_bool (tptp.hAPP_b1630757474l_bool tptp.cOMBK_1994329625t_bool tptp.fFalse))) (= tptp.bot_bo1055319631e_bool (tptp.collec727977250_state (tptp.hAPP_b1245957081e_bool tptp.cOMBK_1079618832_state tptp.fFalse))) (forall ((A_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a A_1) A)) (= (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a A_1) A) A))) (forall ((A_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_1) A)) (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_1) A) A))) (forall ((A_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state A_1) A)) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A_1) A) A))) (forall ((Ba $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a A_1))) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 B)) (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a Ba) B)))))) (forall ((Ba $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat A_1))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat Ba) B)))))) (forall ((Ba $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H248360617l_bool tptp.member1758697444_state A_1))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 B)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state Ba) B)))))) (forall ((B $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a X_1))) (let ((_let_2 (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a X_1))) (=> (not (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_2 A))) (=> (not (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_2 B))) (= (= (tptp.hAPP_f1591852335a_bool _let_1 A) (tptp.hAPP_f1591852335a_bool _let_1 B)) (= A B))))))) (forall ((B $$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 $$unsorted)) (let ((_let_1 (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state X_1))) (let ((_let_2 (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_1))) (=> (not (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_2 A))) (=> (not (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_2 B))) (= (= (tptp.hAPP_f921536533e_bool _let_1 A) (tptp.hAPP_f921536533e_bool _let_1 B)) (= A B))))))) (forall ((Y_7 $$unsorted) (A $$unsorted) (X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_H1421470952a_bool (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a Y_7) A) X_1)) (or (= Y_7 X_1) (tptp.hBOOL (tptp.hAPP_H1421470952a_bool A X_1))))) (forall ((Y_7 $$unsorted) (A $$unsorted) (X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat Y_7) A) X_1)) (or (= Y_7 X_1) (tptp.hBOOL (tptp.hAPP_nat_bool A X_1))))) (forall ((Y_7 $$unsorted) (A $$unsorted) (X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_H513860823e_bool (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state Y_7) A) X_1)) (or (= Y_7 X_1) (tptp.hBOOL (tptp.hAPP_H513860823e_bool A X_1))))) (forall ((A_1 $$unsorted) (Ba $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a A_1))) (= (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a Ba) A))) (or (= A_1 Ba) (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 A)))))) (forall ((A_1 $$unsorted) (Ba $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat A_1))) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat Ba) A))) (or (= A_1 Ba) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 A)))))) (forall ((A_1 $$unsorted) (Ba $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_H248360617l_bool tptp.member1758697444_state A_1))) (= (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state Ba) A))) (or (= A_1 Ba) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 A)))))) (forall ((X_1 $$unsorted) (Y_7 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a X_1))) (let ((_let_2 (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a Y_7))) (= (tptp.hAPP_f1591852335a_bool _let_1 (tptp.hAPP_f1591852335a_bool _let_2 A)) (tptp.hAPP_f1591852335a_bool _let_2 (tptp.hAPP_f1591852335a_bool _let_1 A)))))) (forall ((X_1 $$unsorted) (Y_7 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1))) (let ((_let_2 (tptp.hAPP_n1512601776t_bool tptp.insert_nat Y_7))) (= (tptp.hAPP_f800510211t_bool _let_1 (tptp.hAPP_f800510211t_bool _let_2 A)) (tptp.hAPP_f800510211t_bool _let_2 (tptp.hAPP_f800510211t_bool _let_1 A)))))) (forall ((X_1 $$unsorted) (Y_7 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state X_1))) (let ((_let_2 (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state Y_7))) (= (tptp.hAPP_f921536533e_bool _let_1 (tptp.hAPP_f921536533e_bool _let_2 A)) (tptp.hAPP_f921536533e_bool _let_2 (tptp.hAPP_f921536533e_bool _let_1 A)))))) (forall ((X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a X_1))) (let ((_let_2 (tptp.hAPP_f1591852335a_bool _let_1 A))) (= (tptp.hAPP_f1591852335a_bool _let_1 _let_2) _let_2)))) (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_H727730819e_bool tptp.insert1835143293_state X_1))) (let ((_let_2 (tptp.hAPP_f921536533e_bool _let_1 A))) (= (tptp.hAPP_f921536533e_bool _let_1 _let_2) _let_2)))) (forall ((A_1 $$unsorted) (Pa $$unsorted)) (= (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a A_1) (tptp.collec268032053iple_a Pa)) (tptp.collec268032053iple_a (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1203760810a_bool tptp.cOMBS_1148211387l_bool (tptp.hAPP_f997599971l_bool (tptp.hAPP_f439164429l_bool tptp.cOMBB_1782929690iple_a tptp.fimplies) (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f34030599a_bool tptp.cOMBB_1799513916iple_a tptp.fNot) (tptp.hAPP_H1190454433a_bool (tptp.hAPP_f1371755681a_bool tptp.cOMBC_839220826a_bool tptp.fequal879838495iple_a) A_1)))) Pa)))) (forall ((A_1 $$unsorted) (Pa $$unsorted)) (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_1) (tptp.collect_nat Pa)) (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_1)))) Pa)))) (forall ((A_1 $$unsorted) (Pa $$unsorted)) (= (tptp.hAPP_f1246832597l_bool (tptp.hAPP_f633452666l_bool tptp.insert_fun_nat_bool A_1) (tptp.collect_fun_nat_bool Pa)) (tptp.collect_fun_nat_bool (tptp.hAPP_f1246832597l_bool (tptp.hAPP_f1743029098l_bool tptp.cOMBS_1187019125l_bool (tptp.hAPP_f1974927549l_bool (tptp.hAPP_f857404385l_bool tptp.cOMBB_444170502t_bool tptp.fimplies) (tptp.hAPP_f1246832597l_bool (tptp.hAPP_f1164891443l_bool tptp.cOMBB_238756964t_bool tptp.fNot) (tptp.hAPP_f103356543l_bool (tptp.hAPP_f643944041l_bool tptp.cOMBC_1693257480l_bool tptp.fequal_fun_nat_bool) A_1)))) Pa)))) (forall ((A_1 $$unsorted) (Pa $$unsorted)) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A_1) (tptp.collec727977250_state Pa)) (tptp.collec727977250_state (tptp.hAPP_f921536533e_bool (tptp.hAPP_f760664097e_bool tptp.cOMBS_1248383340l_bool (tptp.hAPP_f1558728829l_bool (tptp.hAPP_f1442918689l_bool tptp.cOMBB_1382207997_state tptp.fimplies) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1037965299e_bool tptp.cOMBB_416661851_state tptp.fNot) (tptp.hAPP_H1645666623e_bool (tptp.hAPP_f262880489e_bool tptp.cOMBC_1424981238e_bool tptp.fequal1531560888_state) A_1)))) Pa)))) (forall ((A_1 $$unsorted) (B $$unsorted)) (= (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a A_1) B) (tptp.collec268032053iple_a (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1203760810a_bool tptp.cOMBS_1148211387l_bool (tptp.hAPP_f997599971l_bool (tptp.hAPP_f439164429l_bool tptp.cOMBB_1782929690iple_a tptp.fdisj) (tptp.hAPP_H1190454433a_bool (tptp.hAPP_f1371755681a_bool tptp.cOMBC_839220826a_bool tptp.fequal879838495iple_a) A_1))) (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f672239281a_bool tptp.cOMBC_1552014468l_bool tptp.member1713797107iple_a) B))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_1) B) (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_1))) (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1722879237t_bool tptp.cOMBC_226598744l_bool tptp.member_nat) B))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (= (tptp.hAPP_f1246832597l_bool (tptp.hAPP_f633452666l_bool tptp.insert_fun_nat_bool A_1) B) (tptp.collect_fun_nat_bool (tptp.hAPP_f1246832597l_bool (tptp.hAPP_f1743029098l_bool tptp.cOMBS_1187019125l_bool (tptp.hAPP_f1974927549l_bool (tptp.hAPP_f857404385l_bool tptp.cOMBB_444170502t_bool tptp.fdisj) (tptp.hAPP_f103356543l_bool (tptp.hAPP_f643944041l_bool tptp.cOMBC_1693257480l_bool tptp.fequal_fun_nat_bool) A_1))) (tptp.hAPP_f1246832597l_bool (tptp.hAPP_f1443436725l_bool tptp.cOMBC_1245412066l_bool tptp.member_fun_nat_bool) B))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A_1) B) (tptp.collec727977250_state (tptp.hAPP_f921536533e_bool (tptp.hAPP_f760664097e_bool tptp.cOMBS_1248383340l_bool (tptp.hAPP_f1558728829l_bool (tptp.hAPP_f1442918689l_bool tptp.cOMBB_1382207997_state tptp.fdisj) (tptp.hAPP_H1645666623e_bool (tptp.hAPP_f262880489e_bool tptp.cOMBC_1424981238e_bool tptp.fequal1531560888_state) A_1))) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1262649863e_bool tptp.cOMBC_764456866l_bool tptp.member1758697444_state) B))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a A_1) (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a A_1) B)))) (forall ((A_1 $$unsorted) (B $$unsorted)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_1) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_1) B)))) (forall ((A_1 $$unsorted) (B $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state A_1) (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A_1) B)))) (forall ((X_2 $$unsorted) (Xa $$unsorted)) (= (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a X_2) Xa) (tptp.collec268032053iple_a (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1203760810a_bool tptp.cOMBS_1148211387l_bool (tptp.hAPP_f997599971l_bool (tptp.hAPP_f439164429l_bool tptp.cOMBB_1782929690iple_a tptp.fdisj) (tptp.hAPP_H1190454433a_bool (tptp.hAPP_f1371755681a_bool tptp.cOMBC_839220826a_bool tptp.fequal879838495iple_a) X_2))) (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f672239281a_bool tptp.cOMBC_1552014468l_bool tptp.member1713797107iple_a) Xa))))) (forall ((X_2 $$unsorted) (Xa $$unsorted)) (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_2) Xa) (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_f1246832597l_bool (tptp.hAPP_f633452666l_bool tptp.insert_fun_nat_bool X_2) Xa) (tptp.collect_fun_nat_bool (tptp.hAPP_f1246832597l_bool (tptp.hAPP_f1743029098l_bool tptp.cOMBS_1187019125l_bool (tptp.hAPP_f1974927549l_bool (tptp.hAPP_f857404385l_bool tptp.cOMBB_444170502t_bool tptp.fdisj) (tptp.hAPP_f103356543l_bool (tptp.hAPP_f643944041l_bool tptp.cOMBC_1693257480l_bool tptp.fequal_fun_nat_bool) X_2))) (tptp.hAPP_f1246832597l_bool (tptp.hAPP_f1443436725l_bool tptp.cOMBC_1245412066l_bool tptp.member_fun_nat_bool) Xa))))) (forall ((X_2 $$unsorted) (Xa $$unsorted)) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state X_2) Xa) (tptp.collec727977250_state (tptp.hAPP_f921536533e_bool (tptp.hAPP_f760664097e_bool tptp.cOMBS_1248383340l_bool (tptp.hAPP_f1558728829l_bool (tptp.hAPP_f1442918689l_bool tptp.cOMBB_1382207997_state tptp.fdisj) (tptp.hAPP_H1645666623e_bool (tptp.hAPP_f262880489e_bool tptp.cOMBC_1424981238e_bool tptp.fequal1531560888_state) X_2))) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1262649863e_bool tptp.cOMBC_764456866l_bool tptp.member1758697444_state) Xa))))) (forall ((A_1 $$unsorted) (Ba $$unsorted)) (=> (= (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a A_1) tptp.bot_bo1181479936a_bool) (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a Ba) tptp.bot_bo1181479936a_bool)) (= A_1 Ba))) (forall ((A_1 $$unsorted) (Ba $$unsorted)) (=> (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_1) 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_1 Ba))) (forall ((A_1 $$unsorted) (Ba $$unsorted)) (=> (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A_1) tptp.bot_bo1055319631e_bool) (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state Ba) tptp.bot_bo1055319631e_bool)) (= A_1 Ba))) (forall ((Ba $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a Ba) (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a A_1) tptp.bot_bo1181479936a_bool))) (= Ba A_1))) (forall ((Ba $$unsorted) (A_1 $$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_1) tptp.bot_bot_fun_nat_bool))) (= Ba A_1))) (forall ((Ba $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state Ba) (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A_1) tptp.bot_bo1055319631e_bool))) (= Ba A_1))) (forall ((A_1 $$unsorted) (Ba $$unsorted) (Ca $$unsorted) (D_3 $$unsorted)) (= (= (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a A_1) (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a Ba) tptp.bot_bo1181479936a_bool)) (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a Ca) (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a D_3) tptp.bot_bo1181479936a_bool))) (or (and (= A_1 Ca) (= Ba D_3)) (and (= A_1 D_3) (= Ba Ca))))) (forall ((A_1 $$unsorted) (Ba $$unsorted) (Ca $$unsorted) (D_3 $$unsorted)) (= (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_1) (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_3) tptp.bot_bot_fun_nat_bool))) (or (and (= A_1 Ca) (= Ba D_3)) (and (= A_1 D_3) (= Ba Ca))))) (forall ((A_1 $$unsorted) (Ba $$unsorted) (Ca $$unsorted) (D_3 $$unsorted)) (= (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A_1) (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state Ba) tptp.bot_bo1055319631e_bool)) (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state Ca) (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state D_3) tptp.bot_bo1055319631e_bool))) (or (and (= A_1 Ca) (= Ba D_3)) (and (= A_1 D_3) (= Ba Ca))))) (forall ((Ba $$unsorted) (A_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a Ba) (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a A_1) tptp.bot_bo1181479936a_bool))) (= Ba A_1))) (forall ((Ba $$unsorted) (A_1 $$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_1) tptp.bot_bot_fun_nat_bool))) (= Ba A_1))) (forall ((Ba $$unsorted) (A_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state Ba) (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A_1) tptp.bot_bo1055319631e_bool))) (= Ba A_1))) (forall ((A_1 $$unsorted) (A $$unsorted)) (not (= (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a A_1) A) tptp.bot_bo1181479936a_bool))) (forall ((A_1 $$unsorted) (A $$unsorted)) (not (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_1) A) tptp.bot_bot_fun_nat_bool))) (forall ((A_1 $$unsorted) (A $$unsorted)) (not (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A_1) A) tptp.bot_bo1055319631e_bool))) (forall ((A_1 $$unsorted) (A $$unsorted)) (not (= tptp.bot_bo1181479936a_bool (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a A_1) A)))) (forall ((A_1 $$unsorted) (A $$unsorted)) (not (= tptp.bot_bot_fun_nat_bool (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_1) A)))) (forall ((A_1 $$unsorted) (A $$unsorted)) (not (= tptp.bot_bo1055319631e_bool (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A_1) A)))) (forall ((X_1 $$unsorted)) (= (tptp.hAPP_f124283079iple_a tptp.the_el1436340927iple_a (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a X_1) tptp.bot_bo1181479936a_bool)) X_1)) (forall ((X_1 $$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 $$unsorted)) (= (tptp.hAPP_f2143211163_state tptp.the_el23965208_state (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state X_1) tptp.bot_bo1055319631e_bool)) X_1)) (forall ((X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_H1421470952a_bool tptp.bot_bo1181479936a_bool X_1)) (tptp.hBOOL tptp.bot_bot_bool))) (forall ((X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_nat_bool tptp.bot_bot_fun_nat_bool X_1)) (tptp.hBOOL tptp.bot_bot_bool))) (forall ((X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_H513860823e_bool tptp.bot_bo1055319631e_bool X_1)) (tptp.hBOOL tptp.bot_bot_bool))) (forall ((X_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_H1421470952a_bool tptp.bot_bo1181479936a_bool X_2)) (tptp.hBOOL tptp.bot_bot_bool))) (forall ((X_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_nat_bool tptp.bot_bot_fun_nat_bool X_2)) (tptp.hBOOL tptp.bot_bot_bool))) (forall ((X_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_H513860823e_bool tptp.bot_bo1055319631e_bool X_2)) (tptp.hBOOL tptp.bot_bot_bool))) (forall ((Ga $$unsorted) (Pa $$unsorted)) (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hoare_606018542rivs_a Ga) (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a (tptp.hoare_1760757500iple_a Pa tptp.skip Pa)) tptp.bot_bo1181479936a_bool)))) (forall ((Ga $$unsorted) (Pa $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hoare_659004819_state Ga) (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state (tptp.hoare_1575745797_state Pa tptp.skip Pa)) tptp.bot_bo1055319631e_bool)))) (forall ((D_3 $$unsorted) (R_1 $$unsorted) (Ga $$unsorted) (Pa $$unsorted) (Ca $$unsorted) (Q_1 $$unsorted)) (let ((_let_1 (tptp.hoare_606018542rivs_a Ga))) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a (tptp.hoare_1760757500iple_a Pa Ca Q_1)) tptp.bot_bo1181479936a_bool))) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a (tptp.hoare_1760757500iple_a Q_1 D_3 R_1)) tptp.bot_bo1181479936a_bool))) (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a (tptp.hoare_1760757500iple_a Pa (tptp.semi Ca D_3) R_1)) tptp.bot_bo1181479936a_bool))))))) (forall ((D_3 $$unsorted) (R_1 $$unsorted) (Ga $$unsorted) (Pa $$unsorted) (Ca $$unsorted) (Q_1 $$unsorted)) (let ((_let_1 (tptp.hoare_659004819_state Ga))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state (tptp.hoare_1575745797_state Pa Ca Q_1)) tptp.bot_bo1055319631e_bool))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state (tptp.hoare_1575745797_state Q_1 D_3 R_1)) tptp.bot_bo1055319631e_bool))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state (tptp.hoare_1575745797_state Pa (tptp.semi Ca D_3) R_1)) tptp.bot_bo1055319631e_bool))))))) (forall ((Y_7 $$unsorted)) (not (forall ((Fun1 $$unsorted) (Com_2 $$unsorted) (Fun2 $$unsorted)) (not (= Y_7 (tptp.hoare_1575745797_state Fun1 Com_2 Fun2)))))) (forall ((Y_7 $$unsorted)) (not (forall ((Fun1 $$unsorted) (Com_2 $$unsorted) (Fun2 $$unsorted)) (not (= Y_7 (tptp.hoare_1760757500iple_a Fun1 Com_2 Fun2)))))) (forall ((X_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a X_1) A)) (not (forall ((B_15 $$unsorted)) (=> (= A (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a X_1) B_15)) (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a X_1) B_15))))))) (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_15 $$unsorted)) (=> (= A (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) B_15)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) B_15))))))) (forall ((X_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_1) A)) (not (forall ((B_15 $$unsorted)) (=> (= A (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state X_1) B_15)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_1) B_15))))))) (forall ((A_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a A_1) A)) (exists ((B_15 $$unsorted)) (and (= A (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a A_1) B_15)) (not (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a A_1) B_15))))))) (forall ((A_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_1) A)) (exists ((B_15 $$unsorted)) (and (= A (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_1) B_15)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_1) B_15))))))) (forall ((A_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state A_1) A)) (exists ((B_15 $$unsorted)) (and (= A (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A_1) B_15)) (not (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state A_1) B_15))))))) (forall ((A $$unsorted)) (=> (forall ((Y_11 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a Y_11) A)))) (= A tptp.bot_bo1181479936a_bool))) (forall ((A $$unsorted)) (=> (forall ((Y_11 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state Y_11) A)))) (= A tptp.bot_bo1055319631e_bool))) (forall ((A $$unsorted)) (=> (forall ((Y_11 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat Y_11) A)))) (= A tptp.bot_bot_fun_nat_bool))) (forall ((Q_1 $$unsorted) (Ga $$unsorted) (Ca $$unsorted) (Pa $$unsorted)) (=> (forall ((Z_7 $$unsorted) (S_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_a2036067514e_bool Pa Z_7) S_2)) (exists ((P_1 $$unsorted) (Q_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hoare_606018542rivs_a Ga) (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a (tptp.hoare_1760757500iple_a P_1 Ca Q_2)) tptp.bot_bo1181479936a_bool))) (forall ((S_3 $$unsorted)) (=> (forall ((Z_8 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_a2036067514e_bool P_1 Z_8) S_2)) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_a2036067514e_bool Q_2 Z_8) S_3)))) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_a2036067514e_bool Q_1 Z_7) S_3)))))))) (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hoare_606018542rivs_a Ga) (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a (tptp.hoare_1760757500iple_a Pa Ca Q_1)) tptp.bot_bo1181479936a_bool))))) (forall ((Q_1 $$unsorted) (Ga $$unsorted) (Ca $$unsorted) (Pa $$unsorted)) (=> (forall ((Z_7 $$unsorted) (S_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool Pa Z_7) S_2)) (exists ((P_1 $$unsorted) (Q_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hoare_659004819_state Ga) (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state (tptp.hoare_1575745797_state P_1 Ca Q_2)) tptp.bot_bo1055319631e_bool))) (forall ((S_3 $$unsorted)) (=> (forall ((Z_8 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool P_1 Z_8) S_2)) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool Q_2 Z_8) S_3)))) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool Q_1 Z_7) S_3)))))))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hoare_659004819_state Ga) (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state (tptp.hoare_1575745797_state Pa Ca Q_1)) tptp.bot_bo1055319631e_bool))))) (forall ((Com1_2 $$unsorted) (Com2_2 $$unsorted)) (not (= (tptp.semi Com1_2 Com2_2) tptp.skip))) (forall ((Com1_2 $$unsorted) (Com2_2 $$unsorted)) (not (= tptp.skip (tptp.semi Com1_2 Com2_2)))) (forall ((X_35 $$unsorted)) (= (tptp.hAPP_f124283079iple_a tptp.the_el1436340927iple_a X_35) (tptp.hAPP_f124283079iple_a tptp.the_Ho746640593iple_a (tptp.hAPP_f772297704a_bool (tptp.hAPP_f390613447a_bool tptp.cOMBB_1501709507iple_a (tptp.hAPP_f430043647l_bool tptp.fequal1258664663a_bool X_35)) (tptp.hAPP_f1665407592a_bool (tptp.hAPP_f549683569a_bool tptp.cOMBC_708118077a_bool tptp.insert873085594iple_a) tptp.bot_bo1181479936a_bool))))) (forall ((X_35 $$unsorted)) (= (tptp.hAPP_f22106695ol_nat tptp.the_elem_nat X_35) (tptp.hAPP_f22106695ol_nat tptp.the_nat (tptp.hAPP_f158894502t_bool (tptp.hAPP_f1777703707t_bool tptp.cOMBB_955900739ol_nat (tptp.hAPP_f103356543l_bool tptp.fequal_fun_nat_bool X_35)) (tptp.hAPP_f1570313510t_bool (tptp.hAPP_f688831301t_bool tptp.cOMBC_178881787t_bool tptp.insert_nat) tptp.bot_bot_fun_nat_bool))))) (forall ((X_35 $$unsorted)) (= (tptp.hAPP_f2143211163_state tptp.the_el23965208_state X_35) (tptp.hAPP_f2143211163_state tptp.the_Ho10452358_state (tptp.hAPP_f1456107715e_bool (tptp.hAPP_f1548785833e_bool tptp.cOMBB_1653402815_state (tptp.hAPP_f854625363l_bool tptp.fequal1746921144e_bool X_35)) (tptp.hAPP_f762269719e_bool (tptp.hAPP_f964290431e_bool tptp.cOMBC_488258100e_bool tptp.insert1835143293_state) tptp.bot_bo1055319631e_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 ((A $$unsorted)) (= (not (= A tptp.bot_bo1181479936a_bool)) (exists ((X_2 $$unsorted) (B_15 $$unsorted)) (and (= A (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a X_2) B_15)) (not (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a X_2) B_15))))))) (forall ((A $$unsorted)) (= (not (= A tptp.bot_bot_fun_nat_bool)) (exists ((X_2 $$unsorted) (B_15 $$unsorted)) (and (= A (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_2) B_15)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) B_15))))))) (forall ((A $$unsorted)) (= (not (= A tptp.bot_bo1055319631e_bool)) (exists ((X_2 $$unsorted) (B_15 $$unsorted)) (and (= A (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state X_2) B_15)) (not (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_2) B_15))))))) (forall ((X_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_H1421470952a_bool tptp.bot_bo1181479936a_bool X_2)) (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a X_2) tptp.bot_bo1181479936a_bool)))) (forall ((X_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_H513860823e_bool tptp.bot_bo1055319631e_bool X_2)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_2) tptp.bot_bo1055319631e_bool)))) _let_11 (forall ((Ga $$unsorted) (Pa $$unsorted) (X_35 $$unsorted) (A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hoare_606018542rivs_a Ga) (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a (tptp.hoare_1760757500iple_a (tptp.hAPP_f100967412e_bool (tptp.hAPP_f1460451647e_bool tptp.cOMBC_524597097e_bool (tptp.hAPP_f1406200875e_bool (tptp.hAPP_f635443597e_bool tptp.cOMBB_2139825703bool_a tptp.cOMBB_844853809_state) Pa)) (tptp.hAPP_f871651461_state (tptp.hAPP_f851239890_state tptp.cOMBS_777315357_state (tptp.hAPP_v365393659_state (tptp.hAPP_f1542232213_state tptp.cOMBC_1193272608_state tptp.update) X_35)) A_1)) (tptp.ass X_35 A_1) Pa)) tptp.bot_bo1181479936a_bool)))) (forall ((Ga $$unsorted) (Pa $$unsorted) (X_35 $$unsorted) (A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hoare_659004819_state Ga) (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state (tptp.hoare_1575745797_state (tptp.hAPP_f1838002347e_bool (tptp.hAPP_f1706273077e_bool tptp.cOMBC_867582640e_bool (tptp.hAPP_f289738463e_bool (tptp.hAPP_f1151843515e_bool tptp.cOMBB_1941618714_state tptp.cOMBB_844853809_state) Pa)) (tptp.hAPP_f871651461_state (tptp.hAPP_f851239890_state tptp.cOMBS_777315357_state (tptp.hAPP_v365393659_state (tptp.hAPP_f1542232213_state tptp.cOMBC_1193272608_state tptp.update) X_35)) A_1)) (tptp.ass X_35 A_1) Pa)) tptp.bot_bo1055319631e_bool)))) (forall ((Ca $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.image_1782127643iple_a (tptp.hAPP_H1450464520iple_a tptp.cOMBK_1505147640_a_nat Ca) A))) (let ((_let_2 (= A tptp.bot_bot_fun_nat_bool))) (and (=> _let_2 (= _let_1 tptp.bot_bo1181479936a_bool)) (=> (not _let_2) (= _let_1 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a Ca) tptp.bot_bo1181479936a_bool))))))) (forall ((Ca $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.image_129517430iple_a (tptp.hAPP_H377435237iple_a tptp.cOMBK_2022976521_state Ca) A))) (let ((_let_2 (= A tptp.bot_bo1055319631e_bool))) (and (=> _let_2 (= _let_1 tptp.bot_bo1181479936a_bool)) (=> (not _let_2) (= _let_1 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a Ca) tptp.bot_bo1181479936a_bool))))))) (forall ((Ca $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.image_194810223_a_nat (tptp.hAPP_n1800114674_a_nat tptp.cOMBK_944981412iple_a Ca) A))) (let ((_let_2 (= A tptp.bot_bo1181479936a_bool))) (and (=> _let_2 (= _let_1 tptp.bot_bot_fun_nat_bool)) (=> (not _let_2) (= _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat Ca) tptp.bot_bot_fun_nat_bool))))))) (forall ((Ca $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.image_1604514514_state (tptp.hAPP_H558669354_state tptp.cOMBK_547979437iple_a Ca) A))) (let ((_let_2 (= A tptp.bot_bo1181479936a_bool))) (and (=> _let_2 (= _let_1 tptp.bot_bo1055319631e_bool)) (=> (not _let_2) (= _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state Ca) tptp.bot_bo1055319631e_bool))))))) (forall ((Ca $$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 $$unsorted)) (let ((_let_1 (tptp.image_650584225_state (tptp.hAPP_H521649881_state tptp.cOMBK_690957994_state Ca) A))) (let ((_let_2 (= A tptp.bot_bo1055319631e_bool))) (and (=> _let_2 (= _let_1 tptp.bot_bo1055319631e_bool)) (=> (not _let_2) (= _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state Ca) tptp.bot_bo1055319631e_bool))))))) (forall ((Ca $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.image_306007685iple_a (tptp.hAPP_H1455657330iple_a tptp.cOMBK_1824972302iple_a Ca) A))) (let ((_let_2 (= A tptp.bot_bo1181479936a_bool))) (and (=> _let_2 (= _let_1 tptp.bot_bo1181479936a_bool)) (=> (not _let_2) (= _let_1 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a Ca) tptp.bot_bo1181479936a_bool))))))) (forall ((Ca $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)) (= (tptp.image_1782127643iple_a (tptp.hAPP_H1450464520iple_a tptp.cOMBK_1505147640_a_nat Ca) A) (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a Ca) tptp.bot_bo1181479936a_bool)))) (forall ((Ca $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a X_1) A)) (= (tptp.image_306007685iple_a (tptp.hAPP_H1455657330iple_a tptp.cOMBK_1824972302iple_a Ca) A) (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a Ca) tptp.bot_bo1181479936a_bool)))) (forall ((Ca $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_1) A)) (= (tptp.image_129517430iple_a (tptp.hAPP_H377435237iple_a tptp.cOMBK_2022976521_state Ca) A) (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a Ca) tptp.bot_bo1181479936a_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_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a X_1) A)) (= (tptp.image_194810223_a_nat (tptp.hAPP_n1800114674_a_nat tptp.cOMBK_944981412iple_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 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_1) A)) (= (tptp.image_1410872416te_nat (tptp.hAPP_n436597305te_nat tptp.cOMBK_1950023923_state Ca) A) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat Ca) tptp.bot_bot_fun_nat_bool)))) (forall ((Ca $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_1) A)) (= (tptp.image_650584225_state (tptp.hAPP_H521649881_state tptp.cOMBK_690957994_state Ca) A) (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state Ca) tptp.bot_bo1055319631e_bool)))) (forall ((Ca $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a X_1) A)) (= (tptp.image_1604514514_state (tptp.hAPP_H558669354_state tptp.cOMBK_547979437iple_a Ca) A) (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state Ca) tptp.bot_bo1055319631e_bool)))) (forall ((A $$unsorted) (Ba $$unsorted) (F_1 $$unsorted) (X_1 $$unsorted)) (=> (= Ba (tptp.hAPP_H563960305_state F_1 X_1)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_1) A)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state Ba) (tptp.image_650584225_state F_1 A)))))) (forall ((A $$unsorted) (Ba $$unsorted) (F_1 $$unsorted) (X_1 $$unsorted)) (=> (= Ba (tptp.hAPP_n1126952044_state F_1 X_1)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state Ba) (tptp.image_1821565372_state F_1 A)))))) (forall ((A $$unsorted) (Ba $$unsorted) (F_1 $$unsorted) (X_1 $$unsorted)) (=> (= Ba (tptp.hAPP_H928324994_state F_1 X_1)) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a X_1) A)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state Ba) (tptp.image_1604514514_state F_1 A)))))) (forall ((A $$unsorted) (Ba $$unsorted) (F_1 $$unsorted) (X_1 $$unsorted)) (=> (= Ba (tptp.hAPP_nat_nat F_1 X_1)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat Ba) (tptp.image_nat_nat F_1 A)))))) (forall ((A $$unsorted) (Ba $$unsorted) (F_1 $$unsorted) (X_1 $$unsorted)) (=> (= Ba (tptp.hAPP_H738206399_a_nat F_1 X_1)) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a X_1) A)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat Ba) (tptp.image_194810223_a_nat F_1 A)))))) (forall ((A $$unsorted) (Ba $$unsorted) (F_1 $$unsorted) (X_1 $$unsorted)) (=> (= Ba (tptp.hAPP_H716259088te_nat F_1 X_1)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_1) A)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat Ba) (tptp.image_1410872416te_nat F_1 A)))))) (forall ((A $$unsorted) (Ba $$unsorted) (F_1 $$unsorted) (X_1 $$unsorted)) (=> (= Ba (tptp.hAPP_H678412245iple_a F_1 X_1)) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a X_1) A)) (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a Ba) (tptp.image_306007685iple_a F_1 A)))))) (forall ((A $$unsorted) (Ba $$unsorted) (F_1 $$unsorted) (X_1 $$unsorted)) (=> (= Ba (tptp.hAPP_H1600811558iple_a F_1 X_1)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_1) A)) (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a Ba) (tptp.image_129517430iple_a F_1 A)))))) (forall ((A $$unsorted) (Ba $$unsorted) (F_1 $$unsorted) (X_1 $$unsorted)) (=> (= Ba (tptp.hAPP_n178040171iple_a F_1 X_1)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)) (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a Ba) (tptp.image_1782127643iple_a F_1 A)))))) (forall ((Y_27 $$unsorted)) (= (tptp.image_nat_nat tptp.cOMBI_nat Y_27) Y_27)) (forall ((Y_27 $$unsorted)) (= (tptp.image_650584225_state tptp.cOMBI_1367665338_state Y_27) Y_27)) (forall ((Y_27 $$unsorted)) (= (tptp.image_306007685iple_a tptp.cOMBI_1218222237iple_a Y_27) Y_27)) (forall ((Vname $$unsorted) (Fun_1 $$unsorted) (Vname_1 $$unsorted) (Fun $$unsorted)) (=> (and (tptp.is_vname Vname) (tptp.is_vname Vname_1)) (= (= (tptp.ass Vname Fun_1) (tptp.ass Vname_1 Fun)) (and (= Vname Vname_1) (= Fun_1 Fun))))) (forall ((Ba $$unsorted) (F_1 $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_1) A)) (=> (= Ba (tptp.hAPP_H563960305_state F_1 X_1)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state Ba) (tptp.image_650584225_state F_1 A)))))) (forall ((Ba $$unsorted) (F_1 $$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_n1126952044_state F_1 X_1)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state Ba) (tptp.image_1821565372_state F_1 A)))))) (forall ((Ba $$unsorted) (F_1 $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a X_1) A)) (=> (= Ba (tptp.hAPP_H928324994_state F_1 X_1)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state Ba) (tptp.image_1604514514_state F_1 A)))))) (forall ((Ba $$unsorted) (F_1 $$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_1 X_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat Ba) (tptp.image_nat_nat F_1 A)))))) (forall ((Ba $$unsorted) (F_1 $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a X_1) A)) (=> (= Ba (tptp.hAPP_H738206399_a_nat F_1 X_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat Ba) (tptp.image_194810223_a_nat F_1 A)))))) (forall ((Ba $$unsorted) (F_1 $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_1) A)) (=> (= Ba (tptp.hAPP_H716259088te_nat F_1 X_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat Ba) (tptp.image_1410872416te_nat F_1 A)))))) (forall ((Ba $$unsorted) (F_1 $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a X_1) A)) (=> (= Ba (tptp.hAPP_H678412245iple_a F_1 X_1)) (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a Ba) (tptp.image_306007685iple_a F_1 A)))))) (forall ((Ba $$unsorted) (F_1 $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_1) A)) (=> (= Ba (tptp.hAPP_H1600811558iple_a F_1 X_1)) (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a Ba) (tptp.image_129517430iple_a F_1 A)))))) (forall ((Ba $$unsorted) (F_1 $$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_n178040171iple_a F_1 X_1)) (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a Ba) (tptp.image_1782127643iple_a F_1 A)))))) (forall ((F_1 $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_1) A)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state (tptp.hAPP_H563960305_state F_1 X_1)) (tptp.image_650584225_state F_1 A))))) (forall ((F_1 $$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_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state (tptp.hAPP_n1126952044_state F_1 X_1)) (tptp.image_1821565372_state F_1 A))))) (forall ((F_1 $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a X_1) A)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state (tptp.hAPP_H928324994_state F_1 X_1)) (tptp.image_1604514514_state F_1 A))))) (forall ((F_1 $$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_1 X_1)) (tptp.image_nat_nat F_1 A))))) (forall ((F_1 $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a X_1) A)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat (tptp.hAPP_H738206399_a_nat F_1 X_1)) (tptp.image_194810223_a_nat F_1 A))))) (forall ((F_1 $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_1) A)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat (tptp.hAPP_H716259088te_nat F_1 X_1)) (tptp.image_1410872416te_nat F_1 A))))) (forall ((F_1 $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a X_1) A)) (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a (tptp.hAPP_H678412245iple_a F_1 X_1)) (tptp.image_306007685iple_a F_1 A))))) (forall ((F_1 $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_1) A)) (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a (tptp.hAPP_H1600811558iple_a F_1 X_1)) (tptp.image_129517430iple_a F_1 A))))) (forall ((F_1 $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)) (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a (tptp.hAPP_n178040171iple_a F_1 X_1)) (tptp.image_1782127643iple_a F_1 A))))) (forall ((Z_2 $$unsorted) (F_1 $$unsorted) (A $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state Z_2) (tptp.image_650584225_state F_1 A))) (exists ((X_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_2) A)) (= Z_2 (tptp.hAPP_H563960305_state F_1 X_2)))))) (forall ((Z_2 $$unsorted) (F_1 $$unsorted) (A $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state Z_2) (tptp.image_1604514514_state F_1 A))) (exists ((X_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a X_2) A)) (= Z_2 (tptp.hAPP_H928324994_state F_1 X_2)))))) (forall ((Z_2 $$unsorted) (F_1 $$unsorted) (A $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat Z_2) (tptp.image_nat_nat F_1 A))) (exists ((X_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) A)) (= Z_2 (tptp.hAPP_nat_nat F_1 X_2)))))) (forall ((Z_2 $$unsorted) (F_1 $$unsorted) (A $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat Z_2) (tptp.image_194810223_a_nat F_1 A))) (exists ((X_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a X_2) A)) (= Z_2 (tptp.hAPP_H738206399_a_nat F_1 X_2)))))) (forall ((Z_2 $$unsorted) (F_1 $$unsorted) (A $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a Z_2) (tptp.image_306007685iple_a F_1 A))) (exists ((X_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a X_2) A)) (= Z_2 (tptp.hAPP_H678412245iple_a F_1 X_2)))))) (forall ((Z_2 $$unsorted) (F_1 $$unsorted) (A $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a Z_2) (tptp.image_129517430iple_a F_1 A))) (exists ((X_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_2) A)) (= Z_2 (tptp.hAPP_H1600811558iple_a F_1 X_2)))))) (forall ((Z_2 $$unsorted) (F_1 $$unsorted) (A $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a Z_2) (tptp.image_1782127643iple_a F_1 A))) (exists ((X_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) A)) (= Z_2 (tptp.hAPP_n178040171iple_a F_1 X_2)))))) (forall ((Vname $$unsorted) (Fun_1 $$unsorted) (Com1 $$unsorted) (Com2 $$unsorted)) (not (= (tptp.ass Vname Fun_1) (tptp.semi Com1 Com2)))) (forall ((Com1 $$unsorted) (Com2 $$unsorted) (Vname $$unsorted) (Fun_1 $$unsorted)) (not (= (tptp.semi Com1 Com2) (tptp.ass Vname Fun_1)))) (forall ((Vname_1 $$unsorted) (Fun $$unsorted)) (not (= tptp.skip (tptp.ass Vname_1 Fun)))) (forall ((Vname_1 $$unsorted) (Fun $$unsorted)) (not (= (tptp.ass Vname_1 Fun) tptp.skip))) (forall ((F_1 $$unsorted) (A $$unsorted)) (= (= (tptp.image_129517430iple_a F_1 A) tptp.bot_bo1181479936a_bool) (= A tptp.bot_bo1055319631e_bool))) (forall ((F_1 $$unsorted) (A $$unsorted)) (= (= (tptp.image_1782127643iple_a F_1 A) tptp.bot_bo1181479936a_bool) (= A tptp.bot_bot_fun_nat_bool))) (forall ((F_1 $$unsorted) (A $$unsorted)) (= (= (tptp.image_1604514514_state F_1 A) tptp.bot_bo1055319631e_bool) (= A tptp.bot_bo1181479936a_bool))) (forall ((F_1 $$unsorted) (A $$unsorted)) (= (= (tptp.image_194810223_a_nat F_1 A) tptp.bot_bot_fun_nat_bool) (= A tptp.bot_bo1181479936a_bool))) (forall ((F_1 $$unsorted)) (= (tptp.image_1604514514_state F_1 tptp.bot_bo1181479936a_bool) tptp.bot_bo1055319631e_bool)) (forall ((F_1 $$unsorted)) (= (tptp.image_194810223_a_nat F_1 tptp.bot_bo1181479936a_bool) tptp.bot_bot_fun_nat_bool)) (forall ((F_1 $$unsorted)) (= (tptp.image_129517430iple_a F_1 tptp.bot_bo1055319631e_bool) tptp.bot_bo1181479936a_bool)) (forall ((F_1 $$unsorted)) (= (tptp.image_1782127643iple_a F_1 tptp.bot_bot_fun_nat_bool) tptp.bot_bo1181479936a_bool)) (forall ((F_1 $$unsorted) (A $$unsorted)) (= (= tptp.bot_bo1181479936a_bool (tptp.image_129517430iple_a F_1 A)) (= A tptp.bot_bo1055319631e_bool))) (forall ((F_1 $$unsorted) (A $$unsorted)) (= (= tptp.bot_bo1181479936a_bool (tptp.image_1782127643iple_a F_1 A)) (= A tptp.bot_bot_fun_nat_bool))) (forall ((F_1 $$unsorted) (A $$unsorted)) (= (= tptp.bot_bo1055319631e_bool (tptp.image_1604514514_state F_1 A)) (= A tptp.bot_bo1181479936a_bool))) (forall ((F_1 $$unsorted) (A $$unsorted)) (= (= tptp.bot_bot_fun_nat_bool (tptp.image_194810223_a_nat F_1 A)) (= A tptp.bot_bo1181479936a_bool))) (forall ((X_1 $$unsorted) (A $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a X_1) A)) (tptp.hBOOL (tptp.hAPP_H1421470952a_bool A X_1)))) (forall ((X_1 $$unsorted) (A $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)) (tptp.hBOOL (tptp.hAPP_nat_bool A X_1)))) (forall ((Pa $$unsorted)) (= (tptp.collec268032053iple_a Pa) Pa)) _let_10 (forall ((F_1 $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.image_306007685iple_a F_1 A))) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a X_1) A)) (= (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a (tptp.hAPP_H678412245iple_a F_1 X_1)) _let_1) _let_1)))) (forall ((F_1 $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.image_1782127643iple_a F_1 A))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)) (= (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a (tptp.hAPP_n178040171iple_a F_1 X_1)) _let_1) _let_1)))) (forall ((F_1 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (= (tptp.image_1604514514_state F_1 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a A_1) B)) (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state (tptp.hAPP_H928324994_state F_1 A_1)) (tptp.image_1604514514_state F_1 B)))) (forall ((F_1 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (= (tptp.image_194810223_a_nat F_1 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a A_1) B)) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat (tptp.hAPP_H738206399_a_nat F_1 A_1)) (tptp.image_194810223_a_nat F_1 B)))) (forall ((F_1 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (= (tptp.image_129517430iple_a F_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A_1) B)) (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a (tptp.hAPP_H1600811558iple_a F_1 A_1)) (tptp.image_129517430iple_a F_1 B)))) (forall ((F_1 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (= (tptp.image_1782127643iple_a F_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_1) B)) (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a (tptp.hAPP_n178040171iple_a F_1 A_1)) (tptp.image_1782127643iple_a F_1 B)))) (forall ((X_1 $$unsorted)) (= (tptp.hAPP_f124283079iple_a tptp.the_Ho746640593iple_a (tptp.hAPP_H1190454433a_bool tptp.fequal879838495iple_a X_1)) X_1)) (forall ((A_1 $$unsorted)) (= (tptp.hAPP_f124283079iple_a tptp.the_Ho746640593iple_a (tptp.hAPP_H1190454433a_bool (tptp.hAPP_f1371755681a_bool tptp.cOMBC_839220826a_bool tptp.fequal879838495iple_a) A_1)) A_1)) (forall ((X_1 $$unsorted) (Y_7 $$unsorted) (Pa $$unsorted)) (let ((_let_1 (tptp.hAPP_f1371755681a_bool tptp.cOMBC_839220826a_bool tptp.fequal879838495iple_a))) (let ((_let_2 (tptp.hAPP_f124283079iple_a tptp.the_Ho746640593iple_a (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1203760810a_bool tptp.cOMBS_1148211387l_bool (tptp.hAPP_f997599971l_bool (tptp.hAPP_f439164429l_bool tptp.cOMBB_1782929690iple_a tptp.fconj) (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f34030599a_bool tptp.cOMBB_1799513916iple_a (tptp.hAPP_b589554111l_bool tptp.fimplies Pa)) (tptp.hAPP_H1190454433a_bool _let_1 X_1)))) (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f34030599a_bool tptp.cOMBB_1799513916iple_a (tptp.hAPP_b589554111l_bool tptp.fimplies (tptp.hAPP_bool_bool tptp.fNot Pa))) (tptp.hAPP_H1190454433a_bool _let_1 Y_7)))))) (let ((_let_3 (tptp.hBOOL Pa))) (and (=> _let_3 (= X_1 _let_2)) (=> (not _let_3) (= Y_7 _let_2))))))) (forall ((F_1 $$unsorted) (A_1 $$unsorted) (Ba $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_H513860823e_bool (tptp.finite9525415_state F_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A_1) tptp.bot_bo1055319631e_bool)) Ba)) (= A_1 Ba))) (forall ((F_1 $$unsorted) (A_1 $$unsorted) (Ba $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.finite_fold1Set_nat F_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_1) tptp.bot_bot_fun_nat_bool)) Ba)) (= A_1 Ba))) (forall ((F_1 $$unsorted) (A_1 $$unsorted) (Ba $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_H1421470952a_bool (tptp.finite1537818352iple_a F_1 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a A_1) tptp.bot_bo1181479936a_bool)) Ba)) (= A_1 Ba))) (forall ((Pa $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_H1421470952a_bool Pa A_1)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_H1421470952a_bool Pa X_2)) (= X_2 A_1))) (= (tptp.hAPP_f124283079iple_a tptp.the_Ho746640593iple_a Pa) A_1)))) (forall ((X_1 $$unsorted) (F_1 $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.finite774711482_state F_1 F)) (= (tptp.hAPP_f2143211163_state F (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state X_1) tptp.bot_bo1055319631e_bool)) X_1))) (forall ((X_1 $$unsorted) (F_1 $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.finite988810631ne_nat F_1 F)) (= (tptp.hAPP_f22106695ol_nat F (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) tptp.bot_bot_fun_nat_bool)) X_1))) (forall ((X_1 $$unsorted) (F_1 $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.finite1669978781iple_a F_1 F)) (= (tptp.hAPP_f124283079iple_a F (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a X_1) tptp.bot_bo1181479936a_bool)) X_1))) (forall ((A_1 $$unsorted) (Ga $$unsorted) (Pa $$unsorted) (Ca $$unsorted) (Q_1 $$unsorted) (X_35 $$unsorted) (S_5 $$unsorted)) (let ((_let_1 (tptp.hAPP_v365393659_state (tptp.hAPP_f1542232213_state tptp.cOMBC_1193272608_state tptp.update) (tptp.loc X_35)))) (let ((_let_2 (tptp.hAPP_f1151843515e_bool tptp.cOMBB_1941618714_state tptp.cOMBB_844853809_state))) (let ((_let_3 (tptp.hoare_659004819_state Ga))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_3 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state (tptp.hoare_1575745797_state Pa Ca (tptp.hAPP_f1838002347e_bool (tptp.hAPP_f1706273077e_bool tptp.cOMBC_867582640e_bool (tptp.hAPP_f289738463e_bool _let_2 Q_1)) (tptp.hAPP_n1547241352_state (tptp.hAPP_f1848060885_state tptp.cOMBC_1777403949_state _let_1) (tptp.getlocs S_5 X_35))))) tptp.bot_bo1055319631e_bool))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_3 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state (tptp.hoare_1575745797_state (tptp.hAPP_f817621513e_bool (tptp.hAPP_f512427579e_bool tptp.cOMBB_572666224_state (tptp.hAPP_f644196280e_bool tptp.cOMBS_1378840469l_bool (tptp.hAPP_f1259673775l_bool (tptp.hAPP_f1561913689l_bool tptp.cOMBB_188601460_state