TSTP Solution File: SWW474_3 by cvc5---1.0.5

%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWW474_3 : TPTP v8.1.2. Released v5.3.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n023.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 00:21:10 EDT 2023

% Result   : Theorem 6.03s 6.25s
% Output   : Proof 6.03s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.37  % Problem    : SWW474_3 : TPTP v8.1.2. Released v5.3.0.
% 0.12/0.38  % Command    : do_cvc5 %s %d
% 0.38/0.59  % Computer : n023.cluster.edu
% 0.38/0.59  % Model    : x86_64 x86_64
% 0.38/0.59  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.38/0.59  % Memory   : 8042.1875MB
% 0.38/0.59  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.38/0.59  % CPULimit   : 300
% 0.38/0.59  % WCLimit    : 300
% 0.38/0.59  % DateTime   : Sun Aug 27 23:13:26 EDT 2023
% 0.38/0.59  % CPUTime    : 
% 0.44/1.00  %----Proving TF0_NAR, FOF, or CNF
% 6.03/6.25  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.tgYPtD88vM/cvc5---1.0.5_5549.p...
% 6.03/6.25  ------- get file name : TPTP file name is SWW474_3
% 6.03/6.25  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_5549.smt2...
% 6.03/6.25  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 6.03/6.25  % SZS status Theorem for SWW474_3
% 6.03/6.25  % SZS output start Proof for SWW474_3
% 6.03/6.25  (
% 6.03/6.25  (let ((_let_1 (tptp.hAPP_c1041435779_state tptp.hoare_Mirabelle_MGT tptp.y))) (let ((_let_2 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state _let_1) tptp.bot_bo39439654e_bool))) (let ((_let_3 (tptp.dom_pname_com tptp.body))) (let ((_let_4 (tptp.cOMBB_424558970_pname tptp.hoare_Mirabelle_MGT))) (let ((_let_5 (tptp.hAPP_f1763243027e_bool (tptp.image_1918575693_state (tptp.hAPP_f481860441_state _let_4 tptp.body_1)) _let_3))) (let ((_let_6 (tptp.hoare_95103338_state _let_5))) (let ((_let_7 (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_6 _let_2)))) (let ((_let_8 (not _let_7))) (let ((_let_9 (= (tptp.hAPP_p799580910on_com tptp.body tptp.pn) (tptp.hAPP_com_option_com tptp.some_com tptp.y)))) (let ((_let_10 (tptp.hBOOL tptp.wT_bodies))) (let ((_let_11 (tptp.hBOOL tptp.hoare_265376576gleton))) (let ((_let_12 (forall ((Pn tptp.pname) (B_4 tptp.com)) (=> (tptp.hBOOL tptp.wT_bodies) (=> (= (tptp.hAPP_p799580910on_com tptp.body Pn) (tptp.hAPP_com_option_com tptp.some_com B_4)) (tptp.hBOOL (tptp.hAPP_com_bool tptp.wt B_4))))))) (let ((_let_13 (forall ((C tptp.com)) (=> (tptp.hBOOL tptp.hoare_265376576gleton) (=> (tptp.hBOOL tptp.wT_bodies) (=> (tptp.hBOOL (tptp.hAPP_com_bool tptp.wt C)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hoare_95103338_state tptp.bot_bo39439654e_bool) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state (tptp.hAPP_c1041435779_state tptp.hoare_Mirabelle_MGT C)) tptp.bot_bo39439654e_bool))))))))) (let ((_let_14 (forall ((G_2 tptp.fun_Ho320143120e_bool) (G_3 tptp.fun_Ho320143120e_bool) (Ts tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hoare_95103338_state G_2))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hoare_95103338_state G_3) Ts)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 G_3)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 Ts)))))))) (let ((_let_15 (forall ((G_2 tptp.fun_Ho320143120e_bool)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hoare_95103338_state G_2) tptp.bot_bo39439654e_bool))))) (let ((_let_16 (forall ((G_2 tptp.fun_Ho320143120e_bool) (G_3 tptp.fun_Ho320143120e_bool) (Ts tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hoare_95103338_state G_2))) (or (not (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hoare_95103338_state G_3) Ts))) (not (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 G_3))) (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 Ts))))))) (let ((_let_17 (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_6 tptp.bot_bo39439654e_bool)))) (let ((_let_18 (not _let_17))) (let ((_let_19 (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hoare_95103338_state tptp.bot_bo39439654e_bool) _let_2)))) (let ((_let_20 (not _let_19))) (let ((_let_21 (or _let_20 _let_18 _let_7))) (let ((_let_22 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_23 (not _let_21))) (let ((_let_24 (tptp.hBOOL (tptp.hAPP_com_bool tptp.wt tptp.y)))) (let ((_let_25 (not _let_24))) (let ((_let_26 (or _let_25 _let_19))) (let ((_let_27 (forall ((C tptp.com)) (or (not (tptp.hBOOL (tptp.hAPP_com_bool tptp.wt C))) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hoare_95103338_state tptp.bot_bo39439654e_bool) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state (tptp.hAPP_c1041435779_state tptp.hoare_Mirabelle_MGT C)) tptp.bot_bo39439654e_bool))))))) (let ((_let_28 (ASSUME :args (_let_10)))) (let ((_let_29 (_let_27))) (let ((_let_30 (not _let_9))) (let ((_let_31 (or _let_30 _let_24))) (let ((_let_32 (forall ((Pn tptp.pname) (B_4 tptp.com)) (or (not (= (tptp.hAPP_p799580910on_com tptp.body Pn) (tptp.hAPP_com_option_com tptp.some_com B_4))) (tptp.hBOOL (tptp.hAPP_com_bool tptp.wt B_4)))))) (let ((_let_33 (_let_32))) (let ((_let_34 (_let_15))) (let ((_let_35 (ASSUME :args _let_34))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_22 :args (_let_5 tptp.bot_bo39439654e_bool _let_2 QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP_f568432088l_bool (tptp.hoare_95103338_state G_3) Ts) (tptp.hoare_95103338_state G_2)))) :args (_let_16))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_21)) :args ((or _let_7 _let_18 _let_20 _let_23))) (ASSUME :args (_let_8)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_35 :args (_let_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.hoare_95103338_state G_2)))) :args _let_34)) _let_35 :args (_let_17 false _let_15)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_26)) :args ((or _let_25 _let_19 (not _let_26)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_31)) :args ((or _let_30 _let_24 (not _let_31)))) (ASSUME :args (_let_9)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_33) :args (tptp.pn tptp.y QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP_p799580910on_com tptp.body Pn) (tptp.hAPP_com_option_com tptp.some_com B_4)))) :args _let_33)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))) _let_28 :args (_let_32 false _let_10)) :args (_let_31 false _let_32)) :args (_let_24 false _let_9 false _let_31)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_29) :args (tptp.y QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.hAPP_c1041435779_state tptp.hoare_Mirabelle_MGT C)))) :args _let_29)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))) (ASSUME :args (_let_11)) _let_28 :args (_let_27 false _let_11 false _let_10)) :args (_let_26 false _let_27)) :args (_let_19 false _let_24 false _let_26)) :args (_let_23 true _let_7 false _let_17 false _let_19)) _let_22 :args (false true _let_21 false _let_16)) :args (_let_15 (forall ((Ts tptp.fun_Ho320143120e_bool) (G_2 tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool Ts) G_2)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hoare_95103338_state G_2) Ts)))) (forall ((Ts tptp.fun_Ho320143120e_bool) (G_2 tptp.fun_Ho320143120e_bool) (Ts_1 tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hoare_95103338_state G_2))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 Ts_1)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool Ts) Ts_1)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 Ts)))))) (forall ((G_2 tptp.fun_Ho320143120e_bool) (G_3 tptp.fun_Ho320143120e_bool) (Ts tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hoare_95103338_state G_3) Ts)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool G_3) G_2)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hoare_95103338_state G_2) Ts))))) _let_14 (forall ((Ts tptp.fun_Ho320143120e_bool) (G_2 tptp.fun_Ho320143120e_bool) (T tptp.hoare_363350478_state)) (let ((_let_1 (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state T))) (let ((_let_2 (tptp.hoare_95103338_state G_2))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_2 (tptp.hAPP_f1749453397e_bool _let_1 tptp.bot_bo39439654e_bool))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_2 Ts)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_2 (tptp.hAPP_f1749453397e_bool _let_1 Ts)))))))) (forall ((G_2 tptp.fun_Ho320143120e_bool) (T tptp.hoare_363350478_state) (Ts tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hoare_95103338_state G_2))) (let ((_let_2 (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state T))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 (tptp.hAPP_f1749453397e_bool _let_2 Ts))) (and (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 (tptp.hAPP_f1749453397e_bool _let_2 tptp.bot_bo39439654e_bool))) (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 Ts))))))) (forall ((Pn_1 tptp.pname) (G_2 tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state (tptp.hAPP_c1041435779_state tptp.hoare_Mirabelle_MGT (tptp.hAPP_pname_com tptp.body_1 Pn_1))))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hoare_95103338_state (tptp.hAPP_f1749453397e_bool _let_1 G_2)) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state (tptp.hAPP_c1041435779_state tptp.hoare_Mirabelle_MGT (tptp.hAPP_option_com_com tptp.the_com (tptp.hAPP_p799580910on_com tptp.body Pn_1)))) tptp.bot_bo39439654e_bool))) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hoare_95103338_state G_2) (tptp.hAPP_f1749453397e_bool _let_1 tptp.bot_bo39439654e_bool)))))) (forall ((A tptp.fun_fu1430349052l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)) (tptp.hBOOL (tptp.hAPP_f389811538l_bool tptp.finite786885583l_bool (tptp.hAPP_f783502055l_bool tptp.collec1613912337l_bool (tptp.hAPP_f510955609l_bool (tptp.hAPP_f1879335953l_bool tptp.cOMBC_7971162l_bool tptp.ord_le675606854l_bool) A)))))) (forall ((A tptp.fun_fu1996308102l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool A)) (tptp.hBOOL (tptp.hAPP_f834704272l_bool tptp.finite393859187l_bool (tptp.hAPP_f891779797l_bool tptp.collec85445553l_bool (tptp.hAPP_f746351743l_bool (tptp.hAPP_f992844137l_bool tptp.cOMBC_736208532l_bool tptp.ord_le2031828156l_bool) A)))))) (forall ((A tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state A)) (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool (tptp.hAPP_f85652879l_bool tptp.collec1243131813e_bool (tptp.hAPP_f726209793l_bool (tptp.hAPP_f205303905l_bool tptp.cOMBC_1250231770l_bool tptp.ord_le704992346e_bool) A)))))) (forall ((A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool (tptp.hAPP_f434788991l_bool (tptp.hAPP_f1297925993l_bool tptp.cOMBC_1284144636l_bool tptp.ord_le313189616e_bool) A)))))) (forall ((H_1 tptp.fun_Ho1262521325e_bool) (Fa tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state Fa)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.hAPP_f766639041l_bool (tptp.image_1660610235e_bool H_1) Fa))))) (forall ((H_1 tptp.fun_Ho424838195e_bool) (Fa tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state Fa)) (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool (tptp.hAPP_f726209793l_bool (tptp.image_1484638543e_bool H_1) Fa))))) (forall ((H_1 tptp.fun_pn800050071e_bool) (Fa tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname Fa)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.hAPP_f434788991l_bool (tptp.image_47868345e_bool H_1) Fa))))) (forall ((H_1 tptp.fun_pn1521100553e_bool) (Fa tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname Fa)) (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool (tptp.hAPP_f682249667l_bool (tptp.image_1637084625e_bool H_1) Fa))))) (forall ((H_1 tptp.fun_fu54631149_state) (Fa tptp.fun_fu1430349052l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool Fa)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state (tptp.hAPP_f1912490857e_bool (tptp.image_431763259_state H_1) Fa))))) (forall ((H_1 tptp.fun_fu700438391_state) (Fa tptp.fun_fu1996308102l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool Fa)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state (tptp.hAPP_f1180969799e_bool (tptp.image_2021386777_state H_1) Fa))))) (forall ((H_1 tptp.fun_fu1499449723_pname) (Fa tptp.fun_fu1430349052l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool Fa)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f674760225e_bool (tptp.image_1283814551_pname H_1) Fa))))) (forall ((H_1 tptp.fun_fu2380401_pname) (Fa tptp.fun_fu1996308102l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool Fa)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f1892738755e_bool (tptp.image_937015865_pname H_1) Fa))))) (forall ((H_1 tptp.fun_pn1262351275_state) (Fa tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname Fa)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state (tptp.hAPP_f1763243027e_bool (tptp.image_1918575693_state H_1) Fa))))) (forall ((A tptp.fun_pname_bool)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool tptp.bot_bo844097828e_bool) A))) (forall ((A tptp.fun_com_bool)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_f273696895l_bool tptp.ord_le1708315510m_bool tptp.bot_bot_fun_com_bool) A))) (forall ((A tptp.fun_Ho320143120e_bool)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool tptp.bot_bo39439654e_bool) A))) (forall ((A_4 tptp.com) (A tptp.fun_com_bool)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool tptp.finite_finite_com A)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool tptp.finite_finite_com (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com A_4) A))))) (forall ((A_4 tptp.fun_pname_bool) (A tptp.fun_fu1430349052l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool A_4) A))))) (forall ((A_4 tptp.fun_Ho320143120e_bool) (A tptp.fun_fu1996308102l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool A)) (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool (tptp.hAPP_f85652879l_bool (tptp.hAPP_f1941218614l_bool tptp.insert975831690e_bool A_4) A))))) (forall ((A_4 tptp.pname) (A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A_4) A))))) (forall ((A_4 tptp.hoare_363350478_state) (A tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state A)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state A_4) A))))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool tptp.bot_bo1649642514l_bool)) (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool tptp.bot_bo133096688l_bool)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool tptp.finite_finite_com tptp.bot_bot_fun_com_bool)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state tptp.bot_bo39439654e_bool)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname tptp.bot_bo844097828e_bool)) (forall ((Q_1 tptp.fun_fu1430349052l_bool) (P_1 tptp.fun_fu1430349052l_bool)) (=> (or (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool P_1))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool Q_1)))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f624840228l_bool tptp.cOMBS_350070575l_bool (tptp.hAPP_f143162813l_bool (tptp.cOMBB_2095475776e_bool tptp.fconj) P_1)) Q_1)))))) (forall ((Q_1 tptp.fun_fu1996308102l_bool) (P_1 tptp.fun_fu1996308102l_bool)) (=> (or (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool (tptp.hAPP_f85652879l_bool tptp.collec1243131813e_bool P_1))) (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool (tptp.hAPP_f85652879l_bool tptp.collec1243131813e_bool Q_1)))) (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool (tptp.hAPP_f85652879l_bool tptp.collec1243131813e_bool (tptp.hAPP_f85652879l_bool (tptp.hAPP_f927797370l_bool tptp.cOMBS_1039407915l_bool (tptp.hAPP_f945781379l_bool (tptp.cOMBB_1004232970e_bool tptp.fconj) P_1)) Q_1)))))) (forall ((Q_1 tptp.fun_Ho320143120e_bool) (P_1 tptp.fun_Ho320143120e_bool)) (=> (or (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state (tptp.hAPP_f1749453397e_bool tptp.collec223185785_state P_1))) (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state (tptp.hAPP_f1749453397e_bool tptp.collec223185785_state Q_1)))) (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state (tptp.hAPP_f1749453397e_bool tptp.collec223185785_state (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1612626488e_bool tptp.cOMBS_56025283l_bool (tptp.hAPP_f1422032445l_bool (tptp.cOMBB_877416532_state tptp.fconj) P_1)) Q_1)))))) (forall ((Q_1 tptp.fun_pname_bool) (P_1 tptp.fun_pname_bool)) (=> (or (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f759274231e_bool tptp.collect_pname P_1))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f759274231e_bool tptp.collect_pname Q_1)))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f759274231e_bool tptp.collect_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_f649174806e_bool tptp.cOMBS_568398431l_bool (tptp.hAPP_f1402196763l_bool (tptp.cOMBB_675860798_pname tptp.fconj) P_1)) Q_1)))))) (forall ((C tptp.pname) (A tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_f773602357e_bool (tptp.image_1927198851_pname (tptp.hAPP_p1379817622_pname tptp.cOMBK_83433476_state C)) A))) (let ((_let_2 (= A tptp.bot_bo39439654e_bool))) (and (=> _let_2 (= _let_1 tptp.bot_bo844097828e_bool)) (=> (not _let_2) (= _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname C) tptp.bot_bo844097828e_bool))))))) (forall ((C tptp.com) (A tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_f497466683m_bool (tptp.image_689867145te_com (tptp.hAPP_c6662434te_com tptp.cOMBK_1864507658_state C)) A))) (let ((_let_2 (= A tptp.bot_bo39439654e_bool))) (and (=> _let_2 (= _let_1 tptp.bot_bot_fun_com_bool)) (=> (not _let_2) (= _let_1 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com C) tptp.bot_bot_fun_com_bool))))))) (forall ((C tptp.hoare_363350478_state) (A tptp.fun_com_bool)) (let ((_let_1 (tptp.hAPP_f1859782925e_bool (tptp.image_1736049107_state (tptp.hAPP_H154362754_state tptp.cOMBK_818325696te_com C)) A))) (let ((_let_2 (= A tptp.bot_bot_fun_com_bool))) (and (=> _let_2 (= _let_1 tptp.bot_bo39439654e_bool)) (=> (not _let_2) (= _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state C) tptp.bot_bo39439654e_bool))))))) (forall ((C tptp.hoare_363350478_state) (A tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f1763243027e_bool (tptp.image_1918575693_state (tptp.hAPP_H1607320188_state tptp.cOMBK_92056634_pname C)) A))) (let ((_let_2 (= A tptp.bot_bo844097828e_bool))) (and (=> _let_2 (= _let_1 tptp.bot_bo39439654e_bool)) (=> (not _let_2) (= _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state C) tptp.bot_bo39439654e_bool))))))) (forall ((C tptp.pname) (X_1 tptp.hoare_363350478_state) (A tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state X_1) A)) (= (tptp.hAPP_f773602357e_bool (tptp.image_1927198851_pname (tptp.hAPP_p1379817622_pname tptp.cOMBK_83433476_state C)) A) (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname C) tptp.bot_bo844097828e_bool)))) (forall ((C tptp.com) (X_1 tptp.hoare_363350478_state) (A tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state X_1) A)) (= (tptp.hAPP_f497466683m_bool (tptp.image_689867145te_com (tptp.hAPP_c6662434te_com tptp.cOMBK_1864507658_state C)) A) (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com C) tptp.bot_bot_fun_com_bool)))) (forall ((C tptp.pname) (X_1 tptp.pname) (A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A)) (= (tptp.hAPP_f759274231e_bool (tptp.image_pname_pname (tptp.hAPP_p1170154830_pname tptp.cOMBK_pname_pname C)) A) (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname C) tptp.bot_bo844097828e_bool)))) (forall ((C tptp.com) (X_1 tptp.pname) (A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A)) (= (tptp.hAPP_f1206115581m_bool (tptp.image_pname_com (tptp.hAPP_c1494068046me_com tptp.cOMBK_com_pname C)) A) (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com C) tptp.bot_bot_fun_com_bool)))) (forall ((C tptp.hoare_363350478_state) (X_1 tptp.com) (A tptp.fun_com_bool)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_1) A)) (= (tptp.hAPP_f1859782925e_bool (tptp.image_1736049107_state (tptp.hAPP_H154362754_state tptp.cOMBK_818325696te_com C)) A) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state C) tptp.bot_bo39439654e_bool)))) (forall ((C tptp.hoare_363350478_state) (X_1 tptp.pname) (A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A)) (= (tptp.hAPP_f1763243027e_bool (tptp.image_1918575693_state (tptp.hAPP_H1607320188_state tptp.cOMBK_92056634_pname C)) A) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state C) tptp.bot_bo39439654e_bool)))) (forall ((F tptp.fun_com_option_com) (X_1 tptp.com) (Y_2 tptp.com)) (let ((_let_1 (tptp.dom_com_com F))) (=> (= (tptp.hAPP_com_option_com F X_1) (tptp.hAPP_com_option_com tptp.some_com Y_2)) (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com X_1) _let_1) _let_1)))) (forall ((F tptp.fun_Ho12798188_pname) (X_1 tptp.hoare_363350478_state) (Y_2 tptp.pname)) (let ((_let_1 (tptp.dom_Ho75493366_pname F))) (=> (= (tptp.hAPP_H134270346_pname F X_1) (tptp.hAPP_p1252095976_pname tptp.some_pname Y_2)) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state X_1) _let_1) _let_1)))) (forall ((F tptp.fun_Ho382349394_state) (X_1 tptp.hoare_363350478_state) (Y_2 tptp.hoare_363350478_state)) (let ((_let_1 (tptp.dom_Ho867270556_state F))) (=> (= (tptp.hAPP_H1942146718_state F X_1) (tptp.hAPP_H1942146718_state tptp.some_H629028223_state Y_2)) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state X_1) _let_1) _let_1)))) (forall ((F tptp.fun_pname_option_com) (X_1 tptp.pname) (Y_2 tptp.com)) (let ((_let_1 (tptp.dom_pname_com F))) (=> (= (tptp.hAPP_p799580910on_com F X_1) (tptp.hAPP_com_option_com tptp.some_com Y_2)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1) _let_1) _let_1)))) (forall ((B tptp.fun_fu1430349052l_bool) (F tptp.fun_Ho1262521325e_bool) (A tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state A)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool B) (tptp.hAPP_f766639041l_bool (tptp.image_1660610235e_bool F) A))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool B))))) (forall ((B tptp.fun_fu1996308102l_bool) (F tptp.fun_Ho424838195e_bool) (A tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state A)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool (tptp.hAPP_f746351743l_bool tptp.ord_le2031828156l_bool B) (tptp.hAPP_f726209793l_bool (tptp.image_1484638543e_bool F) A))) (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool B))))) (forall ((B tptp.fun_pname_bool) (F tptp.fun_Ho713471079_pname) (A tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state A)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) (tptp.hAPP_f773602357e_bool (tptp.image_1927198851_pname F) A))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B))))) (forall ((B tptp.fun_fu1430349052l_bool) (F tptp.fun_pn800050071e_bool) (A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool B) (tptp.hAPP_f434788991l_bool (tptp.image_47868345e_bool F) A))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool B))))) (forall ((B tptp.fun_fu1996308102l_bool) (F tptp.fun_pn1521100553e_bool) (A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool (tptp.hAPP_f746351743l_bool tptp.ord_le2031828156l_bool B) (tptp.hAPP_f682249667l_bool (tptp.image_1637084625e_bool F) A))) (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool B))))) (forall ((B tptp.fun_pname_bool) (F tptp.fun_pname_pname) (A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) (tptp.hAPP_f759274231e_bool (tptp.image_pname_pname F) A))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B))))) (forall ((B tptp.fun_Ho320143120e_bool) (F tptp.fun_fu54631149_state) (A tptp.fun_fu1430349052l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool B) (tptp.hAPP_f1912490857e_bool (tptp.image_431763259_state F) A))) (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state B))))) (forall ((B tptp.fun_Ho320143120e_bool) (F tptp.fun_fu700438391_state) (A tptp.fun_fu1996308102l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool B) (tptp.hAPP_f1180969799e_bool (tptp.image_2021386777_state F) A))) (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state B))))) (forall ((B tptp.fun_pname_bool) (F tptp.fun_fu1499449723_pname) (A tptp.fun_fu1430349052l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) (tptp.hAPP_f674760225e_bool (tptp.image_1283814551_pname F) A))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B))))) (forall ((B tptp.fun_pname_bool) (F tptp.fun_fu2380401_pname) (A tptp.fun_fu1996308102l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) (tptp.hAPP_f1892738755e_bool (tptp.image_937015865_pname F) A))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B))))) (forall ((B tptp.fun_Ho320143120e_bool) (F tptp.fun_pn1262351275_state) (A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool B) (tptp.hAPP_f1763243027e_bool (tptp.image_1918575693_state F) A))) (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state B))))) (forall ((A tptp.fun_pname_bool) (X_1 tptp.pname)) (let ((_let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1) tptp.bot_bo844097828e_bool))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) _let_1)) (or (= A tptp.bot_bo844097828e_bool) (= A _let_1))))) (forall ((A tptp.fun_com_bool) (X_1 tptp.com)) (let ((_let_1 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com X_1) tptp.bot_bot_fun_com_bool))) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_f273696895l_bool tptp.ord_le1708315510m_bool A) _let_1)) (or (= A tptp.bot_bot_fun_com_bool) (= A _let_1))))) (forall ((A tptp.fun_Ho320143120e_bool) (X_1 tptp.hoare_363350478_state)) (let ((_let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state X_1) tptp.bot_bo39439654e_bool))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool A) _let_1)) (or (= A tptp.bot_bo39439654e_bool) (= A _let_1))))) _let_13 (forall ((A_4 tptp.com)) (not (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com A_4) tptp.bot_bot_fun_com_bool)))) (forall ((A_4 tptp.hoare_363350478_state)) (not (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state A_4) tptp.bot_bo39439654e_bool)))) (forall ((A_4 tptp.pname)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A_4) tptp.bot_bo844097828e_bool)))) (forall ((B_1 tptp.com) (A_4 tptp.com) (B tptp.fun_com_bool)) (let ((_let_1 (tptp.hAPP_c667411853l_bool tptp.member_com A_4))) (=> (=> (not (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 B))) (= A_4 B_1)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com B_1) B)))))) (forall ((B_1 tptp.pname) (A_4 tptp.pname) (B tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname A_4))) (=> (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B))) (= A_4 B_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname B_1) B)))))) (forall ((B_1 tptp.hoare_363350478_state) (A_4 tptp.hoare_363350478_state) (B tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_H40373975l_bool tptp.member1253905979_state A_4))) (=> (=> (not (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 B))) (= A_4 B_1)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state B_1) B)))))) (forall ((A_4 tptp.com) (B_1 tptp.com) (A tptp.fun_com_bool)) (let ((_let_1 (tptp.hAPP_c667411853l_bool tptp.member_com A_4))) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com B_1) A))) (=> (not (= A_4 B_1)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 A)))))) (forall ((A_4 tptp.pname) (B_1 tptp.pname) (A tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname A_4))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname B_1) A))) (=> (not (= A_4 B_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A)))))) (forall ((A_4 tptp.hoare_363350478_state) (B_1 tptp.hoare_363350478_state) (A tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_H40373975l_bool tptp.member1253905979_state A_4))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state B_1) A))) (=> (not (= A_4 B_1)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 A)))))) (forall ((A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) A)) (= A B)))) (forall ((A tptp.fun_Ho320143120e_bool) (B tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool B) A)) (= A B)))) (forall ((C tptp.com) (A tptp.fun_com_bool) (B tptp.fun_com_bool)) (let ((_let_1 (tptp.hAPP_c667411853l_bool tptp.member_com C))) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_f273696895l_bool tptp.ord_le1708315510m_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 B)))))) (forall ((C tptp.hoare_363350478_state) (A tptp.fun_Ho320143120e_bool) (B tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_H40373975l_bool tptp.member1253905979_state C))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 B)))))) (forall ((C tptp.pname) (A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname C))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B)))))) (forall ((A tptp.fun_Ho320143120e_bool) (B_1 tptp.com) (F tptp.fun_Ho938602221te_com) (X_1 tptp.hoare_363350478_state)) (=> (= B_1 (tptp.hAPP_H2142737465te_com F X_1)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state X_1) A)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com B_1) (tptp.hAPP_f497466683m_bool (tptp.image_689867145te_com F) A)))))) (forall ((A tptp.fun_pname_bool) (B_1 tptp.com) (F tptp.fun_pname_com) (X_1 tptp.pname)) (=> (= B_1 (tptp.hAPP_pname_com F X_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com B_1) (tptp.hAPP_f1206115581m_bool (tptp.image_pname_com F) A)))))) (forall ((A tptp.fun_com_bool) (B_1 tptp.hoare_363350478_state) (F tptp.fun_co482540593_state) (X_1 tptp.com)) (=> (= B_1 (tptp.hAPP_c1041435779_state F X_1)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_1) A)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state B_1) (tptp.hAPP_f1859782925e_bool (tptp.image_1736049107_state F) A)))))) (forall ((A tptp.fun_com_bool) (B_1 tptp.pname) (F tptp.fun_com_pname) (X_1 tptp.com)) (=> (= B_1 (tptp.hAPP_com_pname F X_1)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_1) A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname B_1) (tptp.hAPP_f1438183293e_bool (tptp.image_com_pname F) A)))))) (forall ((A tptp.fun_pname_bool) (B_1 tptp.hoare_363350478_state) (F tptp.fun_pn1262351275_state) (X_1 tptp.pname)) (=> (= B_1 (tptp.hAPP_p1337579261_state F X_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state B_1) (tptp.hAPP_f1763243027e_bool (tptp.image_1918575693_state F) A)))))) (forall ((A_4 tptp.com) (A tptp.fun_com_bool)) (=> (= A tptp.bot_bot_fun_com_bool) (not (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com A_4) A))))) (forall ((A_4 tptp.hoare_363350478_state) (A tptp.fun_Ho320143120e_bool)) (=> (= A tptp.bot_bo39439654e_bool) (not (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state A_4) A))))) (forall ((A_4 tptp.pname) (A tptp.fun_pname_bool)) (=> (= A tptp.bot_bo844097828e_bool) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A_4) A))))) (forall ((P_1 tptp.fun_pname_bool)) (= (= (tptp.hAPP_f759274231e_bool tptp.collect_pname P_1) tptp.bot_bo844097828e_bool) (forall ((X_2 tptp.pname)) (not (tptp.hBOOL (tptp.hAPP_pname_bool P_1 X_2)))))) (forall ((P_1 tptp.fun_fu1430349052l_bool)) (= (= (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool P_1) tptp.bot_bo1649642514l_bool) (forall ((X_2 tptp.fun_pname_bool)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 X_2)))))) (forall ((P_1 tptp.fun_fu1996308102l_bool)) (= (= (tptp.hAPP_f85652879l_bool tptp.collec1243131813e_bool P_1) tptp.bot_bo133096688l_bool) (forall ((X_2 tptp.fun_Ho320143120e_bool)) (not (tptp.hBOOL (tptp.hAPP_f568432088l_bool P_1 X_2)))))) (forall ((P_1 tptp.fun_com_bool)) (= (= (tptp.hAPP_f1682609283m_bool tptp.collect_com P_1) tptp.bot_bot_fun_com_bool) (forall ((X_2 tptp.com)) (not (tptp.hBOOL (tptp.hAPP_com_bool P_1 X_2)))))) (forall ((P_1 tptp.fun_Ho320143120e_bool)) (= (= (tptp.hAPP_f1749453397e_bool tptp.collec223185785_state P_1) tptp.bot_bo39439654e_bool) (forall ((X_2 tptp.hoare_363350478_state)) (not (tptp.hBOOL (tptp.hAPP_H1645464494e_bool P_1 X_2)))))) (forall ((C tptp.com)) (not (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com C) tptp.bot_bot_fun_com_bool)))) (forall ((C tptp.hoare_363350478_state)) (not (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state C) tptp.bot_bo39439654e_bool)))) (forall ((C tptp.pname)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname C) tptp.bot_bo844097828e_bool)))) (forall ((P_1 tptp.fun_pname_bool)) (= (= tptp.bot_bo844097828e_bool (tptp.hAPP_f759274231e_bool tptp.collect_pname P_1)) (forall ((X_2 tptp.pname)) (not (tptp.hBOOL (tptp.hAPP_pname_bool P_1 X_2)))))) (forall ((P_1 tptp.fun_fu1430349052l_bool)) (= (= tptp.bot_bo1649642514l_bool (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool P_1)) (forall ((X_2 tptp.fun_pname_bool)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 X_2)))))) (forall ((P_1 tptp.fun_fu1996308102l_bool)) (= (= tptp.bot_bo133096688l_bool (tptp.hAPP_f85652879l_bool tptp.collec1243131813e_bool P_1)) (forall ((X_2 tptp.fun_Ho320143120e_bool)) (not (tptp.hBOOL (tptp.hAPP_f568432088l_bool P_1 X_2)))))) (forall ((P_1 tptp.fun_com_bool)) (= (= tptp.bot_bot_fun_com_bool (tptp.hAPP_f1682609283m_bool tptp.collect_com P_1)) (forall ((X_2 tptp.com)) (not (tptp.hBOOL (tptp.hAPP_com_bool P_1 X_2)))))) (forall ((P_1 tptp.fun_Ho320143120e_bool)) (= (= tptp.bot_bo39439654e_bool (tptp.hAPP_f1749453397e_bool tptp.collec223185785_state P_1)) (forall ((X_2 tptp.hoare_363350478_state)) (not (tptp.hBOOL (tptp.hAPP_H1645464494e_bool P_1 X_2)))))) (forall ((A tptp.fun_com_bool)) (= (exists ((X_2 tptp.com)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_2) A))) (not (= A tptp.bot_bot_fun_com_bool)))) (forall ((A tptp.fun_Ho320143120e_bool)) (= (exists ((X_2 tptp.hoare_363350478_state)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state X_2) A))) (not (= A tptp.bot_bo39439654e_bool)))) (forall ((A tptp.fun_pname_bool)) (= (exists ((X_2 tptp.pname)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A))) (not (= A tptp.bot_bo844097828e_bool)))) (forall ((A tptp.fun_com_bool)) (= (forall ((X_2 tptp.com)) (not (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_2) A)))) (= A tptp.bot_bot_fun_com_bool))) (forall ((A tptp.fun_Ho320143120e_bool)) (= (forall ((X_2 tptp.hoare_363350478_state)) (not (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state X_2) A)))) (= A tptp.bot_bo39439654e_bool))) (forall ((A tptp.fun_pname_bool)) (= (forall ((X_2 tptp.pname)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A)))) (= A tptp.bot_bo844097828e_bool))) (= tptp.bot_bo844097828e_bool (tptp.hAPP_f759274231e_bool tptp.collect_pname (tptp.hAPP_b76515610e_bool tptp.cOMBK_bool_pname tptp.fFalse))) (= tptp.bot_bo1649642514l_bool (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool (tptp.hAPP_b357632156l_bool tptp.cOMBK_1857069011e_bool tptp.fFalse))) (= tptp.bot_bo133096688l_bool (tptp.hAPP_f85652879l_bool tptp.collec1243131813e_bool (tptp.hAPP_b1504838374l_bool tptp.cOMBK_1696036407e_bool tptp.fFalse))) (= tptp.bot_bot_fun_com_bool (tptp.hAPP_f1682609283m_bool tptp.collect_com (tptp.hAPP_b1153789088m_bool tptp.cOMBK_bool_com tptp.fFalse))) (= tptp.bot_bo39439654e_bool (tptp.hAPP_f1749453397e_bool tptp.collec223185785_state (tptp.hAPP_b230077104e_bool tptp.cOMBK_574827367_state tptp.fFalse))) (forall ((A_4 tptp.com) (A tptp.fun_com_bool)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com A_4) A)) (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com A_4) A) A))) (forall ((A_4 tptp.pname) (A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A_4) A)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A_4) A) A))) (forall ((A_4 tptp.hoare_363350478_state) (A tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state A_4) A)) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state A_4) A) A))) (forall ((B_1 tptp.com) (A_4 tptp.com) (B tptp.fun_com_bool)) (let ((_let_1 (tptp.hAPP_c667411853l_bool tptp.member_com A_4))) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 B)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com B_1) B)))))) (forall ((B_1 tptp.pname) (A_4 tptp.pname) (B tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname A_4))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname B_1) B)))))) (forall ((B_1 tptp.hoare_363350478_state) (A_4 tptp.hoare_363350478_state) (B tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_H40373975l_bool tptp.member1253905979_state A_4))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 B)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state B_1) B)))))) (forall ((B tptp.fun_com_bool) (X_1 tptp.com) (A tptp.fun_com_bool)) (let ((_let_1 (tptp.hAPP_c566651504m_bool tptp.insert_com X_1))) (let ((_let_2 (tptp.hAPP_c667411853l_bool tptp.member_com X_1))) (=> (not (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_2 A))) (=> (not (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_2 B))) (= (= (tptp.hAPP_f1682609283m_bool _let_1 A) (tptp.hAPP_f1682609283m_bool _let_1 B)) (= A B))))))) (forall ((B tptp.fun_pname_bool) (X_1 tptp.pname) (A tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1))) (let ((_let_2 (tptp.hAPP_p338031245l_bool tptp.member_pname X_1))) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_2 A))) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_2 B))) (= (= (tptp.hAPP_f759274231e_bool _let_1 A) (tptp.hAPP_f759274231e_bool _let_1 B)) (= A B))))))) (forall ((B tptp.fun_Ho320143120e_bool) (X_1 tptp.hoare_363350478_state) (A tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state X_1))) (let ((_let_2 (tptp.hAPP_H40373975l_bool tptp.member1253905979_state X_1))) (=> (not (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_2 A))) (=> (not (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_2 B))) (= (= (tptp.hAPP_f1749453397e_bool _let_1 A) (tptp.hAPP_f1749453397e_bool _let_1 B)) (= A B))))))) (forall ((Y_2 tptp.pname) (A tptp.fun_pname_bool) (X_1 tptp.pname)) (= (tptp.hBOOL (tptp.hAPP_pname_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname Y_2) A) X_1)) (or (= Y_2 X_1) (tptp.hBOOL (tptp.hAPP_pname_bool A X_1))))) (forall ((Y_2 tptp.com) (A tptp.fun_com_bool) (X_1 tptp.com)) (= (tptp.hBOOL (tptp.hAPP_com_bool (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com Y_2) A) X_1)) (or (= Y_2 X_1) (tptp.hBOOL (tptp.hAPP_com_bool A X_1))))) (forall ((Y_2 tptp.hoare_363350478_state) (A tptp.fun_Ho320143120e_bool) (X_1 tptp.hoare_363350478_state)) (= (tptp.hBOOL (tptp.hAPP_H1645464494e_bool (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state Y_2) A) X_1)) (or (= Y_2 X_1) (tptp.hBOOL (tptp.hAPP_H1645464494e_bool A X_1))))) (forall ((A_4 tptp.com) (B_1 tptp.com) (A tptp.fun_com_bool)) (let ((_let_1 (tptp.hAPP_c667411853l_bool tptp.member_com A_4))) (= (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com B_1) A))) (or (= A_4 B_1) (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 A)))))) (forall ((A_4 tptp.pname) (B_1 tptp.pname) (A tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname A_4))) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname B_1) A))) (or (= A_4 B_1) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A)))))) (forall ((A_4 tptp.hoare_363350478_state) (B_1 tptp.hoare_363350478_state) (A tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_H40373975l_bool tptp.member1253905979_state A_4))) (= (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state B_1) A))) (or (= A_4 B_1) (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 A)))))) (forall ((X_1 tptp.pname) (Y_2 tptp.pname) (A tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1))) (let ((_let_2 (tptp.hAPP_p905327722e_bool tptp.insert_pname Y_2))) (= (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool _let_2 A)) (tptp.hAPP_f759274231e_bool _let_2 (tptp.hAPP_f759274231e_bool _let_1 A)))))) (forall ((X_1 tptp.com) (Y_2 tptp.com) (A tptp.fun_com_bool)) (let ((_let_1 (tptp.hAPP_c566651504m_bool tptp.insert_com X_1))) (let ((_let_2 (tptp.hAPP_c566651504m_bool tptp.insert_com Y_2))) (= (tptp.hAPP_f1682609283m_bool _let_1 (tptp.hAPP_f1682609283m_bool _let_2 A)) (tptp.hAPP_f1682609283m_bool _let_2 (tptp.hAPP_f1682609283m_bool _let_1 A)))))) (forall ((X_1 tptp.hoare_363350478_state) (Y_2 tptp.hoare_363350478_state) (A tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state X_1))) (let ((_let_2 (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state Y_2))) (= (tptp.hAPP_f1749453397e_bool _let_1 (tptp.hAPP_f1749453397e_bool _let_2 A)) (tptp.hAPP_f1749453397e_bool _let_2 (tptp.hAPP_f1749453397e_bool _let_1 A)))))) (forall ((X_1 tptp.pname) (A tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1))) (let ((_let_2 (tptp.hAPP_f759274231e_bool _let_1 A))) (= (tptp.hAPP_f759274231e_bool _let_1 _let_2) _let_2)))) (forall ((X_1 tptp.com) (A tptp.fun_com_bool)) (let ((_let_1 (tptp.hAPP_c566651504m_bool tptp.insert_com X_1))) (let ((_let_2 (tptp.hAPP_f1682609283m_bool _let_1 A))) (= (tptp.hAPP_f1682609283m_bool _let_1 _let_2) _let_2)))) (forall ((X_1 tptp.hoare_363350478_state) (A tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state X_1))) (let ((_let_2 (tptp.hAPP_f1749453397e_bool _let_1 A))) (= (tptp.hAPP_f1749453397e_bool _let_1 _let_2) _let_2)))) (forall ((A_4 tptp.pname) (P_1 tptp.fun_pname_bool)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A_4) (tptp.hAPP_f759274231e_bool tptp.collect_pname P_1)) (tptp.hAPP_f759274231e_bool tptp.collect_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_f649174806e_bool tptp.cOMBS_568398431l_bool (tptp.hAPP_f1402196763l_bool (tptp.cOMBB_675860798_pname tptp.fimplies) (tptp.hAPP_f759274231e_bool (tptp.cOMBB_647938656_pname tptp.fNot) (tptp.hAPP_p61793385e_bool (tptp.hAPP_f22061361e_bool tptp.cOMBC_1149511130e_bool tptp.fequal_pname) A_4)))) P_1)))) (forall ((A_4 tptp.com) (P_1 tptp.fun_com_bool)) (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com A_4) (tptp.hAPP_f1682609283m_bool tptp.collect_com P_1)) (tptp.hAPP_f1682609283m_bool tptp.collect_com (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f328772264m_bool tptp.cOMBS_com_bool_bool (tptp.hAPP_f954469007l_bool (tptp.cOMBB_886968260ol_com tptp.fimplies) (tptp.hAPP_f1682609283m_bool (tptp.cOMBB_bool_bool_com tptp.fNot) (tptp.hAPP_c1396316405m_bool (tptp.hAPP_f908845385m_bool tptp.cOMBC_com_com_bool tptp.fequal_com) A_4)))) P_1)))) (forall ((A_4 tptp.fun_pname_bool) (P_1 tptp.fun_fu1430349052l_bool)) (= (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool A_4) (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool P_1)) (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f624840228l_bool tptp.cOMBS_350070575l_bool (tptp.hAPP_f143162813l_bool (tptp.cOMBB_2095475776e_bool tptp.fimplies) (tptp.hAPP_f559147733l_bool (tptp.cOMBB_307249310e_bool tptp.fNot) (tptp.hAPP_f434788991l_bool (tptp.hAPP_f1297925993l_bool tptp.cOMBC_1284144636l_bool tptp.fequal533582459e_bool) A_4)))) P_1)))) (forall ((A_4 tptp.fun_Ho320143120e_bool) (P_1 tptp.fun_fu1996308102l_bool)) (= (tptp.hAPP_f85652879l_bool (tptp.hAPP_f1941218614l_bool tptp.insert975831690e_bool A_4) (tptp.hAPP_f85652879l_bool tptp.collec1243131813e_bool P_1)) (tptp.hAPP_f85652879l_bool tptp.collec1243131813e_bool (tptp.hAPP_f85652879l_bool (tptp.hAPP_f927797370l_bool tptp.cOMBS_1039407915l_bool (tptp.hAPP_f945781379l_bool (tptp.cOMBB_1004232970e_bool tptp.fimplies) (tptp.hAPP_f85652879l_bool (tptp.cOMBB_941362220e_bool tptp.fNot) (tptp.hAPP_f726209793l_bool (tptp.hAPP_f205303905l_bool tptp.cOMBC_1250231770l_bool tptp.fequal731041167e_bool) A_4)))) P_1)))) (forall ((A_4 tptp.hoare_363350478_state) (P_1 tptp.fun_Ho320143120e_bool)) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state A_4) (tptp.hAPP_f1749453397e_bool tptp.collec223185785_state P_1)) (tptp.hAPP_f1749453397e_bool tptp.collec223185785_state (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1612626488e_bool tptp.cOMBS_56025283l_bool (tptp.hAPP_f1422032445l_bool (tptp.cOMBB_877416532_state tptp.fimplies) (tptp.hAPP_f1749453397e_bool (tptp.cOMBB_2059354034_state tptp.fNot) (tptp.hAPP_H705653759e_bool (tptp.hAPP_f114072425e_bool tptp.cOMBC_13083556e_bool tptp.fequal1026769423_state) A_4)))) P_1)))) (forall ((A_4 tptp.com) (B tptp.fun_com_bool)) (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com A_4) B) (tptp.hAPP_f1682609283m_bool tptp.collect_com (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f328772264m_bool tptp.cOMBS_com_bool_bool (tptp.hAPP_f954469007l_bool (tptp.cOMBB_886968260ol_com tptp.fdisj) (tptp.hAPP_c1396316405m_bool (tptp.hAPP_f908845385m_bool tptp.cOMBC_com_com_bool tptp.fequal_com) A_4))) (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f578650245m_bool tptp.cOMBC_1904837336l_bool tptp.member_com) B))))) (forall ((A_4 tptp.fun_pname_bool) (B tptp.fun_fu1430349052l_bool)) (= (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool A_4) B) (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f624840228l_bool tptp.cOMBS_350070575l_bool (tptp.hAPP_f143162813l_bool (tptp.cOMBB_2095475776e_bool tptp.fdisj) (tptp.hAPP_f434788991l_bool (tptp.hAPP_f1297925993l_bool tptp.cOMBC_1284144636l_bool tptp.fequal533582459e_bool) A_4))) (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1145991873l_bool tptp.cOMBC_1988546018l_bool tptp.member799430823e_bool) B))))) (forall ((A_4 tptp.fun_Ho320143120e_bool) (B tptp.fun_fu1996308102l_bool)) (= (tptp.hAPP_f85652879l_bool (tptp.hAPP_f1941218614l_bool tptp.insert975831690e_bool A_4) B) (tptp.hAPP_f85652879l_bool tptp.collec1243131813e_bool (tptp.hAPP_f85652879l_bool (tptp.hAPP_f927797370l_bool tptp.cOMBS_1039407915l_bool (tptp.hAPP_f945781379l_bool (tptp.cOMBB_1004232970e_bool tptp.fdisj) (tptp.hAPP_f726209793l_bool (tptp.hAPP_f205303905l_bool tptp.cOMBC_1250231770l_bool tptp.fequal731041167e_bool) A_4))) (tptp.hAPP_f85652879l_bool (tptp.hAPP_f1854331281l_bool tptp.cOMBC_1522409444l_bool tptp.member1534059107e_bool) B))))) (forall ((A_4 tptp.pname) (B tptp.fun_pname_bool)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A_4) B) (tptp.hAPP_f759274231e_bool tptp.collect_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_f649174806e_bool tptp.cOMBS_568398431l_bool (tptp.hAPP_f1402196763l_bool (tptp.cOMBB_675860798_pname tptp.fdisj) (tptp.hAPP_p61793385e_bool (tptp.hAPP_f22061361e_bool tptp.cOMBC_1149511130e_bool tptp.fequal_pname) A_4))) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f661147897e_bool tptp.cOMBC_1058051404l_bool tptp.member_pname) B))))) (forall ((A_4 tptp.hoare_363350478_state) (B tptp.fun_Ho320143120e_bool)) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state A_4) B) (tptp.hAPP_f1749453397e_bool tptp.collec223185785_state (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1612626488e_bool tptp.cOMBS_56025283l_bool (tptp.hAPP_f1422032445l_bool (tptp.cOMBB_877416532_state tptp.fdisj) (tptp.hAPP_H705653759e_bool (tptp.hAPP_f114072425e_bool tptp.cOMBC_13083556e_bool tptp.fequal1026769423_state) A_4))) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1072682137e_bool tptp.cOMBC_1415895650l_bool tptp.member1253905979_state) B))))) (forall ((A_4 tptp.com) (B tptp.fun_com_bool)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com A_4) (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com A_4) B)))) (forall ((A_4 tptp.pname) (B tptp.fun_pname_bool)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A_4) (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A_4) B)))) (forall ((A_4 tptp.hoare_363350478_state) (B tptp.fun_Ho320143120e_bool)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state A_4) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state A_4) B)))) (forall ((A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (=> (= A B) (not (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) B)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) A))))))) (forall ((A tptp.fun_Ho320143120e_bool) (B tptp.fun_Ho320143120e_bool)) (=> (= A B) (not (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool A) B)) (not (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool B) A))))))) (forall ((C_1 tptp.fun_pname_bool) (A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) C_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 C_1)))))) (forall ((C_1 tptp.fun_Ho320143120e_bool) (A tptp.fun_Ho320143120e_bool) (B tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool A))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 B)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool B) C_1)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 C_1)))))) (forall ((X_1 tptp.com) (A tptp.fun_com_bool) (B tptp.fun_com_bool)) (let ((_let_1 (tptp.hAPP_c667411853l_bool tptp.member_com X_1))) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_f273696895l_bool tptp.ord_le1708315510m_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 B)))))) (forall ((X_1 tptp.hoare_363350478_state) (A tptp.fun_Ho320143120e_bool) (B tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_H40373975l_bool tptp.member1253905979_state X_1))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 B)))))) (forall ((X_1 tptp.pname) (A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname X_1))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B)))))) (forall ((B tptp.fun_com_bool) (X_1 tptp.com) (A tptp.fun_com_bool)) (let ((_let_1 (tptp.hAPP_c667411853l_bool tptp.member_com X_1))) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 A)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_f273696895l_bool tptp.ord_le1708315510m_bool A) B)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 B)))))) (forall ((B tptp.fun_Ho320143120e_bool) (X_1 tptp.hoare_363350478_state) (A tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_H40373975l_bool tptp.member1253905979_state X_1))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 A)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool A) B)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 B)))))) (forall ((B tptp.fun_pname_bool) (X_1 tptp.pname) (A tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname X_1))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) B)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B)))))) (forall ((X_1 tptp.com) (A tptp.fun_com_bool) (B tptp.fun_com_bool)) (let ((_let_1 (tptp.hAPP_c667411853l_bool tptp.member_com X_1))) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_f273696895l_bool tptp.ord_le1708315510m_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 B)))))) (forall ((X_1 tptp.hoare_363350478_state) (A tptp.fun_Ho320143120e_bool) (B tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_H40373975l_bool tptp.member1253905979_state X_1))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 B)))))) (forall ((X_1 tptp.pname) (A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname X_1))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B)))))) (forall ((A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (=> (= A B) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) A)))) (forall ((A tptp.fun_Ho320143120e_bool) (B tptp.fun_Ho320143120e_bool)) (=> (= A B) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool B) A)))) (forall ((A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (=> (= A B) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) B)))) (forall ((A tptp.fun_Ho320143120e_bool) (B tptp.fun_Ho320143120e_bool)) (=> (= A B) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool A) B)))) (forall ((A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (= (= A B) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) B)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) A))))) (forall ((A tptp.fun_Ho320143120e_bool) (B tptp.fun_Ho320143120e_bool)) (= (= A B) (and (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool A) B)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool B) A))))) (forall ((A tptp.fun_pname_bool)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) A))) (forall ((A tptp.fun_Ho320143120e_bool)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool A) A))) (forall ((B_1 tptp.com) (F tptp.fun_Ho938602221te_com) (X_1 tptp.hoare_363350478_state) (A tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state X_1) A)) (=> (= B_1 (tptp.hAPP_H2142737465te_com F X_1)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com B_1) (tptp.hAPP_f497466683m_bool (tptp.image_689867145te_com F) A)))))) (forall ((B_1 tptp.com) (F tptp.fun_pname_com) (X_1 tptp.pname) (A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A)) (=> (= B_1 (tptp.hAPP_pname_com F X_1)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com B_1) (tptp.hAPP_f1206115581m_bool (tptp.image_pname_com F) A)))))) (forall ((B_1 tptp.hoare_363350478_state) (F tptp.fun_co482540593_state) (X_1 tptp.com) (A tptp.fun_com_bool)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_1) A)) (=> (= B_1 (tptp.hAPP_c1041435779_state F X_1)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state B_1) (tptp.hAPP_f1859782925e_bool (tptp.image_1736049107_state F) A)))))) (forall ((B_1 tptp.pname) (F tptp.fun_com_pname) (X_1 tptp.com) (A tptp.fun_com_bool)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_1) A)) (=> (= B_1 (tptp.hAPP_com_pname F X_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname B_1) (tptp.hAPP_f1438183293e_bool (tptp.image_com_pname F) A)))))) (forall ((B_1 tptp.hoare_363350478_state) (F tptp.fun_pn1262351275_state) (X_1 tptp.pname) (A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A)) (=> (= B_1 (tptp.hAPP_p1337579261_state F X_1)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state B_1) (tptp.hAPP_f1763243027e_bool (tptp.image_1918575693_state F) A)))))) (forall ((F tptp.fun_Ho938602221te_com) (X_1 tptp.hoare_363350478_state) (A tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state X_1) A)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com (tptp.hAPP_H2142737465te_com F X_1)) (tptp.hAPP_f497466683m_bool (tptp.image_689867145te_com F) A))))) (forall ((F tptp.fun_pname_com) (X_1 tptp.pname) (A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com (tptp.hAPP_pname_com F X_1)) (tptp.hAPP_f1206115581m_bool (tptp.image_pname_com F) A))))) (forall ((F tptp.fun_co482540593_state) (X_1 tptp.com) (A tptp.fun_com_bool)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_1) A)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state (tptp.hAPP_c1041435779_state F X_1)) (tptp.hAPP_f1859782925e_bool (tptp.image_1736049107_state F) A))))) (forall ((F tptp.fun_com_pname) (X_1 tptp.com) (A tptp.fun_com_bool)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_1) A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname (tptp.hAPP_com_pname F X_1)) (tptp.hAPP_f1438183293e_bool (tptp.image_com_pname F) A))))) (forall ((F tptp.fun_pn1262351275_state) (X_1 tptp.pname) (A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state (tptp.hAPP_p1337579261_state F X_1)) (tptp.hAPP_f1763243027e_bool (tptp.image_1918575693_state F) A))))) (forall ((Z tptp.hoare_363350478_state) (F tptp.fun_pn1262351275_state) (A tptp.fun_pname_bool)) (= (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state Z) (tptp.hAPP_f1763243027e_bool (tptp.image_1918575693_state F) A))) (exists ((X_2 tptp.pname)) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A)) (= Z (tptp.hAPP_p1337579261_state F X_2)))))) (forall ((P_1 tptp.fun_fu1430349052l_bool) (Q_1 tptp.fun_fu1430349052l_bool)) (= (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f624840228l_bool tptp.cOMBS_350070575l_bool (tptp.hAPP_f143162813l_bool (tptp.cOMBB_2095475776e_bool tptp.fdisj) P_1)) Q_1)))) (and (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool P_1))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool Q_1)))))) (forall ((P_1 tptp.fun_fu1996308102l_bool) (Q_1 tptp.fun_fu1996308102l_bool)) (= (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool (tptp.hAPP_f85652879l_bool tptp.collec1243131813e_bool (tptp.hAPP_f85652879l_bool (tptp.hAPP_f927797370l_bool tptp.cOMBS_1039407915l_bool (tptp.hAPP_f945781379l_bool (tptp.cOMBB_1004232970e_bool tptp.fdisj) P_1)) Q_1)))) (and (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool (tptp.hAPP_f85652879l_bool tptp.collec1243131813e_bool P_1))) (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool (tptp.hAPP_f85652879l_bool tptp.collec1243131813e_bool Q_1)))))) (forall ((P_1 tptp.fun_Ho320143120e_bool) (Q_1 tptp.fun_Ho320143120e_bool)) (= (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state (tptp.hAPP_f1749453397e_bool tptp.collec223185785_state (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1612626488e_bool tptp.cOMBS_56025283l_bool (tptp.hAPP_f1422032445l_bool (tptp.cOMBB_877416532_state tptp.fdisj) P_1)) Q_1)))) (and (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state (tptp.hAPP_f1749453397e_bool tptp.collec223185785_state P_1))) (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state (tptp.hAPP_f1749453397e_bool tptp.collec223185785_state Q_1)))))) (forall ((P_1 tptp.fun_pname_bool) (Q_1 tptp.fun_pname_bool)) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f759274231e_bool tptp.collect_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_f649174806e_bool tptp.cOMBS_568398431l_bool (tptp.hAPP_f1402196763l_bool (tptp.cOMBB_675860798_pname tptp.fdisj) P_1)) Q_1)))) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f759274231e_bool tptp.collect_pname P_1))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f759274231e_bool tptp.collect_pname Q_1)))))) (forall ((X_2 tptp.com) (Xa tptp.fun_com_bool)) (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com X_2) Xa) (tptp.hAPP_f1682609283m_bool tptp.collect_com (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f328772264m_bool tptp.cOMBS_com_bool_bool (tptp.hAPP_f954469007l_bool (tptp.cOMBB_886968260ol_com tptp.fdisj) (tptp.hAPP_c1396316405m_bool (tptp.hAPP_f908845385m_bool tptp.cOMBC_com_com_bool tptp.fequal_com) X_2))) (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f578650245m_bool tptp.cOMBC_1904837336l_bool tptp.member_com) Xa))))) (forall ((X_2 tptp.fun_pname_bool) (Xa tptp.fun_fu1430349052l_bool)) (= (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool X_2) Xa) (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f624840228l_bool tptp.cOMBS_350070575l_bool (tptp.hAPP_f143162813l_bool (tptp.cOMBB_2095475776e_bool tptp.fdisj) (tptp.hAPP_f434788991l_bool (tptp.hAPP_f1297925993l_bool tptp.cOMBC_1284144636l_bool tptp.fequal533582459e_bool) X_2))) (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1145991873l_bool tptp.cOMBC_1988546018l_bool tptp.member799430823e_bool) Xa))))) (forall ((X_2 tptp.fun_Ho320143120e_bool) (Xa tptp.fun_fu1996308102l_bool)) (= (tptp.hAPP_f85652879l_bool (tptp.hAPP_f1941218614l_bool tptp.insert975831690e_bool X_2) Xa) (tptp.hAPP_f85652879l_bool tptp.collec1243131813e_bool (tptp.hAPP_f85652879l_bool (tptp.hAPP_f927797370l_bool tptp.cOMBS_1039407915l_bool (tptp.hAPP_f945781379l_bool (tptp.cOMBB_1004232970e_bool tptp.fdisj) (tptp.hAPP_f726209793l_bool (tptp.hAPP_f205303905l_bool tptp.cOMBC_1250231770l_bool tptp.fequal731041167e_bool) X_2))) (tptp.hAPP_f85652879l_bool (tptp.hAPP_f1854331281l_bool tptp.cOMBC_1522409444l_bool tptp.member1534059107e_bool) Xa))))) (forall ((X_2 tptp.pname) (Xa tptp.fun_pname_bool)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname X_2) Xa) (tptp.hAPP_f759274231e_bool tptp.collect_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_f649174806e_bool tptp.cOMBS_568398431l_bool (tptp.hAPP_f1402196763l_bool (tptp.cOMBB_675860798_pname tptp.fdisj) (tptp.hAPP_p61793385e_bool (tptp.hAPP_f22061361e_bool tptp.cOMBC_1149511130e_bool tptp.fequal_pname) X_2))) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f661147897e_bool tptp.cOMBC_1058051404l_bool tptp.member_pname) Xa))))) (forall ((X_2 tptp.hoare_363350478_state) (Xa tptp.fun_Ho320143120e_bool)) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state X_2) Xa) (tptp.hAPP_f1749453397e_bool tptp.collec223185785_state (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1612626488e_bool tptp.cOMBS_56025283l_bool (tptp.hAPP_f1422032445l_bool (tptp.cOMBB_877416532_state tptp.fdisj) (tptp.hAPP_H705653759e_bool (tptp.hAPP_f114072425e_bool tptp.cOMBC_13083556e_bool tptp.fequal1026769423_state) X_2))) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1072682137e_bool tptp.cOMBC_1415895650l_bool tptp.member1253905979_state) Xa))))) (forall ((A_4 tptp.pname) (B_1 tptp.pname)) (=> (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A_4) tptp.bot_bo844097828e_bool) (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname B_1) tptp.bot_bo844097828e_bool)) (= A_4 B_1))) (forall ((A_4 tptp.com) (B_1 tptp.com)) (=> (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com A_4) tptp.bot_bot_fun_com_bool) (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com B_1) tptp.bot_bot_fun_com_bool)) (= A_4 B_1))) (forall ((A_4 tptp.hoare_363350478_state) (B_1 tptp.hoare_363350478_state)) (=> (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state A_4) tptp.bot_bo39439654e_bool) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state B_1) tptp.bot_bo39439654e_bool)) (= A_4 B_1))) (forall ((B_1 tptp.com) (A_4 tptp.com)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com B_1) (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com A_4) tptp.bot_bot_fun_com_bool))) (= B_1 A_4))) (forall ((B_1 tptp.pname) (A_4 tptp.pname)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname B_1) (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A_4) tptp.bot_bo844097828e_bool))) (= B_1 A_4))) (forall ((B_1 tptp.hoare_363350478_state) (A_4 tptp.hoare_363350478_state)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state B_1) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state A_4) tptp.bot_bo39439654e_bool))) (= B_1 A_4))) (forall ((A_4 tptp.pname) (B_1 tptp.pname) (C tptp.pname) (D_1 tptp.pname)) (= (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A_4) (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname B_1) tptp.bot_bo844097828e_bool)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname C) (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname D_1) tptp.bot_bo844097828e_bool))) (or (and (= A_4 C) (= B_1 D_1)) (and (= A_4 D_1) (= B_1 C))))) (forall ((A_4 tptp.com) (B_1 tptp.com) (C tptp.com) (D_1 tptp.com)) (= (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com A_4) (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com B_1) tptp.bot_bot_fun_com_bool)) (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com C) (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com D_1) tptp.bot_bot_fun_com_bool))) (or (and (= A_4 C) (= B_1 D_1)) (and (= A_4 D_1) (= B_1 C))))) (forall ((A_4 tptp.hoare_363350478_state) (B_1 tptp.hoare_363350478_state) (C tptp.hoare_363350478_state) (D_1 tptp.hoare_363350478_state)) (= (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state A_4) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state B_1) tptp.bot_bo39439654e_bool)) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state C) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state D_1) tptp.bot_bo39439654e_bool))) (or (and (= A_4 C) (= B_1 D_1)) (and (= A_4 D_1) (= B_1 C))))) (forall ((B_1 tptp.com) (A_4 tptp.com)) (= (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com B_1) (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com A_4) tptp.bot_bot_fun_com_bool))) (= B_1 A_4))) (forall ((B_1 tptp.pname) (A_4 tptp.pname)) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname B_1) (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A_4) tptp.bot_bo844097828e_bool))) (= B_1 A_4))) (forall ((B_1 tptp.hoare_363350478_state) (A_4 tptp.hoare_363350478_state)) (= (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state B_1) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state A_4) tptp.bot_bo39439654e_bool))) (= B_1 A_4))) (forall ((A_4 tptp.pname) (A tptp.fun_pname_bool)) (not (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A_4) A) tptp.bot_bo844097828e_bool))) (forall ((A_4 tptp.com) (A tptp.fun_com_bool)) (not (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com A_4) A) tptp.bot_bot_fun_com_bool))) (forall ((A_4 tptp.hoare_363350478_state) (A tptp.fun_Ho320143120e_bool)) (not (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state A_4) A) tptp.bot_bo39439654e_bool))) (forall ((A_4 tptp.pname) (A tptp.fun_pname_bool)) (not (= tptp.bot_bo844097828e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A_4) A)))) (forall ((A_4 tptp.com) (A tptp.fun_com_bool)) (not (= tptp.bot_bot_fun_com_bool (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com A_4) A)))) (forall ((A_4 tptp.hoare_363350478_state) (A tptp.fun_Ho320143120e_bool)) (not (= tptp.bot_bo39439654e_bool (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state A_4) A)))) (forall ((A_4 tptp.com) (A tptp.fun_com_bool)) (= (tptp.hBOOL (tptp.hAPP_f990396704l_bool tptp.finite_finite_com (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com A_4) A))) (tptp.hBOOL (tptp.hAPP_f990396704l_bool tptp.finite_finite_com A)))) (forall ((A_4 tptp.fun_pname_bool) (A tptp.fun_fu1430349052l_bool)) (= (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool A_4) A))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)))) (forall ((A_4 tptp.fun_Ho320143120e_bool) (A tptp.fun_fu1996308102l_bool)) (= (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool (tptp.hAPP_f85652879l_bool (tptp.hAPP_f1941218614l_bool tptp.insert975831690e_bool A_4) A))) (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool A)))) (forall ((A_4 tptp.pname) (A tptp.fun_pname_bool)) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A_4) A))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)))) (forall ((A_4 tptp.hoare_363350478_state) (A tptp.fun_Ho320143120e_bool)) (= (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state A_4) A))) (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state A)))) (forall ((A tptp.fun_pname_bool)) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) tptp.bot_bo844097828e_bool)) (= A tptp.bot_bo844097828e_bool))) (forall ((A tptp.fun_com_bool)) (= (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_f273696895l_bool tptp.ord_le1708315510m_bool A) tptp.bot_bot_fun_com_bool)) (= A tptp.bot_bot_fun_com_bool))) (forall ((A tptp.fun_Ho320143120e_bool)) (= (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool A) tptp.bot_bo39439654e_bool)) (= A tptp.bot_bo39439654e_bool))) (forall ((F tptp.fun_co482540593_state) (A tptp.fun_com_bool)) (= (= (tptp.hAPP_f1859782925e_bool (tptp.image_1736049107_state F) A) tptp.bot_bo39439654e_bool) (= A tptp.bot_bot_fun_com_bool))) (forall ((F tptp.fun_Ho713471079_pname) (A tptp.fun_Ho320143120e_bool)) (= (= (tptp.hAPP_f773602357e_bool (tptp.image_1927198851_pname F) A) tptp.bot_bo844097828e_bool) (= A tptp.bot_bo39439654e_bool))) (forall ((F tptp.fun_Ho938602221te_com) (A tptp.fun_Ho320143120e_bool)) (= (= (tptp.hAPP_f497466683m_bool (tptp.image_689867145te_com F) A) tptp.bot_bot_fun_com_bool) (= A tptp.bot_bo39439654e_bool))) (forall ((F tptp.fun_pn1262351275_state) (A tptp.fun_pname_bool)) (= (= (tptp.hAPP_f1763243027e_bool (tptp.image_1918575693_state F) A) tptp.bot_bo39439654e_bool) (= A tptp.bot_bo844097828e_bool))) (forall ((F tptp.fun_Ho713471079_pname)) (= (tptp.hAPP_f773602357e_bool (tptp.image_1927198851_pname F) tptp.bot_bo39439654e_bool) tptp.bot_bo844097828e_bool)) (forall ((F tptp.fun_Ho938602221te_com)) (= (tptp.hAPP_f497466683m_bool (tptp.image_689867145te_com F) tptp.bot_bo39439654e_bool) tptp.bot_bot_fun_com_bool)) (forall ((F tptp.fun_co482540593_state)) (= (tptp.hAPP_f1859782925e_bool (tptp.image_1736049107_state F) tptp.bot_bot_fun_com_bool) tptp.bot_bo39439654e_bool)) (forall ((F tptp.fun_pn1262351275_state)) (= (tptp.hAPP_f1763243027e_bool (tptp.image_1918575693_state F) tptp.bot_bo844097828e_bool) tptp.bot_bo39439654e_bool)) (forall ((F tptp.fun_co482540593_state) (A tptp.fun_com_bool)) (= (= tptp.bot_bo39439654e_bool (tptp.hAPP_f1859782925e_bool (tptp.image_1736049107_state F) A)) (= A tptp.bot_bot_fun_com_bool))) (forall ((F tptp.fun_Ho713471079_pname) (A tptp.fun_Ho320143120e_bool)) (= (= tptp.bot_bo844097828e_bool (tptp.hAPP_f773602357e_bool (tptp.image_1927198851_pname F) A)) (= A tptp.bot_bo39439654e_bool))) (forall ((F tptp.fun_Ho938602221te_com) (A tptp.fun_Ho320143120e_bool)) (= (= tptp.bot_bot_fun_com_bool (tptp.hAPP_f497466683m_bool (tptp.image_689867145te_com F) A)) (= A tptp.bot_bo39439654e_bool))) (forall ((F tptp.fun_pn1262351275_state) (A tptp.fun_pname_bool)) (= (= tptp.bot_bo39439654e_bool (tptp.hAPP_f1763243027e_bool (tptp.image_1918575693_state F) A)) (= A tptp.bot_bo844097828e_bool))) (forall ((A tptp.fun_fu1430349052l_bool) (B tptp.fun_fu1430349052l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool B)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A))))) (forall ((A tptp.fun_fu1996308102l_bool) (B tptp.fun_fu1996308102l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool (tptp.hAPP_f746351743l_bool tptp.ord_le2031828156l_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool B)) (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool A))))) (forall ((A tptp.fun_Ho320143120e_bool) (B tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state B)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state A))))) (forall ((A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A))))) (forall ((A tptp.fun_fu1430349052l_bool) (B tptp.fun_fu1430349052l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool B)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool A) B)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A))))) (forall ((A tptp.fun_fu1996308102l_bool) (B tptp.fun_fu1996308102l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool B)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool (tptp.hAPP_f746351743l_bool tptp.ord_le2031828156l_bool A) B)) (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool A))))) (forall ((A tptp.fun_Ho320143120e_bool) (B tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state B)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool A) B)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state A))))) (forall ((A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) B)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A))))) (forall ((A_4 tptp.pname) (C_1 tptp.fun_pname_bool) (D tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p905327722e_bool tptp.insert_pname A_4))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool C_1) D)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool _let_1 C_1)) (tptp.hAPP_f759274231e_bool _let_1 D)))))) (forall ((A_4 tptp.com) (C_1 tptp.fun_com_bool) (D tptp.fun_com_bool)) (let ((_let_1 (tptp.hAPP_c566651504m_bool tptp.insert_com A_4))) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_f273696895l_bool tptp.ord_le1708315510m_bool C_1) D)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_f273696895l_bool tptp.ord_le1708315510m_bool (tptp.hAPP_f1682609283m_bool _let_1 C_1)) (tptp.hAPP_f1682609283m_bool _let_1 D)))))) (forall ((A_4 tptp.hoare_363350478_state) (C_1 tptp.fun_Ho320143120e_bool) (D tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state A_4))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool C_1) D)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool (tptp.hAPP_f1749453397e_bool _let_1 C_1)) (tptp.hAPP_f1749453397e_bool _let_1 D)))))) (forall ((X_1 tptp.com) (A tptp.fun_com_bool)) (= (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_1) A)) (tptp.hBOOL (tptp.hAPP_com_bool A X_1)))) (forall ((X_1 tptp.hoare_363350478_state) (A tptp.fun_Ho320143120e_bool)) (= (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state X_1) A)) (tptp.hBOOL (tptp.hAPP_H1645464494e_bool A X_1)))) (forall ((X_1 tptp.pname) (A tptp.fun_pname_bool)) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A)) (tptp.hBOOL (tptp.hAPP_pname_bool A X_1)))) (forall ((P_1 tptp.fun_Ho320143120e_bool)) (= (tptp.hAPP_f1749453397e_bool tptp.collec223185785_state P_1) P_1)) (forall ((P_1 tptp.fun_pname_bool)) (= (tptp.hAPP_f759274231e_bool tptp.collect_pname P_1) P_1)) (forall ((P_1 tptp.fun_fu1430349052l_bool)) (= (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool P_1) P_1)) (forall ((P_1 tptp.fun_fu1996308102l_bool)) (= (tptp.hAPP_f85652879l_bool tptp.collec1243131813e_bool P_1) P_1)) (forall ((B_1 tptp.pname) (A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname B_1) B)))))) (forall ((B_1 tptp.com) (A tptp.fun_com_bool) (B tptp.fun_com_bool)) (let ((_let_1 (tptp.hAPP_f273696895l_bool tptp.ord_le1708315510m_bool A))) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 B)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com B_1) B)))))) (forall ((B_1 tptp.hoare_363350478_state) (A tptp.fun_Ho320143120e_bool) (B tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool A))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 B)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state B_1) B)))))) (forall ((B tptp.fun_com_bool) (X_1 tptp.com) (A tptp.fun_com_bool)) (let ((_let_1 (tptp.hAPP_f273696895l_bool tptp.ord_le1708315510m_bool A))) (=> (not (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_1) A))) (= (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com X_1) B))) (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 B)))))) (forall ((B tptp.fun_pname_bool) (X_1 tptp.pname) (A tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A))) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A))) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1) B))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B)))))) (forall ((B tptp.fun_Ho320143120e_bool) (X_1 tptp.hoare_363350478_state) (A tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool A))) (=> (not (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state X_1) A))) (= (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state X_1) B))) (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 B)))))) (forall ((X_1 tptp.com) (A tptp.fun_com_bool) (B tptp.fun_com_bool)) (= (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_f273696895l_bool tptp.ord_le1708315510m_bool (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com X_1) A)) B)) (and (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_1) B)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_f273696895l_bool tptp.ord_le1708315510m_bool A) B))))) (forall ((X_1 tptp.pname) (A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1) A)) B)) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) B)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) B))))) (forall ((X_1 tptp.hoare_363350478_state) (A tptp.fun_Ho320143120e_bool) (B tptp.fun_Ho320143120e_bool)) (= (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state X_1) A)) B)) (and (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state X_1) B)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool A) B))))) (forall ((B tptp.fun_pname_bool) (A_4 tptp.pname)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A_4) B)))) (forall ((B tptp.fun_com_bool) (A_4 tptp.com)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_f273696895l_bool tptp.ord_le1708315510m_bool B) (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com A_4) B)))) (forall ((B tptp.fun_Ho320143120e_bool) (A_4 tptp.hoare_363350478_state)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool B) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state A_4) B)))) (forall ((F tptp.fun_Ho713471079_pname) (X_1 tptp.hoare_363350478_state) (A tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_f773602357e_bool (tptp.image_1927198851_pname F) A))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state X_1) A)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname (tptp.hAPP_H1346202419_pname F X_1)) _let_1) _let_1)))) (forall ((F tptp.fun_Ho938602221te_com) (X_1 tptp.hoare_363350478_state) (A tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_f497466683m_bool (tptp.image_689867145te_com F) A))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state X_1) A)) (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com (tptp.hAPP_H2142737465te_com F X_1)) _let_1) _let_1)))) (forall ((F tptp.fun_pname_pname) (X_1 tptp.pname) (A tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f759274231e_bool (tptp.image_pname_pname F) A))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname (tptp.hAPP_pname_pname F X_1)) _let_1) _let_1)))) (forall ((F tptp.fun_pname_com) (X_1 tptp.pname) (A tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f1206115581m_bool (tptp.image_pname_com F) A))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A)) (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com (tptp.hAPP_pname_com F X_1)) _let_1) _let_1)))) (forall ((F tptp.fun_co482540593_state) (X_1 tptp.com) (A tptp.fun_com_bool)) (let ((_let_1 (tptp.hAPP_f1859782925e_bool (tptp.image_1736049107_state F) A))) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_1) A)) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state (tptp.hAPP_c1041435779_state F X_1)) _let_1) _let_1)))) (forall ((F tptp.fun_pn1262351275_state) (X_1 tptp.pname) (A tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f1763243027e_bool (tptp.image_1918575693_state F) A))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A)) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state (tptp.hAPP_p1337579261_state F X_1)) _let_1) _let_1)))) (forall ((F tptp.fun_Ho713471079_pname) (A_4 tptp.hoare_363350478_state) (B tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.image_1927198851_pname F))) (= (tptp.hAPP_f773602357e_bool _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state A_4) B)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname (tptp.hAPP_H1346202419_pname F A_4)) (tptp.hAPP_f773602357e_bool _let_1 B))))) (forall ((F tptp.fun_Ho938602221te_com) (A_4 tptp.hoare_363350478_state) (B tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.image_689867145te_com F))) (= (tptp.hAPP_f497466683m_bool _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state A_4) B)) (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com (tptp.hAPP_H2142737465te_com F A_4)) (tptp.hAPP_f497466683m_bool _let_1 B))))) (forall ((F tptp.fun_co482540593_state) (A_4 tptp.com) (B tptp.fun_com_bool)) (let ((_let_1 (tptp.image_1736049107_state F))) (= (tptp.hAPP_f1859782925e_bool _let_1 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com A_4) B)) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state (tptp.hAPP_c1041435779_state F A_4)) (tptp.hAPP_f1859782925e_bool _let_1 B))))) (forall ((F tptp.fun_pn1262351275_state) (A_4 tptp.pname) (B tptp.fun_pname_bool)) (let ((_let_1 (tptp.image_1918575693_state F))) (= (tptp.hAPP_f1763243027e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A_4) B)) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state (tptp.hAPP_p1337579261_state F A_4)) (tptp.hAPP_f1763243027e_bool _let_1 B))))) (forall ((F tptp.fun_Ho713471079_pname) (A tptp.fun_Ho320143120e_bool) (B tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.image_1927198851_pname F))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool A) B)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f773602357e_bool _let_1 A)) (tptp.hAPP_f773602357e_bool _let_1 B)))))) (forall ((F tptp.fun_pn1262351275_state) (A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (let ((_let_1 (tptp.image_1918575693_state F))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) B)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool (tptp.hAPP_f1763243027e_bool _let_1 A)) (tptp.hAPP_f1763243027e_bool _let_1 B)))))) (forall ((B tptp.fun_pname_bool) (F tptp.fun_Ho713471079_pname) (A tptp.fun_Ho320143120e_bool)) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) (tptp.hAPP_f773602357e_bool (tptp.image_1927198851_pname F) A))) (exists ((AA tptp.fun_Ho320143120e_bool)) (and (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool AA) A)) (= B (tptp.hAPP_f773602357e_bool (tptp.image_1927198851_pname F) AA)))))) (forall ((B tptp.fun_Ho320143120e_bool) (F tptp.fun_pn1262351275_state) (A tptp.fun_pname_bool)) (= (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool B) (tptp.hAPP_f1763243027e_bool (tptp.image_1918575693_state F) A))) (exists ((AA tptp.fun_pname_bool)) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool AA) A)) (= B (tptp.hAPP_f1763243027e_bool (tptp.image_1918575693_state F) AA)))))) (forall ((M tptp.fun_com_option_com) (A_4 tptp.com) (B_1 tptp.com)) (=> (= (tptp.hAPP_com_option_com M A_4) (tptp.hAPP_com_option_com tptp.some_com B_1)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com A_4) (tptp.dom_com_com M))))) (forall ((M tptp.fun_Ho12798188_pname) (A_4 tptp.hoare_363350478_state) (B_1 tptp.pname)) (=> (= (tptp.hAPP_H134270346_pname M A_4) (tptp.hAPP_p1252095976_pname tptp.some_pname B_1)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state A_4) (tptp.dom_Ho75493366_pname M))))) (forall ((M tptp.fun_Ho382349394_state) (A_4 tptp.hoare_363350478_state) (B_1 tptp.hoare_363350478_state)) (=> (= (tptp.hAPP_H1942146718_state M A_4) (tptp.hAPP_H1942146718_state tptp.some_H629028223_state B_1)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state A_4) (tptp.dom_Ho867270556_state M))))) (forall ((M tptp.fun_pn1342468758_pname) (A_4 tptp.pname) (B_1 tptp.pname)) (=> (= (tptp.hAPP_p1252095976_pname M A_4) (tptp.hAPP_p1252095976_pname tptp.some_pname B_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A_4) (tptp.dom_pname_pname M))))) (forall ((M tptp.fun_pn1405249832_state) (A_4 tptp.pname) (B_1 tptp.hoare_363350478_state)) (=> (= (tptp.hAPP_p1737106368_state M A_4) (tptp.hAPP_H1942146718_state tptp.some_H629028223_state B_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A_4) (tptp.dom_pn66870208_state M))))) (forall ((M tptp.fun_pname_option_com) (A_4 tptp.pname) (B_1 tptp.com)) (=> (= (tptp.hAPP_p799580910on_com M A_4) (tptp.hAPP_com_option_com tptp.some_com B_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A_4) (tptp.dom_pname_com M))))) (forall ((P_1 tptp.fun_pname_bool) (A_4 tptp.pname)) (let ((_let_1 (tptp.hAPP_f759274231e_bool tptp.collect_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_f649174806e_bool tptp.cOMBS_568398431l_bool (tptp.hAPP_f1402196763l_bool (tptp.cOMBB_675860798_pname tptp.fconj) (tptp.hAPP_p61793385e_bool (tptp.hAPP_f22061361e_bool tptp.cOMBC_1149511130e_bool tptp.fequal_pname) A_4))) P_1)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_pname_bool P_1 A_4)))) (and (=> _let_2 (= _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A_4) tptp.bot_bo844097828e_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bo844097828e_bool)))))) (forall ((P_1 tptp.fun_com_bool) (A_4 tptp.com)) (let ((_let_1 (tptp.hAPP_f1682609283m_bool tptp.collect_com (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f328772264m_bool tptp.cOMBS_com_bool_bool (tptp.hAPP_f954469007l_bool (tptp.cOMBB_886968260ol_com tptp.fconj) (tptp.hAPP_c1396316405m_bool (tptp.hAPP_f908845385m_bool tptp.cOMBC_com_com_bool tptp.fequal_com) A_4))) P_1)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_com_bool P_1 A_4)))) (and (=> _let_2 (= _let_1 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com A_4) tptp.bot_bot_fun_com_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bot_fun_com_bool)))))) (forall ((P_1 tptp.fun_fu1430349052l_bool) (A_4 tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f624840228l_bool tptp.cOMBS_350070575l_bool (tptp.hAPP_f143162813l_bool (tptp.cOMBB_2095475776e_bool tptp.fconj) (tptp.hAPP_f434788991l_bool (tptp.hAPP_f1297925993l_bool tptp.cOMBC_1284144636l_bool tptp.fequal533582459e_bool) A_4))) P_1)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 A_4)))) (and (=> _let_2 (= _let_1 (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool A_4) tptp.bot_bo1649642514l_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bo1649642514l_bool)))))) (forall ((P_1 tptp.fun_fu1996308102l_bool) (A_4 tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_f85652879l_bool tptp.collec1243131813e_bool (tptp.hAPP_f85652879l_bool (tptp.hAPP_f927797370l_bool tptp.cOMBS_1039407915l_bool (tptp.hAPP_f945781379l_bool (tptp.cOMBB_1004232970e_bool tptp.fconj) (tptp.hAPP_f726209793l_bool (tptp.hAPP_f205303905l_bool tptp.cOMBC_1250231770l_bool tptp.fequal731041167e_bool) A_4))) P_1)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_f568432088l_bool P_1 A_4)))) (and (=> _let_2 (= _let_1 (tptp.hAPP_f85652879l_bool (tptp.hAPP_f1941218614l_bool tptp.insert975831690e_bool A_4) tptp.bot_bo133096688l_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bo133096688l_bool)))))) (forall ((P_1 tptp.fun_Ho320143120e_bool) (A_4 tptp.hoare_363350478_state)) (let ((_let_1 (tptp.hAPP_f1749453397e_bool tptp.collec223185785_state (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1612626488e_bool tptp.cOMBS_56025283l_bool (tptp.hAPP_f1422032445l_bool (tptp.cOMBB_877416532_state tptp.fconj) (tptp.hAPP_H705653759e_bool (tptp.hAPP_f114072425e_bool tptp.cOMBC_13083556e_bool tptp.fequal1026769423_state) A_4))) P_1)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_H1645464494e_bool P_1 A_4)))) (and (=> _let_2 (= _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state A_4) tptp.bot_bo39439654e_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bo39439654e_bool)))))) (forall ((P_1 tptp.fun_pname_bool) (A_4 tptp.pname)) (let ((_let_1 (tptp.hAPP_f759274231e_bool tptp.collect_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_f649174806e_bool tptp.cOMBS_568398431l_bool (tptp.hAPP_f1402196763l_bool (tptp.cOMBB_675860798_pname tptp.fconj) (tptp.hAPP_p61793385e_bool tptp.fequal_pname A_4))) P_1)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_pname_bool P_1 A_4)))) (and (=> _let_2 (= _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A_4) tptp.bot_bo844097828e_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bo844097828e_bool)))))) (forall ((P_1 tptp.fun_com_bool) (A_4 tptp.com)) (let ((_let_1 (tptp.hAPP_f1682609283m_bool tptp.collect_com (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f328772264m_bool tptp.cOMBS_com_bool_bool (tptp.hAPP_f954469007l_bool (tptp.cOMBB_886968260ol_com tptp.fconj) (tptp.hAPP_c1396316405m_bool tptp.fequal_com A_4))) P_1)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_com_bool P_1 A_4)))) (and (=> _let_2 (= _let_1 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com A_4) tptp.bot_bot_fun_com_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bot_fun_com_bool)))))) (forall ((P_1 tptp.fun_fu1430349052l_bool) (A_4 tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f624840228l_bool tptp.cOMBS_350070575l_bool (tptp.hAPP_f143162813l_bool (tptp.cOMBB_2095475776e_bool tptp.fconj) (tptp.hAPP_f434788991l_bool tptp.fequal533582459e_bool A_4))) P_1)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 A_4)))) (and (=> _let_2 (= _let_1 (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool A_4) tptp.bot_bo1649642514l_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bo1649642514l_bool)))))) (forall ((P_1 tptp.fun_fu1996308102l_bool) (A_4 tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_f85652879l_bool tptp.collec1243131813e_bool (tptp.hAPP_f85652879l_bool (tptp.hAPP_f927797370l_bool tptp.cOMBS_1039407915l_bool (tptp.hAPP_f945781379l_bool (tptp.cOMBB_1004232970e_bool tptp.fconj) (tptp.hAPP_f726209793l_bool tptp.fequal731041167e_bool A_4))) P_1)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_f568432088l_bool P_1 A_4)))) (and (=> _let_2 (= _let_1 (tptp.hAPP_f85652879l_bool (tptp.hAPP_f1941218614l_bool tptp.insert975831690e_bool A_4) tptp.bot_bo133096688l_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bo133096688l_bool)))))) (forall ((P_1 tptp.fun_Ho320143120e_bool) (A_4 tptp.hoare_363350478_state)) (let ((_let_1 (tptp.hAPP_f1749453397e_bool tptp.collec223185785_state (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1612626488e_bool tptp.cOMBS_56025283l_bool (tptp.hAPP_f1422032445l_bool (tptp.cOMBB_877416532_state tptp.fconj) (tptp.hAPP_H705653759e_bool tptp.fequal1026769423_state A_4))) P_1)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_H1645464494e_bool P_1 A_4)))) (and (=> _let_2 (= _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state A_4) tptp.bot_bo39439654e_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bo39439654e_bool)))))) (forall ((A_4 tptp.pname)) (= (tptp.hAPP_f759274231e_bool tptp.collect_pname (tptp.hAPP_p61793385e_bool (tptp.hAPP_f22061361e_bool tptp.cOMBC_1149511130e_bool tptp.fequal_pname) A_4)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A_4) tptp.bot_bo844097828e_bool))) (forall ((A_4 tptp.com)) (= (tptp.hAPP_f1682609283m_bool tptp.collect_com (tptp.hAPP_c1396316405m_bool (tptp.hAPP_f908845385m_bool tptp.cOMBC_com_com_bool tptp.fequal_com) A_4)) (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com A_4) tptp.bot_bot_fun_com_bool))) (forall ((A_4 tptp.fun_pname_bool)) (= (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool (tptp.hAPP_f434788991l_bool (tptp.hAPP_f1297925993l_bool tptp.cOMBC_1284144636l_bool tptp.fequal533582459e_bool) A_4)) (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool A_4) tptp.bot_bo1649642514l_bool))) (forall ((A_4 tptp.fun_Ho320143120e_bool)) (= (tptp.hAPP_f85652879l_bool tptp.collec1243131813e_bool (tptp.hAPP_f726209793l_bool (tptp.hAPP_f205303905l_bool tptp.cOMBC_1250231770l_bool tptp.fequal731041167e_bool) A_4)) (tptp.hAPP_f85652879l_bool (tptp.hAPP_f1941218614l_bool tptp.insert975831690e_bool A_4) tptp.bot_bo133096688l_bool))) (forall ((A_4 tptp.hoare_363350478_state)) (= (tptp.hAPP_f1749453397e_bool tptp.collec223185785_state (tptp.hAPP_H705653759e_bool (tptp.hAPP_f114072425e_bool tptp.cOMBC_13083556e_bool tptp.fequal1026769423_state) A_4)) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state A_4) tptp.bot_bo39439654e_bool))) (forall ((A_4 tptp.pname)) (= (tptp.hAPP_f759274231e_bool tptp.collect_pname (tptp.hAPP_p61793385e_bool tptp.fequal_pname A_4)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A_4) tptp.bot_bo844097828e_bool))) (forall ((A_4 tptp.com)) (= (tptp.hAPP_f1682609283m_bool tptp.collect_com (tptp.hAPP_c1396316405m_bool tptp.fequal_com A_4)) (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com A_4) tptp.bot_bot_fun_com_bool))) (forall ((A_4 tptp.fun_pname_bool)) (= (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool (tptp.hAPP_f434788991l_bool tptp.fequal533582459e_bool A_4)) (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool A_4) tptp.bot_bo1649642514l_bool))) (forall ((A_4 tptp.fun_Ho320143120e_bool)) (= (tptp.hAPP_f85652879l_bool tptp.collec1243131813e_bool (tptp.hAPP_f726209793l_bool tptp.fequal731041167e_bool A_4)) (tptp.hAPP_f85652879l_bool (tptp.hAPP_f1941218614l_bool tptp.insert975831690e_bool A_4) tptp.bot_bo133096688l_bool))) (forall ((A_4 tptp.hoare_363350478_state)) (= (tptp.hAPP_f1749453397e_bool tptp.collec223185785_state (tptp.hAPP_H705653759e_bool tptp.fequal1026769423_state A_4)) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state A_4) tptp.bot_bo39439654e_bool))) (forall ((C tptp.com) (G_2 tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL tptp.hoare_265376576gleton) (=> (forall ((X_2 tptp.pname)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) (tptp.dom_pname_com tptp.body))) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hoare_95103338_state G_2) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state (tptp.hAPP_c1041435779_state tptp.hoare_Mirabelle_MGT (tptp.hAPP_pname_com tptp.body_1 X_2))) tptp.bot_bo39439654e_bool))))) (=> (tptp.hBOOL (tptp.hAPP_com_bool tptp.wt C)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hoare_95103338_state G_2) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state (tptp.hAPP_c1041435779_state tptp.hoare_Mirabelle_MGT C)) tptp.bot_bo39439654e_bool))))))) _let_12 (forall ((B_1 tptp.hoare_363350478_state) (F tptp.fun_co482540593_state) (A tptp.fun_com_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state B_1) (tptp.hAPP_f1859782925e_bool (tptp.image_1736049107_state F) A))) (not (forall ((X_2 tptp.com)) (=> (= B_1 (tptp.hAPP_c1041435779_state F X_2)) (not (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_2) A)))))))) (forall ((B_1 tptp.pname) (F tptp.fun_com_pname) (A tptp.fun_com_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname B_1) (tptp.hAPP_f1438183293e_bool (tptp.image_com_pname F) A))) (not (forall ((X_2 tptp.com)) (=> (= B_1 (tptp.hAPP_com_pname F X_2)) (not (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_2) A)))))))) (forall ((B_1 tptp.com) (F tptp.fun_Ho938602221te_com) (A tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com B_1) (tptp.hAPP_f497466683m_bool (tptp.image_689867145te_com F) A))) (not (forall ((X_2 tptp.hoare_363350478_state)) (=> (= B_1 (tptp.hAPP_H2142737465te_com F X_2)) (not (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state X_2) A)))))))) (forall ((B_1 tptp.com) (F tptp.fun_pname_com) (A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com B_1) (tptp.hAPP_f1206115581m_bool (tptp.image_pname_com F) A))) (not (forall ((X_2 tptp.pname)) (=> (= B_1 (tptp.hAPP_pname_com F X_2)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A)))))))) (forall ((B_1 tptp.hoare_363350478_state) (F tptp.fun_pn1262351275_state) (A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state B_1) (tptp.hAPP_f1763243027e_bool (tptp.image_1918575693_state F) A))) (not (forall ((X_2 tptp.pname)) (=> (= B_1 (tptp.hAPP_p1337579261_state F X_2)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A)))))))) (forall ((P_1 tptp.fun_fu1362071682l_bool) (A tptp.fun_com_bool) (Fa tptp.fun_com_bool)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool tptp.finite_finite_com Fa)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_f273696895l_bool tptp.ord_le1708315510m_bool Fa) A)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool P_1 tptp.bot_bot_fun_com_bool)) (=> (forall ((A_2 tptp.com) (F_2 tptp.fun_com_bool)) (let ((_let_1 (tptp.hAPP_c667411853l_bool tptp.member_com A_2))) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool tptp.finite_finite_com F_2)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 A)) (=> (not (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 F_2))) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool P_1 F_2)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool P_1 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com A_2) F_2))))))))) (tptp.hBOOL (tptp.hAPP_f990396704l_bool P_1 Fa))))))) (forall ((P_1 tptp.fun_fu399576434l_bool) (A tptp.fun_fu1430349052l_bool) (Fa tptp.fun_fu1430349052l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool Fa) A)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool P_1 tptp.bot_bo1649642514l_bool)) (=> (forall ((A_2 tptp.fun_pname_bool) (F_2 tptp.fun_fu1430349052l_bool)) (let ((_let_1 (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool A_2))) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool F_2)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool _let_1 A)) (=> (not (tptp.hBOOL (tptp.hAPP_f1935102916l_bool _let_1 F_2))) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool P_1 F_2)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool P_1 (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool A_2) F_2))))))))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool P_1 Fa))))))) (forall ((P_1 tptp.fun_fu1972704968l_bool) (A tptp.fun_fu1996308102l_bool) (Fa tptp.fun_fu1996308102l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool (tptp.hAPP_f746351743l_bool tptp.ord_le2031828156l_bool Fa) A)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool P_1 tptp.bot_bo133096688l_bool)) (=> (forall ((A_2 tptp.fun_Ho320143120e_bool) (F_2 tptp.fun_fu1996308102l_bool)) (let ((_let_1 (tptp.hAPP_f1610329741l_bool tptp.member1534059107e_bool A_2))) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool F_2)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool _let_1 A)) (=> (not (tptp.hBOOL (tptp.hAPP_f1287348838l_bool _let_1 F_2))) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool P_1 F_2)) (tptp.hBOOL (tptp.hAPP_f1287348838l_bool P_1 (tptp.hAPP_f85652879l_bool (tptp.hAPP_f1941218614l_bool tptp.insert975831690e_bool A_2) F_2))))))))) (tptp.hBOOL (tptp.hAPP_f1287348838l_bool P_1 Fa))))))) (forall ((P_1 tptp.fun_fu1430349052l_bool) (A tptp.fun_pname_bool) (Fa tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool Fa) A)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 tptp.bot_bo844097828e_bool)) (=> (forall ((A_2 tptp.pname) (F_2 tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname A_2))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname F_2)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A)) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 F_2))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 F_2)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A_2) F_2))))))))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 Fa))))))) (forall ((P_1 tptp.fun_fu1996308102l_bool) (A tptp.fun_Ho320143120e_bool) (Fa tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state Fa)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool Fa) A)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool P_1 tptp.bot_bo39439654e_bool)) (=> (forall ((A_2 tptp.hoare_363350478_state) (F_2 tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_H40373975l_bool tptp.member1253905979_state A_2))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state F_2)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 A)) (=> (not (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 F_2))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool P_1 F_2)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool P_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state A_2) F_2))))))))) (tptp.hBOOL (tptp.hAPP_f568432088l_bool P_1 Fa))))))) (forall ((P tptp.pname)) (=> (tptp.hBOOL (tptp.hAPP_com_bool tptp.wt (tptp.hAPP_pname_com tptp.body_1 P))) (not (forall ((Y_3 tptp.com)) (not (= (tptp.hAPP_p799580910on_com tptp.body P) (tptp.hAPP_com_option_com tptp.some_com Y_3))))))) (forall ((B tptp.fun_com_bool) (A tptp.fun_com_bool)) (=> (forall ((X_2 tptp.com)) (let ((_let_1 (tptp.hAPP_c667411853l_bool tptp.member_com X_2))) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 B))))) (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_f273696895l_bool tptp.ord_le1708315510m_bool A) B)))) (forall ((B tptp.fun_Ho320143120e_bool) (A tptp.fun_Ho320143120e_bool)) (=> (forall ((X_2 tptp.hoare_363350478_state)) (let ((_let_1 (tptp.hAPP_H40373975l_bool tptp.member1253905979_state X_2))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 B))))) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool A) B)))) (forall ((B tptp.fun_pname_bool) (A tptp.fun_pname_bool)) (=> (forall ((X_2 tptp.pname)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname X_2))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B))))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) B)))) (forall ((F tptp.fun_fu54631149_state) (A tptp.fun_fu1430349052l_bool) (B tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state B)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool B) (tptp.hAPP_f1912490857e_bool (tptp.image_431763259_state F) A))) (exists ((C_3 tptp.fun_fu1430349052l_bool)) (and (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool C_3) A)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool C_3)) (= B (tptp.hAPP_f1912490857e_bool (tptp.image_431763259_state F) C_3))))))) (forall ((F tptp.fun_fu700438391_state) (A tptp.fun_fu1996308102l_bool) (B tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state B)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool B) (tptp.hAPP_f1180969799e_bool (tptp.image_2021386777_state F) A))) (exists ((C_3 tptp.fun_fu1996308102l_bool)) (and (tptp.hBOOL (tptp.hAPP_f1287348838l_bool (tptp.hAPP_f746351743l_bool tptp.ord_le2031828156l_bool C_3) A)) (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool C_3)) (= B (tptp.hAPP_f1180969799e_bool (tptp.image_2021386777_state F) C_3))))))) (forall ((F tptp.fun_fu1499449723_pname) (A tptp.fun_fu1430349052l_bool) (B tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) (tptp.hAPP_f674760225e_bool (tptp.image_1283814551_pname F) A))) (exists ((C_3 tptp.fun_fu1430349052l_bool)) (and (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool C_3) A)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool C_3)) (= B (tptp.hAPP_f674760225e_bool (tptp.image_1283814551_pname F) C_3))))))) (forall ((F tptp.fun_fu2380401_pname) (A tptp.fun_fu1996308102l_bool) (B tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) (tptp.hAPP_f1892738755e_bool (tptp.image_937015865_pname F) A))) (exists ((C_3 tptp.fun_fu1996308102l_bool)) (and (tptp.hBOOL (tptp.hAPP_f1287348838l_bool (tptp.hAPP_f746351743l_bool tptp.ord_le2031828156l_bool C_3) A)) (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool C_3)) (= B (tptp.hAPP_f1892738755e_bool (tptp.image_937015865_pname F) C_3))))))) (forall ((F tptp.fun_Ho1262521325e_bool) (A tptp.fun_Ho320143120e_bool) (B tptp.fun_fu1430349052l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool B)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool B) (tptp.hAPP_f766639041l_bool (tptp.image_1660610235e_bool F) A))) (exists ((C_3 tptp.fun_Ho320143120e_bool)) (and (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool C_3) A)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state C_3)) (= B (tptp.hAPP_f766639041l_bool (tptp.image_1660610235e_bool F) C_3))))))) (forall ((F tptp.fun_Ho424838195e_bool) (A tptp.fun_Ho320143120e_bool) (B tptp.fun_fu1996308102l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool B)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool (tptp.hAPP_f746351743l_bool tptp.ord_le2031828156l_bool B) (tptp.hAPP_f726209793l_bool (tptp.image_1484638543e_bool F) A))) (exists ((C_3 tptp.fun_Ho320143120e_bool)) (and (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool C_3) A)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state C_3)) (= B (tptp.hAPP_f726209793l_bool (tptp.image_1484638543e_bool F) C_3))))))) (forall ((F tptp.fun_Ho713471079_pname) (A tptp.fun_Ho320143120e_bool) (B tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) (tptp.hAPP_f773602357e_bool (tptp.image_1927198851_pname F) A))) (exists ((C_3 tptp.fun_Ho320143120e_bool)) (and (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool C_3) A)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state C_3)) (= B (tptp.hAPP_f773602357e_bool (tptp.image_1927198851_pname F) C_3))))))) (forall ((F tptp.fun_pn800050071e_bool) (A tptp.fun_pname_bool) (B tptp.fun_fu1430349052l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool B)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool B) (tptp.hAPP_f434788991l_bool (tptp.image_47868345e_bool F) A))) (exists ((C_3 tptp.fun_pname_bool)) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool C_3) A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname C_3)) (= B (tptp.hAPP_f434788991l_bool (tptp.image_47868345e_bool F) C_3))))))) (forall ((F tptp.fun_pn1521100553e_bool) (A tptp.fun_pname_bool) (B tptp.fun_fu1996308102l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool B)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool (tptp.hAPP_f746351743l_bool tptp.ord_le2031828156l_bool B) (tptp.hAPP_f682249667l_bool (tptp.image_1637084625e_bool F) A))) (exists ((C_3 tptp.fun_pname_bool)) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool C_3) A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname C_3)) (= B (tptp.hAPP_f682249667l_bool (tptp.image_1637084625e_bool F) C_3))))))) (forall ((F tptp.fun_pname_pname) (A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) (tptp.hAPP_f759274231e_bool (tptp.image_pname_pname F) A))) (exists ((C_3 tptp.fun_pname_bool)) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool C_3) A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname C_3)) (= B (tptp.hAPP_f759274231e_bool (tptp.image_pname_pname