tptp.fconj) (tptp.hAPP_s1806633685e_bool tptp.fequal_state S_5)))) (tptp.hAPP_f1838002347e_bool (tptp.hAPP_f1706273077e_bool tptp.cOMBC_867582640e_bool (tptp.hAPP_f289738463e_bool _let_2 Pa)) (tptp.hAPP_f871651461_state (tptp.hAPP_f851239890_state tptp.cOMBS_777315357_state _let_1) A_1))) (tptp.local X_35 A_1 Ca) Q_1)) tptp.bot_bo1055319631e_bool)))))))) (forall ((A_1 $$unsorted) (Ga $$unsorted) (Pa $$unsorted) (Ca $$unsorted) (Q_1 $$unsorted) (X_35 $$unsorted) (S_5 $$unsorted)) (let ((_let_1 (tptp.hAPP_v365393659_state (tptp.hAPP_f1542232213_state tptp.cOMBC_1193272608_state tptp.update) (tptp.loc X_35)))) (let ((_let_2 (tptp.hAPP_f635443597e_bool tptp.cOMBB_2139825703bool_a tptp.cOMBB_844853809_state))) (let ((_let_3 (tptp.hoare_606018542rivs_a Ga))) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_3 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a (tptp.hoare_1760757500iple_a Pa Ca (tptp.hAPP_f100967412e_bool (tptp.hAPP_f1460451647e_bool tptp.cOMBC_524597097e_bool (tptp.hAPP_f1406200875e_bool _let_2 Q_1)) (tptp.hAPP_n1547241352_state (tptp.hAPP_f1848060885_state tptp.cOMBC_1777403949_state _let_1) (tptp.getlocs S_5 X_35))))) tptp.bot_bo1181479936a_bool))) (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_3 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a (tptp.hoare_1760757500iple_a (tptp.hAPP_f769584981e_bool (tptp.hAPP_f1159960589e_bool tptp.cOMBB_237455441bool_a (tptp.hAPP_f644196280e_bool tptp.cOMBS_1378840469l_bool (tptp.hAPP_f1259673775l_bool (tptp.hAPP_f1561913689l_bool tptp.cOMBB_188601460_state tptp.fconj) (tptp.hAPP_s1806633685e_bool tptp.fequal_state S_5)))) (tptp.hAPP_f100967412e_bool (tptp.hAPP_f1460451647e_bool tptp.cOMBC_524597097e_bool (tptp.hAPP_f1406200875e_bool _let_2 Pa)) (tptp.hAPP_f871651461_state (tptp.hAPP_f851239890_state tptp.cOMBS_777315357_state _let_1) A_1))) (tptp.local X_35 A_1 Ca) Q_1)) tptp.bot_bo1181479936a_bool)))))))) (forall ((Loc_3 $$unsorted) (Loc_2 $$unsorted)) (=> (and (tptp.is_loc Loc_3) (tptp.is_loc Loc_2)) (= (= (tptp.loc Loc_3) (tptp.loc Loc_2)) (= Loc_3 Loc_2)))) (forall ((Loc_3 $$unsorted) (Fun_1 $$unsorted) (Com_1 $$unsorted) (Loc_2 $$unsorted) (Fun $$unsorted) (Com $$unsorted)) (=> (and (tptp.is_loc Loc_3) (tptp.is_loc Loc_2)) (= (= (tptp.local Loc_3 Fun_1 Com_1) (tptp.local Loc_2 Fun Com)) (and (= Loc_3 Loc_2) (= Fun_1 Fun) (= Com_1 Com))))) (forall ((Loc_3 $$unsorted) (Fun_1 $$unsorted) (Com_1 $$unsorted) (Com1 $$unsorted) (Com2 $$unsorted)) (not (= (tptp.local Loc_3 Fun_1 Com_1) (tptp.semi Com1 Com2)))) (forall ((Com1 $$unsorted) (Com2 $$unsorted) (Loc_3 $$unsorted) (Fun_1 $$unsorted) (Com_1 $$unsorted)) (not (= (tptp.semi Com1 Com2) (tptp.local Loc_3 Fun_1 Com_1)))) (forall ((Loc_2 $$unsorted) (Fun $$unsorted) (Com $$unsorted) (Vname $$unsorted) (Fun_1 $$unsorted)) (not (= (tptp.local Loc_2 Fun Com) (tptp.ass Vname Fun_1)))) (forall ((Vname $$unsorted) (Fun_1 $$unsorted) (Loc_2 $$unsorted) (Fun $$unsorted) (Com $$unsorted)) (not (= (tptp.ass Vname Fun_1) (tptp.local Loc_2 Fun Com)))) (forall ((Loc_2 $$unsorted) (Fun $$unsorted) (Com $$unsorted)) (not (= (tptp.local Loc_2 Fun Com) tptp.skip))) (forall ((Loc_2 $$unsorted) (Fun $$unsorted) (Com $$unsorted)) (not (= tptp.skip (tptp.local Loc_2 Fun Com)))) (forall ((F_1 $$unsorted) (X_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_H513860823e_bool (tptp.finite9525415_state F_1 tptp.bot_bo1055319631e_bool) X_1)))) (forall ((F_1 $$unsorted) (X_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.finite_fold1Set_nat F_1 tptp.bot_bot_fun_nat_bool) X_1)))) (forall ((F_1 $$unsorted) (X_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_H1421470952a_bool (tptp.finite1537818352iple_a F_1 tptp.bot_bo1181479936a_bool) X_1)))) (forall ((F_1 $$unsorted) (A $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_H513860823e_bool (tptp.finite9525415_state F_1 A) X_1)) (not (= A tptp.bot_bo1055319631e_bool)))) (forall ((F_1 $$unsorted) (A $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.finite_fold1Set_nat F_1 A) X_1)) (not (= A tptp.bot_bot_fun_nat_bool)))) (forall ((F_1 $$unsorted) (A $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_H1421470952a_bool (tptp.finite1537818352iple_a F_1 A) X_1)) (not (= A tptp.bot_bo1181479936a_bool)))) (forall ((Pa $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_H1421470952a_bool Pa A_1)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_H1421470952a_bool Pa X_2)) (= X_2 A_1))) (tptp.hBOOL (tptp.hAPP_H1421470952a_bool Pa (tptp.hAPP_f124283079iple_a tptp.the_Ho746640593iple_a Pa)))))) (forall ((A_1 $$unsorted) (Pa $$unsorted)) (=> (exists ((X_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_H1421470952a_bool Pa X_2)) (forall ((Y_11 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_H1421470952a_bool Pa Y_11)) (= Y_11 X_2))))) (=> (tptp.hBOOL (tptp.hAPP_H1421470952a_bool Pa A_1)) (= (tptp.hAPP_f124283079iple_a tptp.the_Ho746640593iple_a Pa) A_1)))) (forall ((Pa $$unsorted)) (=> (exists ((X_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_H1421470952a_bool Pa X_2)) (forall ((Y_11 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_H1421470952a_bool Pa Y_11)) (= Y_11 X_2))))) (tptp.hBOOL (tptp.hAPP_H1421470952a_bool Pa (tptp.hAPP_f124283079iple_a tptp.the_Ho746640593iple_a Pa))))) (forall ((Ca $$unsorted) (S0_1 $$unsorted) (Y_27 $$unsorted) (A_1 $$unsorted) (S1_2 $$unsorted)) (let ((_let_1 (tptp.loc Y_27))) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool (tptp.evalc Ca) (tptp.hAPP_nat_state (tptp.hAPP_v594194232_state (tptp.hAPP_s712361723_state tptp.update S0_1) _let_1) (tptp.hAPP_state_nat A_1 S0_1))) S1_2)) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool (tptp.evalc (tptp.local Y_27 A_1 Ca)) S0_1) (tptp.hAPP_nat_state (tptp.hAPP_v594194232_state (tptp.hAPP_s712361723_state tptp.update S1_2) _let_1) (tptp.getlocs S0_1 Y_27))))))) (forall ((Ca $$unsorted) (S0_1 $$unsorted) (Y_27 $$unsorted) (A_1 $$unsorted) (N_3 $$unsorted) (S1_2 $$unsorted)) (let ((_let_1 (tptp.loc Y_27))) (=> (tptp.hBOOL (tptp.evaln Ca (tptp.hAPP_nat_state (tptp.hAPP_v594194232_state (tptp.hAPP_s712361723_state tptp.update S0_1) _let_1) (tptp.hAPP_state_nat A_1 S0_1)) N_3 S1_2)) (tptp.hBOOL (tptp.evaln (tptp.local Y_27 A_1 Ca) S0_1 N_3 (tptp.hAPP_nat_state (tptp.hAPP_v594194232_state (tptp.hAPP_s712361723_state tptp.update S1_2) _let_1) (tptp.getlocs S0_1 Y_27))))))) (forall ((F_1 $$unsorted) (A_1 $$unsorted) (A $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_H513860823e_bool (tptp.finite1935632226_state F_1 A_1 A) X_1)) (=> (not (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state A_1) A))) (tptp.hBOOL (tptp.hAPP_H513860823e_bool (tptp.finite9525415_state F_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A_1) A)) X_1))))) (forall ((F_1 $$unsorted) (A_1 $$unsorted) (A $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.finite929467206at_nat F_1 A_1 A) X_1)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_1) A))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.finite_fold1Set_nat F_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_1) A)) X_1))))) (forall ((F_1 $$unsorted) (A_1 $$unsorted) (A $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_H1421470952a_bool (tptp.finite2010942150iple_a F_1 A_1 A) X_1)) (=> (not (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a A_1) A))) (tptp.hBOOL (tptp.hAPP_H1421470952a_bool (tptp.finite1537818352iple_a F_1 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a A_1) A)) X_1))))) (forall ((C1 $$unsorted) (S2 $$unsorted) (C0 $$unsorted) (S0 $$unsorted) (N_2 $$unsorted) (S1 $$unsorted)) (=> (tptp.hBOOL (tptp.evaln C0 S0 N_2 S1)) (=> (tptp.hBOOL (tptp.evaln C1 S1 N_2 S2)) (tptp.hBOOL (tptp.evaln (tptp.semi C0 C1) S0 N_2 S2))))) (forall ((S_1 $$unsorted) (N_2 $$unsorted)) (tptp.hBOOL (tptp.evaln tptp.skip S_1 N_2 S_1))) (forall ((S_1 $$unsorted) (N_2 $$unsorted) (T $$unsorted)) (=> (tptp.hBOOL (tptp.evaln tptp.skip S_1 N_2 T)) (= T S_1))) (forall ((C1 $$unsorted) (S2 $$unsorted) (C0 $$unsorted) (S0 $$unsorted) (S1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool (tptp.evalc C0) S0) S1)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool (tptp.evalc C1) S1) S2)) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool (tptp.evalc (tptp.semi C0 C1)) S0) S2))))) (forall ((S_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool (tptp.evalc tptp.skip) S_1) S_1))) (forall ((S_1 $$unsorted) (T $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool (tptp.evalc tptp.skip) S_1) T)) (= T S_1))) (forall ((X_35 $$unsorted) (A_1 $$unsorted) (S_4 $$unsorted) (N_3 $$unsorted)) (tptp.hBOOL (tptp.evaln (tptp.ass X_35 A_1) S_4 N_3 (tptp.hAPP_nat_state (tptp.hAPP_v594194232_state (tptp.hAPP_s712361723_state tptp.update S_4) X_35) (tptp.hAPP_state_nat A_1 S_4))))) (forall ((X_35 $$unsorted) (A_1 $$unsorted) (S_4 $$unsorted) (N_3 $$unsorted) (T_1 $$unsorted)) (=> (tptp.hBOOL (tptp.evaln (tptp.ass X_35 A_1) S_4 N_3 T_1)) (= T_1 (tptp.hAPP_nat_state (tptp.hAPP_v594194232_state (tptp.hAPP_s712361723_state tptp.update S_4) X_35) (tptp.hAPP_state_nat A_1 S_4))))) (forall ((X_35 $$unsorted) (A_1 $$unsorted) (S_4 $$unsorted)) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool (tptp.evalc (tptp.ass X_35 A_1)) S_4) (tptp.hAPP_nat_state (tptp.hAPP_v594194232_state (tptp.hAPP_s712361723_state tptp.update S_4) X_35) (tptp.hAPP_state_nat A_1 S_4))))) (forall ((X_35 $$unsorted) (A_1 $$unsorted) (S_4 $$unsorted) (T_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool (tptp.evalc (tptp.ass X_35 A_1)) S_4) T_1)) (= T_1 (tptp.hAPP_nat_state (tptp.hAPP_v594194232_state (tptp.hAPP_s712361723_state tptp.update S_4) X_35) (tptp.hAPP_state_nat A_1 S_4))))) (forall ((Ca $$unsorted) (S_4 $$unsorted) (T_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool (tptp.evalc Ca) S_4) T_1)) (exists ((N_1 $$unsorted)) (tptp.hBOOL (tptp.evaln Ca S_4 N_1 T_1))))) (forall ((U_1 $$unsorted) (C_2 $$unsorted) (S_1 $$unsorted) (T $$unsorted)) (let ((_let_1 (tptp.hAPP_s1806633685e_bool (tptp.evalc C_2) S_1))) (=> (tptp.hBOOL (tptp.hAPP_state_bool _let_1 T)) (=> (tptp.hBOOL (tptp.hAPP_state_bool _let_1 U_1)) (= U_1 T))))) (forall ((C_2 $$unsorted) (S_1 $$unsorted) (N_2 $$unsorted) (T $$unsorted)) (=> (tptp.hBOOL (tptp.evaln C_2 S_1 N_2 T)) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool (tptp.evalc C_2) S_1) T)))) (forall ((F_1 $$unsorted) (Z_2 $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_H1421470952a_bool (tptp.finite2010942150iple_a F_1 Z_2 tptp.bot_bo1181479936a_bool) X_1)) (= X_1 Z_2))) (forall ((F_1 $$unsorted) (Z_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_H1421470952a_bool (tptp.finite2010942150iple_a F_1 Z_2 tptp.bot_bo1181479936a_bool) Z_2))) (forall ((F_1 $$unsorted) (Z_2 $$unsorted) (Y_7 $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a X_1) A))) (=> (tptp.hBOOL (tptp.hAPP_H1421470952a_bool (tptp.finite2010942150iple_a F_1 Z_2 A) Y_7)) (tptp.hBOOL (tptp.hAPP_H1421470952a_bool (tptp.finite2010942150iple_a F_1 Z_2 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a X_1) A)) (tptp.hAPP_H678412245iple_a (tptp.hAPP_H1455657330iple_a F_1 X_1) Y_7)))))) (forall ((Y_27 $$unsorted) (A_1 $$unsorted) (Ca $$unsorted) (S_4 $$unsorted) (T_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool (tptp.evalc (tptp.local Y_27 A_1 Ca)) S_4) T_1)) (not (forall ((S1_1 $$unsorted)) (let ((_let_1 (tptp.loc Y_27))) (=> (= T_1 (tptp.hAPP_nat_state (tptp.hAPP_v594194232_state (tptp.hAPP_s712361723_state tptp.update S1_1) _let_1) (tptp.getlocs S_4 Y_27))) (not (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool (tptp.evalc Ca) (tptp.hAPP_nat_state (tptp.hAPP_v594194232_state (tptp.hAPP_s712361723_state tptp.update S_4) _let_1) (tptp.hAPP_state_nat A_1 S_4))) S1_1))))))))) (forall ((Y_27 $$unsorted) (A_1 $$unsorted) (Ca $$unsorted) (S_4 $$unsorted) (N_3 $$unsorted) (T_1 $$unsorted)) (=> (tptp.hBOOL (tptp.evaln (tptp.local Y_27 A_1 Ca) S_4 N_3 T_1)) (not (forall ((S1_1 $$unsorted)) (let ((_let_1 (tptp.loc Y_27))) (=> (= T_1 (tptp.hAPP_nat_state (tptp.hAPP_v594194232_state (tptp.hAPP_s712361723_state tptp.update S1_1) _let_1) (tptp.getlocs S_4 Y_27))) (not (tptp.hBOOL (tptp.evaln Ca (tptp.hAPP_nat_state (tptp.hAPP_v594194232_state (tptp.hAPP_s712361723_state tptp.update S_4) _let_1) (tptp.hAPP_state_nat A_1 S_4)) N_3 S1_1))))))))) (forall ((C1 $$unsorted) (C2 $$unsorted) (S_1 $$unsorted) (T $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool (tptp.evalc (tptp.semi C1 C2)) S_1) T)) (not (forall ((S1_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool (tptp.evalc C1) S_1) S1_1)) (not (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool (tptp.evalc C2) S1_1) T)))))))) (forall ((C1 $$unsorted) (C2 $$unsorted) (S_1 $$unsorted) (N_2 $$unsorted) (T $$unsorted)) (=> (tptp.hBOOL (tptp.evaln (tptp.semi C1 C2) S_1 N_2 T)) (not (forall ((S1_1 $$unsorted)) (=> (tptp.hBOOL (tptp.evaln C1 S_1 N_2 S1_1)) (not (tptp.hBOOL (tptp.evaln C2 S1_1 N_2 T)))))))) (forall ((F_1 $$unsorted) (A_1 $$unsorted) (X_35 $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.finite_fold1Set_nat F_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_1) X_35)) X_1)) (not (forall ((A_7 $$unsorted) (A_19 $$unsorted)) (=> (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_1) X_35) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_7) A_19)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.finite929467206at_nat F_1 A_7 A_19) X_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_7) A_19)))))))) (forall ((F_1 $$unsorted) (A_1 $$unsorted) (X_35 $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_H513860823e_bool (tptp.finite9525415_state F_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A_1) X_35)) X_1)) (not (forall ((A_7 $$unsorted) (A_19 $$unsorted)) (=> (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A_1) X_35) (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A_7) A_19)) (=> (tptp.hBOOL (tptp.hAPP_H513860823e_bool (tptp.finite1935632226_state F_1 A_7 A_19) X_1)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state A_7) A_19)))))))) (forall ((F_1 $$unsorted) (A_1 $$unsorted) (X_35 $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_H1421470952a_bool (tptp.finite1537818352iple_a F_1 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a A_1) X_35)) X_1)) (not (forall ((A_7 $$unsorted) (A_19 $$unsorted)) (=> (= (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a A_1) X_35) (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a A_7) A_19)) (=> (tptp.hBOOL (tptp.hAPP_H1421470952a_bool (tptp.finite2010942150iple_a F_1 A_7 A_19) X_1)) (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a A_7) A_19)))))))) (forall ((Ca $$unsorted)) (= (tptp.hoare_Mirabelle_MGT Ca) (tptp.hoare_1575745797_state tptp.fequal_state Ca (tptp.evalc Ca)))) (forall ((C_2 $$unsorted) (S_1 $$unsorted) (T $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool (tptp.evalc C_2) S_1) T)) (exists ((N_1 $$unsorted)) (tptp.hBOOL (tptp.evaln C_2 S_1 N_1 T))))) (forall ((F_1 $$unsorted) (A1 $$unsorted) (A2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.finite_fold1Set_nat F_1 A1) A2)) (exists ((A_7 $$unsorted) (A_19 $$unsorted) (X_2 $$unsorted)) (and (= A1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_7) A_19)) (= A2 X_2) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.finite929467206at_nat F_1 A_7 A_19) X_2)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_7) A_19))))))) (forall ((F_1 $$unsorted) (A1 $$unsorted) (A2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_H513860823e_bool (tptp.finite9525415_state F_1 A1) A2)) (exists ((A_7 $$unsorted) (A_19 $$unsorted) (X_2 $$unsorted)) (and (= A1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A_7) A_19)) (= A2 X_2) (tptp.hBOOL (tptp.hAPP_H513860823e_bool (tptp.finite1935632226_state F_1 A_7 A_19) X_2)) (not (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state A_7) A_19))))))) (forall ((F_1 $$unsorted) (A1 $$unsorted) (A2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_H1421470952a_bool (tptp.finite1537818352iple_a F_1 A1) A2)) (exists ((A_7 $$unsorted) (A_19 $$unsorted) (X_2 $$unsorted)) (and (= A1 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a A_7) A_19)) (= A2 X_2) (tptp.hBOOL (tptp.hAPP_H1421470952a_bool (tptp.finite2010942150iple_a F_1 A_7 A_19) X_2)) (not (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a A_7) A_19))))))) (forall ((F_1 $$unsorted) (Z_2 $$unsorted) (A1 $$unsorted) (A2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_H1421470952a_bool (tptp.finite2010942150iple_a F_1 Z_2 A1) A2)) (or (and (= A1 tptp.bot_bo1181479936a_bool) (= A2 Z_2)) (exists ((X_2 $$unsorted) (A_19 $$unsorted) (Y_11 $$unsorted)) (and (= A1 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a X_2) A_19)) (= A2 (tptp.hAPP_H678412245iple_a (tptp.hAPP_H1455657330iple_a F_1 X_2) Y_11)) (not (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a X_2) A_19))) (tptp.hBOOL (tptp.hAPP_H1421470952a_bool (tptp.finite2010942150iple_a F_1 Z_2 A_19) Y_11))))))) (forall ((C2 $$unsorted) (S2 $$unsorted) (N2 $$unsorted) (T2 $$unsorted) (C1 $$unsorted) (S1 $$unsorted) (N1 $$unsorted) (T1 $$unsorted)) (=> (tptp.hBOOL (tptp.evaln C1 S1 N1 T1)) (=> (tptp.hBOOL (tptp.evaln C2 S2 N2 T2)) (exists ((N_1 $$unsorted)) (and (tptp.hBOOL (tptp.evaln C1 S1 N_1 T1)) (tptp.hBOOL (tptp.evaln C2 S2 N_1 T2))))))) (forall ((N_3 $$unsorted) (Pa $$unsorted) (Ca $$unsorted) (Q_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_H513860823e_bool (tptp.hoare_592710359_state N_3) (tptp.hoare_1575745797_state Pa Ca Q_1))) (forall ((Z_7 $$unsorted) (S_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool Pa Z_7) S_2)) (forall ((S_3 $$unsorted)) (=> (tptp.hBOOL (tptp.evaln Ca S_2 N_3 S_3)) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool Q_1 Z_7) S_3)))))))) (forall ((N_3 $$unsorted) (Pa $$unsorted) (Ca $$unsorted) (Q_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_H1421470952a_bool (tptp.hoare_560051114alid_a N_3) (tptp.hoare_1760757500iple_a Pa Ca Q_1))) (forall ((Z_7 $$unsorted) (S_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_a2036067514e_bool Pa Z_7) S_2)) (forall ((S_3 $$unsorted)) (=> (tptp.hBOOL (tptp.evaln Ca S_2 N_3 S_3)) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_a2036067514e_bool Q_1 Z_7) S_3)))))))) (forall ((X_1 $$unsorted) (A $$unsorted) (F_1 $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.finite988810631ne_nat F_1 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))) (=> (not (= A tptp.bot_bot_fun_nat_bool)) (= (tptp.hAPP_f22106695ol_nat F (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_1 X_1) (tptp.hAPP_f22106695ol_nat F A)))))))) (forall ((X_1 $$unsorted) (A $$unsorted) (F_1 $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.finite774711482_state F_1 F)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state A)) (=> (not (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_1) A))) (=> (not (= A tptp.bot_bo1055319631e_bool)) (= (tptp.hAPP_f2143211163_state F (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state X_1) A)) (tptp.hAPP_H563960305_state (tptp.hAPP_H521649881_state F_1 X_1) (tptp.hAPP_f2143211163_state F A)))))))) (forall ((X_1 $$unsorted) (A $$unsorted) (F_1 $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.finite1669978781iple_a F_1 F)) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool tptp.finite1655202547iple_a A)) (=> (not (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a X_1) A))) (=> (not (= A tptp.bot_bo1181479936a_bool)) (= (tptp.hAPP_f124283079iple_a F (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a X_1) A)) (tptp.hAPP_H678412245iple_a (tptp.hAPP_H1455657330iple_a F_1 X_1) (tptp.hAPP_f124283079iple_a F A)))))))) (forall ((Q_1 $$unsorted) (Pa $$unsorted)) (=> (or (tptp.hBOOL (tptp.hAPP_f540970102l_bool tptp.finite1655202547iple_a (tptp.collec268032053iple_a Pa))) (tptp.hBOOL (tptp.hAPP_f540970102l_bool tptp.finite1655202547iple_a (tptp.collec268032053iple_a Q_1)))) (tptp.hBOOL (tptp.hAPP_f540970102l_bool tptp.finite1655202547iple_a (tptp.collec268032053iple_a (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1203760810a_bool tptp.cOMBS_1148211387l_bool (tptp.hAPP_f997599971l_bool (tptp.hAPP_f439164429l_bool tptp.cOMBB_1782929690iple_a tptp.fconj) Pa)) Q_1)))))) (forall ((Q_1 $$unsorted) (Pa $$unsorted)) (=> (or (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.collect_nat Pa))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.collect_nat Q_1)))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (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_f54304608l_bool tptp.finite_finite_nat tptp.bot_bot_fun_nat_bool)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state tptp.bot_bo1055319631e_bool)) (tptp.hBOOL (tptp.hAPP_f540970102l_bool tptp.finite1655202547iple_a tptp.bot_bo1181479936a_bool)) (forall ((A_1 $$unsorted) (A $$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_1) A))))) (forall ((A_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state A)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A_1) A))))) (forall ((A_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool tptp.finite1655202547iple_a A)) (tptp.hBOOL (tptp.hAPP_f540970102l_bool tptp.finite1655202547iple_a (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a A_1) A))))) (forall ((Pa $$unsorted) (Q_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f540970102l_bool tptp.finite1655202547iple_a (tptp.collec268032053iple_a (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1203760810a_bool tptp.cOMBS_1148211387l_bool (tptp.hAPP_f997599971l_bool (tptp.hAPP_f439164429l_bool tptp.cOMBB_1782929690iple_a tptp.fdisj) Pa)) Q_1)))) (and (tptp.hBOOL (tptp.hAPP_f540970102l_bool tptp.finite1655202547iple_a (tptp.collec268032053iple_a Pa))) (tptp.hBOOL (tptp.hAPP_f540970102l_bool tptp.finite1655202547iple_a (tptp.collec268032053iple_a Q_1)))))) (forall ((Pa $$unsorted) (Q_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (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.collect_nat Pa))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.collect_nat Q_1)))))) (forall ((Glb_3 $$unsorted) (Glb_2 $$unsorted)) (=> (and (tptp.is_glb Glb_3) (tptp.is_glb Glb_2)) (= (= (tptp.glb Glb_3) (tptp.glb Glb_2)) (= Glb_3 Glb_2)))) (forall ((A_1 $$unsorted) (A $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_1) A))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)))) (forall ((A_1 $$unsorted) (A $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A_1) A))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state A)))) (forall ((A_1 $$unsorted) (A $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f540970102l_bool tptp.finite1655202547iple_a (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a A_1) A))) (tptp.hBOOL (tptp.hAPP_f540970102l_bool tptp.finite1655202547iple_a A)))) (forall ((Loc_1 $$unsorted) (Glb_1 $$unsorted)) (not (= (tptp.loc Loc_1) (tptp.glb Glb_1)))) (forall ((Glb_1 $$unsorted) (Loc_1 $$unsorted)) (not (= (tptp.glb Glb_1) (tptp.loc Loc_1)))) (forall ((A $$unsorted) (F_1 $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.finite988810631ne_nat F_1 F)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (not (= A tptp.bot_bot_fun_nat_bool)) (=> (forall ((X_2 $$unsorted) (Y_11 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat F_1 X_2) Y_11)) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_2) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat Y_11) tptp.bot_bot_fun_nat_bool))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat (tptp.hAPP_f22106695ol_nat F A)) A))))))) (forall ((A $$unsorted) (F_1 $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.finite774711482_state F_1 F)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state A)) (=> (not (= A tptp.bot_bo1055319631e_bool)) (=> (forall ((X_2 $$unsorted) (Y_11 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state (tptp.hAPP_H563960305_state (tptp.hAPP_H521649881_state F_1 X_2) Y_11)) (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state X_2) (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state Y_11) tptp.bot_bo1055319631e_bool))))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state (tptp.hAPP_f2143211163_state F A)) A))))))) (forall ((A $$unsorted) (F_1 $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.finite1669978781iple_a F_1 F)) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool tptp.finite1655202547iple_a A)) (=> (not (= A tptp.bot_bo1181479936a_bool)) (=> (forall ((X_2 $$unsorted) (Y_11 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a (tptp.hAPP_H678412245iple_a (tptp.hAPP_H1455657330iple_a F_1 X_2) Y_11)) (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a X_2) (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a Y_11) tptp.bot_bo1181479936a_bool))))) (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a (tptp.hAPP_f124283079iple_a F A)) A))))))) (forall ((F_1 $$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_1 A) X1)))))) (forall ((F_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool tptp.finite1655202547iple_a A)) (=> (not (= A tptp.bot_bo1181479936a_bool)) (exists ((X1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_H1421470952a_bool (tptp.finite1537818352iple_a F_1 A) X1)))))) (forall ((F_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state A)) (=> (not (= A tptp.bot_bo1055319631e_bool)) (exists ((X1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_H513860823e_bool (tptp.finite9525415_state F_1 A) X1)))))) (forall ((Pa $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat F)) (=> (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)))))) (forall ((Pa $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state F)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool Pa tptp.bot_bo1055319631e_bool)) (=> (forall ((X_2 $$unsorted) (F_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state F_2)) (=> (not (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_2) F_2))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool Pa F_2)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool Pa (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state X_2) F_2))))))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool Pa F)))))) (forall ((Pa $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool tptp.finite1655202547iple_a F)) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool Pa tptp.bot_bo1181479936a_bool)) (=> (forall ((X_2 $$unsorted) (F_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool tptp.finite1655202547iple_a F_2)) (=> (not (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a X_2) F_2))) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool Pa F_2)) (tptp.hBOOL (tptp.hAPP_f540970102l_bool Pa (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a X_2) F_2))))))) (tptp.hBOOL (tptp.hAPP_f540970102l_bool Pa F)))))) (forall ((A_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A_1)) (or (= A_1 tptp.bot_bot_fun_nat_bool) (exists ((A_19 $$unsorted) (A_7 $$unsorted)) (and (= A_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_7) A_19)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A_19))))))) (forall ((A_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state A_1)) (or (= A_1 tptp.bot_bo1055319631e_bool) (exists ((A_19 $$unsorted) (A_7 $$unsorted)) (and (= A_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A_7) A_19)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state A_19))))))) (forall ((A_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f540970102l_bool tptp.finite1655202547iple_a A_1)) (or (= A_1 tptp.bot_bo1181479936a_bool) (exists ((A_19 $$unsorted) (A_7 $$unsorted)) (and (= A_1 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a A_7) A_19)) (tptp.hBOOL (tptp.hAPP_f540970102l_bool tptp.finite1655202547iple_a A_19))))))) (forall ((F_1 $$unsorted) (Z_2 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool tptp.finite1655202547iple_a A)) (exists ((X1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_H1421470952a_bool (tptp.finite2010942150iple_a F_1 Z_2 A) X1))))) (forall ((X_1 $$unsorted) (A $$unsorted) (F_1 $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.finite795500164em_nat F_1 F)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (not (= A tptp.bot_bot_fun_nat_bool)) (= (tptp.hAPP_f22106695ol_nat F (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) A)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat F_1 X_1) (tptp.hAPP_f22106695ol_nat F A))))))) (forall ((X_1 $$unsorted) (A $$unsorted) (F_1 $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.finite506823037_state F_1 F)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state A)) (=> (not (= A tptp.bot_bo1055319631e_bool)) (= (tptp.hAPP_f2143211163_state F (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state X_1) A)) (tptp.hAPP_H563960305_state (tptp.hAPP_H521649881_state F_1 X_1) (tptp.hAPP_f2143211163_state F A))))))) (forall ((X_1 $$unsorted) (A $$unsorted) (F_1 $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.finite950012314iple_a F_1 F)) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool tptp.finite1655202547iple_a A)) (=> (not (= A tptp.bot_bo1181479936a_bool)) (= (tptp.hAPP_f124283079iple_a F (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a X_1) A)) (tptp.hAPP_H678412245iple_a (tptp.hAPP_H1455657330iple_a F_1 X_1) (tptp.hAPP_f124283079iple_a F A))))))) (forall ((Pa $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat F)) (=> (not (= F tptp.bot_bot_fun_nat_bool)) (=> (forall ((X_2 $$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))))))) (forall ((Pa $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state F)) (=> (not (= F tptp.bot_bo1055319631e_bool)) (=> (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool Pa (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state X_2) tptp.bot_bo1055319631e_bool)))) (=> (forall ((X_2 $$unsorted) (F_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state F_2)) (=> (not (= F_2 tptp.bot_bo1055319631e_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_2) F_2))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool Pa F_2)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool Pa (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state X_2) F_2)))))))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool Pa F))))))) (forall ((Pa $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool tptp.finite1655202547iple_a F)) (=> (not (= F tptp.bot_bo1181479936a_bool)) (=> (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f540970102l_bool Pa (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a X_2) tptp.bot_bo1181479936a_bool)))) (=> (forall ((X_2 $$unsorted) (F_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool tptp.finite1655202547iple_a F_2)) (=> (not (= F_2 tptp.bot_bo1181479936a_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a X_2) F_2))) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool Pa F_2)) (tptp.hBOOL (tptp.hAPP_f540970102l_bool Pa (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a X_2) F_2)))))))) (tptp.hBOOL (tptp.hAPP_f540970102l_bool Pa F))))))) (forall ((Y $$unsorted)) (=> (tptp.is_vname Y) (=> (forall ((Glb $$unsorted)) (=> (tptp.is_glb Glb) (not (= Y (tptp.glb Glb))))) (not (forall ((Loc $$unsorted)) (=> (tptp.is_loc Loc) (not (= Y (tptp.loc Loc))))))))) (forall ((X_1 $$unsorted) (A $$unsorted) (F_1 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) tptp.bot_bot_fun_nat_bool)))) (let ((_let_2 (tptp.hAPP_f22106695ol_nat F A))) (let ((_let_3 (= _let_1 tptp.bot_bot_fun_nat_bool))) (=> (tptp.hBOOL (tptp.finite988810631ne_nat F_1 F)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)) (and (=> _let_3 (= _let_2 X_1)) (=> (not _let_3) (= _let_2 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat F_1 X_1) (tptp.hAPP_f22106695ol_nat F _let_1)))))))))))) (forall ((X_1 $$unsorted) (A $$unsorted) (F_1 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.minus_2076558538e_bool A) (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state X_1) tptp.bot_bo1055319631e_bool)))) (let ((_let_2 (tptp.hAPP_f2143211163_state F A))) (let ((_let_3 (= _let_1 tptp.bot_bo1055319631e_bool))) (=> (tptp.hBOOL (tptp.finite774711482_state F_1 F)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state A)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_1) A)) (and (=> _let_3 (= _let_2 X_1)) (=> (not _let_3) (= _let_2 (tptp.hAPP_H563960305_state (tptp.hAPP_H521649881_state F_1 X_1) (tptp.hAPP_f2143211163_state F _let_1)))))))))))) (forall ((X_1 $$unsorted) (A $$unsorted) (F_1 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.minus_469558085a_bool A) (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a X_1) tptp.bot_bo1181479936a_bool)))) (let ((_let_2 (tptp.hAPP_f124283079iple_a F A))) (let ((_let_3 (= _let_1 tptp.bot_bo1181479936a_bool))) (=> (tptp.hBOOL (tptp.finite1669978781iple_a F_1 F)) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool tptp.finite1655202547iple_a A)) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a X_1) A)) (and (=> _let_3 (= _let_2 X_1)) (=> (not _let_3) (= _let_2 (tptp.hAPP_H678412245iple_a (tptp.hAPP_H1455657330iple_a F_1 X_1) (tptp.hAPP_f124283079iple_a F _let_1)))))))))))) (forall ((X_1 $$unsorted) (A $$unsorted) (F_1 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1))) (let ((_let_2 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) (tptp.hAPP_f800510211t_bool _let_1 tptp.bot_bot_fun_nat_bool)))) (let ((_let_3 (tptp.hAPP_f22106695ol_nat F (tptp.hAPP_f800510211t_bool _let_1 A)))) (let ((_let_4 (= _let_2 tptp.bot_bot_fun_nat_bool))) (=> (tptp.hBOOL (tptp.finite988810631ne_nat F_1 F)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (and (=> _let_4 (= _let_3 X_1)) (=> (not _let_4) (= _let_3 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat F_1 X_1) (tptp.hAPP_f22106695ol_nat F _let_2)))))))))))) (forall ((X_1 $$unsorted) (A $$unsorted) (F_1 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state X_1))) (let ((_let_2 (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.minus_2076558538e_bool A) (tptp.hAPP_f921536533e_bool _let_1 tptp.bot_bo1055319631e_bool)))) (let ((_let_3 (tptp.hAPP_f2143211163_state F (tptp.hAPP_f921536533e_bool _let_1 A)))) (let ((_let_4 (= _let_2 tptp.bot_bo1055319631e_bool))) (=> (tptp.hBOOL (tptp.finite774711482_state F_1 F)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state A)) (and (=> _let_4 (= _let_3 X_1)) (=> (not _let_4) (= _let_3 (tptp.hAPP_H563960305_state (tptp.hAPP_H521649881_state F_1 X_1) (tptp.hAPP_f2143211163_state F _let_2)))))))))))) (forall ((X_1 $$unsorted) (A $$unsorted) (F_1 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a X_1))) (let ((_let_2 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.minus_469558085a_bool A) (tptp.hAPP_f1591852335a_bool _let_1 tptp.bot_bo1181479936a_bool)))) (let ((_let_3 (tptp.hAPP_f124283079iple_a F (tptp.hAPP_f1591852335a_bool _let_1 A)))) (let ((_let_4 (= _let_2 tptp.bot_bo1181479936a_bool))) (=> (tptp.hBOOL (tptp.finite1669978781iple_a F_1 F)) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool tptp.finite1655202547iple_a A)) (and (=> _let_4 (= _let_3 X_1)) (=> (not _let_4) (= _let_3 (tptp.hAPP_H678412245iple_a (tptp.hAPP_H1455657330iple_a F_1 X_1) (tptp.hAPP_f124283079iple_a F _let_2)))))))))))) (forall ((Ca $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a Ca))) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.minus_469558085a_bool A) B))) (not (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 B))))))) (forall ((Ca $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat Ca))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) B))) (not (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B))))))) (forall ((B $$unsorted) (Ca $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a Ca))) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 A)) (=> (not (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 B))) (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.minus_469558085a_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) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) B))))) (forall ((Ca $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a Ca))) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.minus_469558085a_bool A) B))) (not (tptp.hBOOL (tptp.hAPP_f540970102l_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_H1840393229l_bool tptp.member1713797107iple_a Ca))) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.minus_469558085a_bool A) B))) (tptp.hBOOL (tptp.hAPP_f540970102l_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_H1840393229l_bool tptp.member1713797107iple_a Ca))) (= (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.minus_469558085a_bool A) B))) (and (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 A)) (not (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 B))))))) (forall ((Ca $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat Ca))) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) B))) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 A)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B))))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f672239281a_bool tptp.cOMBC_1552014468l_bool tptp.member1713797107iple_a))) (= (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.minus_469558085a_bool A) B) (tptp.collec268032053iple_a (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1203760810a_bool tptp.cOMBS_1148211387l_bool (tptp.hAPP_f997599971l_bool (tptp.hAPP_f439164429l_bool tptp.cOMBB_1782929690iple_a tptp.fconj) (tptp.hAPP_f1591852335a_bool _let_1 A))) (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f34030599a_bool tptp.cOMBB_1799513916iple_a tptp.fNot) (tptp.hAPP_f1591852335a_bool _let_1 B))))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f1722879237t_bool tptp.cOMBC_226598744l_bool tptp.member_nat))) (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) B) (tptp.collect_nat (tptp.hAPP_f800510211t_bool (tptp.hAPP_f561022312t_bool tptp.cOMBS_nat_bool_bool (tptp.hAPP_f1146629647l_bool (tptp.hAPP_f1080886329l_bool tptp.cOMBB_1015721476ol_nat tptp.fconj) (tptp.hAPP_f800510211t_bool _let_1 A))) (tptp.hAPP_f800510211t_bool (tptp.hAPP_f894608603t_bool tptp.cOMBB_bool_bool_nat tptp.fNot) (tptp.hAPP_f800510211t_bool _let_1 B))))))) (forall ((A $$unsorted)) (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) A) tptp.bot_bot_fun_nat_bool)) (forall ((A $$unsorted)) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.minus_2076558538e_bool A) A) tptp.bot_bo1055319631e_bool)) (forall ((A $$unsorted)) (= (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.minus_469558085a_bool A) A) tptp.bot_bo1181479936a_bool)) (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_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.minus_2076558538e_bool A) tptp.bot_bo1055319631e_bool) A)) (forall ((A $$unsorted)) (= (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.minus_469558085a_bool A) tptp.bot_bo1181479936a_bool) A)) (forall ((A $$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 $$unsorted)) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.minus_2076558538e_bool tptp.bot_bo1055319631e_bool) A) tptp.bot_bo1055319631e_bool)) (forall ((A $$unsorted)) (= (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.minus_469558085a_bool tptp.bot_bo1181479936a_bool) A) tptp.bot_bo1181479936a_bool)) (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 $$unsorted) (X_1 $$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_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_1) B)) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.minus_2076558538e_bool (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state X_1) A)) B) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.minus_2076558538e_bool A) B)))) (forall ((A $$unsorted) (X_1 $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a X_1) B)) (= (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.minus_469558085a_bool (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a X_1) A)) B) (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.minus_469558085a_bool A) B)))) (forall ((A $$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 $$unsorted)) (let ((_let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.minus_2076558538e_bool A) B))) (let ((_let_2 (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state X_1))) (let ((_let_3 (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.minus_2076558538e_bool (tptp.hAPP_f921536533e_bool _let_2 A)) B))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_1) B)))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (tptp.hAPP_f921536533e_bool _let_2 _let_1))))))))) (forall ((A $$unsorted) (X_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.minus_469558085a_bool A) B))) (let ((_let_2 (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a X_1))) (let ((_let_3 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.minus_469558085a_bool (tptp.hAPP_f1591852335a_bool _let_2 A)) B))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a X_1) B)))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (tptp.hAPP_f1591852335a_bool _let_2 _let_1))))))))) (forall ((A_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_1))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_1) 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_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A_1))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state A_1) A)) (= (tptp.hAPP_f921536533e_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.minus_2076558538e_bool A) (tptp.hAPP_f921536533e_bool _let_1 tptp.bot_bo1055319631e_bool))) A)))) (forall ((A_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a A_1))) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a A_1) A)) (= (tptp.hAPP_f1591852335a_bool _let_1 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.minus_469558085a_bool A) (tptp.hAPP_f1591852335a_bool _let_1 tptp.bot_bo1181479936a_bool))) 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_H727730819e_bool tptp.insert1835143293_state X_1))) (=> (not (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_1) A))) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.minus_2076558538e_bool (tptp.hAPP_f921536533e_bool _let_1 A)) (tptp.hAPP_f921536533e_bool _let_1 tptp.bot_bo1055319631e_bool)) A)))) (forall ((X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a X_1))) (=> (not (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a X_1) A))) (= (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.minus_469558085a_bool (tptp.hAPP_f1591852335a_bool _let_1 A)) (tptp.hAPP_f1591852335a_bool _let_1 tptp.bot_bo1181479936a_bool)) A)))) (forall ((A_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_1))) (= (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_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A_1))) (= (tptp.hAPP_f921536533e_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.minus_2076558538e_bool A) (tptp.hAPP_f921536533e_bool _let_1 tptp.bot_bo1055319631e_bool))) (tptp.hAPP_f921536533e_bool _let_1 A)))) (forall ((A_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a A_1))) (= (tptp.hAPP_f1591852335a_bool _let_1 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.minus_469558085a_bool A) (tptp.hAPP_f1591852335a_bool _let_1 tptp.bot_bo1181479936a_bool))) (tptp.hAPP_f1591852335a_bool _let_1 A)))) (forall ((A $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_1))) (let ((_let_2 (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A))) (= (tptp.hAPP_f800510211t_bool _let_2 (tptp.hAPP_f800510211t_bool _let_1 B)) (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool (tptp.hAPP_f800510211t_bool _let_2 (tptp.hAPP_f800510211t_bool _let_1 tptp.bot_bot_fun_nat_bool))) B))))) (forall ((A $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A_1))) (let ((_let_2 (tptp.hAPP_f1583986009e_bool tptp.minus_2076558538e_bool A))) (= (tptp.hAPP_f921536533e_bool _let_2 (tptp.hAPP_f921536533e_bool _let_1 B)) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.minus_2076558538e_bool (tptp.hAPP_f921536533e_bool _let_2 (tptp.hAPP_f921536533e_bool _let_1 tptp.bot_bo1055319631e_bool))) B))))) (forall ((A $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a A_1))) (let ((_let_2 (tptp.hAPP_f1026156344a_bool tptp.minus_469558085a_bool A))) (= (tptp.hAPP_f1591852335a_bool _let_2 (tptp.hAPP_f1591852335a_bool _let_1 B)) (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.minus_469558085a_bool (tptp.hAPP_f1591852335a_bool _let_2 (tptp.hAPP_f1591852335a_bool _let_1 tptp.bot_bo1181479936a_bool))) B))))) (forall ((A $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_1))) (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 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A_1))) (let ((_let_2 (tptp.hAPP_f1583986009e_bool tptp.minus_2076558538e_bool A))) (= (tptp.hAPP_f921536533e_bool _let_2 (tptp.hAPP_f921536533e_bool _let_1 B)) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.minus_2076558538e_bool (tptp.hAPP_f921536533e_bool _let_2 B)) (tptp.hAPP_f921536533e_bool _let_1 tptp.bot_bo1055319631e_bool)))))) (forall ((A $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a A_1))) (let ((_let_2 (tptp.hAPP_f1026156344a_bool tptp.minus_469558085a_bool A))) (= (tptp.hAPP_f1591852335a_bool _let_2 (tptp.hAPP_f1591852335a_bool _let_1 B)) (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.minus_469558085a_bool (tptp.hAPP_f1591852335a_bool _let_2 B)) (tptp.hAPP_f1591852335a_bool _let_1 tptp.bot_bo1181479936a_bool)))))) (forall ((A $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A))) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.hAPP_f800510211t_bool _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_1) B)))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.hAPP_f800510211t_bool _let_1 B)))))) (forall ((A $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f1583986009e_bool tptp.minus_2076558538e_bool A))) (= (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state (tptp.hAPP_f921536533e_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A_1) B)))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state (tptp.hAPP_f921536533e_bool _let_1 B)))))) (forall ((A $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f1026156344a_bool tptp.minus_469558085a_bool A))) (= (tptp.hBOOL (tptp.hAPP_f540970102l_bool tptp.finite1655202547iple_a (tptp.hAPP_f1591852335a_bool _let_1 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a A_1) B)))) (tptp.hBOOL (tptp.hAPP_f540970102l_bool tptp.finite1655202547iple_a (tptp.hAPP_f1591852335a_bool _let_1 B)))))) (forall ((X_1 $$unsorted) (A $$unsorted) (F_1 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.hAPP_f124283079iple_a F A))) (=> (tptp.hBOOL (tptp.finite950012314iple_a F_1 F)) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool tptp.finite1655202547iple_a A)) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a X_1) A)) (= (tptp.hAPP_H678412245iple_a (tptp.hAPP_H1455657330iple_a F_1 X_1) _let_1) _let_1)))))) (forall ((X_1 $$unsorted) (A $$unsorted) (F_1 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.hAPP_f22106695ol_nat F A))) (=> (tptp.hBOOL (tptp.finite795500164em_nat F_1 F)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat F_1 X_1) _let_1) _let_1)))))) (forall ((N $$unsorted) (H $$unsorted) (F_1 $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.finite795500164em_nat F_1 F)) (=> (forall ((X_2 $$unsorted) (Y_11 $$unsorted)) (= (tptp.hAPP_nat_nat H (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat F_1 X_2) Y_11)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat F_1 (tptp.hAPP_nat_nat H X_2)) (tptp.hAPP_nat_nat H Y_11)))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat N)) (=> (not (= N tptp.bot_bot_fun_nat_bool)) (= (tptp.hAPP_nat_nat H (tptp.hAPP_f22106695ol_nat F N)) (tptp.hAPP_f22106695ol_nat F (tptp.image_nat_nat H N)))))))) (forall ((N $$unsorted) (H $$unsorted) (F_1 $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.finite506823037_state F_1 F)) (=> (forall ((X_2 $$unsorted) (Y_11 $$unsorted)) (= (tptp.hAPP_H563960305_state H (tptp.hAPP_H563960305_state (tptp.hAPP_H521649881_state F_1 X_2) Y_11)) (tptp.hAPP_H563960305_state (tptp.hAPP_H521649881_state F_1 (tptp.hAPP_H563960305_state H X_2)) (tptp.hAPP_H563960305_state H Y_11)))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state N)) (=> (not (= N tptp.bot_bo1055319631e_bool)) (= (tptp.hAPP_H563960305_state H (tptp.hAPP_f2143211163_state F N)) (tptp.hAPP_f2143211163_state F (tptp.image_650584225_state H N)))))))) (forall ((N $$unsorted) (H $$unsorted) (F_1 $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.finite950012314iple_a F_1 F)) (=> (forall ((X_2 $$unsorted) (Y_11 $$unsorted)) (= (tptp.hAPP_H678412245iple_a H (tptp.hAPP_H678412245iple_a (tptp.hAPP_H1455657330iple_a F_1 X_2) Y_11)) (tptp.hAPP_H678412245iple_a (tptp.hAPP_H1455657330iple_a F_1 (tptp.hAPP_H678412245iple_a H X_2)) (tptp.hAPP_H678412245iple_a H Y_11)))) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool tptp.finite1655202547iple_a N)) (=> (not (= N tptp.bot_bo1181479936a_bool)) (= (tptp.hAPP_H678412245iple_a H (tptp.hAPP_f124283079iple_a F N)) (tptp.hAPP_f124283079iple_a F (tptp.image_306007685iple_a H N)))))))) (forall ((Pa $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool Pa A)) (=> (forall ((A_7 $$unsorted) (A_19 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A_19)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_7) A_19)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool Pa A_19)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool Pa (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A_19) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_7) tptp.bot_bot_fun_nat_bool)))))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool Pa tptp.bot_bot_fun_nat_bool)))))) (forall ((Pa $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state A)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool Pa A)) (=> (forall ((A_7 $$unsorted) (A_19 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state A_19)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state A_7) A_19)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool Pa A_19)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool Pa (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.minus_2076558538e_bool A_19) (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A_7) tptp.bot_bo1055319631e_bool)))))))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool Pa tptp.bot_bo1055319631e_bool)))))) (forall ((Pa $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool tptp.finite1655202547iple_a A)) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool Pa A)) (=> (forall ((A_7 $$unsorted) (A_19 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool tptp.finite1655202547iple_a A_19)) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a A_7) A_19)) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool Pa A_19)) (tptp.hBOOL (tptp.hAPP_f540970102l_bool Pa (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.minus_469558085a_bool A_19) (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a A_7) tptp.bot_bo1181479936a_bool)))))))) (tptp.hBOOL (tptp.hAPP_f540970102l_bool Pa tptp.bot_bo1181479936a_bool)))))) (tptp.hBOOL (tptp.finite1956789438t_bool (tptp.hAPP_f10625010t_bool (tptp.hAPP_f1115950719t_bool tptp.cOMBB_1654519265ol_nat (tptp.hAPP_f1311642927t_bool tptp.cOMBC_646315179t_bool tptp.minus_2067140911t_bool)) (tptp.hAPP_f1570313510t_bool (tptp.hAPP_f688831301t_bool tptp.cOMBC_178881787t_bool tptp.insert_nat) tptp.bot_bot_fun_nat_bool)))) (tptp.hBOOL (tptp.finite1317819144e_bool (tptp.hAPP_f531275309e_bool (tptp.hAPP_f1470644835e_bool tptp.cOMBB_946224375_state (tptp.hAPP_f2049746453e_bool tptp.cOMBC_872426556e_bool tptp.minus_2076558538e_bool)) (tptp.hAPP_f762269719e_bool (tptp.hAPP_f964290431e_bool tptp.cOMBC_488258100e_bool tptp.insert1835143293_state) tptp.bot_bo1055319631e_bool)))) (tptp.hBOOL (tptp.finite419198954a_bool (tptp.hAPP_f485051996a_bool (tptp.hAPP_f2085120383a_bool tptp.cOMBB_2080540641iple_a (tptp.hAPP_f450029403a_bool tptp.cOMBC_314077933a_bool tptp.minus_469558085a_bool)) (tptp.hAPP_f1665407592a_bool (tptp.hAPP_f549683569a_bool tptp.cOMBC_708118077a_bool tptp.insert873085594iple_a) tptp.bot_bo1181479936a_bool)))) (forall ((A_1 $$unsorted) (Z_2 $$unsorted) (A $$unsorted) (Y_7 $$unsorted) (F_1 $$unsorted)) (=> (tptp.hBOOL (tptp.finite1200705745iple_a F_1)) (=> (tptp.hBOOL (tptp.hAPP_H1421470952a_bool (tptp.finite2010942150iple_a F_1 Z_2 A) Y_7)) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a A_1) A)) (exists ((Y_26 $$unsorted)) (and (= Y_7 (tptp.hAPP_H678412245iple_a (tptp.hAPP_H1455657330iple_a F_1 A_1) Y_26)) (tptp.hBOOL (tptp.hAPP_H1421470952a_bool (tptp.finite2010942150iple_a F_1 Z_2 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.minus_469558085a_bool A) (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a A_1) tptp.bot_bo1181479936a_bool))) Y_26)))))))) (forall ((A_1 $$unsorted) (Ba $$unsorted) (A $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.finite929467206at_nat tptp.times_times_nat Ba A) X_1)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_1) A)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat Ba) A))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.finite929467206at_nat tptp.times_times_nat A_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat Ba) (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_1) tptp.bot_bot_fun_nat_bool)))) X_1)))))) (tptp.hBOOL (tptp.finite1956789438t_bool tptp.insert_nat)) (tptp.hBOOL (tptp.finite1317819144e_bool tptp.insert1835143293_state)) (tptp.hBOOL (tptp.finite419198954a_bool tptp.insert873085594iple_a)) (forall ((Y_7 $$unsorted) (Z_2 $$unsorted) (A $$unsorted) (X_1 $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.finite2010942150iple_a F_1 Z_2 A))) (=> (tptp.hBOOL (tptp.finite1200705745iple_a F_1)) (=> (tptp.hBOOL (tptp.hAPP_H1421470952a_bool _let_1 X_1)) (=> (tptp.hBOOL (tptp.hAPP_H1421470952a_bool _let_1 Y_7)) (= Y_7 X_1)))))) (forall ((Z_2 $$unsorted) (Ba $$unsorted) (A $$unsorted) (Y_7 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.finite929467206at_nat tptp.times_times_nat Ba A) Y_7)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat Ba) A))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.finite929467206at_nat tptp.times_times_nat Z_2 (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_2) Y_7)))))) (forall ((Z_2 $$unsorted) (X_1 $$unsorted) (A $$unsorted) (V $$unsorted) (F_1 $$unsorted)) (=> (tptp.hBOOL (tptp.finite1200705745iple_a F_1)) (=> (tptp.hBOOL (tptp.hAPP_H1421470952a_bool (tptp.finite2010942150iple_a F_1 Z_2 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a X_1) A)) V)) (=> (not (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a X_1) A))) (not (forall ((Y_11 $$unsorted)) (=> (= V (tptp.hAPP_H678412245iple_a (tptp.hAPP_H1455657330iple_a F_1 X_1) Y_11)) (not (tptp.hBOOL (tptp.hAPP_H1421470952a_bool (tptp.finite2010942150iple_a F_1 Z_2 A) Y_11)))))))))) (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 ((A_1 $$unsorted) (A $$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_1) 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_1) A)) (tptp.hAPP_f22106695ol_nat (tptp.finite_fold_nat_nat tptp.times_times_nat A_1) A))))) (forall ((F_1 $$unsorted) (A_1 $$unsorted)) (= (tptp.hAPP_f22106695ol_nat (tptp.finite_fold1_nat F_1) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_1) tptp.bot_bot_fun_nat_bool)) A_1)) (forall ((F_1 $$unsorted) (A_1 $$unsorted)) (= (tptp.hAPP_f2143211163_state (tptp.finite1346402327_state F_1) (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A_1) tptp.bot_bo1055319631e_bool)) A_1)) (forall ((F_1 $$unsorted) (A_1 $$unsorted)) (= (tptp.hAPP_f124283079iple_a (tptp.finite1382394752iple_a F_1) (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a A_1) tptp.bot_bo1181479936a_bool)) A_1)) (forall ((A_1 $$unsorted) (G $$unsorted) (F_1 $$unsorted)) (=> (= G (tptp.finite_fold1_nat F_1)) (= (tptp.hAPP_f22106695ol_nat G (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_1) tptp.bot_bot_fun_nat_bool)) A_1))) (forall ((A_1 $$unsorted) (G $$unsorted) (F_1 $$unsorted)) (=> (= G (tptp.finite1346402327_state F_1)) (= (tptp.hAPP_f2143211163_state G (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A_1) tptp.bot_bo1055319631e_bool)) A_1))) (forall ((A_1 $$unsorted) (G $$unsorted) (F_1 $$unsorted)) (=> (= G (tptp.finite1382394752iple_a F_1)) (= (tptp.hAPP_f124283079iple_a G (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a A_1) tptp.bot_bo1181479936a_bool)) A_1))) (forall ((Z_2 $$unsorted) (A $$unsorted) (Y_7 $$unsorted) (F_1 $$unsorted)) (=> (tptp.hBOOL (tptp.finite1200705745iple_a F_1)) (=> (tptp.hBOOL (tptp.hAPP_H1421470952a_bool (tptp.finite2010942150iple_a F_1 Z_2 A) Y_7)) (= (tptp.hAPP_f124283079iple_a (tptp.finite978536264iple_a F_1 Z_2) A) Y_7)))) (forall ((F_1 $$unsorted) (Z_2 $$unsorted) (A $$unsorted)) (= (tptp.hAPP_f124283079iple_a (tptp.finite978536264iple_a F_1 Z_2) A) (tptp.hAPP_f124283079iple_a tptp.the_Ho746640593iple_a (tptp.finite2010942150iple_a F_1 Z_2 A)))) (forall ((A $$unsorted) (F_1 $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.finite988810631ne_nat F_1 F)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (= (tptp.hAPP_f22106695ol_nat F A) (tptp.hAPP_f22106695ol_nat (tptp.finite_fold1_nat F_1) A))))) (forall ((A $$unsorted) (F_1 $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.finite1669978781iple_a F_1 F)) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool tptp.finite1655202547iple_a A)) (= (tptp.hAPP_f124283079iple_a F A) (tptp.hAPP_f124283079iple_a (tptp.finite1382394752iple_a F_1) A))))) (forall ((X_1 $$unsorted) (A $$unsorted) (F_1 $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.finite988810631ne_nat F_1 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 F (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) A)) (tptp.hAPP_f22106695ol_nat (tptp.finite_fold_nat_nat F_1 X_1) A)))))) (forall ((X_1 $$unsorted) (A $$unsorted) (F_1 $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.finite774711482_state F_1 F)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state A)) (=> (not (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_1) A))) (= (tptp.hAPP_f2143211163_state F (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state X_1) A)) (tptp.hAPP_f2143211163_state (tptp.finite202520804_state F_1 X_1) A)))))) (forall ((X_1 $$unsorted) (A $$unsorted) (F_1 $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.finite1669978781iple_a F_1 F)) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool tptp.finite1655202547iple_a A)) (=> (not (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a X_1) A))) (= (tptp.hAPP_f124283079iple_a F (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a X_1) A)) (tptp.hAPP_f124283079iple_a (tptp.finite978536264iple_a F_1 X_1) A)))))) (forall ((A_1 $$unsorted) (A $$unsorted) (F_1 $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.finite795500164em_nat F_1 F)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (= (tptp.hAPP_f22106695ol_nat F (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_1) A)) (tptp.hAPP_f22106695ol_nat (tptp.finite_fold_nat_nat F_1 A_1) A))))) (forall ((A_1 $$unsorted) (A $$unsorted) (F_1 $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.finite506823037_state F_1 F)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state A)) (= (tptp.hAPP_f2143211163_state F (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A_1) A)) (tptp.hAPP_f2143211163_state (tptp.finite202520804_state F_1 A_1) A))))) (forall ((A_1 $$unsorted) (A $$unsorted) (F_1 $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.finite950012314iple_a F_1 F)) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool tptp.finite1655202547iple_a A)) (= (tptp.hAPP_f124283079iple_a F (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a A_1) A)) (tptp.hAPP_f124283079iple_a (tptp.finite978536264iple_a F_1 A_1) A))))) (forall ((Z_2 $$unsorted) (A $$unsorted) (F_1 $$unsorted)) (=> (tptp.hBOOL (tptp.finite1200705745iple_a F_1)) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool tptp.finite1655202547iple_a A)) (tptp.hBOOL (tptp.hAPP_H1421470952a_bool (tptp.finite2010942150iple_a F_1 Z_2 A) (tptp.hAPP_f124283079iple_a (tptp.finite978536264iple_a F_1 Z_2) A)))))) (forall ((F_1 $$unsorted) (A $$unsorted)) (= (tptp.hAPP_f124283079iple_a (tptp.finite1382394752iple_a F_1) A) (tptp.hAPP_f124283079iple_a tptp.the_Ho746640593iple_a (tptp.finite1537818352iple_a F_1 A)))) (forall ((B $$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 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state A)) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.minus_2076558538e_bool B) A) (tptp.hAPP_f921536533e_bool (tptp.finite512563852e_bool (tptp.hAPP_f531275309e_bool (tptp.hAPP_f1470644835e_bool tptp.cOMBB_946224375_state (tptp.hAPP_f2049746453e_bool tptp.cOMBC_872426556e_bool tptp.minus_2076558538e_bool)) (tptp.hAPP_f762269719e_bool (tptp.hAPP_f964290431e_bool tptp.cOMBC_488258100e_bool tptp.insert1835143293_state) tptp.bot_bo1055319631e_bool)) B) A)))) (forall ((B $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool tptp.finite1655202547iple_a A)) (= (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.minus_469558085a_bool B) A) (tptp.hAPP_f1591852335a_bool (tptp.finite1979045230a_bool (tptp.hAPP_f485051996a_bool (tptp.hAPP_f2085120383a_bool tptp.cOMBB_2080540641iple_a (tptp.hAPP_f450029403a_bool tptp.cOMBC_314077933a_bool tptp.minus_469558085a_bool)) (tptp.hAPP_f1665407592a_bool (tptp.hAPP_f549683569a_bool tptp.cOMBC_708118077a_bool tptp.insert873085594iple_a) tptp.bot_bo1181479936a_bool)) B) A)))) (forall ((A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (not (= A tptp.bot_bot_fun_nat_bool)) (=> (forall ((X_2 $$unsorted) (Y_11 $$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_11)) (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_11) 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 $$unsorted) (F_1 $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.big_se275732192ig_nat F_1 F)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (= (tptp.hAPP_f22106695ol_nat F A) (tptp.hAPP_f22106695ol_nat (tptp.finite_fold1_nat F_1) A))))) (forall ((B $$unsorted) (A $$unsorted) (F_1 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.hAPP_f22106695ol_nat F A))) (=> (tptp.hBOOL (tptp.finite795500164em_nat F_1 F)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (not (= B tptp.bot_bot_fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool B) A)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat F_1 (tptp.hAPP_f22106695ol_nat F B)) _let_1) _let_1))))))) (forall ((B $$unsorted) (A $$unsorted) (F_1 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.hAPP_f2143211163_state F A))) (=> (tptp.hBOOL (tptp.finite506823037_state F_1 F)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state A)) (=> (not (= B tptp.bot_bo1055319631e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool B) A)) (= (tptp.hAPP_H563960305_state (tptp.hAPP_H521649881_state F_1 (tptp.hAPP_f2143211163_state F B)) _let_1) _let_1))))))) (forall ((B $$unsorted) (A $$unsorted) (F_1 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.hAPP_f124283079iple_a F A))) (=> (tptp.hBOOL (tptp.finite950012314iple_a F_1 F)) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool tptp.finite1655202547iple_a A)) (=> (not (= B tptp.bot_bo1181479936a_bool)) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_f430043647l_bool tptp.ord_le1908022732a_bool B) A)) (= (tptp.hAPP_H678412245iple_a (tptp.hAPP_H1455657330iple_a F_1 (tptp.hAPP_f124283079iple_a F B)) _let_1) _let_1))))))) (forall ((X_34 $$unsorted)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_34) X_34))) (forall ((Ca $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a Ca))) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_f430043647l_bool tptp.ord_le1908022732a_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 B)))))) (forall ((Ca $$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 $$unsorted) (Ca $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a Ca))) (=> (=> (not (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 B))) (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 A))) (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.semila1498788770a_bool A) B)))))) (forall ((A $$unsorted) (Ca $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat Ca))) (=> (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 A))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.semila465093516t_bool A) B)))))) (forall ((Ca $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a Ca))) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.semila1498788770a_bool A) B))) (=> (not (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 A))) (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 B)))))) (forall ((Ca $$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.semila465093516t_bool A) B))) (=> (not (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_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool tptp.bot_bo1055319631e_bool) A))) (forall ((A $$unsorted)) (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_f430043647l_bool tptp.ord_le1908022732a_bool tptp.bot_bo1181479936a_bool) A))) (forall ((A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool (tptp.collect_fun_nat_bool (tptp.hAPP_f103356543l_bool (tptp.hAPP_f643944041l_bool tptp.cOMBC_1693257480l_bool tptp.ord_le1568362934t_bool) A)))))) (forall ((Ba $$unsorted) (A_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_1) A)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.semila972727038up_nat A_1) Ba)) (tptp.hAPP_f22106695ol_nat (tptp.finite_fold_nat_nat tptp.semila972727038up_nat Ba) A)))))) (forall ((A $$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 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool A) tptp.bot_bo1055319631e_bool)) (= A tptp.bot_bo1055319631e_bool))) (forall ((A $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_f430043647l_bool tptp.ord_le1908022732a_bool A) tptp.bot_bo1181479936a_bool)) (= A tptp.bot_bo1181479936a_bool))) (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 $$unsorted) (B $$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 ((B $$unsorted) (A_1 $$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_1) B)))) (forall ((B $$unsorted) (A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool B) (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A_1) B)))) (forall ((B $$unsorted) (A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_f430043647l_bool tptp.ord_le1908022732a_bool B) (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a A_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_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state X_1) A)) B)) (and (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_1) B)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool A) B))))) (forall ((X_1 $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_f430043647l_bool tptp.ord_le1908022732a_bool (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a X_1) A)) B)) (and (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a X_1) B)) (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_f430043647l_bool tptp.ord_le1908022732a_bool A) B))))) (forall ((B $$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 $$unsorted)) (let ((_let_1 (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool A))) (=> (not (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_1) A))) (= (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state X_1) B))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 B)))))) (forall ((B $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f430043647l_bool tptp.ord_le1908022732a_bool A))) (=> (not (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a X_1) A))) (= (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a X_1) B))) (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 B)))))) (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_f854625363l_bool tptp.ord_le1720872323e_bool A))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 B)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state Ba) B)))))) (forall ((Ba $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f430043647l_bool tptp.ord_le1908022732a_bool A))) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 B)) (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a Ba) B)))))) (forall ((A_1 $$unsorted) (C $$unsorted) (D_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_1))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool C) D_2)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_f800510211t_bool _let_1 C)) (tptp.hAPP_f800510211t_bool _let_1 D_2)))))) (forall ((A_1 $$unsorted) (C $$unsorted) (D_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A_1))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool C) D_2)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool (tptp.hAPP_f921536533e_bool _let_1 C)) (tptp.hAPP_f921536533e_bool _let_1 D_2)))))) (forall ((A_1 $$unsorted) (C $$unsorted) (D_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a A_1))) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_f430043647l_bool tptp.ord_le1908022732a_bool C) D_2)) (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_f430043647l_bool tptp.ord_le1908022732a_bool (tptp.hAPP_f1591852335a_bool _let_1 C)) (tptp.hAPP_f1591852335a_bool _let_1 D_2)))))) (forall ((A_18 $$unsorted) (B_14 $$unsorted) (X_33 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.semila972727038up_nat A_18) B_14)) X_33)) (not (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_18) X_33)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat B_14) X_33))))))) (forall ((B_13 $$unsorted) (D_1 $$unsorted) (A_17 $$unsorted) (C_7 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_17) C_7)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat B_13) D_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.semila972727038up_nat A_17) B_13)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.semila972727038up_nat C_7) D_1)))))) (forall ((Z_6 $$unsorted) (Y_25 $$unsorted) (X_32 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_25) X_32)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Z_6) X_32)) (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.semila972727038up_nat Y_25) Z_6)) X_32))))) (forall ((B_12 $$unsorted) (A_16 $$unsorted) (X_31 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_16) X_31)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat B_12) X_31)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.semila972727038up_nat