F) C_3))))))) (forall ((F tptp.fun_pn1262351275_state) (A tptp.fun_pname_bool) (B tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state B)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool B) (tptp.hAPP_f1763243027e_bool (tptp.image_1918575693_state F) A))) (exists ((C_3 tptp.fun_pname_bool)) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool C_3) A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname C_3)) (= B (tptp.hAPP_f1763243027e_bool (tptp.image_1918575693_state F) C_3))))))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname _let_3)) (forall ((P_1 tptp.fun_fu1362071682l_bool) (Fa tptp.fun_com_bool)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool tptp.finite_finite_com Fa)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool P_1 tptp.bot_bot_fun_com_bool)) (=> (forall ((X_2 tptp.com) (F_2 tptp.fun_com_bool)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool tptp.finite_finite_com F_2)) (=> (not (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_2) F_2))) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool P_1 F_2)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool P_1 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com X_2) F_2))))))) (tptp.hBOOL (tptp.hAPP_f990396704l_bool P_1 Fa)))))) (forall ((P_1 tptp.fun_fu399576434l_bool) (Fa tptp.fun_fu1430349052l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool P_1 tptp.bot_bo1649642514l_bool)) (=> (forall ((X_2 tptp.fun_pname_bool) (F_2 tptp.fun_fu1430349052l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool F_2)) (=> (not (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool X_2) F_2))) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool P_1 F_2)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool P_1 (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool X_2) F_2))))))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool P_1 Fa)))))) (forall ((P_1 tptp.fun_fu1972704968l_bool) (Fa tptp.fun_fu1996308102l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool P_1 tptp.bot_bo133096688l_bool)) (=> (forall ((X_2 tptp.fun_Ho320143120e_bool) (F_2 tptp.fun_fu1996308102l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool F_2)) (=> (not (tptp.hBOOL (tptp.hAPP_f1287348838l_bool (tptp.hAPP_f1610329741l_bool tptp.member1534059107e_bool X_2) F_2))) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool P_1 F_2)) (tptp.hBOOL (tptp.hAPP_f1287348838l_bool P_1 (tptp.hAPP_f85652879l_bool (tptp.hAPP_f1941218614l_bool tptp.insert975831690e_bool X_2) F_2))))))) (tptp.hBOOL (tptp.hAPP_f1287348838l_bool P_1 Fa)))))) (forall ((P_1 tptp.fun_fu1430349052l_bool) (Fa tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 tptp.bot_bo844097828e_bool)) (=> (forall ((X_2 tptp.pname) (F_2 tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname F_2)) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) F_2))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 F_2)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname X_2) F_2))))))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 Fa)))))) (forall ((P_1 tptp.fun_fu1996308102l_bool) (Fa tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state Fa)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool P_1 tptp.bot_bo39439654e_bool)) (=> (forall ((X_2 tptp.hoare_363350478_state) (F_2 tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state F_2)) (=> (not (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state X_2) F_2))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool P_1 F_2)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool P_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state X_2) F_2))))))) (tptp.hBOOL (tptp.hAPP_f568432088l_bool P_1 Fa)))))) (forall ((A_4 tptp.fun_com_bool)) (= (tptp.hBOOL (tptp.hAPP_f990396704l_bool tptp.finite_finite_com A_4)) (or (= A_4 tptp.bot_bot_fun_com_bool) (exists ((A_7 tptp.fun_com_bool) (A_2 tptp.com)) (and (= A_4 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com A_2) A_7)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool tptp.finite_finite_com A_7))))))) (forall ((A_4 tptp.fun_fu1430349052l_bool)) (= (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A_4)) (or (= A_4 tptp.bot_bo1649642514l_bool) (exists ((A_7 tptp.fun_fu1430349052l_bool) (A_2 tptp.fun_pname_bool)) (and (= A_4 (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool A_2) A_7)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A_7))))))) (forall ((A_4 tptp.fun_fu1996308102l_bool)) (= (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool A_4)) (or (= A_4 tptp.bot_bo133096688l_bool) (exists ((A_7 tptp.fun_fu1996308102l_bool) (A_2 tptp.fun_Ho320143120e_bool)) (and (= A_4 (tptp.hAPP_f85652879l_bool (tptp.hAPP_f1941218614l_bool tptp.insert975831690e_bool A_2) A_7)) (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool A_7))))))) (forall ((A_4 tptp.fun_pname_bool)) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A_4)) (or (= A_4 tptp.bot_bo844097828e_bool) (exists ((A_7 tptp.fun_pname_bool) (A_2 tptp.pname)) (and (= A_4 (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A_2) A_7)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A_7))))))) (forall ((A_4 tptp.fun_Ho320143120e_bool)) (= (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state A_4)) (or (= A_4 tptp.bot_bo39439654e_bool) (exists ((A_7 tptp.fun_Ho320143120e_bool) (A_2 tptp.hoare_363350478_state)) (and (= A_4 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state A_2) A_7)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state A_7))))))) (forall ((F tptp.fun_co482540593_state) (A tptp.fun_com_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_f990396704l_bool tptp.finite_finite_com A))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state (tptp.hAPP_f1859782925e_bool (tptp.image_1736049107_state F) A))) (exists ((X_2 tptp.com)) (and (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_2) A)) (not (tptp.hBOOL (tptp.hAPP_f990396704l_bool tptp.finite_finite_com (tptp.hAPP_f1682609283m_bool tptp.collect_com (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f328772264m_bool tptp.cOMBS_com_bool_bool (tptp.hAPP_f954469007l_bool (tptp.cOMBB_886968260ol_com tptp.fconj) (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f578650245m_bool tptp.cOMBC_1904837336l_bool tptp.member_com) A))) (tptp.hAPP_H176808977m_bool (tptp.hAPP_f1375689733m_bool tptp.cOMBC_1517337958e_bool (tptp.hAPP_f1813061839e_bool (tptp.cOMBB_147383684ol_com tptp.fequal1026769423_state) F)) (tptp.hAPP_c1041435779_state F X_2)))))))))))) (forall ((F tptp.fun_Ho901937921_state) (A tptp.fun_Ho320143120e_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state A))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state (tptp.hAPP_f1749453397e_bool (tptp.image_2068641359_state F) A))) (exists ((X_2 tptp.hoare_363350478_state)) (and (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state X_2) A)) (not (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state (tptp.hAPP_f1749453397e_bool tptp.collec223185785_state (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1612626488e_bool tptp.cOMBS_56025283l_bool (tptp.hAPP_f1422032445l_bool (tptp.cOMBB_877416532_state tptp.fconj) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1072682137e_bool tptp.cOMBC_1415895650l_bool tptp.member1253905979_state) A))) (tptp.hAPP_H705653759e_bool (tptp.hAPP_f114072425e_bool tptp.cOMBC_13083556e_bool (tptp.hAPP_f355123231e_bool (tptp.cOMBB_496159380_state tptp.fequal1026769423_state) F)) (tptp.hAPP_H1982017439_state F X_2)))))))))))) (forall ((F tptp.fun_fu54631149_state) (A tptp.fun_fu1430349052l_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state (tptp.hAPP_f1912490857e_bool (tptp.image_431763259_state F) A))) (exists ((X_2 tptp.fun_pname_bool)) (and (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool X_2) A)) (not (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f624840228l_bool tptp.cOMBS_350070575l_bool (tptp.hAPP_f143162813l_bool (tptp.cOMBB_2095475776e_bool tptp.fconj) (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1145991873l_bool tptp.cOMBC_1988546018l_bool tptp.member799430823e_bool) A))) (tptp.hAPP_H444605547l_bool (tptp.hAPP_f1075942761l_bool tptp.cOMBC_1091669008e_bool (tptp.hAPP_f272807711e_bool (tptp.cOMBB_543245952e_bool tptp.fequal1026769423_state) F)) (tptp.hAPP_f804167819_state F X_2)))))))))))) (forall ((F tptp.fun_fu700438391_state) (A tptp.fun_fu1996308102l_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool A))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state (tptp.hAPP_f1180969799e_bool (tptp.image_2021386777_state F) A))) (exists ((X_2 tptp.fun_Ho320143120e_bool)) (and (tptp.hBOOL (tptp.hAPP_f1287348838l_bool (tptp.hAPP_f1610329741l_bool tptp.member1534059107e_bool X_2) A)) (not (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool (tptp.hAPP_f85652879l_bool tptp.collec1243131813e_bool (tptp.hAPP_f85652879l_bool (tptp.hAPP_f927797370l_bool tptp.cOMBS_1039407915l_bool (tptp.hAPP_f945781379l_bool (tptp.cOMBB_1004232970e_bool tptp.fconj) (tptp.hAPP_f85652879l_bool (tptp.hAPP_f1854331281l_bool tptp.cOMBC_1522409444l_bool tptp.member1534059107e_bool) A))) (tptp.hAPP_H40373975l_bool (tptp.hAPP_f1585300113l_bool tptp.cOMBC_497487404e_bool (tptp.hAPP_f440040771e_bool (tptp.cOMBB_238163658e_bool tptp.fequal1026769423_state) F)) (tptp.hAPP_f1242401993_state F X_2)))))))))))) (forall ((F tptp.fun_com_pname) (A tptp.fun_com_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_f990396704l_bool tptp.finite_finite_com A))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f1438183293e_bool (tptp.image_com_pname F) A))) (exists ((X_2 tptp.com)) (and (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_2) A)) (not (tptp.hBOOL (tptp.hAPP_f990396704l_bool tptp.finite_finite_com (tptp.hAPP_f1682609283m_bool tptp.collect_com (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f328772264m_bool tptp.cOMBS_com_bool_bool (tptp.hAPP_f954469007l_bool (tptp.cOMBB_886968260ol_com tptp.fconj) (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f578650245m_bool tptp.cOMBC_1904837336l_bool tptp.member_com) A))) (tptp.hAPP_p1639923567m_bool (tptp.hAPP_f734198589m_bool tptp.cOMBC_com_pname_bool (tptp.hAPP_f835719487e_bool (tptp.cOMBB_1083901850ol_com tptp.fequal_pname) F)) (tptp.hAPP_com_pname F X_2)))))))))))) (forall ((F tptp.fun_Ho713471079_pname) (A tptp.fun_Ho320143120e_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state A))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f773602357e_bool (tptp.image_1927198851_pname F) A))) (exists ((X_2 tptp.hoare_363350478_state)) (and (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state X_2) A)) (not (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state (tptp.hAPP_f1749453397e_bool tptp.collec223185785_state (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1612626488e_bool tptp.cOMBS_56025283l_bool (tptp.hAPP_f1422032445l_bool (tptp.cOMBB_877416532_state tptp.fconj) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1072682137e_bool tptp.cOMBC_1415895650l_bool tptp.member1253905979_state) A))) (tptp.hAPP_p2009489185e_bool (tptp.hAPP_f626747953e_bool tptp.cOMBC_1026256022e_bool (tptp.hAPP_f875047427e_bool (tptp.cOMBB_951329022_state tptp.fequal_pname) F)) (tptp.hAPP_H1346202419_pname F X_2)))))))))))) (forall ((F tptp.fun_pname_pname) (A tptp.fun_pname_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f759274231e_bool (tptp.image_pname_pname F) A))) (exists ((X_2 tptp.pname)) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f759274231e_bool tptp.collect_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_f649174806e_bool tptp.cOMBS_568398431l_bool (tptp.hAPP_f1402196763l_bool (tptp.cOMBB_675860798_pname tptp.fconj) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f661147897e_bool tptp.cOMBC_1058051404l_bool tptp.member_pname) A))) (tptp.hAPP_p61793385e_bool (tptp.hAPP_f22061361e_bool tptp.cOMBC_1149511130e_bool (tptp.hAPP_f1336811455e_bool (tptp.cOMBB_542850580_pname tptp.fequal_pname) F)) (tptp.hAPP_pname_pname F X_2)))))))))))) (forall ((F tptp.fun_fu1499449723_pname) (A tptp.fun_fu1430349052l_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f674760225e_bool (tptp.image_1283814551_pname F) A))) (exists ((X_2 tptp.fun_pname_bool)) (and (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool X_2) A)) (not (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f624840228l_bool tptp.cOMBS_350070575l_bool (tptp.hAPP_f143162813l_bool (tptp.cOMBB_2095475776e_bool tptp.fconj) (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1145991873l_bool tptp.cOMBC_1988546018l_bool tptp.member799430823e_bool) A))) (tptp.hAPP_p338031245l_bool (tptp.hAPP_f2082757169l_bool tptp.cOMBC_1004116266e_bool (tptp.hAPP_f1385420507e_bool (tptp.cOMBB_598082538e_bool tptp.fequal_pname) F)) (tptp.hAPP_f1297739591_pname F X_2)))))))))))) (forall ((F tptp.fun_fu2380401_pname) (A tptp.fun_fu1996308102l_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool A))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f1892738755e_bool (tptp.image_937015865_pname F) A))) (exists ((X_2 tptp.fun_Ho320143120e_bool)) (and (tptp.hBOOL (tptp.hAPP_f1287348838l_bool (tptp.hAPP_f1610329741l_bool tptp.member1534059107e_bool X_2) A)) (not (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool (tptp.hAPP_f85652879l_bool tptp.collec1243131813e_bool (tptp.hAPP_f85652879l_bool (tptp.hAPP_f927797370l_bool tptp.cOMBS_1039407915l_bool (tptp.hAPP_f945781379l_bool (tptp.cOMBB_1004232970e_bool tptp.fconj) (tptp.hAPP_f85652879l_bool (tptp.hAPP_f1854331281l_bool tptp.cOMBC_1522409444l_bool tptp.member1534059107e_bool) A))) (tptp.hAPP_p425615669l_bool (tptp.hAPP_f883421385l_bool tptp.cOMBC_1845395470e_bool (tptp.hAPP_f1544555711e_bool (tptp.cOMBB_655928288e_bool tptp.fequal_pname) F)) (tptp.hAPP_f1309420425_pname F X_2)))))))))))) (forall ((F tptp.fun_Ho1262521325e_bool) (A tptp.fun_Ho320143120e_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state A))) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.hAPP_f766639041l_bool (tptp.image_1660610235e_bool F) A))) (exists ((X_2 tptp.hoare_363350478_state)) (and (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state X_2) A)) (not (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state (tptp.hAPP_f1749453397e_bool tptp.collec223185785_state (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1612626488e_bool tptp.cOMBS_56025283l_bool (tptp.hAPP_f1422032445l_bool (tptp.cOMBB_877416532_state tptp.fconj) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1072682137e_bool tptp.cOMBC_1415895650l_bool tptp.member1253905979_state) A))) (tptp.hAPP_f1763243027e_bool (tptp.hAPP_f1421439337e_bool tptp.cOMBC_1674478480l_bool (tptp.hAPP_f399561463l_bool (tptp.cOMBB_1217374484_state tptp.fequal533582459e_bool) F)) (tptp.hAPP_H2033014795e_bool F X_2)))))))))))) (forall ((F tptp.fun_Ho424838195e_bool) (A tptp.fun_Ho320143120e_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state A))) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool (tptp.hAPP_f726209793l_bool (tptp.image_1484638543e_bool F) A))) (exists ((X_2 tptp.hoare_363350478_state)) (and (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state X_2) A)) (not (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state (tptp.hAPP_f1749453397e_bool tptp.collec223185785_state (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1612626488e_bool tptp.cOMBS_56025283l_bool (tptp.hAPP_f1422032445l_bool (tptp.cOMBB_877416532_state tptp.fconj) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1072682137e_bool tptp.cOMBC_1415895650l_bool tptp.member1253905979_state) A))) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1072682137e_bool tptp.cOMBC_1415895650l_bool (tptp.hAPP_f565239043l_bool (tptp.cOMBB_867654038_state tptp.fequal731041167e_bool) F)) (tptp.hAPP_H705653759e_bool F X_2)))))))))))) (forall ((F tptp.fun_pn800050071e_bool) (A tptp.fun_pname_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A))) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.hAPP_f434788991l_bool (tptp.image_47868345e_bool F) A))) (exists ((X_2 tptp.pname)) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f759274231e_bool tptp.collect_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_f649174806e_bool tptp.cOMBS_568398431l_bool (tptp.hAPP_f1402196763l_bool (tptp.cOMBB_675860798_pname tptp.fconj) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f661147897e_bool tptp.cOMBC_1058051404l_bool tptp.member_pname) A))) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f661147897e_bool tptp.cOMBC_1058051404l_bool (tptp.hAPP_f567934427l_bool (tptp.cOMBB_408569982_pname tptp.fequal533582459e_bool) F)) (tptp.hAPP_p61793385e_bool F X_2)))))))))))) (forall ((F tptp.fun_pn1521100553e_bool) (A tptp.fun_pname_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A))) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool (tptp.hAPP_f682249667l_bool (tptp.image_1637084625e_bool F) A))) (exists ((X_2 tptp.pname)) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f759274231e_bool tptp.collect_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_f649174806e_bool tptp.cOMBS_568398431l_bool (tptp.hAPP_f1402196763l_bool (tptp.cOMBB_675860798_pname tptp.fconj) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f661147897e_bool tptp.cOMBC_1058051404l_bool tptp.member_pname) A))) (tptp.hAPP_f773602357e_bool (tptp.hAPP_f1863577801e_bool tptp.cOMBC_947783590l_bool (tptp.hAPP_f1841796439l_bool (tptp.cOMBB_343228284_pname tptp.fequal731041167e_bool) F)) (tptp.hAPP_p2009489185e_bool F X_2)))))))))))) (forall ((F tptp.fun_pn1262351275_state) (A tptp.fun_pname_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state (tptp.hAPP_f1763243027e_bool (tptp.image_1918575693_state F) A))) (exists ((X_2 tptp.pname)) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f759274231e_bool tptp.collect_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_f649174806e_bool tptp.cOMBS_568398431l_bool (tptp.hAPP_f1402196763l_bool (tptp.cOMBB_675860798_pname tptp.fconj) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f661147897e_bool tptp.cOMBC_1058051404l_bool tptp.member_pname) A))) (tptp.hAPP_H2033014795e_bool (tptp.hAPP_f443781369e_bool tptp.cOMBC_1422551904e_bool (tptp.hAPP_f1284518107e_bool (tptp.cOMBB_1755629310_pname tptp.fequal1026769423_state) F)) (tptp.hAPP_p1337579261_state F X_2)))))))))))) (forall ((Pname_2 tptp.pname) (Pname_1 tptp.pname)) (= (= (tptp.hAPP_pname_com tptp.body_1 Pname_2) (tptp.hAPP_pname_com tptp.body_1 Pname_1)) (= Pname_2 Pname_1))) (forall ((G_2 tptp.fun_Ho320143120e_bool) (Procs tptp.fun_pname_bool)) (let ((_let_1 (tptp.cOMBB_424558970_pname tptp.hoare_Mirabelle_MGT))) (let ((_let_2 (tptp.hAPP_f1763243027e_bool (tptp.image_1918575693_state (tptp.hAPP_f481860441_state _let_1 tptp.body_1)) Procs))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hoare_95103338_state (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool G_2) _let_2)) (tptp.hAPP_f1763243027e_bool (tptp.image_1918575693_state (tptp.hAPP_f481860441_state _let_1 (tptp.hAPP_f96342628me_com (tptp.cOMBB_923936821_pname tptp.the_com) tptp.body))) Procs))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname Procs)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hoare_95103338_state G_2) _let_2))))))) (forall ((A_4 tptp.com) (M tptp.fun_com_option_com)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com A_4) (tptp.dom_com_com M))) (exists ((B_3 tptp.com)) (= (tptp.hAPP_com_option_com M A_4) (tptp.hAPP_com_option_com tptp.some_com B_3))))) (forall ((A_4 tptp.hoare_363350478_state) (M tptp.fun_Ho12798188_pname)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state A_4) (tptp.dom_Ho75493366_pname M))) (exists ((B_3 tptp.pname)) (= (tptp.hAPP_H134270346_pname M A_4) (tptp.hAPP_p1252095976_pname tptp.some_pname B_3))))) (forall ((A_4 tptp.hoare_363350478_state) (M tptp.fun_Ho382349394_state)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state A_4) (tptp.dom_Ho867270556_state M))) (exists ((B_3 tptp.hoare_363350478_state)) (= (tptp.hAPP_H1942146718_state M A_4) (tptp.hAPP_H1942146718_state tptp.some_H629028223_state B_3))))) (forall ((A_4 tptp.pname) (M tptp.fun_pn1342468758_pname)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A_4) (tptp.dom_pname_pname M))) (exists ((B_3 tptp.pname)) (= (tptp.hAPP_p1252095976_pname M A_4) (tptp.hAPP_p1252095976_pname tptp.some_pname B_3))))) (forall ((A_4 tptp.pname) (M tptp.fun_pn1405249832_state)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A_4) (tptp.dom_pn66870208_state M))) (exists ((B_3 tptp.hoare_363350478_state)) (= (tptp.hAPP_p1737106368_state M A_4) (tptp.hAPP_H1942146718_state tptp.some_H629028223_state B_3))))) (forall ((A_4 tptp.pname) (M tptp.fun_pname_option_com)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A_4) (tptp.dom_pname_com M))) (exists ((B_3 tptp.com)) (= (tptp.hAPP_p799580910on_com M A_4) (tptp.hAPP_com_option_com tptp.some_com B_3))))) (forall ((X_1 tptp.pname)) (= (tptp.hAPP_f1297739591_pname tptp.the_elem_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1) tptp.bot_bo844097828e_bool)) X_1)) (forall ((X_1 tptp.com)) (= (tptp.hAPP_f1276420679ol_com tptp.the_elem_com (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com X_1) tptp.bot_bot_fun_com_bool)) X_1)) (forall ((X_1 tptp.hoare_363350478_state)) (= (tptp.hAPP_f1242401993_state tptp.the_el1666657391_state (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state X_1) tptp.bot_bo39439654e_bool)) X_1)) (forall ((F tptp.fun_Ho938602221te_com) (B tptp.fun_com_bool) (A tptp.fun_Ho320143120e_bool)) (=> (forall ((X_2 tptp.hoare_363350478_state)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state X_2) A)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com (tptp.hAPP_H2142737465te_com F X_2)) B)))) (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_f273696895l_bool tptp.ord_le1708315510m_bool (tptp.hAPP_f497466683m_bool (tptp.image_689867145te_com F) A)) B)))) (forall ((F tptp.fun_Ho713471079_pname) (B tptp.fun_pname_bool) (A tptp.fun_Ho320143120e_bool)) (=> (forall ((X_2 tptp.hoare_363350478_state)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state X_2) A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname (tptp.hAPP_H1346202419_pname F X_2)) B)))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f773602357e_bool (tptp.image_1927198851_pname F) A)) B)))) (forall ((F tptp.fun_pname_com) (B tptp.fun_com_bool) (A tptp.fun_pname_bool)) (=> (forall ((X_2 tptp.pname)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com (tptp.hAPP_pname_com F X_2)) B)))) (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_f273696895l_bool tptp.ord_le1708315510m_bool (tptp.hAPP_f1206115581m_bool (tptp.image_pname_com F) A)) B)))) (forall ((F tptp.fun_pname_pname) (B tptp.fun_pname_bool) (A tptp.fun_pname_bool)) (=> (forall ((X_2 tptp.pname)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname (tptp.hAPP_pname_pname F X_2)) B)))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool (tptp.image_pname_pname F) A)) B)))) (forall ((F tptp.fun_co482540593_state) (B tptp.fun_Ho320143120e_bool) (A tptp.fun_com_bool)) (=> (forall ((X_2 tptp.com)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_2) A)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state (tptp.hAPP_c1041435779_state F X_2)) B)))) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool (tptp.hAPP_f1859782925e_bool (tptp.image_1736049107_state F) A)) B)))) (forall ((F tptp.fun_com_pname) (B tptp.fun_pname_bool) (A tptp.fun_com_bool)) (=> (forall ((X_2 tptp.com)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_2) A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname (tptp.hAPP_com_pname F X_2)) B)))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f1438183293e_bool (tptp.image_com_pname F) A)) B)))) (forall ((F tptp.fun_pn1262351275_state) (B tptp.fun_Ho320143120e_bool) (A tptp.fun_pname_bool)) (=> (forall ((X_2 tptp.pname)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state (tptp.hAPP_p1337579261_state F X_2)) B)))) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool (tptp.hAPP_f1763243027e_bool (tptp.image_1918575693_state F) A)) B)))) (forall ((X_1 tptp.fun_pname_bool)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool X_1) X_1))) (forall ((X_1 tptp.bool)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool X_1) X_1))) (forall ((X_1 tptp.fun_Ho320143120e_bool)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool X_1) X_1))) (forall ((A tptp.fun_com_bool)) (= (not (= A tptp.bot_bot_fun_com_bool)) (exists ((X_2 tptp.com) (B_2 tptp.fun_com_bool)) (and (= A (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com X_2) B_2)) (not (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_2) B_2))))))) (forall ((A tptp.fun_pname_bool)) (= (not (= A tptp.bot_bo844097828e_bool)) (exists ((X_2 tptp.pname) (B_2 tptp.fun_pname_bool)) (and (= A (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname X_2) B_2)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) B_2))))))) (forall ((A tptp.fun_Ho320143120e_bool)) (= (not (= A tptp.bot_bo39439654e_bool)) (exists ((X_2 tptp.hoare_363350478_state) (B_2 tptp.fun_Ho320143120e_bool)) (and (= A (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state X_2) B_2)) (not (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state X_2) B_2))))))) (forall ((X_5 tptp.pname)) (= (tptp.hAPP_o593586696_pname tptp.the_pname_1 (tptp.hAPP_p1252095976_pname tptp.some_pname X_5)) X_5)) (forall ((X_5 tptp.hoare_363350478_state)) (= (tptp.hAPP_o1390191976_state tptp.the_Ho1765868149_state (tptp.hAPP_H1942146718_state tptp.some_H629028223_state X_5)) X_5)) (forall ((X_5 tptp.com)) (= (tptp.hAPP_option_com_com tptp.the_com (tptp.hAPP_com_option_com tptp.some_com X_5)) X_5)) (forall ((G_2 tptp.fun_Ho320143120e_bool) (P_1 tptp.fun_st1506752259e_bool) (Pn_1 tptp.pname) (Q_1 tptp.fun_st1506752259e_bool)) (let ((_let_1 (tptp.hAPP_f960042659_state tptp.hoare_608330478_state P_1))) (let ((_let_2 (tptp.hoare_95103338_state G_2))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_2 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state (tptp.hAPP_f83715540_state (tptp.hAPP_c1279058753_state _let_1 (tptp.hAPP_option_com_com tptp.the_com (tptp.hAPP_p799580910on_com tptp.body Pn_1))) Q_1)) tptp.bot_bo39439654e_bool))) (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_2 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state (tptp.hAPP_f83715540_state (tptp.hAPP_c1279058753_state _let_1 (tptp.hAPP_pname_com tptp.body_1 Pn_1)) Q_1)) tptp.bot_bo39439654e_bool))))))) (forall ((P_1 tptp.fun_st1506752259e_bool) (Pn_1 tptp.pname) (Q_1 tptp.fun_st1506752259e_bool) (G_2 tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_f960042659_state tptp.hoare_608330478_state P_1))) (let ((_let_2 (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state (tptp.hAPP_f83715540_state (tptp.hAPP_c1279058753_state _let_1 (tptp.hAPP_pname_com tptp.body_1 Pn_1)) Q_1)))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hoare_95103338_state (tptp.hAPP_f1749453397e_bool _let_2 G_2)) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state (tptp.hAPP_f83715540_state (tptp.hAPP_c1279058753_state _let_1 (tptp.hAPP_option_com_com tptp.the_com (tptp.hAPP_p799580910on_com tptp.body Pn_1))) Q_1)) tptp.bot_bo39439654e_bool))) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hoare_95103338_state G_2) (tptp.hAPP_f1749453397e_bool _let_2 tptp.bot_bo39439654e_bool))))))) (= _let_11 (exists ((S_1 tptp.state) (T_2 tptp.state)) (not (= S_1 T_2)))) (forall ((A tptp.fun_com_bool) (C tptp.com) (B tptp.fun_com_bool)) (let ((_let_1 (tptp.hAPP_c667411853l_bool tptp.member_com C))) (=> (=> (not (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 B))) (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 A))) (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila605046092m_bool A) B)))))) (forall ((A tptp.fun_Ho320143120e_bool) (C tptp.hoare_363350478_state) (B tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_H40373975l_bool tptp.member1253905979_state C))) (=> (=> (not (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 B))) (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 A))) (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool A) B)))))) (forall ((A tptp.fun_pname_bool) (C tptp.pname) (B tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname C))) (=> (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A) B)))))) (forall ((C tptp.com) (A tptp.fun_com_bool) (B tptp.fun_com_bool)) (let ((_let_1 (tptp.hAPP_c667411853l_bool tptp.member_com C))) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila605046092m_bool A) B))) (=> (not (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 A))) (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 B)))))) (forall ((C tptp.hoare_363350478_state) (A tptp.fun_Ho320143120e_bool) (B tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_H40373975l_bool tptp.member1253905979_state C))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool A) B))) (=> (not (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 A))) (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 B)))))) (forall ((C tptp.pname) (A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname C))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A) B))) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B)))))) (forall ((Fun1_2 tptp.fun_st1506752259e_bool) (Com_1 tptp.com) (Fun2_2 tptp.fun_st1506752259e_bool) (Fun1_1 tptp.fun_st1506752259e_bool) (Com_2 tptp.com) (Fun2_1 tptp.fun_st1506752259e_bool)) (= (= (tptp.hAPP_f83715540_state (tptp.hAPP_c1279058753_state (tptp.hAPP_f960042659_state tptp.hoare_608330478_state Fun1_2) Com_1) Fun2_2) (tptp.hAPP_f83715540_state (tptp.hAPP_c1279058753_state (tptp.hAPP_f960042659_state tptp.hoare_608330478_state Fun1_1) Com_2) Fun2_1)) (and (= Fun1_2 Fun1_1) (= Com_1 Com_2) (= Fun2_2 Fun2_1)))) (forall ((A tptp.fun_com_bool) (C tptp.com) (B tptp.fun_com_bool)) (let ((_let_1 (tptp.hAPP_c667411853l_bool tptp.member_com C))) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 B)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila605046092m_bool A) B)))))) (forall ((A tptp.fun_Ho320143120e_bool) (C tptp.hoare_363350478_state) (B tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_H40373975l_bool tptp.member1253905979_state C))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 B)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool A) B)))))) (forall ((A tptp.fun_pname_bool) (C tptp.pname) (B tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname C))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A) B)))))) (forall ((B tptp.fun_com_bool) (C tptp.com) (A tptp.fun_com_bool)) (let ((_let_1 (tptp.hAPP_c667411853l_bool tptp.member_com C))) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila605046092m_bool A) B)))))) (forall ((B tptp.fun_Ho320143120e_bool) (C tptp.hoare_363350478_state) (A tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_H40373975l_bool tptp.member1253905979_state C))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool A) B)))))) (forall ((B tptp.fun_pname_bool) (C tptp.pname) (A tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname C))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A) B)))))) (forall ((P_1 tptp.fun_pname_bool) (A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (= (forall ((X_2 tptp.pname)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A) B))) (tptp.hBOOL (tptp.hAPP_pname_bool P_1 X_2)))) (and (forall ((X_2 tptp.pname)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A)) (tptp.hBOOL (tptp.hAPP_pname_bool P_1 X_2)))) (forall ((X_2 tptp.pname)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) B)) (tptp.hBOOL (tptp.hAPP_pname_bool P_1 X_2))))))) (forall ((P_1 tptp.fun_Ho320143120e_bool) (A tptp.fun_Ho320143120e_bool) (B tptp.fun_Ho320143120e_bool)) (= (forall ((X_2 tptp.hoare_363350478_state)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state X_2) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool A) B))) (tptp.hBOOL (tptp.hAPP_H1645464494e_bool P_1 X_2)))) (and (forall ((X_2 tptp.hoare_363350478_state)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state X_2) A)) (tptp.hBOOL (tptp.hAPP_H1645464494e_bool P_1 X_2)))) (forall ((X_2 tptp.hoare_363350478_state)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state X_2) B)) (tptp.hBOOL (tptp.hAPP_H1645464494e_bool P_1 X_2))))))) (forall ((P_1 tptp.fun_pname_bool) (A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (= (exists ((X_2 tptp.pname)) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A) B))) (tptp.hBOOL (tptp.hAPP_pname_bool P_1 X_2)))) (or (exists ((X_2 tptp.pname)) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A)) (tptp.hBOOL (tptp.hAPP_pname_bool P_1 X_2)))) (exists ((X_2 tptp.pname)) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) B)) (tptp.hBOOL (tptp.hAPP_pname_bool P_1 X_2))))))) (forall ((P_1 tptp.fun_Ho320143120e_bool) (A tptp.fun_Ho320143120e_bool) (B tptp.fun_Ho320143120e_bool)) (= (exists ((X_2 tptp.hoare_363350478_state)) (and (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state X_2) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool A) B))) (tptp.hBOOL (tptp.hAPP_H1645464494e_bool P_1 X_2)))) (or (exists ((X_2 tptp.hoare_363350478_state)) (and (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state X_2) A)) (tptp.hBOOL (tptp.hAPP_H1645464494e_bool P_1 X_2)))) (exists ((X_2 tptp.hoare_363350478_state)) (and (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state X_2) B)) (tptp.hBOOL (tptp.hAPP_H1645464494e_bool P_1 X_2))))))) (forall ((A tptp.fun_pname_bool) (B tptp.fun_pname_bool) (C_1 tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A))) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool (tptp.hAPP_f759274231e_bool _let_1 B)) C_1) (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool B) C_1))))) (forall ((A tptp.fun_Ho320143120e_bool) (B tptp.fun_Ho320143120e_bool) (C_1 tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool A))) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool (tptp.hAPP_f1749453397e_bool _let_1 B)) C_1) (tptp.hAPP_f1749453397e_bool _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool B) C_1))))) (forall ((C tptp.com) (A tptp.fun_com_bool) (B tptp.fun_com_bool)) (let ((_let_1 (tptp.hAPP_c667411853l_bool tptp.member_com C))) (= (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila605046092m_bool A) B))) (or (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 B)))))) (forall ((C tptp.hoare_363350478_state) (A tptp.fun_Ho320143120e_bool) (B tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_H40373975l_bool tptp.member1253905979_state C))) (= (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool A) B))) (or (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 B)))))) (forall ((C tptp.pname) (A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname C))) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A) B))) (or (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B)))))) (forall ((A tptp.fun_pname_bool) (B tptp.fun_pname_bool) (C_1 tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A))) (let ((_let_2 (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool B))) (= (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool _let_2 C_1)) (tptp.hAPP_f759274231e_bool _let_2 (tptp.hAPP_f759274231e_bool _let_1 C_1)))))) (forall ((A tptp.fun_Ho320143120e_bool) (B tptp.fun_Ho320143120e_bool) (C_1 tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool A))) (let ((_let_2 (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool B))) (= (tptp.hAPP_f1749453397e_bool _let_1 (tptp.hAPP_f1749453397e_bool _let_2 C_1)) (tptp.hAPP_f1749453397e_bool _let_2 (tptp.hAPP_f1749453397e_bool _let_1 C_1)))))) (forall ((A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A))) (let ((_let_2 (tptp.hAPP_f759274231e_bool _let_1 B))) (= (tptp.hAPP_f759274231e_bool _let_1 _let_2) _let_2)))) (forall ((A tptp.fun_Ho320143120e_bool) (B tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool A))) (let ((_let_2 (tptp.hAPP_f1749453397e_bool _let_1 B))) (= (tptp.hAPP_f1749453397e_bool _let_1 _let_2) _let_2)))) (forall ((A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A) B) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool B) A))) (forall ((A tptp.fun_Ho320143120e_bool) (B tptp.fun_Ho320143120e_bool)) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool A) B) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool B) A))) (forall ((A tptp.fun_com_bool) (B tptp.fun_com_bool)) (let ((_let_1 (tptp.hAPP_f578650245m_bool tptp.cOMBC_1904837336l_bool tptp.member_com))) (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila605046092m_bool A) B) (tptp.hAPP_f1682609283m_bool tptp.collect_com (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f328772264m_bool tptp.cOMBS_com_bool_bool (tptp.hAPP_f954469007l_bool (tptp.cOMBB_886968260ol_com tptp.fdisj) (tptp.hAPP_f1682609283m_bool _let_1 A))) (tptp.hAPP_f1682609283m_bool _let_1 B)))))) (forall ((A tptp.fun_fu1430349052l_bool) (B tptp.fun_fu1430349052l_bool)) (let ((_let_1 (tptp.hAPP_f1145991873l_bool tptp.cOMBC_1988546018l_bool tptp.member799430823e_bool))) (= (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.semila1782091504l_bool A) B) (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f624840228l_bool tptp.cOMBS_350070575l_bool (tptp.hAPP_f143162813l_bool (tptp.cOMBB_2095475776e_bool tptp.fdisj) (tptp.hAPP_f559147733l_bool _let_1 A))) (tptp.hAPP_f559147733l_bool _let_1 B)))))) (forall ((A tptp.fun_fu1996308102l_bool) (B tptp.fun_fu1996308102l_bool)) (let ((_let_1 (tptp.hAPP_f1854331281l_bool tptp.cOMBC_1522409444l_bool tptp.member1534059107e_bool))) (= (tptp.hAPP_f85652879l_bool (tptp.hAPP_f1175211816l_bool tptp.semila862847378l_bool A) B) (tptp.hAPP_f85652879l_bool tptp.collec1243131813e_bool (tptp.hAPP_f85652879l_bool (tptp.hAPP_f927797370l_bool tptp.cOMBS_1039407915l_bool (tptp.hAPP_f945781379l_bool (tptp.cOMBB_1004232970e_bool tptp.fdisj) (tptp.hAPP_f85652879l_bool _let_1 A))) (tptp.hAPP_f85652879l_bool _let_1 B)))))) (forall ((A tptp.fun_Ho320143120e_bool) (B tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_f1072682137e_bool tptp.cOMBC_1415895650l_bool tptp.member1253905979_state))) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool A) B) (tptp.hAPP_f1749453397e_bool tptp.collec223185785_state (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1612626488e_bool tptp.cOMBS_56025283l_bool (tptp.hAPP_f1422032445l_bool (tptp.cOMBB_877416532_state tptp.fdisj) (tptp.hAPP_f1749453397e_bool _let_1 A))) (tptp.hAPP_f1749453397e_bool _let_1 B)))))) (forall ((A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f661147897e_bool tptp.cOMBC_1058051404l_bool tptp.member_pname))) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A) B) (tptp.hAPP_f759274231e_bool tptp.collect_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_f649174806e_bool tptp.cOMBS_568398431l_bool (tptp.hAPP_f1402196763l_bool (tptp.cOMBB_675860798_pname tptp.fdisj) (tptp.hAPP_f759274231e_bool _let_1 A))) (tptp.hAPP_f759274231e_bool _let_1 B)))))) (forall ((A tptp.fun_pname_bool)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A) A) A)) (forall ((A tptp.fun_Ho320143120e_bool)) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool A) A) A)) (forall ((P_1 tptp.fun_pname_bool) (Q_1 tptp.fun_pname_bool)) (= (tptp.hAPP_f759274231e_bool tptp.collect_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_f649174806e_bool tptp.cOMBS_568398431l_bool (tptp.hAPP_f1402196763l_bool (tptp.cOMBB_675860798_pname tptp.fdisj) P_1)) Q_1)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool (tptp.hAPP_f759274231e_bool tptp.collect_pname P_1)) (tptp.hAPP_f759274231e_bool tptp.collect_pname Q_1)))) (forall ((P_1 tptp.fun_fu1430349052l_bool) (Q_1 tptp.fun_fu1430349052l_bool)) (= (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f624840228l_bool tptp.cOMBS_350070575l_bool (tptp.hAPP_f143162813l_bool (tptp.cOMBB_2095475776e_bool tptp.fdisj) P_1)) Q_1)) (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.semila1782091504l_bool (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool P_1)) (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool Q_1)))) (forall ((P_1 tptp.fun_fu1996308102l_bool) (Q_1 tptp.fun_fu1996308102l_bool)) (= (tptp.hAPP_f85652879l_bool tptp.collec1243131813e_bool (tptp.hAPP_f85652879l_bool (tptp.hAPP_f927797370l_bool tptp.cOMBS_1039407915l_bool (tptp.hAPP_f945781379l_bool (tptp.cOMBB_1004232970e_bool tptp.fdisj) P_1)) Q_1)) (tptp.hAPP_f85652879l_bool (tptp.hAPP_f1175211816l_bool tptp.semila862847378l_bool (tptp.hAPP_f85652879l_bool tptp.collec1243131813e_bool P_1)) (tptp.hAPP_f85652879l_bool tptp.collec1243131813e_bool Q_1)))) (forall ((P_1 tptp.fun_Ho320143120e_bool) (Q_1 tptp.fun_Ho320143120e_bool)) (= (tptp.hAPP_f1749453397e_bool tptp.collec223185785_state (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1612626488e_bool tptp.cOMBS_56025283l_bool (tptp.hAPP_f1422032445l_bool (tptp.cOMBB_877416532_state tptp.fdisj) P_1)) Q_1)) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool (tptp.hAPP_f1749453397e_bool tptp.collec223185785_state P_1)) (tptp.hAPP_f1749453397e_bool tptp.collec223185785_state Q_1)))) (forall ((A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (= (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A) B) tptp.bot_bo844097828e_bool) (and (= A tptp.bot_bo844097828e_bool) (= B tptp.bot_bo844097828e_bool)))) (forall ((A tptp.fun_com_bool) (B tptp.fun_com_bool)) (= (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila605046092m_bool A) B) tptp.bot_bot_fun_com_bool) (and (= A tptp.bot_bot_fun_com_bool) (= B tptp.bot_bot_fun_com_bool)))) (forall ((A tptp.fun_Ho320143120e_bool) (B tptp.fun_Ho320143120e_bool)) (= (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool A) B) tptp.bot_bo39439654e_bool) (and (= A tptp.bot_bo39439654e_bool) (= B tptp.bot_bo39439654e_bool)))) (forall ((A tptp.fun_pname_bool)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A) tptp.bot_bo844097828e_bool) A)) (forall ((A tptp.fun_com_bool)) (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila605046092m_bool A) tptp.bot_bot_fun_com_bool) A)) (forall ((A tptp.fun_Ho320143120e_bool)) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool A) tptp.bot_bo39439654e_bool) A)) (forall ((B tptp.fun_pname_bool)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool tptp.bot_bo844097828e_bool) B) B)) (forall ((B tptp.fun_com_bool)) (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila605046092m_bool tptp.bot_bot_fun_com_bool) B) B)) (forall ((B tptp.fun_Ho320143120e_bool)) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool tptp.bot_bo39439654e_bool) B) B)) (forall ((G_2 tptp.fun_fu1430349052l_bool) (Fa tptp.fun_fu1430349052l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool G_2)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.semila1782091504l_bool Fa) G_2)))))) (forall ((G_2 tptp.fun_fu1996308102l_bool) (Fa tptp.fun_fu1996308102l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool G_2)) (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool (tptp.hAPP_f85652879l_bool (tptp.hAPP_f1175211816l_bool tptp.semila862847378l_bool Fa) G_2)))))) (forall ((G_2 tptp.fun_Ho320143120e_bool) (Fa tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state Fa)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state G_2)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool Fa) G_2)))))) (forall ((G_2 tptp.fun_pname_bool) (Fa tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname G_2)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool Fa) G_2)))))) (forall ((Fa tptp.fun_fu1430349052l_bool) (G_2 tptp.fun_fu1430349052l_bool)) (= (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.semila1782091504l_bool Fa) G_2))) (and (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool Fa)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool G_2))))) (forall ((Fa tptp.fun_fu1996308102l_bool) (G_2 tptp.fun_fu1996308102l_bool)) (= (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool (tptp.hAPP_f85652879l_bool (tptp.hAPP_f1175211816l_bool tptp.semila862847378l_bool Fa) G_2))) (and (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool Fa)) (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool G_2))))) (forall ((Fa tptp.fun_Ho320143120e_bool) (G_2 tptp.fun_Ho320143120e_bool)) (= (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool Fa) G_2))) (and (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state Fa)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state G_2))))) (forall ((Fa tptp.fun_pname_bool) (G_2 tptp.fun_pname_bool)) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool Fa) G_2))) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname Fa)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname G_2))))) (forall ((A_4 tptp.pname) (B tptp.fun_pname_bool) (C_1 tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p905327722e_bool tptp.insert_pname A_4))) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool (tptp.hAPP_f759274231e_bool _let_1 B)) C_1) (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool B) C_1))))) (forall ((A_4 tptp.com) (B tptp.fun_com_bool) (C_1 tptp.fun_com_bool)) (let ((_let_1 (tptp.hAPP_c566651504m_bool tptp.insert_com A_4))) (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila605046092m_bool (tptp.hAPP_f1682609283m_bool _let_1 B)) C_1) (tptp.hAPP_f1682609283m_bool _let_1 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila605046092m_bool B) C_1))))) (forall ((A_4 tptp.hoare_363350478_state) (B tptp.fun_Ho320143120e_bool) (C_1 tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state A_4))) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool (tptp.hAPP_f1749453397e_bool _let_1 B)) C_1) (tptp.hAPP_f1749453397e_bool _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool B) C_1))))) (forall ((A tptp.fun_pname_bool) (A_4 tptp.pname) (B tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A))) (let ((_let_2 (tptp.hAPP_p905327722e_bool tptp.insert_pname A_4))) (= (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool _let_2 B)) (tptp.hAPP_f759274231e_bool _let_2 (tptp.hAPP_f759274231e_bool _let_1 B)))))) (forall ((A tptp.fun_com_bool) (A_4 tptp.com) (B tptp.fun_com_bool)) (let ((_let_1 (tptp.hAPP_f1120618594m_bool tptp.semila605046092m_bool A))) (let ((_let_2 (tptp.hAPP_c566651504m_bool tptp.insert_com A_4))) (= (tptp.hAPP_f1682609283m_bool _let_1 (tptp.hAPP_f1682609283m_bool _let_2 B)) (tptp.hAPP_f1682609283m_bool _let_2 (tptp.hAPP_f1682609283m_bool _let_1 B)))))) (forall ((A tptp.fun_Ho320143120e_bool) (A_4 tptp.hoare_363350478_state) (B tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool A))) (let ((_let_2 (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state A_4))) (= (tptp.hAPP_f1749453397e_bool _let_1 (tptp.hAPP_f1749453397e_bool _let_2 B)) (tptp.hAPP_f1749453397e_bool _let_2 (tptp.hAPP_f1749453397e_bool _let_1 B)))))) (forall ((B tptp.fun_pname_bool) (D tptp.fun_pname_bool) (A tptp.fun_pname_bool) (C_1 tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) C_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) D)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A) B)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool C_1) D)))))) (forall ((B tptp.fun_Ho320143120e_bool) (D tptp.fun_Ho320143120e_bool) (A tptp.fun_Ho320143120e_bool) (C_1 tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool A) C_1)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool B) D)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool A) B)) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool C_1) D)))))) (forall ((B tptp.fun_pname_bool) (A tptp.fun_pname_bool) (C_1 tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) C_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) C_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A) B)) C_1))))) (forall ((B tptp.fun_Ho320143120e_bool) (A tptp.fun_Ho320143120e_bool) (C_1 tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool A) C_1)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool B) C_1)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool A) B)) C_1))))) (forall ((B tptp.fun_pname_bool) (A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) A)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A) B) A))) (forall ((B tptp.fun_Ho320143120e_bool) (A tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool B) A)) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool A) B) A))) (forall ((A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) B)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A) B) B))) (forall ((A tptp.fun_Ho320143120e_bool) (B tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool A) B)) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool A) B) B))) (forall ((A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) B)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A) B) B))) (forall ((A tptp.fun_Ho320143120e_bool) (B tptp.fun_Ho320143120e_bool)) (= (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool A) B)) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool A) B) B))) (forall ((B tptp.fun_pname_bool) (A tptp.fun_pname_bool)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A) B)))) (forall ((B tptp.fun_Ho320143120e_bool) (A tptp.fun_Ho320143120e_bool)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool B) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool A) B)))) (forall ((A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A) B)))) (forall ((A tptp.fun_Ho320143120e_bool) (B tptp.fun_Ho320143120e_bool)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool A) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool A) B)))) (forall ((F tptp.fun_Ho713471079_pname) (A tptp.fun_Ho320143120e_bool) (B tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.image_1927198851_pname F))) (= (tptp.hAPP_f773602357e_bool _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool A) B)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool (tptp.hAPP_f773602357e_bool _let_1 A)) (tptp.hAPP_f773602357e_bool _let_1 B))))) (forall ((F tptp.fun_pn1262351275_state) (A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (let ((_let_1 (tptp.image_1918575693_state F))) (= (tptp.hAPP_f1763243027e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A) B)) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool (tptp.hAPP_f1763243027e_bool _let_1 A)) (tptp.hAPP_f1763243027e_bool _let_1 B))))) (forall ((A_4 tptp.pname) (B tptp.fun_pname_bool)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A_4) B) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool (tptp.hAPP_f759274231e_bool tptp.collect_pname (tptp.hAPP_p61793385e_bool (tptp.hAPP_f22061361e_bool tptp.cOMBC_1149511130e_bool tptp.fequal_pname) A_4))) B))) (forall ((A_4 tptp.com) (B tptp.fun_com_bool)) (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com A_4) B) (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila605046092m_bool (tptp.hAPP_f1682609283m_bool tptp.collect_com (tptp.hAPP_c1396316405m_bool (tptp.hAPP_f908845385m_bool tptp.cOMBC_com_com_bool tptp.fequal_com) A_4))) B))) (forall ((A_4 tptp.fun_pname_bool) (B tptp.fun_fu1430349052l_bool)) (= (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool A_4) B) (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.semila1782091504l_bool (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool (tptp.hAPP_f434788991l_bool (tptp.hAPP_f1297925993l_bool tptp.cOMBC_1284144636l_bool tptp.fequal533582459e_bool) A_4))) B))) (forall ((A_4 tptp.fun_Ho320143120e_bool) (B tptp.fun_fu1996308102l_bool)) (= (tptp.hAPP_f85652879l_bool (tptp.hAPP_f1941218614l_bool tptp.insert975831690e_bool A_4) B) (tptp.hAPP_f85652879l_bool (tptp.hAPP_f1175211816l_bool tptp.semila862847378l_bool (tptp.hAPP_f85652879l_bool tptp.collec1243131813e_bool (tptp.hAPP_f726209793l_bool (tptp.hAPP_f205303905l_bool tptp.cOMBC_1250231770l_bool tptp.fequal731041167e_bool) A_4))) B))) (forall ((A_4 tptp.hoare_363350478_state) (B tptp.fun_Ho320143120e_bool)) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state A_4) B) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool (tptp.hAPP_f1749453397e_bool tptp.collec223185785_state (tptp.hAPP_H705653759e_bool (tptp.hAPP_f114072425e_bool tptp.cOMBC_13083556e_bool tptp.fequal1026769423_state) A_4))) B))) (forall ((A_4 tptp.pname) (A tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p905327722e_bool tptp.insert_pname A_4))) (= (tptp.hAPP_f759274231e_bool _let_1 A) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool (tptp.hAPP_f759274231e_bool _let_1 tptp.bot_bo844097828e_bool)) A)))) (forall ((A_4 tptp.com) (A tptp.fun_com_bool)) (let ((_let_1 (tptp.hAPP_c566651504m_bool tptp.insert_com A_4))) (= (tptp.hAPP_f1682609283m_bool _let_1 A) (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila605046092m_bool (tptp.hAPP_f1682609283m_bool _let_1 tptp.bot_bot_fun_com_bool)) A)))) (forall ((A_4 tptp.hoare_363350478_state) (A tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state A_4))) (= (tptp.hAPP_f1749453397e_bool _let_1 A) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool (tptp.hAPP_f1749453397e_bool _let_1 tptp.bot_bo39439654e_bool)) A)))) (forall ((G_2 tptp.fun_Ho320143120e_bool) (P_1 tptp.fun_pn12888928e_bool) (Q_1 tptp.fun_pn12888928e_bool) (Procs tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f1311198492_state tptp.cOMBS_124505571_state (tptp.hAPP_f387017471_state (tptp.cOMBB_1212270426_pname tptp.hoare_608330478_state) P_1)))) (let ((_let_2 (tptp.hAPP_f1763243027e_bool (tptp.image_1918575693_state (tptp.hAPP_f19336718_state (tptp.hAPP_f720869462_state tptp.cOMBS_1110920566_state (tptp.hAPP_f1146170881_state _let_1 tptp.body_1)) Q_1)) Procs))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hoare_95103338_state (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool G_2) _let_2)) (tptp.hAPP_f1763243027e_bool (tptp.image_1918575693_state (tptp.hAPP_f19336718_state (tptp.hAPP_f720869462_state tptp.cOMBS_1110920566_state (tptp.hAPP_f1146170881_state _let_1 (tptp.hAPP_f96342628me_com (tptp.cOMBB_923936821_pname tptp.the_com) tptp.body))) Q_1)) Procs))) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hoare_95103338_state G_2) _let_2)))))) (forall ((Z tptp.fun_pname_bool) (Y_2 tptp.fun_pname_bool) (X_1 tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool Z))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool Y_2) X_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 Y_2)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 X_1)))))) (forall ((Z tptp.bool) (Y_2 tptp.bool) (X_1 tptp.bool)) (let ((_let_1 (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Z))) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Y_2) X_1)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 Y_2)) (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 X_1)))))) (forall ((Z tptp.fun_Ho320143120e_bool) (Y_2 tptp.fun_Ho320143120e_bool) (X_1 tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool Z))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool Y_2) X_1)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 Y_2)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 X_1)))))) (forall ((Y_2 tptp.fun_pname_bool) (X_1 tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool Y_2) X_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool X_1) Y_2)) (= X_1 Y_2)))) (forall ((Y_2 tptp.bool) (X_1 tptp.bool)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Y_2) X_1)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool X_1) Y_2)) (= (tptp.hBOOL X_1) (tptp.hBOOL Y_2))))) (forall ((Y_2 tptp.fun_Ho320143120e_bool) (X_1 tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool Y_2) X_1)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool X_1) Y_2)) (= X_1 Y_2)))) (forall ((Z tptp.fun_pname_bool) (X_1 tptp.fun_pname_bool) (Y_2 tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool X_1))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 Y_2)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool Y_2) Z)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 Z)))))) (forall ((Z tptp.bool) (X_1 tptp.bool) (Y_2 tptp.bool)) (let ((_let_1 (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool X_1))) (=> (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 Y_2)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Y_2) Z)) (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 Z)))))) (forall ((Z tptp.fun_Ho320143120e_bool) (X_1 tptp.fun_Ho320143120e_bool) (Y_2 tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool X_1))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 Y_2)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool Y_2) Z)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 Z)))))) (forall ((X_1 tptp.fun_pname_bool) (Y_2 tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool X_1) Y_2)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool Y_2) X_1)) (= X_1 Y_2)))) (forall ((X_1 tptp.bool) (Y_2 tptp.bool)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool X_1) Y_2)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Y_2) X_1)) (= (tptp.hBOOL X_1) (tptp.hBOOL Y_2))))) (forall ((X_1 tptp.fun_Ho320143120e_bool) (Y_2 tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool X_1) Y_2)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool Y_2) X_1)) (= X_1 Y_2)))) (forall ((C tptp.fun_pname_bool) (B_1 tptp.fun_pname_bool) (A_4 tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B_1) A_4)) (=> (= B_1 C) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool C) A_4))))) (forall ((C tptp.bool) (B_1 tptp.bool) (A_4 tptp.bool)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool B_1) A_4)) (=> (= (tptp.hBOOL B_1) (tptp.hBOOL C)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool C) A_4))))) (forall ((C tptp.fun_Ho320143120e_bool) (B_1 tptp.fun_Ho320143120e_bool) (A_4 tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool B_1) A_4)) (=> (= B_1 C) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool C) A_4))))) (forall ((C tptp.fun_pname_bool) (A_4 tptp.fun_pname_bool) (B_1 tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_4))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B_1)) (=> (= B_1 C) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 C)))))) (forall ((C tptp.bool) (A_4 tptp.bool) (B_1 tptp.bool)) (let ((_let_1 (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool A_4))) (=> (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 B_1)) (=> (= (tptp.hBOOL B_1) (tptp.hBOOL C)) (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 C)))))) (forall ((C tptp.fun_Ho320143120e_bool) (A_4 tptp.fun_Ho320143120e_bool) (B_1 tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool A_4))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 B_1)) (=> (= B_1 C) (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 C)))))) (forall ((C tptp.fun_pname_bool) (A_4 tptp.fun_pname_bool) (B_1 tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool C))) (=> (= A_4 B_1) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A_4)))))) (forall ((C tptp.bool) (B_1 tptp.bool) (A_4 tptp.bool)) (let ((_let_1 (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool C))) (=> (= (tptp.hBOOL A_4) (tptp.hBOOL B_1)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 B_1)) (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 A_4)))))) (forall ((C tptp.fun_Ho320143120e_bool) (A_4 tptp.fun_Ho320143120e_bool) (B_1 tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool C))) (=> (= A_4 B_1) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 B_1)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 A_4)))))) (forall ((C tptp.fun_pname_bool) (A_4 tptp.fun_pname_bool) (B_1 tptp.fun_pname_bool)) (=> (= A_4 B_1) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B_1) C)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_4) C))))) (forall ((C tptp.bool) (B_1 tptp.bool) (A_4 tptp.bool)) (=> (= (tptp.hBOOL A_4) (tptp.hBOOL B_1)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool B_1) C)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool A_4) C))))) (forall ((C tptp.fun_Ho320143120e_bool) (A_4 tptp.fun_Ho320143120e_bool) (B_1 tptp.fun_Ho320143120e_bool)) (=> (= A_4 B_1) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool B_1) C)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool A_4) C))))) (forall ((Y_2 tptp.fun_pname_bool) (X_1 tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool Y_2) X_1)) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool X_1) Y_2)) (= X_1 Y_2)))) (forall ((Y_2 tptp.bool) (X_1 tptp.bool)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Y_2) X_1)) (= (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool X_1) Y_2)) (= (tptp.hBOOL X_1) (tptp.hBOOL Y_2))))) (forall ((Y_2 tptp.fun_Ho320143120e_bool) (X_1 tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool Y_2) X_1)) (= (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool X_1) Y_2)) (= X_1 Y_2)))) (forall ((X_1 tptp.fun_pname_bool) (Y_2 tptp.fun_pname_bool)) (=> (= X_1 Y_2) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool X_1) Y_2)))) (forall ((Y_2 tptp.bool) (X_1 tptp.bool)) (=> (= (tptp.hBOOL X_1) (tptp.hBOOL Y_2)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool X_1) Y_2)))) (forall ((X_1 tptp.fun_Ho320143120e_bool) (Y_2 tptp.fun_Ho320143120e_bool)) (=> (= X_1 Y_2) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool X_1) Y_2)))) (forall ((X_1 tptp.fun_pname_bool) (Y_2 tptp.fun_pname_bool)) (= (= X_1 Y_2) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool X_1) Y_2)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool Y_2) X_1))))) (forall ((Y_2 tptp.bool) (X_1 tptp.bool)) (= (= (tptp.hBOOL X_1) (tptp.hBOOL Y_2)) (and (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool X_1) Y_2)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Y_2) X_1))))) (forall ((X_1 tptp.fun_Ho320143120e_bool) (Y_2 tptp.fun_Ho320143120e_bool)) (= (= X_1 Y_2) (and (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool X_1) Y_2)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool Y_2) X_1))))) (forall ((A_4 tptp.pname) (A_8 tptp.pname)) (= (= (tptp.hAPP_p1252095976_pname tptp.some_pname A_4) (tptp.hAPP_p1252095976_pname tptp.some_pname A_8)) (= A_4 A_8))) (forall ((A_4 tptp.hoare_363350478_state) (A_8 tptp.hoare_363350478_state)) (= (= (tptp.hAPP_H1942146718_state tptp.some_H629028223_state A_4) (tptp.hAPP_H1942146718_state tptp.some_H629028223_state A_8)) (= A_4 A_8))) (forall ((A_4 tptp.com) (A_8 tptp.com)) (= (= (tptp.hAPP_com_option_com tptp.some_com A_4) (tptp.hAPP_com_option_com tptp.some_com A_8)) (= A_4 A_8))) (forall ((G_2 tptp.fun_Ho320143120e_bool) (P_1 tptp.fun_st1506752259e_bool) (C tptp.com) (Q_1 tptp.fun_st1506752259e_bool) (C_1 tptp.bool)) (let ((_let_1 (tptp.hoare_95103338_state G_2))) (=> (=> (tptp.hBOOL C_1) (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state (tptp.hAPP_f83715540_state (tptp.hAPP_c1279058753_state (tptp.hAPP_f960042659_state tptp.hoare_608330478_state P_1) C) Q_1)) tptp.bot_bo39439654e_bool)))) (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state (tptp.hAPP_f83715540_state (tptp.hAPP_c1279058753_state (tptp.hAPP_f960042659_state tptp.hoare_608330478_state (tptp.hAPP_b1095269219e_bool (tptp.hAPP_f701449317e_bool tptp.cOMBC_471052088e_bool (tptp.hAPP_f873506917e_bool (tptp.cOMBB_1757942702_state tptp.cOMBC_231445413l_bool) (tptp.hAPP_f1283379615l_bool (tptp.cOMBB_1759179140_state (tptp.cOMBB_188601460_state tptp.fconj)) P_1))) C_1)) C) Q_1)) tptp.bot_bo39439654e_bool)))))) (forall ((Pn_1 tptp.pname) (G_2 tptp.fun_Ho320143120e_bool) (P_1 tptp.fun_pn12888928e_bool) (Q_1 tptp.fun_pn12888928e_bool) (Procs tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f1311198492_state tptp.cOMBS_124505571_state (tptp.hAPP_f387017471_state (tptp.cOMBB_1212270426_pname tptp.hoare_608330478_state) P_1)))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hoare_95103338_state (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool G_2) (tptp.hAPP_f1763243027e_bool (tptp.image_1918575693_state (tptp.hAPP_f19336718_state (tptp.hAPP_f720869462_state tptp.cOMBS_1110920566_state (tptp.hAPP_f1146170881_state _let_1 tptp.body_1)) Q_1)) Procs))) (tptp.hAPP_f1763243027e_bool (tptp.image_1918575693_state (tptp.hAPP_f19336718_state (tptp.hAPP_f720869462_state tptp.cOMBS_1110920566_state (tptp.hAPP_f1146170881_state _let_1 (tptp.hAPP_f96342628me_com (tptp.cOMBB_923936821_pname tptp.the_com) tptp.body))) Q_1)) Procs))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname Pn_1) Procs)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hoare_95103338_state G_2) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state (tptp.hAPP_f83715540_state (tptp.hAPP_c1279058753_state (tptp.hAPP_f960042659_state tptp.hoare_608330478_state (tptp.hAPP_p1637813682e_bool P_1 Pn_1)) (tptp.hAPP_pname_com tptp.body_1 Pn_1)) (tptp.hAPP_p1637813682e_bool Q_1 Pn_1))) tptp.bot_bo39439654e_bool))))))) (forall ((A_4 tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_4) tptp.bot_bo844097828e_bool)) (= A_4 tptp.bot_bo844097828e_bool))) (forall ((A_4 tptp.fun_com_bool)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_f273696895l_bool tptp.ord_le1708315510m_bool A_4) tptp.bot_bot_fun_com_bool)) (= A_4 tptp.bot_bot_fun_com_bool))) (forall ((A_4 tptp.bool)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool A_4) tptp.bot_bot_bool)) (= (tptp.hBOOL A_4) (tptp.hBOOL tptp.bot_bot_bool)))) (forall ((A_4 tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool A_4) tptp.bot_bo39439654e_bool)) (= A_4 tptp.bot_bo39439654e_bool))) (forall ((A_4 tptp.fun_pname_bool)) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_4) tptp.bot_bo844097828e_bool)) (= A_4 tptp.bot_bo844097828e_bool))) (forall ((A_4 tptp.fun_com_bool)) (= (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_f273696895l_bool tptp.ord_le1708315510m_bool A_4) tptp.bot_bot_fun_com_bool)) (= A_4 tptp.bot_bot_fun_com_bool))) (forall ((A_4 tptp.bool)) (= (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool A_4) tptp.bot_bot_bool)) (= (tptp.hBOOL A_4) (tptp.hBOOL tptp.bot_bot_bool)))) (forall ((A_4 tptp.fun_Ho320143120e_bool)) (= (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool A_4) tptp.bot_bo39439654e_bool)) (= A_4 tptp.bot_bo39439654e_bool))) (forall ((A_4 tptp.fun_pname_bool)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool tptp.bot_bo844097828e_bool) A_4))) (forall ((A_4 tptp.fun_com_bool)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_f273696895l_bool tptp.ord_le1708315510m_bool tptp.bot_bot_fun_com_bool) A_4))) (forall ((A_4 tptp.bool)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool tptp.bot_bot_bool) A_4))) (forall ((A_4 tptp.fun_Ho320143120e_bool)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool tptp.bot_bo39439654e_bool) A_4))) (forall ((X_1 tptp.pname) (F tptp.fun_pname_bool) (G tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool F) G)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_pname_bool F X_1)) (tptp.hAPP_pname_bool G X_1))))) (forall ((X_1 tptp.hoare_363350478_state) (F tptp.fun_Ho320143120e_bool) (G tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool F) G)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_H1645464494e_bool F X_1)) (tptp.hAPP_H1645464494e_bool G X_1))))) (forall ((X_1 tptp.pname) (F tptp.fun_pname_bool) (G tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool F) G)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_pname_bool F X_1)) (tptp.hAPP_pname_bool G X_1))))) (forall ((X_1 tptp.hoare_363350478_state) (F tptp.fun_Ho320143120e_bool) (G tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool F) G)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_H1645464494e_bool F X_1)) (tptp.hAPP_H1645464494e_bool G X_1))))) (forall ((F tptp.fun_pname_bool) (G tptp.fun_pname_bool)) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool F) G)) (forall ((X_2 tptp.pname)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_pname_bool F X_2)) (tptp.hAPP_pname_bool G X_2)))))) (forall ((F tptp.fun_Ho320143120e_bool) (G tptp.fun_Ho320143120e_bool)) (= (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool F) G)) (forall ((X_2 tptp.hoare_363350478_state)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_H1645464494e_bool F X_2)) (tptp.hAPP_H1645464494e_bool G X_2)))))) (forall ((X_1 tptp.pname)) (= (tptp.hBOOL (tptp.hAPP_pname_bool tptp.bot_bo844097828e_bool X_1)) (tptp.hBOOL tptp.bot_bot_bool))) (forall ((X_1 tptp.com)) (= (tptp.hBOOL (tptp.hAPP_com_bool tptp.bot_bot_fun_com_bool X_1)) (tptp.hBOOL tptp.bot_bot_bool))) (forall ((X_1 tptp.hoare_363350478_state)) (= (tptp.hBOOL (tptp.hAPP_H1645464494e_bool tptp.bot_bo39439654e_bool X_1)) (tptp.hBOOL tptp.bot_bot_bool))) (forall ((X_2 tptp.pname)) (= (tptp.hBOOL (tptp.hAPP_pname_bool tptp.bot_bo844097828e_bool X_2)) (tptp.hBOOL tptp.bot_bot_bool))) (forall ((X_2 tptp.com)) (= (tptp.hBOOL (tptp.hAPP_com_bool tptp.bot_bot_fun_com_bool X_2)) (tptp.hBOOL tptp.bot_bot_bool))) (forall ((X_2 tptp.hoare_363350478_state)) (= (tptp.hBOOL (tptp.hAPP_H1645464494e_bool tptp.bot_bo39439654e_bool X_2)) (tptp.hBOOL