A_16) B_12)) X_31))))) (forall ((Y_24 $$unsorted) (X_30 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_24) X_30)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.semila972727038up_nat X_30) Y_24) X_30))) (forall ((X_29 $$unsorted) (Y_23 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_29) Y_23)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.semila972727038up_nat X_29) Y_23) Y_23))) (forall ((A_15 $$unsorted) (X_28 $$unsorted) (B_11 $$unsorted)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_28))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_11)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.semila972727038up_nat A_15) B_11)))))) (forall ((B_10 $$unsorted) (X_27 $$unsorted) (A_14 $$unsorted)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_27))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A_14)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.semila972727038up_nat A_14) B_10)))))) (forall ((X_1 $$unsorted) (Y_7 $$unsorted) (Z_2 $$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.semila972727038up_nat X_1) Y_7)) Z_2)) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_1) Z_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_7) Z_2))))) (forall ((X_1 $$unsorted) (Y_7 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_1) Y_7)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.semila972727038up_nat X_1) Y_7) Y_7))) (forall ((Y_22 $$unsorted) (X_26 $$unsorted)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_22) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.semila972727038up_nat X_26) Y_22)))) (forall ((Y_21 $$unsorted) (X_25 $$unsorted)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_21) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.semila972727038up_nat X_25) Y_21)))) (forall ((X_24 $$unsorted) (Y_20 $$unsorted)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_24) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.semila972727038up_nat X_24) Y_20)))) (forall ((X_23 $$unsorted) (Y_19 $$unsorted)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_23) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.semila972727038up_nat X_23) Y_19)))) (forall ((X_1 $$unsorted) (Y_7 $$unsorted)) (let ((_let_1 (tptp.hBOOL tptp.bot_bot_bool))) (= (= (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool X_1) Y_7)) _let_1) (and (= (tptp.hBOOL X_1) _let_1) (= (tptp.hBOOL Y_7) _let_1))))) (forall ((X_1 $$unsorted) (Y_7 $$unsorted)) (= (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.semila465093516t_bool X_1) Y_7) tptp.bot_bot_fun_nat_bool) (and (= X_1 tptp.bot_bot_fun_nat_bool) (= Y_7 tptp.bot_bot_fun_nat_bool)))) (forall ((X_1 $$unsorted) (Y_7 $$unsorted)) (= (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool X_1) Y_7) tptp.bot_bo1055319631e_bool) (and (= X_1 tptp.bot_bo1055319631e_bool) (= Y_7 tptp.bot_bo1055319631e_bool)))) (forall ((X_1 $$unsorted) (Y_7 $$unsorted)) (= (= (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.semila1498788770a_bool X_1) Y_7) tptp.bot_bo1181479936a_bool) (and (= X_1 tptp.bot_bo1181479936a_bool) (= Y_7 tptp.bot_bo1181479936a_bool)))) (forall ((X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool X_1) tptp.bot_bot_bool)) (tptp.hBOOL X_1))) (forall ((X_1 $$unsorted)) (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.semila465093516t_bool X_1) tptp.bot_bot_fun_nat_bool) X_1)) (forall ((X_1 $$unsorted)) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool X_1) tptp.bot_bo1055319631e_bool) X_1)) (forall ((X_1 $$unsorted)) (= (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.semila1498788770a_bool X_1) tptp.bot_bo1181479936a_bool) X_1)) (forall ((X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool tptp.bot_bot_bool) X_1)) (tptp.hBOOL X_1))) (forall ((X_1 $$unsorted)) (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.semila465093516t_bool tptp.bot_bot_fun_nat_bool) X_1) X_1)) (forall ((X_1 $$unsorted)) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool tptp.bot_bo1055319631e_bool) X_1) X_1)) (forall ((X_1 $$unsorted)) (= (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.semila1498788770a_bool tptp.bot_bo1181479936a_bool) X_1) X_1)) (forall ((B $$unsorted)) (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.semila465093516t_bool tptp.bot_bot_fun_nat_bool) B) B)) (forall ((B $$unsorted)) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool tptp.bot_bo1055319631e_bool) B) B)) (forall ((B $$unsorted)) (= (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.semila1498788770a_bool tptp.bot_bo1181479936a_bool) B) B)) (forall ((A $$unsorted)) (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.semila465093516t_bool A) tptp.bot_bot_fun_nat_bool) A)) (forall ((A $$unsorted)) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool A) tptp.bot_bo1055319631e_bool) A)) (forall ((A $$unsorted)) (= (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.semila1498788770a_bool A) tptp.bot_bo1181479936a_bool) A)) (forall ((A $$unsorted) (B $$unsorted)) (= (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.semila465093516t_bool A) B) tptp.bot_bot_fun_nat_bool) (and (= A tptp.bot_bot_fun_nat_bool) (= B tptp.bot_bot_fun_nat_bool)))) (forall ((A $$unsorted) (B $$unsorted)) (= (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool A) B) tptp.bot_bo1055319631e_bool) (and (= A tptp.bot_bo1055319631e_bool) (= B tptp.bot_bo1055319631e_bool)))) (forall ((A $$unsorted) (B $$unsorted)) (= (= (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.semila1498788770a_bool A) B) tptp.bot_bo1181479936a_bool) (and (= A tptp.bot_bo1181479936a_bool) (= B tptp.bot_bo1181479936a_bool)))) (forall ((F $$unsorted) (Ga $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.semila465093516t_bool F) Ga))) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat F)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat Ga))))) (forall ((Ga $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat F)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat Ga)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.semila465093516t_bool F) Ga)))))) (forall ((X_22 $$unsorted) (Y_18 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_22) Y_18))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_18) X_22)))) (forall ((Z_5 $$unsorted) (Y_17 $$unsorted) (X_21 $$unsorted)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Z_5))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_17) X_21)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Y_17)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 X_21)))))) (forall ((Y_16 $$unsorted) (X_20 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_16) X_20)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_20) Y_16)) (= X_20 Y_16)))) (forall ((Z_4 $$unsorted) (X_19 $$unsorted) (Y_15 $$unsorted)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_19))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Y_15)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_15) Z_4)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Z_4)))))) (forall ((X_18 $$unsorted) (Y_14 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_18) Y_14)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_14) X_18)) (= X_18 Y_14)))) (forall ((C_6 $$unsorted) (B_9 $$unsorted) (A_13 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat B_9) A_13)) (=> (= B_9 C_6) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat C_6) A_13))))) (forall ((C_5 $$unsorted) (A_12 $$unsorted) (B_8 $$unsorted)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_12))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_8)) (=> (= B_8 C_5) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 C_5)))))) (forall ((C_4 $$unsorted) (A_11 $$unsorted) (B_7 $$unsorted)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat C_4))) (=> (= A_11 B_7) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_7)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A_11)))))) (forall ((C_3 $$unsorted) (A_10 $$unsorted) (B_6 $$unsorted)) (=> (= A_10 B_6) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat B_6) C_3)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_10) C_3))))) (forall ((Y_7 $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_7) X_1)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_1) Y_7)) (= X_1 Y_7)))) (forall ((X_17 $$unsorted) (Y_13 $$unsorted)) (=> (= X_17 Y_13) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_17) Y_13)))) (forall ((X_1 $$unsorted) (Y_7 $$unsorted)) (= (= X_1 Y_7) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_1) Y_7)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_7) X_1))))) (forall ((X_16 $$unsorted) (Y_12 $$unsorted)) (or (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_16) Y_12)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_12) X_16)))) (forall ((Pa $$unsorted) (Q_1 $$unsorted)) (= (tptp.collec268032053iple_a (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1203760810a_bool tptp.cOMBS_1148211387l_bool (tptp.hAPP_f997599971l_bool (tptp.hAPP_f439164429l_bool tptp.cOMBB_1782929690iple_a tptp.fdisj) Pa)) Q_1)) (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.semila1498788770a_bool (tptp.collec268032053iple_a Pa)) (tptp.collec268032053iple_a Q_1)))) (forall ((Pa $$unsorted) (Q_1 $$unsorted)) (= (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)) (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.semila465093516t_bool (tptp.collect_nat Pa)) (tptp.collect_nat Q_1)))) (forall ((X_1 $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a X_1))) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_f430043647l_bool tptp.ord_le1908022732a_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 B)))))) (forall ((X_1 $$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 $$unsorted)) (let ((_let_1 (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a X_1))) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 A)) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_f430043647l_bool tptp.ord_le1908022732a_bool A) B)) (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 B)))))) (forall ((B $$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 $$unsorted)) (let ((_let_1 (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a X_1))) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_f430043647l_bool tptp.ord_le1908022732a_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 B)))))) (forall ((X_1 $$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 $$unsorted) (Ca $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a Ca))) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 B)) (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.semila1498788770a_bool A) B)))))) (forall ((A $$unsorted) (Ca $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat Ca))) (=> (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.semila465093516t_bool A) B)))))) (forall ((B $$unsorted) (Ca $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a Ca))) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.semila1498788770a_bool A) B)))))) (forall ((B $$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)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.semila465093516t_bool A) B)))))) (forall ((Ca $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a Ca))) (= (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.semila1498788770a_bool A) B))) (or (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 B)))))) (forall ((Ca $$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.semila465093516t_bool A) B))) (or (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B)))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f672239281a_bool tptp.cOMBC_1552014468l_bool tptp.member1713797107iple_a))) (= (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.semila1498788770a_bool A) B) (tptp.collec268032053iple_a (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1203760810a_bool tptp.cOMBS_1148211387l_bool (tptp.hAPP_f997599971l_bool (tptp.hAPP_f439164429l_bool tptp.cOMBB_1782929690iple_a tptp.fdisj) (tptp.hAPP_f1591852335a_bool _let_1 A))) (tptp.hAPP_f1591852335a_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.semila465093516t_bool A) B) (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_f800510211t_bool _let_1 A))) (tptp.hAPP_f800510211t_bool _let_1 B)))))) (forall ((R_1 $$unsorted) (S $$unsorted)) (let ((_let_1 (tptp.hAPP_f672239281a_bool tptp.cOMBC_1552014468l_bool tptp.member1713797107iple_a))) (= (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_f430043647l_bool tptp.ord_le1908022732a_bool (tptp.hAPP_f1591852335a_bool _let_1 R_1)) (tptp.hAPP_f1591852335a_bool _let_1 S))) (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_f430043647l_bool tptp.ord_le1908022732a_bool R_1) S))))) (forall ((R_1 $$unsorted) (S $$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))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool R_1) S))))) (forall ((R_1 $$unsorted) (S $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_f672239281a_bool tptp.cOMBC_1552014468l_bool tptp.member1713797107iple_a))) (= (tptp.hBOOL (tptp.hAPP_H1421470952a_bool (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.semila1498788770a_bool (tptp.hAPP_f1591852335a_bool _let_1 R_1)) (tptp.hAPP_f1591852335a_bool _let_1 S)) X_2)) (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a X_2) (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.semila1498788770a_bool R_1) S)))))) (forall ((R_1 $$unsorted) (S $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1722879237t_bool tptp.cOMBC_226598744l_bool tptp.member_nat))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.semila465093516t_bool (tptp.hAPP_f800510211t_bool _let_1 R_1)) (tptp.hAPP_f800510211t_bool _let_1 S)) X_2)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.semila465093516t_bool R_1) S)))))) (forall ((A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool tptp.bot_bot_bool) A_1))) (forall ((A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool tptp.bot_bot_fun_nat_bool) A_1))) (forall ((A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool tptp.bot_bo1055319631e_bool) A_1))) (forall ((A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_f430043647l_bool tptp.ord_le1908022732a_bool tptp.bot_bo1181479936a_bool) A_1))) (forall ((A_9 $$unsorted)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.bot_bot_nat) A_9))) (forall ((A_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool A_1) tptp.bot_bot_bool)) (= (tptp.hBOOL A_1) (tptp.hBOOL tptp.bot_bot_bool)))) (forall ((A_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A_1) tptp.bot_bot_fun_nat_bool)) (= A_1 tptp.bot_bot_fun_nat_bool))) (forall ((A_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool A_1) tptp.bot_bo1055319631e_bool)) (= A_1 tptp.bot_bo1055319631e_bool))) (forall ((A_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_f430043647l_bool tptp.ord_le1908022732a_bool A_1) tptp.bot_bo1181479936a_bool)) (= A_1 tptp.bot_bo1181479936a_bool))) (forall ((A_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_1) tptp.bot_bot_nat)) (= A_1 tptp.bot_bot_nat))) (forall ((A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool A_1) tptp.bot_bot_bool)) (= (tptp.hBOOL A_1) (tptp.hBOOL tptp.bot_bot_bool)))) (forall ((A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A_1) tptp.bot_bot_fun_nat_bool)) (= A_1 tptp.bot_bot_fun_nat_bool))) (forall ((A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool A_1) tptp.bot_bo1055319631e_bool)) (= A_1 tptp.bot_bo1055319631e_bool))) (forall ((A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_f430043647l_bool tptp.ord_le1908022732a_bool A_1) tptp.bot_bo1181479936a_bool)) (= A_1 tptp.bot_bo1181479936a_bool))) (forall ((A_8 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_8) tptp.bot_bot_nat)) (= A_8 tptp.bot_bot_nat))) (forall ((A $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f1730770594t_bool tptp.semila465093516t_bool A))) (let ((_let_2 (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_1))) (= (tptp.hAPP_f800510211t_bool _let_1 (tptp.hAPP_f800510211t_bool _let_2 B)) (tptp.hAPP_f800510211t_bool _let_2 (tptp.hAPP_f800510211t_bool _let_1 B)))))) (forall ((A $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool A))) (let ((_let_2 (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A_1))) (= (tptp.hAPP_f921536533e_bool _let_1 (tptp.hAPP_f921536533e_bool _let_2 B)) (tptp.hAPP_f921536533e_bool _let_2 (tptp.hAPP_f921536533e_bool _let_1 B)))))) (forall ((A $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f1026156344a_bool tptp.semila1498788770a_bool A))) (let ((_let_2 (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a A_1))) (= (tptp.hAPP_f1591852335a_bool _let_1 (tptp.hAPP_f1591852335a_bool _let_2 B)) (tptp.hAPP_f1591852335a_bool _let_2 (tptp.hAPP_f1591852335a_bool _let_1 B)))))) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_1))) (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.semila465093516t_bool (tptp.hAPP_f800510211t_bool _let_1 B)) C) (tptp.hAPP_f800510211t_bool _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.semila465093516t_bool B) C))))) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A_1))) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool (tptp.hAPP_f921536533e_bool _let_1 B)) C) (tptp.hAPP_f921536533e_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool B) C))))) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a A_1))) (= (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.semila1498788770a_bool (tptp.hAPP_f1591852335a_bool _let_1 B)) C) (tptp.hAPP_f1591852335a_bool _let_1 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.semila1498788770a_bool B) C))))) (forall ((Ts $$unsorted) (Ga $$unsorted) (Ts_1 $$unsorted)) (let ((_let_1 (tptp.hoare_659004819_state Ga))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 Ts_1)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool Ts) Ts_1)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 Ts)))))) (forall ((Ts $$unsorted) (Ga $$unsorted) (Ts_1 $$unsorted)) (let ((_let_1 (tptp.hoare_606018542rivs_a Ga))) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 Ts_1)) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_f430043647l_bool tptp.ord_le1908022732a_bool Ts) Ts_1)) (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 Ts)))))) (forall ((Ts $$unsorted) (Ga $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool Ts) Ga)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hoare_659004819_state Ga) Ts)))) (forall ((Ts $$unsorted) (Ga $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_f430043647l_bool tptp.ord_le1908022732a_bool Ts) Ga)) (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hoare_606018542rivs_a Ga) Ts)))) (forall ((A_1 $$unsorted) (B $$unsorted)) (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_1) B) (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.semila465093516t_bool (tptp.collect_nat (tptp.hAPP_n1699378549t_bool (tptp.hAPP_f229349961t_bool tptp.cOMBC_nat_nat_bool tptp.fequal_nat) A_1))) B))) (forall ((A_1 $$unsorted) (B $$unsorted)) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A_1) B) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool (tptp.collec727977250_state (tptp.hAPP_H1645666623e_bool (tptp.hAPP_f262880489e_bool tptp.cOMBC_1424981238e_bool tptp.fequal1531560888_state) A_1))) B))) (forall ((A_1 $$unsorted) (B $$unsorted)) (= (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a A_1) B) (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.semila1498788770a_bool (tptp.collec268032053iple_a (tptp.hAPP_H1190454433a_bool (tptp.hAPP_f1371755681a_bool tptp.cOMBC_839220826a_bool tptp.fequal879838495iple_a) A_1))) B))) (forall ((A_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_1))) (= (tptp.hAPP_f800510211t_bool _let_1 A) (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.semila465093516t_bool (tptp.hAPP_f800510211t_bool _let_1 tptp.bot_bot_fun_nat_bool)) A)))) (forall ((A_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A_1))) (= (tptp.hAPP_f921536533e_bool _let_1 A) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool (tptp.hAPP_f921536533e_bool _let_1 tptp.bot_bo1055319631e_bool)) A)))) (forall ((A_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a A_1))) (= (tptp.hAPP_f1591852335a_bool _let_1 A) (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.semila1498788770a_bool (tptp.hAPP_f1591852335a_bool _let_1 tptp.bot_bo1181479936a_bool)) A)))) (forall ((Ba $$unsorted) (A_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.finite_fold_nat_nat tptp.semila972727038up_nat Ba))) (=> (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 A_1) A)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.semila972727038up_nat A_1) (tptp.hAPP_f22106695ol_nat _let_1 A)))))) (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.semila465093516t_bool A) B) (tptp.hAPP_f800510211t_bool (tptp.finite1578363458t_bool tptp.insert_nat B) A)))) (forall ((B $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state A)) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool A) B) (tptp.hAPP_f921536533e_bool (tptp.finite512563852e_bool tptp.insert1835143293_state B) A)))) (forall ((B $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool tptp.finite1655202547iple_a A)) (= (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.semila1498788770a_bool A) B) (tptp.hAPP_f1591852335a_bool (tptp.finite1979045230a_bool tptp.insert873085594iple_a B) A)))) (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_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state X_1) tptp.bot_bo1055319631e_bool))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool A) _let_1)) (or (= A tptp.bot_bo1055319631e_bool) (= A _let_1))))) (forall ((A $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a X_1) tptp.bot_bo1181479936a_bool))) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_f430043647l_bool tptp.ord_le1908022732a_bool A) _let_1)) (or (= A tptp.bot_bo1181479936a_bool) (= A _let_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_H727730819e_bool tptp.insert1835143293_state X_1))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.minus_2076558538e_bool A) (tptp.hAPP_f921536533e_bool _let_1 tptp.bot_bo1055319631e_bool))) B)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_1) A)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool A) (tptp.hAPP_f921536533e_bool _let_1 B))))))) (forall ((A $$unsorted) (X_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a X_1))) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_f430043647l_bool tptp.ord_le1908022732a_bool (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.minus_469558085a_bool A) (tptp.hAPP_f1591852335a_bool _let_1 tptp.bot_bo1181479936a_bool))) B)) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a X_1) A)) (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_f430043647l_bool tptp.ord_le1908022732a_bool A) (tptp.hAPP_f1591852335a_bool _let_1 B))))))) (forall ((A $$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 $$unsorted)) (let ((_let_1 (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool A))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_1) A)))) (let ((_let_3 (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state X_1))) (= (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 (tptp.hAPP_f921536533e_bool _let_3 B))) (and (=> _let_2 (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.minus_2076558538e_bool A) (tptp.hAPP_f921536533e_bool _let_3 tptp.bot_bo1055319631e_bool))) B))) (=> (not _let_2) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 B))))))))) (forall ((A $$unsorted) (X_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f430043647l_bool tptp.ord_le1908022732a_bool A))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a X_1) A)))) (let ((_let_3 (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a X_1))) (= (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 (tptp.hAPP_f1591852335a_bool _let_3 B))) (and (=> _let_2 (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_f430043647l_bool tptp.ord_le1908022732a_bool (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.minus_469558085a_bool A) (tptp.hAPP_f1591852335a_bool _let_3 tptp.bot_bo1181479936a_bool))) B))) (=> (not _let_2) (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 B))))))))) (forall ((B $$unsorted) (A $$unsorted) (F_1 $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.finite795500164em_nat F_1 F)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (not (= A tptp.bot_bot_fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat B)) (=> (not (= B tptp.bot_bot_fun_nat_bool)) (= (tptp.hAPP_f22106695ol_nat F (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.semila465093516t_bool A) B)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat F_1 (tptp.hAPP_f22106695ol_nat F A)) (tptp.hAPP_f22106695ol_nat F B))))))))) (forall ((B $$unsorted) (A $$unsorted) (F_1 $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.finite506823037_state F_1 F)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state A)) (=> (not (= A tptp.bot_bo1055319631e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state B)) (=> (not (= B tptp.bot_bo1055319631e_bool)) (= (tptp.hAPP_f2143211163_state F (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool A) B)) (tptp.hAPP_H563960305_state (tptp.hAPP_H521649881_state F_1 (tptp.hAPP_f2143211163_state F A)) (tptp.hAPP_f2143211163_state F B))))))))) (forall ((B $$unsorted) (A $$unsorted) (F_1 $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.finite950012314iple_a F_1 F)) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool tptp.finite1655202547iple_a A)) (=> (not (= A tptp.bot_bo1181479936a_bool)) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool tptp.finite1655202547iple_a B)) (=> (not (= B tptp.bot_bo1181479936a_bool)) (= (tptp.hAPP_f124283079iple_a F (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.semila1498788770a_bool A) B)) (tptp.hAPP_H678412245iple_a (tptp.hAPP_H1455657330iple_a F_1 (tptp.hAPP_f124283079iple_a F A)) (tptp.hAPP_f124283079iple_a F B))))))))) (forall ((Ca $$unsorted) (Ba $$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.