tptp.bot_bot_bool))) (forall ((P_1 tptp.fun_fu1022316450e_bool) (Q_1 tptp.fun_fu1022316450e_bool) (G_2 tptp.fun_Ho320143120e_bool) (P_3 tptp.fun_fu1022316450e_bool) (C0_1 tptp.fun_fu78728705ol_com) (Q_3 tptp.fun_fu1022316450e_bool) (U_1 tptp.fun_fu1430349052l_bool)) (let ((_let_1 (tptp.cOMBB_151548708e_bool tptp.hoare_608330478_state))) (let ((_let_2 (tptp.hoare_95103338_state G_2))) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool U_1)) (=> (forall ((P_4 tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f792846925ol_com C0_1 P_4))) (let ((_let_2 (tptp.hoare_95103338_state G_2))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_2 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state (tptp.hAPP_f83715540_state (tptp.hAPP_c1279058753_state (tptp.hAPP_f960042659_state tptp.hoare_608330478_state (tptp.hAPP_f887530048e_bool P_3 P_4)) _let_1) (tptp.hAPP_f887530048e_bool Q_3 P_4))) tptp.bot_bo39439654e_bool))) (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_2 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state (tptp.hAPP_f83715540_state (tptp.hAPP_c1279058753_state (tptp.hAPP_f960042659_state tptp.hoare_608330478_state (tptp.hAPP_f887530048e_bool P_1 P_4)) _let_1) (tptp.hAPP_f887530048e_bool Q_1 P_4))) tptp.bot_bo39439654e_bool))))))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_2 (tptp.hAPP_f1912490857e_bool (tptp.image_431763259_state (tptp.hAPP_f2070959648_state (tptp.hAPP_f820078872_state tptp.cOMBS_444947014_state (tptp.hAPP_f926121585_state (tptp.hAPP_f907647536_state tptp.cOMBS_1636274867_state (tptp.hAPP_f1215319405_state _let_1 P_3)) C0_1)) Q_3)) U_1))) (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_2 (tptp.hAPP_f1912490857e_bool (tptp.image_431763259_state (tptp.hAPP_f2070959648_state (tptp.hAPP_f820078872_state tptp.cOMBS_444947014_state (tptp.hAPP_f926121585_state (tptp.hAPP_f907647536_state tptp.cOMBS_1636274867_state (tptp.hAPP_f1215319405_state _let_1 P_1)) C0_1)) Q_1)) U_1))))))))) (forall ((P_1 tptp.fun_fu1232608556e_bool) (Q_1 tptp.fun_fu1232608556e_bool) (G_2 tptp.fun_Ho320143120e_bool) (P_3 tptp.fun_fu1232608556e_bool) (C0_1 tptp.fun_fu1203007991ol_com) (Q_3 tptp.fun_fu1232608556e_bool) (U_1 tptp.fun_fu1996308102l_bool)) (let ((_let_1 (tptp.cOMBB_188465958e_bool tptp.hoare_608330478_state))) (let ((_let_2 (tptp.hoare_95103338_state G_2))) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool U_1)) (=> (forall ((P_4 tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_f1577230223ol_com C0_1 P_4))) (let ((_let_2 (tptp.hoare_95103338_state G_2))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_2 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state (tptp.hAPP_f83715540_state (tptp.hAPP_c1279058753_state (tptp.hAPP_f960042659_state tptp.hoare_608330478_state (tptp.hAPP_f877220222e_bool P_3 P_4)) _let_1) (tptp.hAPP_f877220222e_bool Q_3 P_4))) tptp.bot_bo39439654e_bool))) (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_2 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state (tptp.hAPP_f83715540_state (tptp.hAPP_c1279058753_state (tptp.hAPP_f960042659_state tptp.hoare_608330478_state (tptp.hAPP_f877220222e_bool P_1 P_4)) _let_1) (tptp.hAPP_f877220222e_bool Q_1 P_4))) tptp.bot_bo39439654e_bool))))))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_2 (tptp.hAPP_f1180969799e_bool (tptp.image_2021386777_state (tptp.hAPP_f605405862_state (tptp.hAPP_f1593397690_state tptp.cOMBS_1452472386_state (tptp.hAPP_f153770241_state (tptp.hAPP_f2014973160_state tptp.cOMBS_319359663_state (tptp.hAPP_f1323754599_state _let_1 P_3)) C0_1)) Q_3)) U_1))) (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_2 (tptp.hAPP_f1180969799e_bool (tptp.image_2021386777_state (tptp.hAPP_f605405862_state (tptp.hAPP_f1593397690_state tptp.cOMBS_1452472386_state (tptp.hAPP_f153770241_state (tptp.hAPP_f2014973160_state tptp.cOMBS_319359663_state (tptp.hAPP_f1323754599_state _let_1 P_1)) C0_1)) Q_1)) U_1))))))))) (forall ((P_1 tptp.fun_pn12888928e_bool) (Q_1 tptp.fun_pn12888928e_bool) (G_2 tptp.fun_Ho320143120e_bool) (P_3 tptp.fun_pn12888928e_bool) (C0_1 tptp.fun_pname_com) (Q_3 tptp.fun_pn12888928e_bool) (U_1 tptp.fun_pname_bool)) (let ((_let_1 (tptp.cOMBB_1212270426_pname tptp.hoare_608330478_state))) (let ((_let_2 (tptp.hoare_95103338_state G_2))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname U_1)) (=> (forall ((P_4 tptp.pname)) (let ((_let_1 (tptp.hAPP_pname_com C0_1 P_4))) (let ((_let_2 (tptp.hoare_95103338_state G_2))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_2 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state (tptp.hAPP_f83715540_state (tptp.hAPP_c1279058753_state (tptp.hAPP_f960042659_state tptp.hoare_608330478_state (tptp.hAPP_p1637813682e_bool P_3 P_4)) _let_1) (tptp.hAPP_p1637813682e_bool Q_3 P_4))) tptp.bot_bo39439654e_bool))) (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_2 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state (tptp.hAPP_f83715540_state (tptp.hAPP_c1279058753_state (tptp.hAPP_f960042659_state tptp.hoare_608330478_state (tptp.hAPP_p1637813682e_bool P_1 P_4)) _let_1) (tptp.hAPP_p1637813682e_bool Q_1 P_4))) tptp.bot_bo39439654e_bool))))))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_2 (tptp.hAPP_f1763243027e_bool (tptp.image_1918575693_state (tptp.hAPP_f19336718_state (tptp.hAPP_f720869462_state tptp.cOMBS_1110920566_state (tptp.hAPP_f1146170881_state (tptp.hAPP_f1311198492_state tptp.cOMBS_124505571_state (tptp.hAPP_f387017471_state _let_1 P_3)) C0_1)) Q_3)) U_1))) (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_2 (tptp.hAPP_f1763243027e_bool (tptp.image_1918575693_state (tptp.hAPP_f19336718_state (tptp.hAPP_f720869462_state tptp.cOMBS_1110920566_state (tptp.hAPP_f1146170881_state (tptp.hAPP_f1311198492_state tptp.cOMBS_124505571_state (tptp.hAPP_f387017471_state _let_1 P_1)) C0_1)) Q_1)) U_1))))))))) (forall ((G_2 tptp.fun_Ho320143120e_bool) (C tptp.com) (Q_1 tptp.fun_st1506752259e_bool) (P_1 tptp.fun_st1506752259e_bool)) (=> (forall ((Z_2 tptp.state) (S_1 tptp.state)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool P_1 Z_2) S_1)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hoare_95103338_state G_2) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state (tptp.hAPP_f83715540_state (tptp.hAPP_c1279058753_state (tptp.hAPP_f960042659_state tptp.hoare_608330478_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_1))) C) (tptp.hAPP_f1863945078e_bool tptp.cOMBK_631994958_state (tptp.hAPP_s1806633685e_bool Q_1 Z_2)))) tptp.bot_bo39439654e_bool))))) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hoare_95103338_state G_2) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state (tptp.hAPP_f83715540_state (tptp.hAPP_c1279058753_state (tptp.hAPP_f960042659_state tptp.hoare_608330478_state P_1) C) Q_1)) tptp.bot_bo39439654e_bool))))) (forall ((G_2 tptp.fun_Ho320143120e_bool) (P_1 tptp.fun_pn12888928e_bool) (Q_1 tptp.fun_pn12888928e_bool) (Procs tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f1311198492_state tptp.cOMBS_124505571_state (tptp.hAPP_f387017471_state (tptp.cOMBB_1212270426_pname tptp.hoare_608330478_state) P_1)))) (let ((_let_2 (tptp.hAPP_f1763243027e_bool (tptp.image_1918575693_state (tptp.hAPP_f19336718_state (tptp.hAPP_f720869462_state tptp.cOMBS_1110920566_state (tptp.hAPP_f1146170881_state _let_1 tptp.body_1)) Q_1)) Procs))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hoare_501514600_state (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool G_2) _let_2)) (tptp.hAPP_f1763243027e_bool (tptp.image_1918575693_state (tptp.hAPP_f19336718_state (tptp.hAPP_f720869462_state tptp.cOMBS_1110920566_state (tptp.hAPP_f1146170881_state _let_1 (tptp.hAPP_f96342628me_com (tptp.cOMBB_923936821_pname tptp.the_com) tptp.body))) Q_1)) Procs))) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hoare_501514600_state G_2) _let_2)))))) (forall ((P_1 tptp.fun_st1506752259e_bool) (G_2 tptp.fun_Ho320143120e_bool) (P_3 tptp.fun_st1506752259e_bool) (C tptp.com) (Q_1 tptp.fun_st1506752259e_bool)) (let ((_let_1 (tptp.hoare_95103338_state G_2))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state (tptp.hAPP_f83715540_state (tptp.hAPP_c1279058753_state (tptp.hAPP_f960042659_state tptp.hoare_608330478_state P_3) C) Q_1)) tptp.bot_bo39439654e_bool))) (=> (forall ((Z_2 tptp.state) (S_1 tptp.state)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool P_1 Z_2) S_1)) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool P_3 Z_2) S_1)))) (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state (tptp.hAPP_f83715540_state (tptp.hAPP_c1279058753_state (tptp.hAPP_f960042659_state tptp.hoare_608330478_state P_1) C) Q_1)) tptp.bot_bo39439654e_bool))))))) (forall ((Q_1 tptp.fun_st1506752259e_bool) (G_2 tptp.fun_Ho320143120e_bool) (P_1 tptp.fun_st1506752259e_bool) (C tptp.com) (Q_3 tptp.fun_st1506752259e_bool)) (let ((_let_1 (tptp.hAPP_c1279058753_state (tptp.hAPP_f960042659_state tptp.hoare_608330478_state P_1) C))) (let ((_let_2 (tptp.hoare_95103338_state G_2))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_2 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state (tptp.hAPP_f83715540_state _let_1 Q_3)) tptp.bot_bo39439654e_bool))) (=> (forall ((Z_2 tptp.state) (S_1 tptp.state)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool Q_3 Z_2) S_1)) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool Q_1 Z_2) S_1)))) (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_2 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state (tptp.hAPP_f83715540_state _let_1 Q_1)) tptp.bot_bo39439654e_bool)))))))) (forall ((P_1 tptp.fun_st1506752259e_bool) (Q_1 tptp.fun_st1506752259e_bool) (C tptp.com)) (let ((_let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state (tptp.hAPP_f83715540_state (tptp.hAPP_c1279058753_state (tptp.hAPP_f960042659_state tptp.hoare_608330478_state P_1) C) Q_1)) tptp.bot_bo39439654e_bool))) (let ((_let_2 (tptp.hoare_95103338_state tptp.bot_bo39439654e_bool))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_2 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state (tptp.hAPP_c1041435779_state tptp.hoare_Mirabelle_MGT C)) tptp.bot_bo39439654e_bool))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hoare_501514600_state tptp.bot_bo39439654e_bool) _let_1)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_2 _let_1))))))) (forall ((A tptp.fun_pname_bool) (B tptp.fun_pname_bool) (X_1 tptp.pname)) (=> (tptp.hBOOL (tptp.hAPP_pname_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A) B) X_1)) (=> (not (tptp.hBOOL (tptp.hAPP_pname_bool A X_1))) (tptp.hBOOL (tptp.hAPP_pname_bool B X_1))))) (forall ((A tptp.fun_Ho320143120e_bool) (B tptp.fun_Ho320143120e_bool) (X_1 tptp.hoare_363350478_state)) (=> (tptp.hBOOL (tptp.hAPP_H1645464494e_bool (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool A) B) X_1)) (=> (not (tptp.hBOOL (tptp.hAPP_H1645464494e_bool A X_1))) (tptp.hBOOL (tptp.hAPP_H1645464494e_bool B X_1))))) (forall ((A tptp.fun_pname_bool) (B tptp.fun_pname_bool) (X_1 tptp.pname)) (=> (=> (not (tptp.hBOOL (tptp.hAPP_pname_bool B X_1))) (tptp.hBOOL (tptp.hAPP_pname_bool A X_1))) (tptp.hBOOL (tptp.hAPP_pname_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A) B) X_1)))) (forall ((A tptp.fun_Ho320143120e_bool) (B tptp.fun_Ho320143120e_bool) (X_1 tptp.hoare_363350478_state)) (=> (=> (not (tptp.hBOOL (tptp.hAPP_H1645464494e_bool B X_1))) (tptp.hBOOL (tptp.hAPP_H1645464494e_bool A X_1))) (tptp.hBOOL (tptp.hAPP_H1645464494e_bool (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool A) B) X_1)))) (forall ((Q_1 tptp.fun_st1506752259e_bool) (P_1 tptp.fun_st1506752259e_bool) (G_2 tptp.fun_Ho320143120e_bool) (P_3 tptp.fun_st1506752259e_bool) (C tptp.com) (Q_3 tptp.fun_st1506752259e_bool)) (let ((_let_1 (tptp.hoare_95103338_state G_2))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state (tptp.hAPP_f83715540_state (tptp.hAPP_c1279058753_state (tptp.hAPP_f960042659_state tptp.hoare_608330478_state P_3) C) Q_3)) tptp.bot_bo39439654e_bool))) (=> (forall ((Z_2 tptp.state) (S_1 tptp.state)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool P_1 Z_2) S_1)) (forall ((S_2 tptp.state)) (=> (forall ((Z_3 tptp.state)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool P_3 Z_3) S_1)) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool Q_3 Z_3) S_2)))) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool Q_1 Z_2) S_2)))))) (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state (tptp.hAPP_f83715540_state (tptp.hAPP_c1279058753_state (tptp.hAPP_f960042659_state tptp.hoare_608330478_state P_1) C) Q_1)) tptp.bot_bo39439654e_bool))))))) (forall ((G_2 tptp.fun_Ho320143120e_bool) (Ts tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hoare_95103338_state G_2) Ts)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hoare_501514600_state G_2) Ts)))) (forall ((X_2 tptp.com)) (= (tptp.hBOOL (tptp.hAPP_com_bool tptp.bot_bot_fun_com_bool X_2)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_2) tptp.bot_bot_fun_com_bool)))) (forall ((X_2 tptp.hoare_363350478_state)) (= (tptp.hBOOL (tptp.hAPP_H1645464494e_bool tptp.bot_bo39439654e_bool X_2)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state X_2) tptp.bot_bo39439654e_bool)))) (forall ((X_2 tptp.pname)) (= (tptp.hBOOL (tptp.hAPP_pname_bool tptp.bot_bo844097828e_bool X_2)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) tptp.bot_bo844097828e_bool)))) (forall ((Q_1 tptp.fun_pname_bool) (P_1 tptp.fun_pname_bool) (X_1 tptp.pname)) (=> (tptp.hBOOL (tptp.hAPP_pname_bool P_1 X_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool P_1) Q_1)) (tptp.hBOOL (tptp.hAPP_pname_bool Q_1 X_1))))) (forall ((Q_1 tptp.fun_Ho320143120e_bool) (P_1 tptp.fun_Ho320143120e_bool) (X_1 tptp.hoare_363350478_state)) (=> (tptp.hBOOL (tptp.hAPP_H1645464494e_bool P_1 X_1)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool P_1) Q_1)) (tptp.hBOOL (tptp.hAPP_H1645464494e_bool Q_1 X_1))))) (forall ((X_1 tptp.pname) (P_1 tptp.fun_pname_bool) (Q_1 tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool P_1) Q_1)) (=> (tptp.hBOOL (tptp.hAPP_pname_bool P_1 X_1)) (tptp.hBOOL (tptp.hAPP_pname_bool Q_1 X_1))))) (forall ((X_1 tptp.hoare_363350478_state) (P_1 tptp.fun_Ho320143120e_bool) (Q_1 tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool P_1) Q_1)) (=> (tptp.hBOOL (tptp.hAPP_H1645464494e_bool P_1 X_1)) (tptp.hBOOL (tptp.hAPP_H1645464494e_bool Q_1 X_1))))) (forall ((A tptp.fun_pname_bool) (B tptp.fun_pname_bool) (X_1 tptp.pname)) (=> (tptp.hBOOL (tptp.hAPP_pname_bool B X_1)) (tptp.hBOOL (tptp.hAPP_pname_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A) B) X_1)))) (forall ((A tptp.fun_Ho320143120e_bool) (B tptp.fun_Ho320143120e_bool) (X_1 tptp.hoare_363350478_state)) (=> (tptp.hBOOL (tptp.hAPP_H1645464494e_bool B X_1)) (tptp.hBOOL (tptp.hAPP_H1645464494e_bool (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool A) B) X_1)))) (forall ((B tptp.fun_pname_bool) (A tptp.fun_pname_bool) (X_1 tptp.pname)) (=> (tptp.hBOOL (tptp.hAPP_pname_bool A X_1)) (tptp.hBOOL (tptp.hAPP_pname_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A) B) X_1)))) (forall ((B tptp.fun_Ho320143120e_bool) (A tptp.fun_Ho320143120e_bool) (X_1 tptp.hoare_363350478_state)) (=> (tptp.hBOOL (tptp.hAPP_H1645464494e_bool A X_1)) (tptp.hBOOL (tptp.hAPP_H1645464494e_bool (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool A) B) X_1)))) (forall ((R_1 tptp.fun_com_bool) (S tptp.fun_com_bool)) (let ((_let_1 (tptp.hAPP_f578650245m_bool tptp.cOMBC_1904837336l_bool tptp.member_com))) (= (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_f273696895l_bool tptp.ord_le1708315510m_bool (tptp.hAPP_f1682609283m_bool _let_1 R_1)) (tptp.hAPP_f1682609283m_bool _let_1 S))) (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_f273696895l_bool tptp.ord_le1708315510m_bool R_1) S))))) (forall ((R_1 tptp.fun_Ho320143120e_bool) (S tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_f1072682137e_bool tptp.cOMBC_1415895650l_bool tptp.member1253905979_state))) (= (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool (tptp.hAPP_f1749453397e_bool _let_1 R_1)) (tptp.hAPP_f1749453397e_bool _let_1 S))) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool R_1) S))))) (forall ((R_1 tptp.fun_pname_bool) (S tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f661147897e_bool tptp.cOMBC_1058051404l_bool tptp.member_pname))) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool _let_1 R_1)) (tptp.hAPP_f759274231e_bool _let_1 S))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool R_1) S))))) (forall ((R_1 tptp.fun_com_bool) (S tptp.fun_com_bool) (X_2 tptp.com)) (let ((_let_1 (tptp.hAPP_f578650245m_bool tptp.cOMBC_1904837336l_bool tptp.member_com))) (= (tptp.hBOOL (tptp.hAPP_com_bool (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila605046092m_bool (tptp.hAPP_f1682609283m_bool _let_1 R_1)) (tptp.hAPP_f1682609283m_bool _let_1 S)) X_2)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_2) (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila605046092m_bool R_1) S)))))) (forall ((R_1 tptp.fun_Ho320143120e_bool) (S tptp.fun_Ho320143120e_bool) (X_2 tptp.hoare_363350478_state)) (let ((_let_1 (tptp.hAPP_f1072682137e_bool tptp.cOMBC_1415895650l_bool tptp.member1253905979_state))) (= (tptp.hBOOL (tptp.hAPP_H1645464494e_bool (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool (tptp.hAPP_f1749453397e_bool _let_1 R_1)) (tptp.hAPP_f1749453397e_bool _let_1 S)) X_2)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state X_2) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool R_1) S)))))) (forall ((R_1 tptp.fun_pname_bool) (S tptp.fun_pname_bool) (X_2 tptp.pname)) (let ((_let_1 (tptp.hAPP_f661147897e_bool tptp.cOMBC_1058051404l_bool tptp.member_pname))) (= (tptp.hBOOL (tptp.hAPP_pname_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool (tptp.hAPP_f759274231e_bool _let_1 R_1)) (tptp.hAPP_f759274231e_bool _let_1 S)) X_2)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool R_1) S)))))) (forall ((F tptp.fun_pname_bool) (G tptp.fun_pname_bool)) (=> (forall ((X_2 tptp.pname)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_pname_bool F X_2)) (tptp.hAPP_pname_bool G X_2)))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool F) G)))) (forall ((F tptp.fun_Ho320143120e_bool) (G tptp.fun_Ho320143120e_bool)) (=> (forall ((X_2 tptp.hoare_363350478_state)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_H1645464494e_bool F X_2)) (tptp.hAPP_H1645464494e_bool G X_2)))) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool F) G)))) (forall ((X_1 tptp.pname)) (= (tptp.set_pname (tptp.hAPP_p1252095976_pname tptp.some_pname X_1)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1) tptp.bot_bo844097828e_bool))) (forall ((X_1 tptp.com)) (= (tptp.set_com (tptp.hAPP_com_option_com tptp.some_com X_1)) (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com X_1) tptp.bot_bot_fun_com_bool))) (forall ((X_1 tptp.hoare_363350478_state)) (= (tptp.set_Ho1327198534_state (tptp.hAPP_H1942146718_state tptp.some_H629028223_state X_1)) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state X_1) tptp.bot_bo39439654e_bool))) (forall ((F tptp.fun_pname_bool) (G tptp.fun_pname_bool) (X_1 tptp.pname)) (= (tptp.hBOOL (tptp.hAPP_pname_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool F) G) X_1)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool (tptp.hAPP_pname_bool F X_1)) (tptp.hAPP_pname_bool G X_1))))) (forall ((F tptp.fun_Ho320143120e_bool) (G tptp.fun_Ho320143120e_bool) (X_1 tptp.hoare_363350478_state)) (= (tptp.hBOOL (tptp.hAPP_H1645464494e_bool (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool F) G) X_1)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool (tptp.hAPP_H1645464494e_bool F X_1)) (tptp.hAPP_H1645464494e_bool G X_1))))) (forall ((F tptp.fun_pname_bool) (G tptp.fun_pname_bool) (X_2 tptp.pname)) (= (tptp.hBOOL (tptp.hAPP_pname_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool F) G) X_2)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool (tptp.hAPP_pname_bool F X_2)) (tptp.hAPP_pname_bool G X_2))))) (forall ((F tptp.fun_Ho320143120e_bool) (G tptp.fun_Ho320143120e_bool) (X_2 tptp.hoare_363350478_state)) (= (tptp.hBOOL (tptp.hAPP_H1645464494e_bool (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool F) G) X_2)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool (tptp.hAPP_H1645464494e_bool F X_2)) (tptp.hAPP_H1645464494e_bool G X_2))))) (=> _let_11 (forall ((T_2 tptp.state)) (not (forall ((S_1 tptp.state)) (= S_1 T_2))))) (forall ((X_1 tptp.fun_pname_bool) (Y_2 tptp.fun_pname_bool)) (= (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool X_1) Y_2) tptp.bot_bo844097828e_bool) (and (= X_1 tptp.bot_bo844097828e_bool) (= Y_2 tptp.bot_bo844097828e_bool)))) (forall ((X_1 tptp.fun_com_bool) (Y_2 tptp.fun_com_bool)) (= (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila605046092m_bool X_1) Y_2) tptp.bot_bot_fun_com_bool) (and (= X_1 tptp.bot_bot_fun_com_bool) (= Y_2 tptp.bot_bot_fun_com_bool)))) (forall ((X_1 tptp.bool) (Y_2 tptp.bool)) (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_2)) _let_1) (and (= (tptp.hBOOL X_1) _let_1) (= (tptp.hBOOL Y_2) _let_1))))) (forall ((X_1 tptp.fun_Ho320143120e_bool) (Y_2 tptp.fun_Ho320143120e_bool)) (= (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool X_1) Y_2) tptp.bot_bo39439654e_bool) (and (= X_1 tptp.bot_bo39439654e_bool) (= Y_2 tptp.bot_bo39439654e_bool)))) (forall ((X_1 tptp.com) (Xo tptp.option_com)) (= (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_1) (tptp.set_com Xo))) (= Xo (tptp.hAPP_com_option_com tptp.some_com X_1)))) (forall ((X_1 tptp.hoare_363350478_state) (Xo tptp.option131732143_state)) (= (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state X_1) (tptp.set_Ho1327198534_state Xo))) (= Xo (tptp.hAPP_H1942146718_state tptp.some_H629028223_state X_1)))) (forall ((X_1 tptp.pname) (Xo tptp.option_pname)) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) (tptp.set_pname Xo))) (= Xo (tptp.hAPP_p1252095976_pname tptp.some_pname X_1)))) (forall ((A_4 tptp.fun_pname_bool)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A_4) A_4) A_4)) (forall ((A_4 tptp.bool)) (= (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool A_4) A_4)) (tptp.hBOOL A_4))) (forall ((A_4 tptp.fun_Ho320143120e_bool)) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool A_4) A_4) A_4)) (forall ((X_1 tptp.fun_pname_bool)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool X_1) X_1) X_1)) (forall ((X_1 tptp.bool)) (= (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool X_1) X_1)) (tptp.hBOOL X_1))) (forall ((X_1 tptp.fun_Ho320143120e_bool)) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool X_1) X_1) X_1)) (forall ((A_4 tptp.fun_pname_bool) (B_1 tptp.fun_pname_bool)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A_4) B_1) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool B_1) A_4))) (forall ((A_4 tptp.bool) (B_1 tptp.bool)) (= (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool A_4) B_1)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool B_1) A_4)))) (forall ((A_4 tptp.fun_Ho320143120e_bool) (B_1 tptp.fun_Ho320143120e_bool)) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool A_4) B_1) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool B_1) A_4))) (forall ((X_1 tptp.fun_pname_bool) (Y_2 tptp.fun_pname_bool)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool X_1) Y_2) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool Y_2) X_1))) (forall ((X_1 tptp.bool) (Y_2 tptp.bool)) (= (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool X_1) Y_2)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool Y_2) X_1)))) (forall ((X_1 tptp.fun_Ho320143120e_bool) (Y_2 tptp.fun_Ho320143120e_bool)) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool X_1) Y_2) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool Y_2) X_1))) (forall ((X_1 tptp.fun_pname_bool) (Y_2 tptp.fun_pname_bool)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool X_1) Y_2) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool Y_2) X_1))) (forall ((X_1 tptp.bool) (Y_2 tptp.bool)) (= (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool X_1) Y_2)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool Y_2) X_1)))) (forall ((X_1 tptp.fun_Ho320143120e_bool) (Y_2 tptp.fun_Ho320143120e_bool)) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool X_1) Y_2) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool Y_2) X_1))) (forall ((A_4 tptp.fun_pname_bool) (B_1 tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A_4))) (let ((_let_2 (tptp.hAPP_f759274231e_bool _let_1 B_1))) (= (tptp.hAPP_f759274231e_bool _let_1 _let_2) _let_2)))) (forall ((A_4 tptp.bool) (B_1 tptp.bool)) (let ((_let_1 (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool A_4))) (let ((_let_2 (tptp.hAPP_bool_bool _let_1 B_1))) (= (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 _let_2)) (tptp.hBOOL _let_2))))) (forall ((A_4 tptp.fun_Ho320143120e_bool) (B_1 tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool A_4))) (let ((_let_2 (tptp.hAPP_f1749453397e_bool _let_1 B_1))) (= (tptp.hAPP_f1749453397e_bool _let_1 _let_2) _let_2)))) (forall ((X_1 tptp.fun_pname_bool) (Y_2 tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool X_1))) (let ((_let_2 (tptp.hAPP_f759274231e_bool _let_1 Y_2))) (= (tptp.hAPP_f759274231e_bool _let_1 _let_2) _let_2)))) (forall ((X_1 tptp.bool) (Y_2 tptp.bool)) (let ((_let_1 (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool X_1))) (let ((_let_2 (tptp.hAPP_bool_bool _let_1 Y_2))) (= (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 _let_2)) (tptp.hBOOL _let_2))))) (forall ((X_1 tptp.fun_Ho320143120e_bool) (Y_2 tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool X_1))) (let ((_let_2 (tptp.hAPP_f1749453397e_bool _let_1 Y_2))) (= (tptp.hAPP_f1749453397e_bool _let_1 _let_2) _let_2)))) (forall ((X_1 tptp.fun_pname_bool) (Y_2 tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool X_1))) (let ((_let_2 (tptp.hAPP_f759274231e_bool _let_1 Y_2))) (= (tptp.hAPP_f759274231e_bool _let_1 _let_2) _let_2)))) (forall ((X_1 tptp.bool) (Y_2 tptp.bool)) (let ((_let_1 (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool X_1))) (let ((_let_2 (tptp.hAPP_bool_bool _let_1 Y_2))) (= (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 _let_2)) (tptp.hBOOL _let_2))))) (forall ((X_1 tptp.fun_Ho320143120e_bool) (Y_2 tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool X_1))) (let ((_let_2 (tptp.hAPP_f1749453397e_bool _let_1 Y_2))) (= (tptp.hAPP_f1749453397e_bool _let_1 _let_2) _let_2)))) (forall ((B_1 tptp.fun_pname_bool) (A_4 tptp.fun_pname_bool) (C tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool B_1))) (let ((_let_2 (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A_4))) (= (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool _let_2 C)) (tptp.hAPP_f759274231e_bool _let_2 (tptp.hAPP_f759274231e_bool _let_1 C)))))) (forall ((B_1 tptp.bool) (A_4 tptp.bool) (C tptp.bool)) (let ((_let_1 (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool B_1))) (let ((_let_2 (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool A_4))) (= (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 (tptp.hAPP_bool_bool _let_2 C))) (tptp.hBOOL (tptp.hAPP_bool_bool _let_2 (tptp.hAPP_bool_bool _let_1 C))))))) (forall ((B_1 tptp.fun_Ho320143120e_bool) (A_4 tptp.fun_Ho320143120e_bool) (C tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool B_1))) (let ((_let_2 (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool A_4))) (= (tptp.hAPP_f1749453397e_bool _let_1 (tptp.hAPP_f1749453397e_bool _let_2 C)) (tptp.hAPP_f1749453397e_bool _let_2 (tptp.hAPP_f1749453397e_bool _let_1 C)))))) (forall ((X_1 tptp.fun_pname_bool) (Y_2 tptp.fun_pname_bool) (Z tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool X_1))) (let ((_let_2 (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool Y_2))) (= (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool _let_2 Z)) (tptp.hAPP_f759274231e_bool _let_2 (tptp.hAPP_f759274231e_bool _let_1 Z)))))) (forall ((X_1 tptp.bool) (Y_2 tptp.bool) (Z tptp.bool)) (let ((_let_1 (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool X_1))) (let ((_let_2 (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool Y_2))) (= (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 (tptp.hAPP_bool_bool _let_2 Z))) (tptp.hBOOL (tptp.hAPP_bool_bool _let_2 (tptp.hAPP_bool_bool _let_1 Z))))))) (forall ((X_1 tptp.fun_Ho320143120e_bool) (Y_2 tptp.fun_Ho320143120e_bool) (Z tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool X_1))) (let ((_let_2 (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool Y_2))) (= (tptp.hAPP_f1749453397e_bool _let_1 (tptp.hAPP_f1749453397e_bool _let_2 Z)) (tptp.hAPP_f1749453397e_bool _let_2 (tptp.hAPP_f1749453397e_bool _let_1 Z)))))) (forall ((X_1 tptp.fun_pname_bool) (Y_2 tptp.fun_pname_bool) (Z tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool X_1))) (let ((_let_2 (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool Y_2))) (= (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool _let_2 Z)) (tptp.hAPP_f759274231e_bool _let_2 (tptp.hAPP_f759274231e_bool _let_1 Z)))))) (forall ((X_1 tptp.bool) (Y_2 tptp.bool) (Z tptp.bool)) (let ((_let_1 (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool X_1))) (let ((_let_2 (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool Y_2))) (= (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 (tptp.hAPP_bool_bool _let_2 Z))) (tptp.hBOOL (tptp.hAPP_bool_bool _let_2 (tptp.hAPP_bool_bool _let_1 Z))))))) (forall ((X_1 tptp.fun_Ho320143120e_bool) (Y_2 tptp.fun_Ho320143120e_bool) (Z tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool X_1))) (let ((_let_2 (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool Y_2))) (= (tptp.hAPP_f1749453397e_bool _let_1 (tptp.hAPP_f1749453397e_bool _let_2 Z)) (tptp.hAPP_f1749453397e_bool _let_2 (tptp.hAPP_f1749453397e_bool _let_1 Z)))))) (forall ((A_4 tptp.fun_pname_bool) (B_1 tptp.fun_pname_bool) (C tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A_4))) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool (tptp.hAPP_f759274231e_bool _let_1 B_1)) C) (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool B_1) C))))) (forall ((A_4 tptp.bool) (B_1 tptp.bool) (C tptp.bool)) (let ((_let_1 (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool A_4))) (= (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool (tptp.hAPP_bool_bool _let_1 B_1)) C)) (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool B_1) C)))))) (forall ((A_4 tptp.fun_Ho320143120e_bool) (B_1 tptp.fun_Ho320143120e_bool) (C tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool A_4))) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool (tptp.hAPP_f1749453397e_bool _let_1 B_1)) C) (tptp.hAPP_f1749453397e_bool _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool B_1) C))))) (forall ((X_1 tptp.fun_pname_bool) (Y_2 tptp.fun_pname_bool) (Z tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool X_1))) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool (tptp.hAPP_f759274231e_bool _let_1 Y_2)) Z) (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool Y_2) Z))))) (forall ((X_1 tptp.bool) (Y_2 tptp.bool) (Z tptp.bool)) (let ((_let_1 (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool X_1))) (= (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool (tptp.hAPP_bool_bool _let_1 Y_2)) Z)) (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool Y_2) Z)))))) (forall ((X_1 tptp.fun_Ho320143120e_bool) (Y_2 tptp.fun_Ho320143120e_bool) (Z tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool X_1))) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool (tptp.hAPP_f1749453397e_bool _let_1 Y_2)) Z) (tptp.hAPP_f1749453397e_bool _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool Y_2) Z))))) (forall ((X_1 tptp.fun_pname_bool) (Y_2 tptp.fun_pname_bool) (Z tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool X_1))) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool (tptp.hAPP_f759274231e_bool _let_1 Y_2)) Z) (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool Y_2) Z))))) (forall ((X_1 tptp.bool) (Y_2 tptp.bool) (Z tptp.bool)) (let ((_let_1 (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool X_1))) (= (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool (tptp.hAPP_bool_bool _let_1 Y_2)) Z)) (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool Y_2) Z)))))) (forall ((X_1 tptp.fun_Ho320143120e_bool) (Y_2 tptp.fun_Ho320143120e_bool) (Z tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool X_1))) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool (tptp.hAPP_f1749453397e_bool _let_1 Y_2)) Z) (tptp.hAPP_f1749453397e_bool _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool Y_2) Z))))) (forall ((X_1 tptp.fun_pname_bool) (Y_2 tptp.fun_pname_bool)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool X_1) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool X_1) Y_2)))) (forall ((X_1 tptp.bool) (Y_2 tptp.bool)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool X_1) (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool X_1) Y_2)))) (forall ((X_1 tptp.fun_Ho320143120e_bool) (Y_2 tptp.fun_Ho320143120e_bool)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool X_1) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool X_1) Y_2)))) (forall ((X_1 tptp.fun_pname_bool) (Y_2 tptp.fun_pname_bool)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool X_1) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool X_1) Y_2)))) (forall ((X_1 tptp.bool) (Y_2 tptp.bool)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool X_1) (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool X_1) Y_2)))) (forall ((X_1 tptp.fun_Ho320143120e_bool) (Y_2 tptp.fun_Ho320143120e_bool)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool X_1) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool X_1) Y_2)))) (forall ((Y_2 tptp.fun_pname_bool) (X_1 tptp.fun_pname_bool)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool Y_2) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool X_1) Y_2)))) (forall ((Y_2 tptp.bool) (X_1 tptp.bool)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Y_2) (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool X_1) Y_2)))) (forall ((Y_2 tptp.fun_Ho320143120e_bool) (X_1 tptp.fun_Ho320143120e_bool)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool Y_2) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool X_1) Y_2)))) (forall ((Y_2 tptp.fun_pname_bool) (X_1 tptp.fun_pname_bool)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool Y_2) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool X_1) Y_2)))) (forall ((Y_2 tptp.bool) (X_1 tptp.bool)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Y_2) (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool X_1) Y_2)))) (forall ((Y_2 tptp.fun_Ho320143120e_bool) (X_1 tptp.fun_Ho320143120e_bool)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool Y_2) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool X_1) Y_2)))) (forall ((X_1 tptp.fun_pname_bool) (Y_2 tptp.fun_pname_bool)) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool X_1) Y_2)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool X_1) Y_2) Y_2))) (forall ((X_1 tptp.bool) (Y_2 tptp.bool)) (= (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool X_1) Y_2)) (= (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool X_1) Y_2)) (tptp.hBOOL Y_2)))) (forall ((X_1 tptp.fun_Ho320143120e_bool) (Y_2 tptp.fun_Ho320143120e_bool)) (= (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool X_1) Y_2)) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool X_1) Y_2) Y_2))) (forall ((X_1 tptp.fun_pname_bool) (Y_2 tptp.fun_pname_bool) (Z tptp.fun_pname_bool)) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool X_1) Y_2)) Z)) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool X_1) Z)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool Y_2) Z))))) (forall ((X_1 tptp.bool) (Y_2 tptp.bool) (Z tptp.bool)) (= (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool X_1) Y_2)) Z)) (and (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool X_1) Z)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Y_2) Z))))) (forall ((X_1 tptp.fun_Ho320143120e_bool) (Y_2 tptp.fun_Ho320143120e_bool) (Z tptp.fun_Ho320143120e_bool)) (= (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool X_1) Y_2)) Z)) (and (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool X_1) Z)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool Y_2) Z))))) (forall ((B_1 tptp.fun_pname_bool) (X_1 tptp.fun_pname_bool) (A_4 tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool X_1))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A_4)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A_4) B_1)))))) (forall ((B_1 tptp.bool) (X_1 tptp.bool) (A_4 tptp.bool)) (let ((_let_1 (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool X_1))) (=> (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 A_4)) (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool A_4) B_1)))))) (forall ((B_1 tptp.fun_Ho320143120e_bool) (X_1 tptp.fun_Ho320143120e_bool) (A_4 tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool X_1))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 A_4)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool A_4) B_1)))))) (forall ((A_4 tptp.fun_pname_bool) (X_1 tptp.fun_pname_bool) (B_1 tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool X_1))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A_4) B_1)))))) (forall ((A_4 tptp.bool) (X_1 tptp.bool) (B_1 tptp.bool)) (let ((_let_1 (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool X_1))) (=> (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 B_1)) (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool A_4) B_1)))))) (forall ((A_4 tptp.fun_Ho320143120e_bool) (X_1 tptp.fun_Ho320143120e_bool) (B_1 tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool X_1))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 B_1)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool A_4) B_1)))))) (forall ((X_1 tptp.fun_pname_bool) (Y_2 tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool X_1) Y_2)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool X_1) Y_2) Y_2))) (forall ((X_1 tptp.bool) (Y_2 tptp.bool)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool X_1) Y_2)) (= (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool X_1) Y_2)) (tptp.hBOOL Y_2)))) (forall ((X_1 tptp.fun_Ho320143120e_bool) (Y_2 tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool X_1) Y_2)) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool X_1) Y_2) Y_2))) (forall ((Y_2 tptp.fun_pname_bool) (X_1 tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool Y_2) X_1)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool X_1) Y_2) X_1))) (forall ((Y_2 tptp.bool) (X_1 tptp.bool)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Y_2) X_1)) (= (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool X_1) Y_2)) (tptp.hBOOL X_1)))) (forall ((Y_2 tptp.fun_Ho320143120e_bool) (X_1 tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool Y_2) X_1)) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool X_1) Y_2) X_1))) (forall ((B_1 tptp.fun_pname_bool) (A_4 tptp.fun_pname_bool) (X_1 tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_4) X_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B_1) X_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A_4) B_1)) X_1))))) (forall ((B_1 tptp.bool) (A_4 tptp.bool) (X_1 tptp.bool)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool A_4) X_1)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool B_1) X_1)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool A_4) B_1)) X_1))))) (forall ((B_1 tptp.fun_Ho320143120e_bool) (A_4 tptp.fun_Ho320143120e_bool) (X_1 tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool A_4) X_1)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool B_1) X_1)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool A_4) B_1)) X_1))))) (forall ((Z tptp.fun_pname_bool) (Y_2 tptp.fun_pname_bool) (X_1 tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool Y_2) X_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool Z) X_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool Y_2) Z)) X_1))))) (forall ((Z tptp.bool) (Y_2 tptp.bool) (X_1 tptp.bool)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Y_2) X_1)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Z) X_1)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool Y_2) Z)) X_1))))) (forall ((Z tptp.fun_Ho320143120e_bool) (Y_2 tptp.fun_Ho320143120e_bool) (X_1 tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool Y_2) X_1)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool Z) X_1)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool Y_2) Z)) X_1))))) (forall ((B_1 tptp.fun_pname_bool) (D_1 tptp.fun_pname_bool) (A_4 tptp.fun_pname_bool) (C tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_4) C)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B_1) D_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A_4) B_1)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool C) D_1)))))) (forall ((B_1 tptp.bool) (D_1 tptp.bool) (A_4 tptp.bool) (C tptp.bool)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool A_4) C)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool B_1) D_1)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool A_4) B_1)) (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool C) D_1)))))) (forall ((B_1 tptp.fun_Ho320143120e_bool) (D_1 tptp.fun_Ho320143120e_bool) (A_4 tptp.fun_Ho320143120e_bool) (C tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool A_4) C)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool B_1) D_1)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool A_4) B_1)) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool C) D_1)))))) (forall ((A_4 tptp.fun_pname_bool) (B_1 tptp.fun_pname_bool) (X_1 tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A_4) B_1)) X_1)) (not (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_4) X_1)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B_1) X_1))))))) (forall ((A_4 tptp.bool) (B_1 tptp.bool) (X_1 tptp.bool)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool A_4) B_1)) X_1)) (not (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool A_4) X_1)) (not (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool B_1) X_1))))))) (forall ((A_4 tptp.fun_Ho320143120e_bool) (B_1 tptp.fun_Ho320143120e_bool) (X_1 tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool A_4) B_1)) X_1)) (not (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool A_4) X_1)) (not (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool B_1) X_1))))))) (forall ((X_1 tptp.fun_pname_bool)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool tptp.bot_bo844097828e_bool) X_1) X_1)) (forall ((X_1 tptp.fun_com_bool)) (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila605046092m_bool tptp.bot_bot_fun_com_bool) X_1) X_1)) (forall ((X_1 tptp.bool)) (= (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 tptp.fun_Ho320143120e_bool)) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool tptp.bot_bo39439654e_bool) X_1) X_1)) (forall ((X_1 tptp.fun_pname_bool)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool X_1) tptp.bot_bo844097828e_bool) X_1)) (forall ((X_1 tptp.fun_com_bool)) (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila605046092m_bool X_1) tptp.bot_bot_fun_com_bool) X_1)) (forall ((X_1 tptp.bool)) (= (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 tptp.fun_Ho320143120e_bool)) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool X_1) tptp.bot_bo39439654e_bool) X_1)) (forall ((X_1 tptp.pname) (P_1 tptp.fun_pname_bool) (A tptp.option_pname)) (=> (forall ((X_2 tptp.pname)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) (tptp.set_pname A))) (tptp.hBOOL (tptp.hAPP_pname_bool P_1 X_2)))) (=> (= A (tptp.hAPP_p1252095976_pname tptp.some_pname X_1)) (tptp.hBOOL (tptp.hAPP_pname_bool P_1 X_1))))) (forall ((X_1 tptp.hoare_363350478_state) (P_1 tptp.fun_Ho320143120e_bool) (A tptp.option131732143_state)) (=> (forall ((X_2 tptp.hoare_363350478_state)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state X_2) (tptp.set_Ho1327198534_state A))) (tptp.hBOOL (tptp.hAPP_H1645464494e_bool P_1 X_2)))) (=> (= A (tptp.hAPP_H1942146718_state tptp.some_H629028223_state X_1)) (tptp.hBOOL (tptp.hAPP_H1645464494e_bool P_1 X_1))))) (forall ((X_1 tptp.com) (P_1 tptp.fun_com_bool) (A tptp.option_com)) (=> (forall ((X_2 tptp.com)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_2) (tptp.set_com A))) (tptp.hBOOL (tptp.hAPP_com_bool P_1 X_2)))) (=> (= A (tptp.hAPP_com_option_com tptp.some_com X_1)) (tptp.hBOOL (tptp.hAPP_com_bool P_1 X_1))))) (forall ((B tptp.fun_fu1430349052l_bool) (A tptp.fun_fu1430349052l_bool) (F tptp.fun_fu2101097872e_bool) (Fa tptp.fun_fu608906319e_bool)) (=> (tptp.hBOOL (tptp.finite1268145088e_bool F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)) (=> (not (= A tptp.bot_bo1649642514l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool B)) (=> (not (= B tptp.bot_bo1649642514l_bool)) (= (tptp.hAPP_f674760225e_bool Fa (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.semila1782091504l_bool A) B)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool F (tptp.hAPP_f674760225e_bool Fa A)) (tptp.hAPP_f674760225e_bool Fa B))))))))) (forall ((B tptp.fun_fu1996308102l_bool) (A tptp.fun_fu1996308102l_bool) (F tptp.fun_fu531943146e_bool) (Fa tptp.fun_fu1671561851e_bool)) (=> (tptp.hBOOL (tptp.finite2090946954e_bool F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool A)) (=> (not (= A tptp.bot_bo133096688l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool B)) (=> (not (= B tptp.bot_bo133096688l_bool)) (= (tptp.hAPP_f1180969799e_bool Fa (tptp.hAPP_f85652879l_bool (tptp.hAPP_f1175211816l_bool tptp.semila862847378l_bool A) B)) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool F (tptp.hAPP_f1180969799e_bool Fa A)) (tptp.hAPP_f1180969799e_bool Fa B))))))))) (forall ((B tptp.fun_com_bool) (A tptp.fun_com_bool) (F tptp.fun_com_fun_com_com) (Fa tptp.fun_fun_com_bool_com)) (=> (tptp.hBOOL (tptp.finite666746948em_com F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool tptp.finite_finite_com A)) (=> (not (= A tptp.bot_bot_fun_com_bool)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool tptp.finite_finite_com B)) (=> (not (= B tptp.bot_bot_fun_com_bool)) (= (tptp.hAPP_f1276420679ol_com Fa (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila605046092m_bool A) B)) (tptp.hAPP_com_com (tptp.hAPP_com_fun_com_com F (tptp.hAPP_f1276420679ol_com Fa A)) (tptp.hAPP_f1276420679ol_com Fa B))))))))) (forall ((B tptp.fun_Ho320143120e_bool) (A tptp.fun_Ho320143120e_bool) (F tptp.fun_Ho31865764_state) (Fa tptp.fun_fu700438391_state)) (=> (tptp.hBOOL (tptp.finite2031572_state F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state A)) (=> (not (= A tptp.bot_bo39439654e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state B)) (=> (not (= B tptp.bot_bo39439654e_bool)) (= (tptp.hAPP_f1242401993_state Fa (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool A) B)) (tptp.hAPP_H1982017439_state (tptp.hAPP_H230141040_state F (tptp.hAPP_f1242401993_state Fa A)) (tptp.hAPP_f1242401993_state Fa B))))))))) (forall ((B tptp.fun_pname_bool) (A tptp.fun_pname_bool) (F tptp.fun_pn1208287926_pname) (Fa tptp.fun_fu1499449723_pname)) (=> (tptp.hBOOL (tptp.finite89670078_pname F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (=> (not (= A tptp.bot_bo844097828e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B)) (=> (not (= B tptp.bot_bo844097828e_bool)) (= (tptp.hAPP_f1297739591_pname Fa (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A) B)) (tptp.hAPP_pname_pname (tptp.hAPP_p1170154830_pname F (tptp.hAPP_f1297739591_pname Fa A)) (tptp.hAPP_f1297739591_pname Fa B))))))))) (forall ((B tptp.fun_fu1430349052l_bool) (A tptp.fun_fu1430349052l_bool) (F tptp.fun_fu2101097872e_bool) (Fa tptp.fun_fu608906319e_bool)) (let ((_let_1 (tptp.hAPP_f674760225e_bool Fa A))) (=> (tptp.hBOOL (tptp.finite1268145088e_bool F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)) (=> (not (= B tptp.bot_bo1649642514l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool B) A)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool F (tptp.hAPP_f674760225e_bool Fa B)) _let_1) _let_1))))))) (forall ((B tptp.fun_fu1996308102l_bool) (A tptp.fun_fu1996308102l_bool) (F tptp.fun_fu531943146e_bool) (Fa tptp.fun_fu1671561851e_bool)) (let ((_let_1 (tptp.hAPP_f1180969799e_bool Fa A))) (=> (tptp.hBOOL (tptp.finite2090946954e_bool F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool A)) (=> (not (= B tptp.bot_bo133096688l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool (tptp.hAPP_f746351743l_bool tptp.ord_le2031828156l_bool B) A)) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool F (tptp.hAPP_f1180969799e_bool Fa B)) _let_1) _let_1))))))) (forall ((B tptp.fun_com_bool) (A tptp.fun_com_bool) (F tptp.fun_com_fun_com_com) (Fa tptp.fun_fun_com_bool_com)) (let ((_let_1 (tptp.hAPP_f1276420679ol_com Fa A))) (=> (tptp.hBOOL (tptp.finite666746948em_com F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool tptp.finite_finite_com A)) (=> (not (= B tptp.bot_bot_fun_com_bool)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_f273696895l_bool tptp.ord_le1708315510m_bool B) A)) (= (tptp.hAPP_com_com (tptp.hAPP_com_fun_com_com F (tptp.hAPP_f1276420679ol_com Fa B)) _let_1) _let_1))))))) (forall ((B tptp.fun_Ho320143120e_bool) (A tptp.fun_Ho320143120e_bool) (F tptp.fun_Ho31865764_state) (Fa tptp.fun_fu700438391_state)) (let ((_let_1 (tptp.hAPP_f1242401993_state Fa A))) (=> (tptp.hBOOL (tptp.finite2031572_state F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state A)) (=> (not (= B tptp.bot_bo39439654e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool B) A)) (= (tptp.hAPP_H1982017439_state (tptp.hAPP_H230141040_state F (tptp.hAPP_f1242401993_state Fa B)) _let_1) _let_1))))))) (forall ((B tptp.fun_pname_bool) (A tptp.fun_pname_bool) (F tptp.fun_pn1208287926_pname) (Fa tptp.fun_fu1499449723_pname)) (let ((_let_1 (tptp.hAPP_f1297739591_pname Fa A))) (=> (tptp.hBOOL (tptp.finite89670078_pname F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (=> (not (= B tptp.bot_bo844097828e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) A)) (= (tptp.hAPP_pname_pname (tptp.hAPP_p1170154830_pname F (tptp.hAPP_f1297739591_pname Fa B)) _let_1) _let_1))))))) (forall ((G_2 tptp.fun_Ho320143120e_bool) (P_1 tptp.fun_st1506752259e_bool)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hoare_95103338_state G_2) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state (tptp.hAPP_f83715540_state (tptp.hAPP_c1279058753_state (tptp.hAPP_f960042659_state tptp.hoare_608330478_state P_1) tptp.skip) P_1)) tptp.bot_bo39439654e_bool)))) (forall ((X_1 tptp.com) (A tptp.fun_com_bool) (F tptp.fun_com_fun_com_com) (Fa tptp.fun_fun_com_bool_com)) (=> (tptp.hBOOL (tptp.finite666746948em_com F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool tptp.finite_finite_com A)) (=> (not (= A tptp.bot_bot_fun_com_bool)) (= (tptp.hAPP_f1276420679ol_com Fa (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com X_1) A)) (tptp.hAPP_com_com (tptp.hAPP_com_fun_com_com F X_1) (tptp.hAPP_f1276420679ol_com Fa A))))))) (forall ((X_1 tptp.fun_pname_bool) (A tptp.fun_fu1430349052l_bool) (F tptp.fun_fu2101097872e_bool) (Fa tptp.fun_fu608906319e_bool)) (=> (tptp.hBOOL (tptp.finite1268145088e_bool F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)) (=> (not (= A tptp.bot_bo1649642514l_bool)) (= (tptp.hAPP_f674760225e_bool Fa (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool X_1) A)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool F X_1) (tptp.hAPP_f674760225e_bool Fa A))))))) (forall ((X_1 tptp.fun_Ho320143120e_bool) (A tptp.fun_fu1996308102l_bool) (F tptp.fun_fu531943146e_bool) (Fa tptp.fun_fu1671561851e_bool)) (=> (tptp.hBOOL (tptp.finite2090946954e_bool F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool A)) (=> (not (= A tptp.bot_bo133096688l_bool)) (= (tptp.hAPP_f1180969799e_bool Fa (tptp.hAPP_f85652879l_bool (tptp.hAPP_f1941218614l_bool tptp.insert975831690e_bool X_1) A)) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool F X_1) (tptp.hAPP_f1180969799e_bool Fa A))))))) (forall ((X_1 tptp.pname) (A tptp.fun_pname_bool) (F tptp.fun_pn1208287926_pname) (Fa tptp.fun_fu1499449723_pname)) (=> (tptp.hBOOL (tptp.finite89670078_pname F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (=> (not (= A tptp.bot_bo844097828e_bool)) (= (tptp.hAPP_f1297739591_pname Fa (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1) A)) (tptp.hAPP_pname_pname (tptp.hAPP_p1170154830_pname F X_1) (tptp.hAPP_f1297739591_pname Fa A))))))) (forall ((X_1 tptp.hoare_363350478_state) (A tptp.fun_Ho320143120e_bool) (F tptp.fun_Ho31865764_state) (Fa tptp.fun_fu700438391_state)) (=> (tptp.hBOOL (tptp.finite2031572_state F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state A)) (=> (not (= A tptp.bot_bo39439654e_bool)) (= (tptp.hAPP_f1242401993_state Fa (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state X_1) A)) (tptp.hAPP_H1982017439_state (tptp.hAPP_H230141040_state F X_1) (tptp.hAPP_f1242401993_state Fa A))))))) (forall ((P_1 tptp.fun_fu1362071682l_bool) (Fa tptp.fun_com_bool)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool tptp.finite_finite_com Fa)) (=> (not (= Fa tptp.bot_bot_fun_com_bool)) (=> (forall ((X_2 tptp.com)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool P_1 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com X_2) tptp.bot_bot_fun_com_bool)))) (=> (forall ((X_2 tptp.com) (F_2 tptp.fun_com_bool)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool tptp.finite_finite_com F_2)) (=> (not (= F_2 tptp.bot_bot_fun_com_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_2) F_2))) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool P_1 F_2)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool P_1 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com X_2) F_2)))))))) (tptp.hBOOL (tptp.hAPP_f990396704l_bool P_1 Fa))))))) (forall ((P_1 tptp.fun_fu399576434l_bool) (Fa tptp.fun_fu1430349052l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool Fa)) (=> (not (= Fa tptp.bot_bo1649642514l_bool)) (=> (forall ((X_2 tptp.fun_pname_bool)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool P_1 (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool X_2) tptp.bot_bo1649642514l_bool)))) (=> (forall ((X_2 tptp.fun_pname_bool) (F_2 tptp.fun_fu1430349052l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool F_2)) (=> (not (= F_2 tptp.bot_bo1649642514l_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool X_2) F_2))) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool P_1 F_2)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool P_1 (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool X_2) F_2)))))))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool P_1 Fa))))))) (forall ((P_1 tptp.fun_fu1972704968l_bool) (Fa tptp.fun_fu1996308102l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool Fa)) (=> (not (= Fa tptp.bot_bo133096688l_bool)) (=> (forall ((X_2 tptp.fun_Ho320143120e_bool)) (tptp.hBOOL (tptp.hAPP_f1287348838l_bool P_1 (tptp.hAPP_f85652879l_bool (tptp.hAPP_f1941218614l_bool tptp.insert975831690e_bool X_2) tptp.bot_bo133096688l_bool)))) (=> (forall ((X_2 tptp.fun_Ho320143120e_bool) (F_2 tptp.fun_fu1996308102l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool F_2)) (=> (not (= F_2 tptp.bot_bo133096688l_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_f1287348838l_bool (tptp.hAPP_f1610329741l_bool tptp.member1534059107e_bool X_2) F_2))) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool P_1 F_2)) (tptp.hBOOL (tptp.hAPP_f1287348838l_bool P_1 (tptp.hAPP_f85652879l_bool (tptp.hAPP_f1941218614l_bool tptp.insert975831690e_bool X_2) F_2)))))))) (tptp.hBOOL (tptp.hAPP_f1287348838l_bool P_1 Fa))))))) (forall ((P_1 tptp.fun_fu1430349052l_bool) (Fa tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname Fa)) (=> (not (= Fa tptp.bot_bo844097828e_bool)) (=> (forall ((X_2 tptp.pname)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname X_2) tptp.bot_bo844097828e_bool)))) (=> (forall ((X_2 tptp.pname) (F_2 tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname F_2)) (=> (not (= F_2 tptp.bot_bo844097828e_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) F_2))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 F_2)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname X_2) F_2)))))))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 Fa))))))) (forall ((P_1 tptp.fun_fu1996308102l_bool) (Fa tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state Fa)) (=> (not (= Fa tptp.bot_bo39439654e_bool)) (=> (forall ((X_2 tptp.hoare_363350478_state)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool P_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state X_2) tptp.bot_bo39439654e_bool)))) (=> (forall ((X_2 tptp.hoare_363350478_state) (F_2 tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state F_2)) (=> (not (= F_2 tptp.bot_bo39439654e_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state X_2) F_2))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool P_1 F_2)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool P_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state X_2) F_2)))))))) (tptp.hBOOL (tptp.hAPP_f568432088l_bool P_1 Fa))))))) (forall ((G_2 tptp.fun_Ho320143120e_bool) (P_1 tptp.fun_st1506752259e_bool) (B_1 tptp.fun_state_bool) (C tptp.com)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hoare_95103338_state G_2) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state (tptp.hAPP_f83715540_state (tptp.hAPP_c1279058753_state (tptp.hAPP_f960042659_state tptp.hoare_608330478_state (tptp.hAPP_f1863945078e_bool (tptp.hAPP_f915354021e_bool tptp.cOMBC_952831051e_bool (tptp.hAPP_f1138284024e_bool (tptp.cOMBB_20296667_state tptp.cOMBS_1378840469l_bool) (tptp.hAPP_f1283379615l_bool (tptp.cOMBB_1759179140_state (tptp.cOMBB_188601460_state tptp.fconj)) P_1))) (tptp.hAPP_f1759915619e_bool (tptp.cOMBB_160679318_state tptp.fNot) B_1))) (tptp.hAPP_com_com (tptp.while B_1) C)) P_1)) tptp.bot_bo39439654e_bool)))) (forall ((D_1 tptp.com) (R_1 tptp.fun_st1506752259e_bool) (G_2 tptp.fun_Ho320143120e_bool) (P_1 tptp.fun_st1506752259e_bool) (C tptp.com) (Q_1 tptp.fun_st1506752259e_bool)) (let ((_let_1 (tptp.hAPP_f960042659_state tptp.hoare_608330478_state P_1))) (let ((_let_2 (tptp.hoare_95103338_state G_2))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_2 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state (tptp.hAPP_f83715540_state (tptp.hAPP_c1279058753_state _let_1 C) Q_1)) tptp.bot_bo39439654e_bool))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_2 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state (tptp.hAPP_f83715540_state (tptp.hAPP_c1279058753_state (tptp.hAPP_f960042659_state tptp.hoare_608330478_state Q_1) D_1) R_1)) tptp.bot_bo39439654e_bool))) (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_2 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state (tptp.hAPP_f83715540_state (tptp.hAPP_c1279058753_state _let_1 (tptp.hAPP_com_com (tptp.hAPP_com_fun_com_com tptp.semi C) D_1)) R_1)) tptp.bot_bo39439654e_bool)))))))) (forall ((B_1 tptp.fun_state_bool) (C tptp.com)) (=> (tptp.hBOOL (tptp.hAPP_com_bool tptp.wt (tptp.hAPP_com_com (tptp.while B_1) C))) (tptp.hBOOL (tptp.hAPP_com_bool tptp.wt C)))) (forall ((C1 tptp.com) (C2 tptp.com)) (=> (tptp.hBOOL (tptp.hAPP_com_bool tptp.wt (tptp.hAPP_com_com (tptp.hAPP_com_fun_com_com tptp.semi C1) C2))) (not (=> (tptp.hBOOL (tptp.hAPP_com_bool tptp.wt C1)) (not (tptp.hBOOL (tptp.hAPP_com_bool tptp.wt C2))))))) (forall ((X_1 tptp.hoare_363350478_state) (F tptp.fun_Ho31865764_state) (Fa tptp.fun_fu700438391_state)) (=> (tptp.hBOOL (tptp.finite2031572_state F Fa)) (= (tptp.hAPP_H1982017439_state (tptp.hAPP_H230141040_state F X_1) X_1) X_1))) (forall ((X_1 tptp.pname) (F tptp.fun_pn1208287926_pname) (Fa tptp.fun_fu1499449723_pname)) (=> (tptp.hBOOL (tptp.finite89670078_pname F Fa)) (= (tptp.hAPP_pname_pname (tptp.hAPP_p1170154830_pname F X_1) X_1) X_1))) (forall ((Com1_3 tptp.com) (Com2_3 tptp.com)) (not (= tptp.skip (tptp.hAPP_com_com (tptp.hAPP_com_fun_com_com tptp.semi Com1_3) Com2_3)))) (forall ((Fun_1 tptp.fun_state_bool) (Com_2 tptp.com)) (not (= tptp.skip (tptp.hAPP_com_com (tptp.while Fun_1) Com_2)))) (forall ((Com1_3 tptp.com) (Com2_3 tptp.com)) (not (= (tptp.hAPP_com_com (tptp.hAPP_com_fun_com_com tptp.semi Com1_3) Com2_3) tptp.skip))) (forall ((Fun_1 tptp.fun_state_bool) (Com_2 tptp.com)) (not (= (tptp.hAPP_com_com (tptp.while Fun_1) Com_2) tptp.skip))) (forall ((Com1_2 tptp.com) (Com2_2 tptp.com) (Fun_1 tptp.fun_state_bool) (Com_2 tptp.com)) (not (= (tptp.hAPP_com_com (tptp.hAPP_com_fun_com_com tptp.semi Com1_2) Com2_2) (tptp.hAPP_com_com (tptp.while Fun_1) Com_2)))) (forall ((Fun_1 tptp.fun_state_bool) (Com_2 tptp.com) (Com1_2 tptp.com) (Com2_2 tptp.com)) (not (= (tptp.hAPP_com_com (tptp.while Fun_1) Com_2) (tptp.hAPP_com_com (tptp.hAPP_com_fun_com_com tptp.semi Com1_2) Com2_2)))) (forall ((Com1_2 tptp.com) (Com2_2 tptp.com) (Com1_1 tptp.com) (Com2_1 tptp.com)) (= (= (tptp.hAPP_com_com (tptp.hAPP_com_fun_com_com tptp.semi Com1_2) Com2_2) (tptp.hAPP_com_com (tptp.hAPP_com_fun_com_com tptp.semi Com1_1) Com2_1)) (and (= Com1_2 Com1_1) (= Com2_2 Com2_1)))) (forall ((Fun tptp.fun_state_bool) (Com_1 tptp.com) (Fun_1 tptp.fun_state_bool) (Com_2 tptp.com)) (= (= (tptp.hAPP_com_com (tptp.while Fun) Com_1) (tptp.hAPP_com_com (tptp.while Fun_1) Com_2)) (and (= Fun Fun_1) (= Com_1 Com_2)))) (forall ((Pname_1 tptp.pname) (Fun tptp.fun_state_bool) (Com_1 tptp.com)) (not (= (tptp.hAPP_pname_com tptp.body_1 Pname_1) (tptp.hAPP_com_com (tptp.while Fun) Com_1)))) (forall ((Fun tptp.fun_state_bool) (Com_1 tptp.com) (Pname_1 tptp.pname)) (not (= (tptp.hAPP_com_com (tptp.while Fun) Com_1) (tptp.hAPP_pname_com tptp.body_1 Pname_1)))) (forall ((B_1 tptp.fun_state_bool) (C tptp.com)) (=> (tptp.hBOOL (tptp.hAPP_com_bool tptp.wt C)) (tptp.hBOOL (tptp.hAPP_com_bool tptp.wt (tptp.hAPP_com_com (tptp.while B_1) C))))) (forall ((Pname tptp.pname) (Com1 tptp.com) (Com2 tptp.com)) (not (= (tptp.hAPP_pname_com tptp.body_1 Pname) (tptp.hAPP_com_com (tptp.hAPP_com_fun_com_com tptp.semi Com1) Com2)))) (forall ((Com1 tptp.com) (Com2 tptp.com) (Pname tptp.pname)) (not (= (tptp.hAPP_com_com (tptp.hAPP_com_fun_com_com tptp.semi Com1) Com2) (tptp.hAPP_pname_com tptp.body_1 Pname)))) (forall ((C1 tptp.com) (C0 tptp.com)) (=> (tptp.hBOOL (tptp.hAPP_com_bool tptp.wt C0)) (=> (tptp.hBOOL (tptp.hAPP_com_bool tptp.wt C1)) (tptp.hBOOL (tptp.hAPP_com_bool tptp.wt (tptp.hAPP_com_com (tptp.hAPP_com_fun_com_com tptp.semi C0) C1)))))) (forall ((Pname tptp.pname)) (not (= tptp.skip (tptp.hAPP_pname_com tptp.body_1 Pname)))) (forall ((Pname tptp.pname)) (not (= (tptp.hAPP_pname_com tptp.body_1 Pname) tptp.skip))) (tptp.hBOOL (tptp.hAPP_com_bool tptp.wt tptp.skip)) (forall ((X_1 tptp.com) (A tptp.fun_com_bool) (F tptp.fun_com_fun_com_com) (Fa tptp.fun_fun_com_bool_com)) (let ((_let_1 (tptp.hAPP_f1276420679ol_com Fa A))) (=> (tptp.hBOOL (tptp.finite666746948em_com F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool tptp.finite_finite_com A)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_1) A)) (= (tptp.hAPP_com_com (tptp.hAPP_com_fun_com_com F X_1) _let_1) _let_1)))))) (forall ((X_1 tptp.pname) (A tptp.fun_pname_bool) (F tptp.fun_pn1208287926_pname) (Fa tptp.fun_fu1499449723_pname)) (let ((_let_1 (tptp.hAPP_f1297739591_pname Fa A))) (=> (tptp.hBOOL (tptp.finite89670078_pname F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A)) (= (tptp.hAPP_pname_pname (tptp.hAPP_p1170154830_pname F X_1) _let_1) _let_1)))))) (forall ((X_1 tptp.hoare_363350478_state) (A tptp.fun_Ho320143120e_bool) (F tptp.fun_Ho31865764_state) (Fa tptp.fun_fu700438391_state)) (let ((_let_1 (tptp.hAPP_f1242401993_state Fa A))) (=> (tptp.hBOOL (tptp.finite2031572_state F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state A)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state X_1) A)) (= (tptp.hAPP_H1982017439_state (tptp.hAPP_H230141040_state F X_1) _let_1) _let_1)))))) (forall ((X_1 tptp.fun_pname_bool) (A tptp.fun_fu1430349052l_bool) (F tptp.fun_fu2101097872e_bool) (Fa tptp.fun_fu608906319e_bool)) (let ((_let_1 (tptp.hAPP_f674760225e_bool Fa A))) (=> (tptp.hBOOL (tptp.finite1268145088e_bool F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool X_1) A)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool F X_1) _let_1) _let_1)))))) (forall ((X_1 tptp.fun_Ho320143120e_bool) (A tptp.fun_fu1996308102l_bool) (F tptp.fun_fu531943146e_bool) (Fa tptp.fun_fu1671561851e_bool)) (let ((_let_1 (tptp.hAPP_f1180969799e_bool Fa A))) (=> (tptp.hBOOL (tptp.finite2090946954e_bool F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool (tptp.hAPP_f1610329741l_bool tptp.member1534059107e_bool X_1) A)) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool F X_1) _let_1) _let_1)))))) (forall ((N tptp.fun_fu1430349052l_bool) (H_1 tptp.fun_fu410713561e_bool) (F tptp.fun_fu2101097872e_bool) (Fa tptp.fun_fu608906319e_bool)) (=> (tptp.hBOOL (tptp.finite1268145088e_bool F Fa)) (=> (forall ((X_2 tptp.fun_pname_bool) (Y_3 tptp.fun_pname_bool)) (= (tptp.hAPP_f759274231e_bool H_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool F X_2) Y_3)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool F (tptp.hAPP_f759274231e_bool H_1 X_2)) (tptp.hAPP_f759274231e_bool H_1 Y_3)))) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool N)) (=> (not (= N tptp.bot_bo1649642514l_bool)) (= (tptp.hAPP_f759274231e_bool H_1 (tptp.hAPP_f674760225e_bool Fa N)) (tptp.hAPP_f674760225e_bool Fa (tptp.hAPP_f559147733l_bool (tptp.image_2063528359e_bool H_1) N)))))))) (forall ((N tptp.fun_fu1996308102l_bool) (H_1 tptp.fun_fu1066574909e_bool) (F tptp.fun_fu531943146e_bool) (Fa tptp.fun_fu1671561851e_bool)) (=> (tptp.hBOOL (tptp.finite2090946954e_bool F Fa)) (=> (forall ((X_2 tptp.fun_Ho320143120e_bool) (Y_3 tptp.fun_Ho320143120e_bool)) (= (tptp.hAPP_f1749453397e_bool H_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool F X_2) Y_3)) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool F (tptp.hAPP_f1749453397e_bool H_1 X_2)) (tptp.hAPP_f1749453397e_bool H_1 Y_3)))) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool N)) (=> (not (= N tptp.bot_bo133096688l_bool)) (= (tptp.hAPP_f1749453397e_bool H_1 (tptp.hAPP_f1180969799e_bool Fa N)) (tptp.hAPP_f1180969799e_bool Fa (tptp.hAPP_f85652879l_bool (tptp.image_1332939013e_bool H_1) N)))))))) (forall ((N tptp.fun_pname_bool) (H_1 tptp.fun_pname_pname) (F tptp.fun_pn1208287926_pname) (Fa tptp.fun_fu1499449723_pname)) (=> (tptp.hBOOL (tptp.finite89670078_pname F Fa)) (=> (forall ((X_2 tptp.pname) (Y_3 tptp.pname)) (= (tptp.hAPP_pname_pname H_1 (tptp.hAPP_pname_pname (tptp.hAPP_p1170154830_pname F X_2) Y_3)) (tptp.hAPP_pname_pname (tptp.hAPP_p1170154830_pname F (tptp.hAPP_pname_pname H_1 X_2)) (tptp.hAPP_pname_pname H_1 Y_3)))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname N)) (=> (not (= N tptp.bot_bo844097828e_bool)) (= (tptp.hAPP_pname_pname H_1 (tptp.hAPP_f1297739591_pname Fa N)) (tptp.hAPP_f1297739591_pname Fa (tptp.hAPP_f759274231e_bool (tptp.image_pname_pname H_1) N)))))))) (forall ((N tptp.fun_Ho320143120e_bool) (H_1 tptp.fun_Ho901937921_state) (F tptp.fun_Ho31865764_state) (Fa tptp.fun_fu700438391_state)) (=> (tptp.hBOOL (tptp.finite2031572_state F Fa)) (=> (forall ((X_2 tptp.hoare_363350478_state) (Y_3 tptp.hoare_363350478_state)) (= (tptp.hAPP_H1982017439_state H_1 (tptp.hAPP_H1982017439_state (tptp.hAPP_H230141040_state F X_2) Y_3)) (tptp.hAPP_H1982017439_state (tptp.hAPP_H230141040_state F (tptp.hAPP_H1982017439_state H_1 X_2)) (tptp.hAPP_H1982017439_state H_1 Y_3)))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state N)) (=> (not (= N tptp.bot_bo39439654e_bool)) (= (tptp.hAPP_H1982017439_state H_1 (tptp.hAPP_f1242401993_state Fa N)) (tptp.hAPP_f1242401993_state Fa (tptp.hAPP_f1749453397e_bool (tptp.image_2068641359_state H_1) N)))))))) (forall ((N tptp.fun_com_bool) (H_1 tptp.fun_com_com) (F tptp.fun_com_fun_com_com) (Fa tptp.fun_fun_com_bool_com)) (=> (tptp.hBOOL (tptp.finite666746948em_com F Fa)) (=> (forall ((X_2 tptp.com) (Y_3 tptp.com)) (= (tptp.hAPP_com_com H_1 (tptp.hAPP_com_com (tptp.hAPP_com_fun_com_com F X_2) Y_3)) (tptp.hAPP_com_com (tptp.hAPP_com_fun_com_com F (tptp.hAPP_com_com H_1 X_2)) (tptp.hAPP_com_com H_1 Y_3)))) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool tptp.finite_finite_com N)) (=> (not (= N tptp.bot_bot_fun_com_bool)) (= (tptp.hAPP_com_com H_1 (tptp.hAPP_f1276420679ol_com Fa N)) (tptp.hAPP_f1276420679ol_com Fa (tptp.hAPP_f1682609283m_bool (tptp.image_com_com H_1) N)))))))) (forall ((X_4 tptp.fun_com_bool)) (= (tptp.hAPP_f1276420679ol_com tptp.the_elem_com X_4) (tptp.hAPP_f1276420679ol_com tptp.the_com_1 (tptp.hAPP_f1998868198m_bool (tptp.cOMBB_298914627ol_com (tptp.hAPP_f273696895l_bool tptp.fequal_fun_com_bool X_4)) (tptp.hAPP_f721468006m_bool (tptp.hAPP_f947797701m_bool