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_2) Ba)))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f22106695ol_nat (tptp.finite_fold_nat_nat tptp.semila972727038up_nat Ca) A)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.semila972727038up_nat Ba) Ca)))))) (forall ((Pa $$unsorted) (A $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat F)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool F) A)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool Pa tptp.bot_bot_fun_nat_bool)) (=> (forall ((A_7 $$unsorted) (F_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat A_7))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat F_2)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 A)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 F_2))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool Pa F_2)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool Pa (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_7) F_2))))))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool Pa F))))))) (forall ((Pa $$unsorted) (A $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state F)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool F) A)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool Pa tptp.bot_bo1055319631e_bool)) (=> (forall ((A_7 $$unsorted) (F_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_H248360617l_bool tptp.member1758697444_state A_7))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state F_2)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 A)) (=> (not (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 F_2))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool Pa F_2)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool Pa (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A_7) F_2))))))))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool Pa F))))))) (forall ((Pa $$unsorted) (A $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool tptp.finite1655202547iple_a F)) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_f430043647l_bool tptp.ord_le1908022732a_bool F) A)) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool Pa tptp.bot_bo1181479936a_bool)) (=> (forall ((A_7 $$unsorted) (F_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a A_7))) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool tptp.finite1655202547iple_a F_2)) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 A)) (=> (not (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 F_2))) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool Pa F_2)) (tptp.hBOOL (tptp.hAPP_f540970102l_bool Pa (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a A_7) F_2))))))))) (tptp.hBOOL (tptp.hAPP_f540970102l_bool Pa F))))))) (forall ((B $$unsorted) (A $$unsorted)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a X_2))) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 B))))) (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_f430043647l_bool tptp.ord_le1908022732a_bool A) B)))) (forall ((B $$unsorted) (A $$unsorted)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat X_2))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) B)))) (forall ((M_1 $$unsorted) (C_2 $$unsorted) (S_1 $$unsorted) (N_2 $$unsorted) (T $$unsorted)) (=> (tptp.hBOOL (tptp.evaln C_2 S_1 N_2 T)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_2) M_1)) (tptp.hBOOL (tptp.evaln C_2 S_1 M_1 T))))) (forall ((K $$unsorted)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.hAPP_n1699378549t_bool (tptp.hAPP_f229349961t_bool tptp.cOMBC_nat_nat_bool tptp.ord_less_eq_nat) K))))) (forall ((A $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a Ba) tptp.bot_bo1181479936a_bool))) (let ((_let_2 (tptp.hAPP_f124283079iple_a (tptp.partia1866111638iple_a Ba) A))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_f430043647l_bool tptp.ord_le1908022732a_bool A) _let_1)))) (and (=> _let_3 (= _let_2 Ba)) (=> (not _let_3) (= _let_2 (tptp.hAPP_f124283079iple_a tptp.the_Ho746640593iple_a (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f672239281a_bool tptp.cOMBC_1552014468l_bool tptp.member1713797107iple_a) (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.minus_469558085a_bool A) _let_1)))))))))) (forall ((A $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat Ba) tptp.bot_bot_fun_nat_bool))) (let ((_let_2 (tptp.hAPP_f22106695ol_nat (tptp.partial_flat_lub_nat Ba) A))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) _let_1)))) (and (=> _let_3 (= _let_2 Ba)) (=> (not _let_3) (= _let_2 (tptp.hAPP_f22106695ol_nat tptp.the_nat (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1722879237t_bool tptp.cOMBC_226598744l_bool tptp.member_nat) (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) _let_1)))))))))) (forall ((A $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state Ba) tptp.bot_bo1055319631e_bool))) (let ((_let_2 (tptp.hAPP_f2143211163_state (tptp.partia415982977_state Ba) A))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool A) _let_1)))) (and (=> _let_3 (= _let_2 Ba)) (=> (not _let_3) (= _let_2 (tptp.hAPP_f2143211163_state tptp.the_Ho10452358_state (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1262649863e_bool tptp.cOMBC_764456866l_bool tptp.member1758697444_state) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.minus_2076558538e_bool A) _let_1)))))))))) (forall ((N $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat N)) (exists ((M $$unsorted)) (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_2) M))))))) (forall ((U $$unsorted) (F_1 $$unsorted)) (=> (forall ((N_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_1) (tptp.hAPP_nat_nat F_1 N_1)))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.hAPP_n1699378549t_bool (tptp.hAPP_f229349961t_bool tptp.cOMBC_nat_nat_bool (tptp.hAPP_f618557131t_bool (tptp.hAPP_f1505651103t_bool tptp.cOMBB_800536526ol_nat tptp.ord_less_eq_nat) F_1)) U)))))) (forall ((X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) tptp.bot_bot_fun_nat_bool)))) (let ((_let_2 (tptp.hAPP_f22106695ol_nat tptp.big_la43341705in_nat A))) (let ((_let_3 (= _let_1 tptp.bot_bot_fun_nat_bool))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)) (and (=> _let_3 (= _let_2 X_1)) (=> (not _let_3) (= _let_2 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.semila972727038up_nat X_1) (tptp.hAPP_f22106695ol_nat tptp.big_la43341705in_nat _let_1))))))))))) (forall ((X_1 $$unsorted)) (= (tptp.hAPP_f22106695ol_nat tptp.big_la43341705in_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 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f22106695ol_nat tptp.big_la43341705in_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.semila972727038up_nat X_1) _let_1) _let_1))))) (forall ((A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (= (tptp.hAPP_f22106695ol_nat tptp.big_la43341705in_nat A) (tptp.hAPP_f22106695ol_nat (tptp.finite_fold1_nat tptp.semila972727038up_nat) A)))) (forall ((X_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (not (= A tptp.bot_bot_fun_nat_bool)) (= (tptp.hAPP_f22106695ol_nat tptp.big_la43341705in_nat (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) A)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.semila972727038up_nat X_1) (tptp.hAPP_f22106695ol_nat tptp.big_la43341705in_nat A)))))) (forall ((X_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A))) (=> (not (= A tptp.bot_bot_fun_nat_bool)) (= (tptp.hAPP_f22106695ol_nat tptp.big_la43341705in_nat (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) A)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.semila972727038up_nat X_1) (tptp.hAPP_f22106695ol_nat tptp.big_la43341705in_nat A))))))) (forall ((B $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f22106695ol_nat tptp.big_la43341705in_nat A))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (not (= B tptp.bot_bot_fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool B) A)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.semila972727038up_nat (tptp.hAPP_f22106695ol_nat tptp.big_la43341705in_nat B)) _let_1) _let_1)))))) (forall ((B $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (not (= A tptp.bot_bot_fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat B)) (=> (not (= B tptp.bot_bot_fun_nat_bool)) (= (tptp.hAPP_f22106695ol_nat tptp.big_la43341705in_nat (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.semila465093516t_bool A) B)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.semila972727038up_nat (tptp.hAPP_f22106695ol_nat tptp.big_la43341705in_nat A)) (tptp.hAPP_f22106695ol_nat tptp.big_la43341705in_nat B)))))))) (forall ((A_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (= (tptp.hAPP_f22106695ol_nat tptp.big_la43341705in_nat (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_1) A)) (tptp.hAPP_f22106695ol_nat (tptp.finite_fold_nat_nat tptp.semila972727038up_nat A_1) A)))) (forall ((X_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A))) (= (tptp.hAPP_f22106695ol_nat tptp.big_la43341705in_nat (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) A)) (tptp.hAPP_f22106695ol_nat (tptp.finite_fold_nat_nat tptp.semila972727038up_nat X_1) A))))) (forall ((X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1))) (let ((_let_2 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) (tptp.hAPP_f800510211t_bool _let_1 tptp.bot_bot_fun_nat_bool)))) (let ((_let_3 (tptp.hAPP_f22106695ol_nat tptp.big_la43341705in_nat (tptp.hAPP_f800510211t_bool _let_1 A)))) (let ((_let_4 (= _let_2 tptp.bot_bot_fun_nat_bool))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (and (=> _let_4 (= _let_3 X_1)) (=> (not _let_4) (= _let_3 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.semila972727038up_nat X_1) (tptp.hAPP_f22106695ol_nat tptp.big_la43341705in_nat _let_2))))))))))) (forall ((N $$unsorted) (H $$unsorted)) (=> (forall ((X_2 $$unsorted) (Y_11 $$unsorted)) (= (tptp.hAPP_nat_nat H (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.semila972727038up_nat X_2) Y_11)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.semila972727038up_nat (tptp.hAPP_nat_nat H X_2)) (tptp.hAPP_nat_nat H Y_11)))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat N)) (=> (not (= N tptp.bot_bot_fun_nat_bool)) (= (tptp.hAPP_nat_nat H (tptp.hAPP_f22106695ol_nat tptp.big_la43341705in_nat N)) (tptp.hAPP_f22106695ol_nat tptp.big_la43341705in_nat (tptp.image_nat_nat H N))))))) (forall ((A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (not (= A tptp.bot_bot_fun_nat_bool)) (=> (forall ((X_2 $$unsorted) (Y_11 $$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.semila972727038up_nat X_2) Y_11)) (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_11) tptp.bot_bot_fun_nat_bool))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat (tptp.hAPP_f22106695ol_nat tptp.big_la43341705in_nat A)) A)))))) (forall ((B $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (not (= A tptp.bot_bot_fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat B)) (=> (not (= B tptp.bot_bot_fun_nat_bool)) (=> (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.semila840543986t_bool A) B) tptp.bot_bot_fun_nat_bool) (= (tptp.hAPP_f22106695ol_nat tptp.big_la43341705in_nat (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.semila465093516t_bool A) B)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.semila972727038up_nat (tptp.hAPP_f22106695ol_nat tptp.big_la43341705in_nat A)) (tptp.hAPP_f22106695ol_nat tptp.big_la43341705in_nat B))))))))) (forall ((B $$unsorted) (Ca $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a Ca))) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 A)) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 B)) (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.semila671163144a_bool A) B))))))) (forall ((B $$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)) (=> (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.semila840543986t_bool A) B))))))) (forall ((Ca $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a Ca))) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.semila671163144a_bool A) B))) (not (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 A)) (not (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 B)))))))) (forall ((Ca $$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.semila840543986t_bool A) B))) (not (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 A)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B)))))))) (forall ((Ga $$unsorted) (F $$unsorted)) (=> (or (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat F)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat Ga))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.semila840543986t_bool F) Ga))))) (forall ((X_15 $$unsorted) (A_6 $$unsorted) (B_5 $$unsorted)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_15))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.semila80283416nf_nat A_6) B_5))) (not (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A_6)) (not (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_5)))))))) (forall ((B_4 $$unsorted) (D $$unsorted) (A_5 $$unsorted) (C_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_5) C_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat B_4) D)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.semila80283416nf_nat A_5) B_4)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.semila80283416nf_nat C_1) D)))))) (forall ((Z_3 $$unsorted) (X_14 $$unsorted) (Y_10 $$unsorted)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_14))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Y_10)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Z_3)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.semila80283416nf_nat Y_10) Z_3))))))) (forall ((B_3 $$unsorted) (X_13 $$unsorted) (A_4 $$unsorted)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_13))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A_4)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_3)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.semila80283416nf_nat A_4) B_3))))))) (forall ((Y_9 $$unsorted) (X_12 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_9) X_12)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.semila80283416nf_nat X_12) Y_9) Y_9))) (forall ((X_11 $$unsorted) (Y_8 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_11) Y_8)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.semila80283416nf_nat X_11) Y_8) X_11))) (forall ((A_3 $$unsorted) (B_2 $$unsorted) (X_10 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat B_2) X_10)) (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.semila80283416nf_nat A_3) B_2)) X_10)))) (forall ((B_1 $$unsorted) (A_2 $$unsorted) (X_9 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_2) X_9)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.semila80283416nf_nat A_2) B_1)) X_9)))) (forall ((X_1 $$unsorted) (Y_7 $$unsorted) (Z_2 $$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.semila80283416nf_nat Y_7) Z_2))) (and (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Y_7)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Z_2)))))) (forall ((X_1 $$unsorted) (Y_7 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_1) Y_7)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.semila80283416nf_nat X_1) Y_7) X_1))) (forall ((X_8 $$unsorted) (Y_6 $$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.semila80283416nf_nat X_8) Y_6)) Y_6))) (forall ((X_7 $$unsorted) (Y_5 $$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.semila80283416nf_nat X_7) Y_5)) Y_5))) (forall ((X_6 $$unsorted) (Y_4 $$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.semila80283416nf_nat X_6) Y_4)) X_6))) (forall ((X_5 $$unsorted) (Y_3 $$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.semila80283416nf_nat X_5) Y_3)) X_5))) (forall ((X_4 $$unsorted) (Y_2 $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.semila972727038up_nat X_4))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.semila80283416nf_nat Y_2) Z_1))) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.semila80283416nf_nat (tptp.hAPP_nat_nat _let_1 Y_2)) (tptp.hAPP_nat_nat _let_1 Z_1)))))) (forall ((X_3 $$unsorted) (Y_1 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.semila80283416nf_nat X_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.semila972727038up_nat (tptp.hAPP_nat_nat _let_1 Y_1)) (tptp.hAPP_nat_nat _let_1 Z))) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.semila972727038up_nat Y_1) Z)))))) (forall ((B $$unsorted) (A_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_1))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_1) C)) (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.semila840543986t_bool (tptp.hAPP_f800510211t_bool _let_1 B)) C) (tptp.hAPP_f800510211t_bool _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.semila840543986t_bool B) C)))))) (forall ((B $$unsorted) (A_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A_1))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state A_1) C)) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool (tptp.hAPP_f921536533e_bool _let_1 B)) C) (tptp.hAPP_f921536533e_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool B) C)))))) (forall ((B $$unsorted) (A_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a A_1))) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a A_1) C)) (= (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.semila671163144a_bool (tptp.hAPP_f1591852335a_bool _let_1 B)) C) (tptp.hAPP_f1591852335a_bool _let_1 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.semila671163144a_bool B) C)))))) (forall ((B $$unsorted) (A_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f1730770594t_bool tptp.semila840543986t_bool A))) (let ((_let_2 (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_1))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_1) A)) (= (tptp.hAPP_f800510211t_bool _let_1 (tptp.hAPP_f800510211t_bool _let_2 B)) (tptp.hAPP_f800510211t_bool _let_2 (tptp.hAPP_f800510211t_bool _let_1 B))))))) (forall ((B $$unsorted) (A_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool A))) (let ((_let_2 (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A_1))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state A_1) A)) (= (tptp.hAPP_f921536533e_bool _let_1 (tptp.hAPP_f921536533e_bool _let_2 B)) (tptp.hAPP_f921536533e_bool _let_2 (tptp.hAPP_f921536533e_bool _let_1 B))))))) (forall ((B $$unsorted) (A_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f1026156344a_bool tptp.semila671163144a_bool A))) (let ((_let_2 (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a A_1))) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a A_1) A)) (= (tptp.hAPP_f1591852335a_bool _let_1 (tptp.hAPP_f1591852335a_bool _let_2 B)) (tptp.hAPP_f1591852335a_bool _let_2 (tptp.hAPP_f1591852335a_bool _let_1 B))))))) (forall ((B $$unsorted) (A_1 $$unsorted) (C $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_1) C))) (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.semila840543986t_bool (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_1) B)) C) (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.semila840543986t_bool B) C)))) (forall ((B $$unsorted) (A_1 $$unsorted) (C $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state A_1) C))) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A_1) B)) C) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool B) C)))) (forall ((B $$unsorted) (A_1 $$unsorted) (C $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a A_1) C))) (= (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.semila671163144a_bool (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a A_1) B)) C) (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.semila671163144a_bool B) C)))) (forall ((B $$unsorted) (A_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f1730770594t_bool tptp.semila840543986t_bool A))) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_1) A))) (= (tptp.hAPP_f800510211t_bool _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_1) B)) (tptp.hAPP_f800510211t_bool _let_1 B))))) (forall ((B $$unsorted) (A_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool A))) (=> (not (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state A_1) A))) (= (tptp.hAPP_f921536533e_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A_1) B)) (tptp.hAPP_f921536533e_bool _let_1 B))))) (forall ((B $$unsorted) (A_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f1026156344a_bool tptp.semila671163144a_bool A))) (=> (not (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a A_1) A))) (= (tptp.hAPP_f1591852335a_bool _let_1 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a A_1) B)) (tptp.hAPP_f1591852335a_bool _let_1 B))))) (forall ((A_1 $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_1))) (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.semila840543986t_bool (tptp.hAPP_f800510211t_bool _let_1 A)) (tptp.hAPP_f800510211t_bool _let_1 B)) (tptp.hAPP_f800510211t_bool _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.semila840543986t_bool A) B))))) (forall ((A_1 $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A_1))) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool (tptp.hAPP_f921536533e_bool _let_1 A)) (tptp.hAPP_f921536533e_bool _let_1 B)) (tptp.hAPP_f921536533e_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool A) B))))) (forall ((A_1 $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a A_1))) (= (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.semila671163144a_bool (tptp.hAPP_f1591852335a_bool _let_1 A)) (tptp.hAPP_f1591852335a_bool _let_1 B)) (tptp.hAPP_f1591852335a_bool _let_1 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.semila671163144a_bool A) B))))) (forall ((B $$unsorted) (A_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.semila840543986t_bool B) C))) (let ((_let_2 (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_1))) (let ((_let_3 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.semila840543986t_bool (tptp.hAPP_f800510211t_bool _let_2 B)) C))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_1) C)))) (and (=> _let_4 (= _let_3 (tptp.hAPP_f800510211t_bool _let_2 _let_1))) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((B $$unsorted) (A_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool B) C))) (let ((_let_2 (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A_1))) (let ((_let_3 (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool (tptp.hAPP_f921536533e_bool _let_2 B)) C))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state A_1) C)))) (and (=> _let_4 (= _let_3 (tptp.hAPP_f921536533e_bool _let_2 _let_1))) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((B $$unsorted) (A_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.semila671163144a_bool B) C))) (let ((_let_2 (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a A_1))) (let ((_let_3 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.semila671163144a_bool (tptp.hAPP_f1591852335a_bool _let_2 B)) C))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a A_1) C)))) (and (=> _let_4 (= _let_3 (tptp.hAPP_f1591852335a_bool _let_2 _let_1))) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((B $$unsorted) (A_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f1730770594t_bool tptp.semila840543986t_bool A))) (let ((_let_2 (tptp.hAPP_f800510211t_bool _let_1 B))) (let ((_let_3 (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_1))) (let ((_let_4 (tptp.hAPP_f800510211t_bool _let_1 (tptp.hAPP_f800510211t_bool _let_3 B)))) (let ((_let_5 (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_1) A)))) (and (=> _let_5 (= _let_4 (tptp.hAPP_f800510211t_bool _let_3 _let_2))) (=> (not _let_5) (= _let_4 _let_2))))))))) (forall ((B $$unsorted) (A_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool A))) (let ((_let_2 (tptp.hAPP_f921536533e_bool _let_1 B))) (let ((_let_3 (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A_1))) (let ((_let_4 (tptp.hAPP_f921536533e_bool _let_1 (tptp.hAPP_f921536533e_bool _let_3 B)))) (let ((_let_5 (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state A_1) A)))) (and (=> _let_5 (= _let_4 (tptp.hAPP_f921536533e_bool _let_3 _let_2))) (=> (not _let_5) (= _let_4 _let_2))))))))) (forall ((B $$unsorted) (A_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f1026156344a_bool tptp.semila671163144a_bool A))) (let ((_let_2 (tptp.hAPP_f1591852335a_bool _let_1 B))) (let ((_let_3 (tptp.hAPP_H1641355846a_bool tptp.insert873085594iple_a A_1))) (let ((_let_4 (tptp.hAPP_f1591852335a_bool _let_1 (tptp.hAPP_f1591852335a_bool _let_3 B)))) (let ((_let_5 (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a A_1) A)))) (and (=> _let_5 (= _let_4 (tptp.hAPP_f1591852335a_bool _let_3 _let_2))) (=> (not _let_5) (= _let_4 _let_2))))))))) (forall ((R_1 $$unsorted) (S $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_f672239281a_bool tptp.cOMBC_1552014468l_bool tptp.member1713797107iple_a))) (= (tptp.hBOOL (tptp.hAPP_H1421470952a_bool (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.semila671163144a_bool (tptp.hAPP_f1591852335a_bool _let_1 R_1)) (tptp.hAPP_f1591852335a_bool _let_1 S)) X_2)) (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a X_2) (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.semila671163144a_bool R_1) S)))))) (forall ((R_1 $$unsorted) (S $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1722879237t_bool tptp.cOMBC_226598744l_bool tptp.member_nat))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.semila840543986t_bool (tptp.hAPP_f800510211t_bool _let_1 R_1)) (tptp.hAPP_f800510211t_bool _let_1 S)) X_2)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.semila840543986t_bool R_1) S)))))) (forall ((Pa $$unsorted) (Q_1 $$unsorted)) (= (tptp.collec268032053iple_a (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1203760810a_bool tptp.cOMBS_1148211387l_bool (tptp.hAPP_f997599971l_bool (tptp.hAPP_f439164429l_bool tptp.cOMBB_1782929690iple_a tptp.fconj) Pa)) Q_1)) (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.semila671163144a_bool (tptp.collec268032053iple_a Pa)) (tptp.collec268032053iple_a Q_1)))) (forall ((Pa $$unsorted) (Q_1 $$unsorted)) (= (tptp.collect_nat (tptp.hAPP_f800510211t_bool (tptp.hAPP_f561022312t_bool tptp.cOMBS_nat_bool_bool (tptp.hAPP_f1146629647l_bool (tptp.hAPP_f1080886329l_bool tptp.cOMBB_1015721476ol_nat tptp.fconj) Pa)) Q_1)) (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.semila840543986t_bool (tptp.collect_nat Pa)) (tptp.collect_nat Q_1)))) (forall ((X_1 $$unsorted) (A $$unsorted) (Pa $$unsorted)) (let ((_let_1 (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a X_1))) (= (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.semila671163144a_bool A) (tptp.collec268032053iple_a Pa)))) (and (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_H1421470952a_bool Pa X_1)))))) (forall ((X_1 $$unsorted) (A $$unsorted) (Pa $$unsorted)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat X_1))) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.semila840543986t_bool A) (tptp.collect_nat Pa)))) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_nat_bool Pa X_1)))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f672239281a_bool tptp.cOMBC_1552014468l_bool tptp.member1713797107iple_a))) (= (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.semila671163144a_bool A) B) (tptp.collec268032053iple_a (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1203760810a_bool tptp.cOMBS_1148211387l_bool (tptp.hAPP_f997599971l_bool (tptp.hAPP_f439164429l_bool tptp.cOMBB_1782929690iple_a tptp.fconj) (tptp.hAPP_f1591852335a_bool _let_1 A))) (tptp.hAPP_f1591852335a_bool _let_1 B)))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f1722879237t_bool tptp.cOMBC_226598744l_bool tptp.member_nat))) (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.semila840543986t_bool A) B) (tptp.collect_nat (tptp.hAPP_f800510211t_bool (tptp.hAPP_f561022312t_bool tptp.cOMBS_nat_bool_bool (tptp.hAPP_f1146629647l_bool (tptp.hAPP_f1080886329l_bool tptp.cOMBB_1015721476ol_nat tptp.fconj) (tptp.hAPP_f800510211t_bool _let_1 A))) (tptp.hAPP_f800510211t_bool _let_1 B)))))) (forall ((Ca $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a Ca))) (= (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.semila671163144a_bool A) B))) (and (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 B)))))) (forall ((Ca $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat Ca))) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.semila840543986t_bool A) B))) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B)))))) (forall ((Ca $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a Ca))) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.semila671163144a_bool A) B))) (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 A))))) (forall ((Ca $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat Ca))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.semila840543986t_bool A) B))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 A))))) (forall ((Ca $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a Ca))) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.semila671163144a_bool A) B))) (tptp.hBOOL (tptp.hAPP_f540970102l_bool _let_1 B))))) (forall ((Ca $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat Ca))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.semila840543986t_bool A) B))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B))))) (forall ((A $$unsorted) (B $$unsorted)) (= (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.semila840543986t_bool A) B) tptp.bot_bot_fun_nat_bool) (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) A)) (forall ((Xa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat Xa) B)) (not (= X_2 Xa)))))))) (forall ((A $$unsorted) (B $$unsorted)) (= (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool A) B) tptp.bot_bo1055319631e_bool) (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_2) A)) (forall ((Xa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state Xa) B)) (not (= X_2 Xa)))))))) (forall ((A $$unsorted) (B $$unsorted)) (= (= (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.semila671163144a_bool A) B) tptp.bot_bo1181479936a_bool) (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a X_2) A)) (forall ((Xa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool tptp.member1713797107iple_a Xa) B)) (not (= X_2 Xa)))))))) (forall ((A $$unsorted)) (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.semila840543986t_bool A) tptp.bot_bot_fun_nat_bool) tptp.bot_bot_fun_nat_bool)) (forall ((A $$unsorted)) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool A) tptp.bot_bo1055319631e_bool) tptp.bot_bo1055319631e_bool)) (forall ((A $$unsorted)) (= (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.semila671163144a_bool A) tptp.bot_bo1181479936a_bool) tptp.bot_bo1181479936a_bool)) (forall ((B $$unsorted)) (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.semila840543986t_bool tptp.bot_bot_fun_nat_bool) B) tptp.bot_bot_fun_nat_bool)) (forall ((B $$unsorted)) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool tptp.bot_bo1055319631e_bool) B) tptp.bot_bo1055319631e_bool)) (forall ((B $$unsorted)) (= (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.semila671163144a_bool tptp.bot_bo1181479936a_bool) B) tptp.bot_bo1181479936a_bool)) (forall ((X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila310582991f_bool tptp.bot_bot_bool) X_1)) (tptp.hBOOL tptp.bot_bot_bool))) (forall ((X_1 $$unsorted)) (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.semila840543986t_bool tptp.bot_bot_fun_nat_bool) X_1) tptp.bot_bot_fun_nat_bool)) (forall ((X_1 $$unsorted)) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool tptp.bot_bo1055319631e_bool) X_1) tptp.bot_bo1055319631e_bool)) (forall ((X_1 $$unsorted)) (= (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.semila671163144a_bool tptp.bot_bo1181479936a_bool) X_1) tptp.bot_bo1181479936a_bool)) (forall ((X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila310582991f_bool X_1) tptp.bot_bot_bool)) (tptp.hBOOL tptp.bot_bot_bool))) (forall ((X_1 $$unsorted)) (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.semila840543986t_bool X_1) tptp.bot_bot_fun_nat_bool) tptp.bot_bot_fun_nat_bool)) (forall ((X_1 $$unsorted)) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool X_1) tptp.bot_bo1055319631e_bool) tptp.bot_bo1055319631e_bool)) (forall ((X_1 $$unsorted)) (= (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.semila671163144a_bool X_1) tptp.bot_bo1181479936a_bool) tptp.bot_bo1181479936a_bool)) (forall ((A $$unsorted) (B $$unsorted)) (=> (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.semila840543986t_bool A) B) tptp.bot_bot_fun_nat_bool) (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) B) A))) (forall ((A $$unsorted) (B $$unsorted)) (=> (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool A) B) tptp.bot_bo1055319631e_bool) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.minus_2076558538e_bool A) B) A))) (forall ((A $$unsorted) (B $$unsorted)) (=> (= (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.semila671163144a_bool A) B) tptp.bot_bo1181479936a_bool) (= (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.minus_469558085a_bool A) B) A))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.semila840543986t_bool A) (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool B) A)) tptp.bot_bot_fun_nat_bool)) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool A) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.minus_2076558538e_bool B) A)) tptp.bot_bo1055319631e_bool)) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.semila671163144a_bool A) (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool tptp.minus_469558085a_bool B) A)) tptp.bot_bo1181479936a_bool)) (forall ((P $$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 ((P $$unsorted)) (= (tptp.hAPP_nat_nat tptp.cOMBI_nat P) P)) (forall ((X $$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 $$unsorted)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.cOMBK_nat_nat P) Q) P)) _let_9 _let_8 (forall ((X $$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_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 $$unsorted)) (= (tptp.hAPP_nat_bool (tptp.hAPP_f800510211t_bool (tptp.hAPP_f894608603t_bool tptp.cOMBB_bool_bool_nat P) Q) R) (tptp.hAPP_bool_bool P (tptp.hAPP_nat_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_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 $$unsorted)) (= (tptp.hAPP_state_state (tptp.hAPP_n1547241352_state (tptp.hAPP_f1848060885_state tptp.cOMBC_1777403949_state P) Q) R) (tptp.hAPP_nat_state (tptp.hAPP_s1892499976_state P R) Q))) (forall ((P $$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_H678412245iple_a tptp.cOMBI_1218222237iple_a P) P)) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP_H1421470952a_bool (tptp.hAPP_H1190454433a_bool tptp.fequal879838495iple_a X) Y))) (= X Y))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_H1421470952a_bool (tptp.hAPP_H1190454433a_bool tptp.fequal879838495iple_a X) Y)))) (forall ((P $$unsorted) (Q $$unsorted)) (=> (tptp.is_bool P) (= (tptp.hAPP_f54304608l_bool (tptp.hAPP_b1630757474l_bool tptp.cOMBK_1994329625t_bool P) Q) P))) (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.hAPP_s1806633685e_bool (tptp.hAPP_f1863945078e_bool tptp.cOMBK_631994958_state P) Q) P)) (forall ((P $$unsorted)) (= (tptp.hAPP_H563960305_state tptp.cOMBI_1367665338_state P) P)) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP_H513860823e_bool (tptp.hAPP_H1645666623e_bool tptp.fequal1531560888_state X) Y))) (= X Y))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_H513860823e_bool (tptp.hAPP_H1645666623e_bool tptp.fequal1531560888_state X) Y)))) (forall ((P $$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_n178040171iple_a (tptp.hAPP_H1450464520iple_a tptp.cOMBK_1505147640_a_nat P) Q) P)) (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.hAPP_H738206399_a_nat (tptp.hAPP_n1800114674_a_nat tptp.cOMBK_944981412iple_a P) Q) P)) (forall ((P $$unsorted) (Q $$unsorted)) (=> (tptp.is_bool P) (= (tptp.hAPP_H1421470952a_bool (tptp.hAPP_b119575286a_bool tptp.cOMBK_151824839iple_a P) Q) P))) (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_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 $$unsorted)) (= (tptp.hAPP_nat_bool (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1722879237t_bool tptp.cOMBC_226598744l_bool P) Q) R) (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f54304608l_bool (tptp.hAPP_f1246832597l_bool (tptp.hAPP_f1164891443l_bool tptp.cOMBB_238756964t_bool P) Q) R) (tptp.hAPP_bool_bool P (tptp.hAPP_f54304608l_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_f54304608l_bool (tptp.hAPP_f1246832597l_bool (tptp.hAPP_f1743029098l_bool tptp.cOMBS_1187019125l_bool P) Q) R) (tptp.hAPP_bool_bool (tptp.hAPP_f1748468828l_bool P R) (tptp.hAPP_f54304608l_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 ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_s1806633685e_bool (tptp.hAPP_b1095269219e_bool (tptp.hAPP_f701449317e_bool tptp.cOMBC_471052088e_bool P) Q) R) (tptp.hAPP_b2019457360e_bool (tptp.hAPP_s1874344717e_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.hAPP_H716259088te_nat (tptp.hAPP_n436597305te_nat tptp.cOMBK_1950023923_state P) Q) P)) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_f430043647l_bool tptp.fequal1258664663a_bool X) Y))) (= X Y))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_f540970102l_bool (tptp.hAPP_f430043647l_bool tptp.fequal1258664663a_bool X) Y)))) (forall ((P $$unsorted) (Q $$unsorted)) (=> (tptp.is_bool P) (= (tptp.hAPP_H513860823e_bool (tptp.hAPP_b1245957081e_bool tptp.cOMBK_1079618832_state P) Q) P))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H1421470952a_bool (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f34030599a_bool tptp.cOMBB_1799513916iple_a P) Q) R) (tptp.hAPP_bool_bool P (tptp.hAPP_H1421470952a_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H1421470952a_bool (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1203760810a_bool tptp.cOMBS_1148211387l_bool P) Q) R) (tptp.hAPP_bool_bool (tptp.hAPP_H1017515220l_bool P R) (tptp.hAPP_H1421470952a_bool Q R)))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.fequal1746921144e_bool X) Y))) (= X Y))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.fequal1746921144e_bool X) Y)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_a2036067514e_bool (tptp.hAPP_f769584981e_bool (tptp.hAPP_f1159960589e_bool tptp.cOMBB_237455441bool_a P) Q) R) (tptp.hAPP_f1759915619e_bool P (tptp.hAPP_a2036067514e_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 $$unsorted)) (= (tptp.hAPP_H513860823e_bool (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1037965299e_bool tptp.cOMBB_416661851_state P) Q) R) (tptp.hAPP_bool_bool P (tptp.hAPP_H513860823e_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H513860823e_bool (tptp.hAPP_f921536533e_bool (tptp.hAPP_f760664097e_bool tptp.cOMBS_1248383340l_bool P) Q) R) (tptp.hAPP_bool_bool (tptp.hAPP_H226398757l_bool P R) (tptp.hAPP_H513860823e_bool Q R)))) (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_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) (R $$unsorted)) (= (tptp.hAPP_f1748468828l_bool (tptp.hAPP_f1974927549l_bool (tptp.hAPP_f857404385l_bool tptp.cOMBB_444170502t_bool P) Q) R) (tptp.hAPP_b589554111l_bool P (tptp.hAPP_f54304608l_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_s1806633685e_bool (tptp.hAPP_f817621513e_bool (tptp.hAPP_f512427579e_bool tptp.cOMBB_572666224_state P) Q) R) (tptp.hAPP_f1759915619e_bool P (tptp.hAPP_s1806633685e_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_s1806633685e_bool (tptp.hAPP_f1838002347e_bool (tptp.hAPP_f1706273077e_bool tptp.cOMBC_867582640e_bool P) Q) R) (tptp.hAPP_f746301080e_bool (tptp.hAPP_s286259371e_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.hAPP_H678412245iple_a (tptp.hAPP_H1455657330iple_a tptp.cOMBK_1824972302iple_a P) Q) P)) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H1017515220l_bool (tptp.hAPP_f997599971l_bool (tptp.hAPP_f439164429l_bool tptp.cOMBB_1782929690iple_a P) Q) R) (tptp.hAPP_b589554111l_bool P (tptp.hAPP_H1421470952a_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.hAPP_H1600811558iple_a (tptp.hAPP_H377435237iple_a tptp.cOMBK_2022976521_state P) Q) P)) (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.hAPP_H928324994_state (tptp.hAPP_H558669354_state tptp.cOMBK_547979437iple_a P) Q) P)) (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_H226398757l_bool (tptp.hAPP_f1558728829l_bool (tptp.hAPP_f1442918689l_bool tptp.cOMBB_1382207997_state P) Q) R) (tptp.hAPP_b589554111l_bool P (tptp.hAPP_H513860823e_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H1421470952a_bool (tptp.hAPP_H1190454433a_bool (tptp.hAPP_f1371755681a_bool tptp.cOMBC_839220826a_bool P) Q) R) (tptp.hAPP_H1421470952a_bool (tptp.hAPP_H1190454433a_bool P R) Q))) (forall ((P $$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 $$unsorted)) (= (tptp.hAPP_f54304608l_bool (tptp.hAPP_f1246832597l_bool (tptp.hAPP_f1443436725l_bool tptp.cOMBC_1245412066l_bool P) Q) R) (tptp.hAPP_f1637334154l_bool (tptp.hAPP_f1951378235l_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.hAPP_H563960305_state (tptp.hAPP_H521649881_state tptp.cOMBK_690957994_state P) Q) P)) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_s2001034685l_bool (tptp.hAPP_f1283379615l_bool (tptp.hAPP_f1345202233l_bool tptp.cOMBB_1759179140_state P) Q) R) (tptp.hAPP_f1259673775l_bool P (tptp.hAPP_s1806633685e_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_H513860823e_bool (tptp.hAPP_H1645666623e_bool (tptp.hAPP_f262880489e_bool tptp.cOMBC_1424981238e_bool P) Q) R) (tptp.hAPP_H513860823e_bool (tptp.hAPP_H1645666623e_bool P R) Q))) (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_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 $$unsorted)) (= (tptp.hAPP_H1421470952a_bool (tptp.hAPP_f772297704a_bool (tptp.hAPP_f390613447a_bool tptp.cOMBB_1501709507iple_a P) Q) R) (tptp.hAPP_f540970102l_bool P (tptp.hAPP_H1190454433a_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H1421470952a_bool (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f672239281a_bool tptp.cOMBC_1552014468l_bool P) Q) R) (tptp.hAPP_f540970102l_bool (tptp.hAPP_H1840393229l_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_s1874344717e_bool (tptp.hAPP_f873506917e_bool (tptp.hAPP_f1398071125e_bool tptp.cOMBB_1757942702_state P) Q) R) (tptp.hAPP_f167292325e_bool P (tptp.hAPP_s2001034685l_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_s286259371e_bool (tptp.hAPP_f289738463e_bool (tptp.hAPP_f1151843515e_bool tptp.cOMBB_1941618714_state P) Q) R) (tptp.hAPP_f162060345e_bool P (tptp.hAPP_s1806633685e_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H513860823e_bool (tptp.hAPP_f1456107715e_bool (tptp.hAPP_f1548785833e_bool tptp.cOMBB_1653402815_state P) Q) R) (tptp.hAPP_f1760790145l_bool P (tptp.hAPP_H1645666623e_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H513860823e_bool (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1262649863e_bool tptp.cOMBC_764456866l_bool P) Q) R) (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool P R) Q))) (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_H1190454433a_bool (tptp.hAPP_f1665407592a_bool (tptp.hAPP_f549683569a_bool tptp.cOMBC_708118077a_bool P) Q) R) (tptp.hAPP_f1591852335a_bool (tptp.hAPP_H1641355846a_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool (tptp.hAPP_f450029403a_bool tptp.cOMBC_314077933a_bool P) Q) R) (tptp.hAPP_f1591852335a_bool (tptp.hAPP_f1026156344a_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H1645666623e_bool (tptp.hAPP_f762269719e_bool (tptp.hAPP_f964290431e_bool tptp.cOMBC_488258100e_bool P) Q) R) (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool (tptp.hAPP_f2049746453e_bool tptp.cOMBC_872426556e_bool P) Q) R) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H1641355846a_bool (tptp.hAPP_f485051996a_bool (tptp.hAPP_f2085120383a_bool tptp.cOMBB_2080540641iple_a P) Q) R) (tptp.hAPP_f1026156344a_bool P (tptp.hAPP_H1190454433a_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H727730819e_bool (tptp.hAPP_f531275309e_bool (tptp.hAPP_f1470644835e_bool tptp.cOMBB_946224375_state P) Q) R) (tptp.hAPP_f1583986009e_bool P (tptp.hAPP_H1645666623e_bool Q R)))) _let_6 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 3.42/3.67  )
% 3.42/3.67  % SZS output end Proof for SWW470+2
% 3.42/3.68  % cvc5---1.0.5 exiting
% 3.42/3.68  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------