tptp.cOMBC_1977231931m_bool tptp.insert_com) tptp.bot_bot_fun_com_bool))))) (forall ((X_4 tptp.fun_pname_bool)) (= (tptp.hAPP_f1297739591_pname tptp.the_elem_pname X_4) (tptp.hAPP_f1297739591_pname tptp.the_pname (tptp.hAPP_f42430548e_bool (tptp.cOMBB_530759491_pname (tptp.hAPP_f434788991l_bool tptp.fequal533582459e_bool X_4)) (tptp.hAPP_f180827860e_bool (tptp.hAPP_f698292281e_bool tptp.cOMBC_1123258281e_bool tptp.insert_pname) tptp.bot_bo844097828e_bool))))) (forall ((X_4 tptp.fun_Ho320143120e_bool)) (= (tptp.hAPP_f1242401993_state tptp.the_el1666657391_state X_4) (tptp.hAPP_f1242401993_state tptp.the_Ho1653144541_state (tptp.hAPP_f265222234e_bool (tptp.cOMBB_1356223341_state (tptp.hAPP_f726209793l_bool tptp.fequal731041167e_bool X_4)) (tptp.hAPP_f596150574e_bool (tptp.hAPP_f961492031e_bool tptp.cOMBC_1774708299e_bool tptp.insert1330351828_state) tptp.bot_bo39439654e_bool))))) (forall ((X_1 tptp.com) (A tptp.fun_com_bool) (F tptp.fun_com_fun_com_com) (Fa tptp.fun_fun_com_bool_com)) (=> (tptp.hBOOL (tptp.finite860057415ne_com F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool tptp.finite_finite_com A)) (=> (not (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_1) A))) (=> (not (= A tptp.bot_bot_fun_com_bool)) (= (tptp.hAPP_f1276420679ol_com Fa (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com X_1) A)) (tptp.hAPP_com_com (tptp.hAPP_com_fun_com_com F X_1) (tptp.hAPP_f1276420679ol_com Fa A)))))))) (forall ((X_1 tptp.pname) (A tptp.fun_pname_bool) (F tptp.fun_pn1208287926_pname) (Fa tptp.fun_fu1499449723_pname)) (=> (tptp.hBOOL (tptp.finite1282449217_pname F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A))) (=> (not (= A tptp.bot_bo844097828e_bool)) (= (tptp.hAPP_f1297739591_pname Fa (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1) A)) (tptp.hAPP_pname_pname (tptp.hAPP_p1170154830_pname F X_1) (tptp.hAPP_f1297739591_pname Fa A)))))))) (forall ((X_1 tptp.hoare_363350478_state) (A tptp.fun_Ho320143120e_bool) (F tptp.fun_Ho31865764_state) (Fa tptp.fun_fu700438391_state)) (=> (tptp.hBOOL (tptp.finite269920017_state F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state A)) (=> (not (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state X_1) A))) (=> (not (= A tptp.bot_bo39439654e_bool)) (= (tptp.hAPP_f1242401993_state Fa (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state X_1) A)) (tptp.hAPP_H1982017439_state (tptp.hAPP_H230141040_state F X_1) (tptp.hAPP_f1242401993_state Fa A)))))))) (forall ((X_1 tptp.fun_pname_bool) (A tptp.fun_fu1430349052l_bool) (F tptp.fun_fu2101097872e_bool) (Fa tptp.fun_fu608906319e_bool)) (=> (tptp.hBOOL (tptp.finite1626890877e_bool F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)) (=> (not (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool X_1) A))) (=> (not (= A tptp.bot_bo1649642514l_bool)) (= (tptp.hAPP_f674760225e_bool Fa (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool X_1) A)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool F X_1) (tptp.hAPP_f674760225e_bool Fa A)))))))) (forall ((X_1 tptp.fun_Ho320143120e_bool) (A tptp.fun_fu1996308102l_bool) (F tptp.fun_fu531943146e_bool) (Fa tptp.fun_fu1671561851e_bool)) (=> (tptp.hBOOL (tptp.finite1264277005e_bool F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool A)) (=> (not (tptp.hBOOL (tptp.hAPP_f1287348838l_bool (tptp.hAPP_f1610329741l_bool tptp.member1534059107e_bool X_1) A))) (=> (not (= A tptp.bot_bo133096688l_bool)) (= (tptp.hAPP_f1180969799e_bool Fa (tptp.hAPP_f85652879l_bool (tptp.hAPP_f1941218614l_bool tptp.insert975831690e_bool X_1) A)) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool F X_1) (tptp.hAPP_f1180969799e_bool Fa A)))))))) (forall ((Y_2 tptp.hoare_363350478_state)) (not (forall ((Fun1 tptp.fun_st1506752259e_bool) (Com tptp.com) (Fun2 tptp.fun_st1506752259e_bool)) (not (= Y_2 (tptp.hAPP_f83715540_state (tptp.hAPP_c1279058753_state (tptp.hAPP_f960042659_state tptp.hoare_608330478_state Fun1) Com) Fun2)))))) (forall ((X_1 tptp.com) (F tptp.fun_com_fun_com_com) (Fa tptp.fun_fun_com_bool_com)) (=> (tptp.hBOOL (tptp.finite860057415ne_com F Fa)) (= (tptp.hAPP_f1276420679ol_com Fa (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com X_1) tptp.bot_bot_fun_com_bool)) X_1))) (forall ((X_1 tptp.pname) (F tptp.fun_pn1208287926_pname) (Fa tptp.fun_fu1499449723_pname)) (=> (tptp.hBOOL (tptp.finite1282449217_pname F Fa)) (= (tptp.hAPP_f1297739591_pname Fa (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1) tptp.bot_bo844097828e_bool)) X_1))) (forall ((X_1 tptp.hoare_363350478_state) (F tptp.fun_Ho31865764_state) (Fa tptp.fun_fu700438391_state)) (=> (tptp.hBOOL (tptp.finite269920017_state F Fa)) (= (tptp.hAPP_f1242401993_state Fa (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state X_1) tptp.bot_bo39439654e_bool)) X_1))) (forall ((A tptp.fun_com_bool) (F tptp.fun_com_fun_com_com) (Fa tptp.fun_fun_com_bool_com)) (=> (tptp.hBOOL (tptp.finite860057415ne_com F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool tptp.finite_finite_com A)) (=> (not (= A tptp.bot_bot_fun_com_bool)) (=> (forall ((X_2 tptp.com) (Y_3 tptp.com)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com (tptp.hAPP_com_com (tptp.hAPP_com_fun_com_com F X_2) Y_3)) (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com X_2) (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com Y_3) tptp.bot_bot_fun_com_bool))))) (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com (tptp.hAPP_f1276420679ol_com Fa A)) A))))))) (forall ((A tptp.fun_pname_bool) (F tptp.fun_pn1208287926_pname) (Fa tptp.fun_fu1499449723_pname)) (=> (tptp.hBOOL (tptp.finite1282449217_pname F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (=> (not (= A tptp.bot_bo844097828e_bool)) (=> (forall ((X_2 tptp.pname) (Y_3 tptp.pname)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname (tptp.hAPP_pname_pname (tptp.hAPP_p1170154830_pname F X_2) Y_3)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname X_2) (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname Y_3) tptp.bot_bo844097828e_bool))))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname (tptp.hAPP_f1297739591_pname Fa A)) A))))))) (forall ((A tptp.fun_Ho320143120e_bool) (F tptp.fun_Ho31865764_state) (Fa tptp.fun_fu700438391_state)) (=> (tptp.hBOOL (tptp.finite269920017_state F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state A)) (=> (not (= A tptp.bot_bo39439654e_bool)) (=> (forall ((X_2 tptp.hoare_363350478_state) (Y_3 tptp.hoare_363350478_state)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state (tptp.hAPP_H1982017439_state (tptp.hAPP_H230141040_state F X_2) Y_3)) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state X_2) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state Y_3) tptp.bot_bo39439654e_bool))))) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state (tptp.hAPP_f1242401993_state Fa A)) A))))))) (forall ((A tptp.fun_fu1430349052l_bool) (F tptp.fun_fu2101097872e_bool) (Fa tptp.fun_fu608906319e_bool)) (=> (tptp.hBOOL (tptp.finite1626890877e_bool F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)) (=> (not (= A tptp.bot_bo1649642514l_bool)) (=> (forall ((X_2 tptp.fun_pname_bool) (Y_3 tptp.fun_pname_bool)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool F X_2) Y_3)) (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool X_2) (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool Y_3) tptp.bot_bo1649642514l_bool))))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool (tptp.hAPP_f674760225e_bool Fa A)) A))))))) (forall ((A tptp.fun_fu1996308102l_bool) (F tptp.fun_fu531943146e_bool) (Fa tptp.fun_fu1671561851e_bool)) (=> (tptp.hBOOL (tptp.finite1264277005e_bool F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool A)) (=> (not (= A tptp.bot_bo133096688l_bool)) (=> (forall ((X_2 tptp.fun_Ho320143120e_bool) (Y_3 tptp.fun_Ho320143120e_bool)) (tptp.hBOOL (tptp.hAPP_f1287348838l_bool (tptp.hAPP_f1610329741l_bool tptp.member1534059107e_bool (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool F X_2) Y_3)) (tptp.hAPP_f85652879l_bool (tptp.hAPP_f1941218614l_bool tptp.insert975831690e_bool X_2) (tptp.hAPP_f85652879l_bool (tptp.hAPP_f1941218614l_bool tptp.insert975831690e_bool Y_3) tptp.bot_bo133096688l_bool))))) (tptp.hBOOL (tptp.hAPP_f1287348838l_bool (tptp.hAPP_f1610329741l_bool tptp.member1534059107e_bool (tptp.hAPP_f1180969799e_bool Fa A)) A))))))) (forall ((F tptp.fun_pn1262351275_state) (G tptp.fun_pn1262351275_state) (M_1 tptp.fun_pname_bool) (N tptp.fun_pname_bool)) (=> (= M_1 N) (=> (forall ((X_2 tptp.pname)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) N)) (= (tptp.hAPP_p1337579261_state F X_2) (tptp.hAPP_p1337579261_state G X_2)))) (= (tptp.hAPP_f1763243027e_bool (tptp.image_1918575693_state F) M_1) (tptp.hAPP_f1763243027e_bool (tptp.image_1918575693_state G) N))))) (forall ((Q_1 tptp.fun_Ho320143120e_bool) (P_1 tptp.fun_Ho320143120e_bool)) (=> (forall ((X_2 tptp.hoare_363350478_state)) (=> (tptp.hBOOL (tptp.hAPP_H1645464494e_bool P_1 X_2)) (tptp.hBOOL (tptp.hAPP_H1645464494e_bool Q_1 X_2)))) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool (tptp.hAPP_f1749453397e_bool tptp.collec223185785_state P_1)) (tptp.hAPP_f1749453397e_bool tptp.collec223185785_state Q_1))))) (forall ((Q_1 tptp.fun_pname_bool) (P_1 tptp.fun_pname_bool)) (=> (forall ((X_2 tptp.pname)) (=> (tptp.hBOOL (tptp.hAPP_pname_bool P_1 X_2)) (tptp.hBOOL (tptp.hAPP_pname_bool Q_1 X_2)))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool tptp.collect_pname P_1)) (tptp.hAPP_f759274231e_bool tptp.collect_pname Q_1))))) (forall ((Q_1 tptp.fun_fu1430349052l_bool) (P_1 tptp.fun_fu1430349052l_bool)) (=> (forall ((X_2 tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 X_2)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool Q_1 X_2)))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool P_1)) (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool Q_1))))) (forall ((Q_1 tptp.fun_fu1996308102l_bool) (P_1 tptp.fun_fu1996308102l_bool)) (=> (forall ((X_2 tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool P_1 X_2)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool Q_1 X_2)))) (tptp.hBOOL (tptp.hAPP_f1287348838l_bool (tptp.hAPP_f746351743l_bool tptp.ord_le2031828156l_bool (tptp.hAPP_f85652879l_bool tptp.collec1243131813e_bool P_1)) (tptp.hAPP_f85652879l_bool tptp.collec1243131813e_bool Q_1))))) (forall ((Q_1 tptp.fun_pname_bool) (P_1 tptp.fun_pname_bool)) (=> (forall ((X_2 tptp.pname)) (=> (tptp.hBOOL (tptp.hAPP_pname_bool P_1 X_2)) (tptp.hBOOL (tptp.hAPP_pname_bool Q_1 X_2)))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool P_1) Q_1)))) (forall ((Q_1 tptp.fun_Ho320143120e_bool) (P_1 tptp.fun_Ho320143120e_bool)) (=> (forall ((X_2 tptp.hoare_363350478_state)) (=> (tptp.hBOOL (tptp.hAPP_H1645464494e_bool P_1 X_2)) (tptp.hBOOL (tptp.hAPP_H1645464494e_bool Q_1 X_2)))) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool P_1) Q_1)))) (forall ((A_4 tptp.com) (A tptp.fun_com_bool)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com A_4) A)) (exists ((B_2 tptp.fun_com_bool)) (and (= A (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com A_4) B_2)) (not (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com A_4) B_2))))))) (forall ((A_4 tptp.pname) (A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A_4) A)) (exists ((B_2 tptp.fun_pname_bool)) (and (= A (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A_4) B_2)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A_4) B_2))))))) (forall ((A_4 tptp.hoare_363350478_state) (A tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state A_4) A)) (exists ((B_2 tptp.fun_Ho320143120e_bool)) (and (= A (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state A_4) B_2)) (not (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state A_4) B_2))))))) (forall ((X_1 tptp.com) (A tptp.fun_com_bool)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_1) A)) (not (forall ((B_2 tptp.fun_com_bool)) (=> (= A (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com X_1) B_2)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_1) B_2))))))) (forall ((X_1 tptp.pname) (A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A)) (not (forall ((B_2 tptp.fun_pname_bool)) (=> (= A (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1) B_2)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) B_2))))))) (forall ((X_1 tptp.hoare_363350478_state) (A tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state X_1) A)) (not (forall ((B_2 tptp.fun_Ho320143120e_bool)) (=> (= A (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state X_1) B_2)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state X_1) B_2))))))) (forall ((A tptp.fun_com_bool)) (=> (forall ((Y_3 tptp.com)) (not (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com Y_3) A)))) (= A tptp.bot_bot_fun_com_bool))) (forall ((A tptp.fun_pname_bool)) (=> (forall ((Y_3 tptp.pname)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname Y_3) A)))) (= A tptp.bot_bo844097828e_bool))) (forall ((A tptp.fun_Ho320143120e_bool)) (=> (forall ((Y_3 tptp.hoare_363350478_state)) (not (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state Y_3) A)))) (= A tptp.bot_bo39439654e_bool))) (forall ((G_2 tptp.fun_Ho320143120e_bool) (C tptp.com)) (let ((_let_1 (tptp.hoare_95103338_state G_2))) (=> (tptp.hBOOL tptp.hoare_265376576gleton) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state (tptp.hAPP_f83715540_state (tptp.hAPP_c1279058753_state (tptp.hAPP_f960042659_state tptp.hoare_608330478_state (tptp.hAPP_f1935169308e_bool (tptp.cOMBB_1036740637_state (tptp.cOMBB_1911358915_state tptp.fAll_state)) (tptp.hAPP_f249262236e_bool (tptp.cOMBB_1476898461_state (tptp.hAPP_f915354021e_bool tptp.cOMBC_952831051e_bool (tptp.hAPP_f1138284024e_bool (tptp.cOMBB_20296667_state tptp.cOMBS_1378840469l_bool) (tptp.hAPP_f1283379615l_bool (tptp.cOMBB_1759179140_state (tptp.cOMBB_188601460_state tptp.fimplies)) (tptp.evalc C))))) tptp.fequal_state))) C) tptp.fequal_state)) tptp.bot_bo39439654e_bool))) (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state (tptp.hAPP_c1041435779_state tptp.hoare_Mirabelle_MGT C)) tptp.bot_bo39439654e_bool))))))) (forall ((C tptp.bool) (F tptp.fun_bool_bool) (B_1 tptp.bool) (A_4 tptp.bool)) (=> (= (tptp.hBOOL A_4) (tptp.hBOOL (tptp.hAPP_bool_bool F B_1))) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool C) B_1)) (=> (forall ((X_2 tptp.bool) (Y_3 tptp.bool)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Y_3) X_2)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_bool_bool F Y_3)) (tptp.hAPP_bool_bool F X_2))))) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_bool_bool F C)) A_4)))))) (forall ((C tptp.fun_pname_bool) (A_4 tptp.fun_pname_bool) (F tptp.fun_fu410713561e_bool) (B_1 tptp.fun_pname_bool)) (=> (= A_4 (tptp.hAPP_f759274231e_bool F B_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool C) B_1)) (=> (forall ((X_2 tptp.fun_pname_bool) (Y_3 tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool Y_3) X_2)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool F Y_3)) (tptp.hAPP_f759274231e_bool F X_2))))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool F C)) A_4)))))) (forall ((C tptp.fun_Ho320143120e_bool) (A_4 tptp.fun_Ho320143120e_bool) (F tptp.fun_fu1066574909e_bool) (B_1 tptp.fun_Ho320143120e_bool)) (=> (= A_4 (tptp.hAPP_f1749453397e_bool F B_1)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool C) B_1)) (=> (forall ((X_2 tptp.fun_Ho320143120e_bool) (Y_3 tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool Y_3) X_2)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool (tptp.hAPP_f1749453397e_bool F Y_3)) (tptp.hAPP_f1749453397e_bool F X_2))))) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool (tptp.hAPP_f1749453397e_bool F C)) A_4)))))) (forall ((G_2 tptp.fun_Ho320143120e_bool) (C tptp.com)) (let ((_let_1 (tptp.hoare_95103338_state G_2))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state (tptp.hAPP_c1041435779_state tptp.hoare_Mirabelle_MGT C)) tptp.bot_bo39439654e_bool))) (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state (tptp.hAPP_f83715540_state (tptp.hAPP_c1279058753_state (tptp.hAPP_f960042659_state tptp.hoare_608330478_state (tptp.hAPP_f1935169308e_bool (tptp.cOMBB_1036740637_state (tptp.cOMBB_1911358915_state tptp.fAll_state)) (tptp.hAPP_f249262236e_bool (tptp.cOMBB_1476898461_state (tptp.hAPP_f915354021e_bool tptp.cOMBC_952831051e_bool (tptp.hAPP_f1138284024e_bool (tptp.cOMBB_20296667_state tptp.cOMBS_1378840469l_bool) (tptp.hAPP_f1283379615l_bool (tptp.cOMBB_1759179140_state (tptp.cOMBB_188601460_state tptp.fimplies)) (tptp.evalc C))))) tptp.fequal_state))) C) tptp.fequal_state)) tptp.bot_bo39439654e_bool)))))) (forall ((C tptp.com)) (= (tptp.hAPP_c1041435779_state tptp.hoare_Mirabelle_MGT C) (tptp.hAPP_f83715540_state (tptp.hAPP_c1279058753_state (tptp.hAPP_f960042659_state tptp.hoare_608330478_state tptp.fequal_state) C) (tptp.evalc C)))) (forall ((P tptp.pname) (S_4 tptp.state) (S1_2 tptp.state)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool (tptp.evalc (tptp.hAPP_pname_com tptp.body_1 P)) S_4) S1_2)) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool (tptp.evalc (tptp.hAPP_option_com_com tptp.the_com (tptp.hAPP_p799580910on_com tptp.body P))) S_4) S1_2)))) (forall ((Pn tptp.pname) (S0_1 tptp.state) (S1_2 tptp.state)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool (tptp.evalc (tptp.hAPP_option_com_com tptp.the_com (tptp.hAPP_p799580910on_com tptp.body Pn))) S0_1) S1_2)) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool (tptp.evalc (tptp.hAPP_pname_com tptp.body_1 Pn)) S0_1) S1_2)))) (forall ((S_4 tptp.state) (T_1 tptp.state)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool (tptp.evalc tptp.skip) S_4) T_1)) (= T_1 S_4))) (forall ((S_4 tptp.state)) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool (tptp.evalc tptp.skip) S_4) S_4))) (forall ((C1 tptp.com) (S2_1 tptp.state) (C0 tptp.com) (S0_1 tptp.state) (S1_2 tptp.state)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool (tptp.evalc C0) S0_1) S1_2)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool (tptp.evalc C1) S1_2) S2_1)) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool (tptp.evalc (tptp.hAPP_com_com (tptp.hAPP_com_fun_com_com tptp.semi C0) C1)) S0_1) S2_1))))) (forall ((S2 tptp.state) (C tptp.com) (S1_1 tptp.state) (B_1 tptp.fun_state_bool) (S0 tptp.state)) (let ((_let_1 (tptp.evalc (tptp.hAPP_com_com (tptp.while B_1) C)))) (=> (tptp.hBOOL (tptp.hAPP_state_bool B_1 S0)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool (tptp.evalc C) S0) S1_1)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool _let_1 S1_1) S2)) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool _let_1 S0) S2))))))) (forall ((C tptp.com) (B_1 tptp.fun_state_bool) (S_3 tptp.state)) (=> (not (tptp.hBOOL (tptp.hAPP_state_bool B_1 S_3))) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool (tptp.evalc (tptp.hAPP_com_com (tptp.while B_1) C)) S_3) S_3)))) (forall ((U tptp.state) (C_2 tptp.com) (S_4 tptp.state) (T_1 tptp.state)) (let ((_let_1 (tptp.hAPP_s1806633685e_bool (tptp.evalc C_2) S_4))) (=> (tptp.hBOOL (tptp.hAPP_state_bool _let_1 T_1)) (=> (tptp.hBOOL (tptp.hAPP_state_bool _let_1 U)) (= U T_1))))) (forall ((C1 tptp.com) (C2 tptp.com) (S_4 tptp.state) (T_1 tptp.state)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool (tptp.evalc (tptp.hAPP_com_com (tptp.hAPP_com_fun_com_com tptp.semi C1) C2)) S_4) T_1)) (not (forall ((S1 tptp.state)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool (tptp.evalc C1) S_4) S1)) (not (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool (tptp.evalc C2) S1) T_1)))))))) (forall ((B_1 tptp.fun_state_bool) (C tptp.com) (S_3 tptp.state) (T tptp.state)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_state_bool B_1 S_3)))) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool (tptp.evalc (tptp.hAPP_com_com (tptp.while B_1) C)) S_3) T)) (=> (=> (= T S_3) _let_1) (not (=> _let_1 (forall ((S1 tptp.state)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool (tptp.evalc C) S_3) S1)) (not (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool (tptp.evalc (tptp.hAPP_com_com (tptp.while B_1) C)) S1) T))))))))))) (forall ((C tptp.bool) (F tptp.fun_bool_bool) (B_1 tptp.bool) (A_4 tptp.bool)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool B_1) A_4)) (=> (= (tptp.hBOOL (tptp.hAPP_bool_bool F B_1)) (tptp.hBOOL C)) (=> (forall ((X_2 tptp.bool) (Y_3 tptp.bool)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Y_3) X_2)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_bool_bool F Y_3)) (tptp.hAPP_bool_bool F X_2))))) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool C) (tptp.hAPP_bool_bool F A_4))))))) (forall ((F tptp.fun_fu410713561e_bool) (C tptp.fun_pname_bool) (B_1 tptp.fun_pname_bool) (A_4 tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B_1) A_4)) (=> (= (tptp.hAPP_f759274231e_bool F B_1) C) (=> (forall ((X_2 tptp.fun_pname_bool) (Y_3 tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool Y_3) X_2)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool F Y_3)) (tptp.hAPP_f759274231e_bool F X_2))))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool C) (tptp.hAPP_f759274231e_bool F A_4))))))) (forall ((F tptp.fun_fu1066574909e_bool) (C tptp.fun_Ho320143120e_bool) (B_1 tptp.fun_Ho320143120e_bool) (A_4 tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool B_1) A_4)) (=> (= (tptp.hAPP_f1749453397e_bool F B_1) C) (=> (forall ((X_2 tptp.fun_Ho320143120e_bool) (Y_3 tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool Y_3) X_2)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool (tptp.hAPP_f1749453397e_bool F Y_3)) (tptp.hAPP_f1749453397e_bool F X_2))))) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool C) (tptp.hAPP_f1749453397e_bool F A_4))))))) (forall ((B tptp.fun_fu1430349052l_bool) (A tptp.fun_fu1430349052l_bool) (F tptp.fun_fu2101097872e_bool) (Fa tptp.fun_fu608906319e_bool)) (let ((_let_1 (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.semila1130628874l_bool A) B))) (=> (tptp.hBOOL (tptp.finite1626890877e_bool F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool B)) (=> (not (= _let_1 tptp.bot_bo1649642514l_bool)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool F (tptp.hAPP_f674760225e_bool Fa (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.semila1782091504l_bool A) B))) (tptp.hAPP_f674760225e_bool Fa _let_1)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool F (tptp.hAPP_f674760225e_bool Fa A)) (tptp.hAPP_f674760225e_bool Fa B))))))))) (forall ((B tptp.fun_fu1996308102l_bool) (A tptp.fun_fu1996308102l_bool) (F tptp.fun_fu531943146e_bool) (Fa tptp.fun_fu1671561851e_bool)) (let ((_let_1 (tptp.hAPP_f85652879l_bool (tptp.hAPP_f1175211816l_bool tptp.semila218417144l_bool A) B))) (=> (tptp.hBOOL (tptp.finite1264277005e_bool F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool B)) (=> (not (= _let_1 tptp.bot_bo133096688l_bool)) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool F (tptp.hAPP_f1180969799e_bool Fa (tptp.hAPP_f85652879l_bool (tptp.hAPP_f1175211816l_bool tptp.semila862847378l_bool A) B))) (tptp.hAPP_f1180969799e_bool Fa _let_1)) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool F (tptp.hAPP_f1180969799e_bool Fa A)) (tptp.hAPP_f1180969799e_bool Fa B))))))))) (forall ((B tptp.fun_pname_bool) (A tptp.fun_pname_bool) (F tptp.fun_pn1208287926_pname) (Fa tptp.fun_fu1499449723_pname)) (let ((_let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A) B))) (=> (tptp.hBOOL (tptp.finite1282449217_pname F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B)) (=> (not (= _let_1 tptp.bot_bo844097828e_bool)) (= (tptp.hAPP_pname_pname (tptp.hAPP_p1170154830_pname F (tptp.hAPP_f1297739591_pname Fa (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A) B))) (tptp.hAPP_f1297739591_pname Fa _let_1)) (tptp.hAPP_pname_pname (tptp.hAPP_p1170154830_pname F (tptp.hAPP_f1297739591_pname Fa A)) (tptp.hAPP_f1297739591_pname Fa B))))))))) (forall ((B tptp.fun_Ho320143120e_bool) (A tptp.fun_Ho320143120e_bool) (F tptp.fun_Ho31865764_state) (Fa tptp.fun_fu700438391_state)) (let ((_let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool A) B))) (=> (tptp.hBOOL (tptp.finite269920017_state F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state A)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state B)) (=> (not (= _let_1 tptp.bot_bo39439654e_bool)) (= (tptp.hAPP_H1982017439_state (tptp.hAPP_H230141040_state F (tptp.hAPP_f1242401993_state Fa (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool A) B))) (tptp.hAPP_f1242401993_state Fa _let_1)) (tptp.hAPP_H1982017439_state (tptp.hAPP_H230141040_state F (tptp.hAPP_f1242401993_state Fa A)) (tptp.hAPP_f1242401993_state Fa B))))))))) (forall ((B tptp.fun_com_bool) (A tptp.fun_com_bool) (F tptp.fun_com_fun_com_com) (Fa tptp.fun_fun_com_bool_com)) (let ((_let_1 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila980496562m_bool A) B))) (=> (tptp.hBOOL (tptp.finite860057415ne_com F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool tptp.finite_finite_com A)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool tptp.finite_finite_com B)) (=> (not (= _let_1 tptp.bot_bot_fun_com_bool)) (= (tptp.hAPP_com_com (tptp.hAPP_com_fun_com_com F (tptp.hAPP_f1276420679ol_com Fa (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila605046092m_bool A) B))) (tptp.hAPP_f1276420679ol_com Fa _let_1)) (tptp.hAPP_com_com (tptp.hAPP_com_fun_com_com F (tptp.hAPP_f1276420679ol_com Fa A)) (tptp.hAPP_f1276420679ol_com Fa B))))))))) (forall ((B tptp.fun_fu1430349052l_bool) (A tptp.fun_fu1430349052l_bool) (F tptp.fun_fu2101097872e_bool) (Fa tptp.fun_fu608906319e_bool)) (=> (tptp.hBOOL (tptp.finite1626890877e_bool F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)) (=> (not (= A tptp.bot_bo1649642514l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool B)) (=> (not (= B tptp.bot_bo1649642514l_bool)) (=> (= (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.semila1130628874l_bool A) B) tptp.bot_bo1649642514l_bool) (= (tptp.hAPP_f674760225e_bool Fa (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.semila1782091504l_bool A) B)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool F (tptp.hAPP_f674760225e_bool Fa A)) (tptp.hAPP_f674760225e_bool Fa B)))))))))) (forall ((B tptp.fun_fu1996308102l_bool) (A tptp.fun_fu1996308102l_bool) (F tptp.fun_fu531943146e_bool) (Fa tptp.fun_fu1671561851e_bool)) (=> (tptp.hBOOL (tptp.finite1264277005e_bool F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool A)) (=> (not (= A tptp.bot_bo133096688l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool B)) (=> (not (= B tptp.bot_bo133096688l_bool)) (=> (= (tptp.hAPP_f85652879l_bool (tptp.hAPP_f1175211816l_bool tptp.semila218417144l_bool A) B) tptp.bot_bo133096688l_bool) (= (tptp.hAPP_f1180969799e_bool Fa (tptp.hAPP_f85652879l_bool (tptp.hAPP_f1175211816l_bool tptp.semila862847378l_bool A) B)) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool F (tptp.hAPP_f1180969799e_bool Fa A)) (tptp.hAPP_f1180969799e_bool Fa B)))))))))) (forall ((B tptp.fun_pname_bool) (A tptp.fun_pname_bool) (F tptp.fun_pn1208287926_pname) (Fa tptp.fun_fu1499449723_pname)) (=> (tptp.hBOOL (tptp.finite1282449217_pname F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (=> (not (= A tptp.bot_bo844097828e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B)) (=> (not (= B tptp.bot_bo844097828e_bool)) (=> (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A) B) tptp.bot_bo844097828e_bool) (= (tptp.hAPP_f1297739591_pname Fa (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A) B)) (tptp.hAPP_pname_pname (tptp.hAPP_p1170154830_pname F (tptp.hAPP_f1297739591_pname Fa A)) (tptp.hAPP_f1297739591_pname Fa B)))))))))) (forall ((B tptp.fun_Ho320143120e_bool) (A tptp.fun_Ho320143120e_bool) (F tptp.fun_Ho31865764_state) (Fa tptp.fun_fu700438391_state)) (=> (tptp.hBOOL (tptp.finite269920017_state F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state A)) (=> (not (= A tptp.bot_bo39439654e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state B)) (=> (not (= B tptp.bot_bo39439654e_bool)) (=> (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool A) B) tptp.bot_bo39439654e_bool) (= (tptp.hAPP_f1242401993_state Fa (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool A) B)) (tptp.hAPP_H1982017439_state (tptp.hAPP_H230141040_state F (tptp.hAPP_f1242401993_state Fa A)) (tptp.hAPP_f1242401993_state Fa B)))))))))) (forall ((B tptp.fun_com_bool) (A tptp.fun_com_bool) (F tptp.fun_com_fun_com_com) (Fa tptp.fun_fun_com_bool_com)) (=> (tptp.hBOOL (tptp.finite860057415ne_com F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool tptp.finite_finite_com A)) (=> (not (= A tptp.bot_bot_fun_com_bool)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool tptp.finite_finite_com B)) (=> (not (= B tptp.bot_bot_fun_com_bool)) (=> (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila980496562m_bool A) B) tptp.bot_bot_fun_com_bool) (= (tptp.hAPP_f1276420679ol_com Fa (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila605046092m_bool A) B)) (tptp.hAPP_com_com (tptp.hAPP_com_fun_com_com F (tptp.hAPP_f1276420679ol_com Fa A)) (tptp.hAPP_f1276420679ol_com Fa B)))))))))) (forall ((X_1 tptp.com) (A tptp.fun_com_bool) (F tptp.fun_com_fun_com_com) (Fa tptp.fun_fun_com_bool_com)) (let ((_let_1 (tptp.hAPP_c566651504m_bool tptp.insert_com X_1))) (let ((_let_2 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.minus_59609839m_bool A) (tptp.hAPP_f1682609283m_bool _let_1 tptp.bot_bot_fun_com_bool)))) (let ((_let_3 (tptp.hAPP_f1276420679ol_com Fa (tptp.hAPP_f1682609283m_bool _let_1 A)))) (let ((_let_4 (= _let_2 tptp.bot_bot_fun_com_bool))) (=> (tptp.hBOOL (tptp.finite860057415ne_com F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool tptp.finite_finite_com A)) (and (=> _let_4 (= _let_3 X_1)) (=> (not _let_4) (= _let_3 (tptp.hAPP_com_com (tptp.hAPP_com_fun_com_com F X_1) (tptp.hAPP_f1276420679ol_com Fa _let_2)))))))))))) (forall ((X_1 tptp.pname) (A tptp.fun_pname_bool) (F tptp.fun_pn1208287926_pname) (Fa tptp.fun_fu1499449723_pname)) (let ((_let_1 (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1))) (let ((_let_2 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A) (tptp.hAPP_f759274231e_bool _let_1 tptp.bot_bo844097828e_bool)))) (let ((_let_3 (tptp.hAPP_f1297739591_pname Fa (tptp.hAPP_f759274231e_bool _let_1 A)))) (let ((_let_4 (= _let_2 tptp.bot_bo844097828e_bool))) (=> (tptp.hBOOL (tptp.finite1282449217_pname F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (and (=> _let_4 (= _let_3 X_1)) (=> (not _let_4) (= _let_3 (tptp.hAPP_pname_pname (tptp.hAPP_p1170154830_pname F X_1) (tptp.hAPP_f1297739591_pname Fa _let_2)))))))))))) (forall ((X_1 tptp.hoare_363350478_state) (A tptp.fun_Ho320143120e_bool) (F tptp.fun_Ho31865764_state) (Fa tptp.fun_fu700438391_state)) (let ((_let_1 (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state X_1))) (let ((_let_2 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.minus_1060678561e_bool A) (tptp.hAPP_f1749453397e_bool _let_1 tptp.bot_bo39439654e_bool)))) (let ((_let_3 (tptp.hAPP_f1242401993_state Fa (tptp.hAPP_f1749453397e_bool _let_1 A)))) (let ((_let_4 (= _let_2 tptp.bot_bo39439654e_bool))) (=> (tptp.hBOOL (tptp.finite269920017_state F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state A)) (and (=> _let_4 (= _let_3 X_1)) (=> (not _let_4) (= _let_3 (tptp.hAPP_H1982017439_state (tptp.hAPP_H230141040_state F X_1) (tptp.hAPP_f1242401993_state Fa _let_2)))))))))))) (forall ((X_1 tptp.fun_pname_bool) (A tptp.fun_fu1430349052l_bool) (F tptp.fun_fu2101097872e_bool) (Fa tptp.fun_fu608906319e_bool)) (let ((_let_1 (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool X_1))) (let ((_let_2 (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.minus_1290075917l_bool A) (tptp.hAPP_f559147733l_bool _let_1 tptp.bot_bo1649642514l_bool)))) (let ((_let_3 (tptp.hAPP_f674760225e_bool Fa (tptp.hAPP_f559147733l_bool _let_1 A)))) (let ((_let_4 (= _let_2 tptp.bot_bo1649642514l_bool))) (=> (tptp.hBOOL (tptp.finite1626890877e_bool F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)) (and (=> _let_4 (= _let_3 X_1)) (=> (not _let_4) (= _let_3 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool F X_1) (tptp.hAPP_f674760225e_bool Fa _let_2)))))))))))) (forall ((X_1 tptp.fun_Ho320143120e_bool) (A tptp.fun_fu1996308102l_bool) (F tptp.fun_fu531943146e_bool) (Fa tptp.fun_fu1671561851e_bool)) (let ((_let_1 (tptp.hAPP_f1941218614l_bool tptp.insert975831690e_bool X_1))) (let ((_let_2 (tptp.hAPP_f85652879l_bool (tptp.hAPP_f1175211816l_bool tptp.minus_1119384757l_bool A) (tptp.hAPP_f85652879l_bool _let_1 tptp.bot_bo133096688l_bool)))) (let ((_let_3 (tptp.hAPP_f1180969799e_bool Fa (tptp.hAPP_f85652879l_bool _let_1 A)))) (let ((_let_4 (= _let_2 tptp.bot_bo133096688l_bool))) (=> (tptp.hBOOL (tptp.finite1264277005e_bool F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool A)) (and (=> _let_4 (= _let_3 X_1)) (=> (not _let_4) (= _let_3 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool F X_1) (tptp.hAPP_f1180969799e_bool Fa _let_2)))))))))))) (forall ((X_1 tptp.com) (A tptp.fun_com_bool) (F tptp.fun_com_fun_com_com) (Fa tptp.fun_fun_com_bool_com)) (let ((_let_1 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.minus_59609839m_bool A) (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com X_1) tptp.bot_bot_fun_com_bool)))) (let ((_let_2 (tptp.hAPP_f1276420679ol_com Fa A))) (let ((_let_3 (= _let_1 tptp.bot_bot_fun_com_bool))) (=> (tptp.hBOOL (tptp.finite860057415ne_com F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool tptp.finite_finite_com A)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_1) A)) (and (=> _let_3 (= _let_2 X_1)) (=> (not _let_3) (= _let_2 (tptp.hAPP_com_com (tptp.hAPP_com_fun_com_com F X_1) (tptp.hAPP_f1276420679ol_com Fa _let_1)))))))))))) (forall ((X_1 tptp.pname) (A tptp.fun_pname_bool) (F tptp.fun_pn1208287926_pname) (Fa tptp.fun_fu1499449723_pname)) (let ((_let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A) (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1) tptp.bot_bo844097828e_bool)))) (let ((_let_2 (tptp.hAPP_f1297739591_pname Fa A))) (let ((_let_3 (= _let_1 tptp.bot_bo844097828e_bool))) (=> (tptp.hBOOL (tptp.finite1282449217_pname F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A)) (and (=> _let_3 (= _let_2 X_1)) (=> (not _let_3) (= _let_2 (tptp.hAPP_pname_pname (tptp.hAPP_p1170154830_pname F X_1) (tptp.hAPP_f1297739591_pname Fa _let_1)))))))))))) (forall ((X_1 tptp.hoare_363350478_state) (A tptp.fun_Ho320143120e_bool) (F tptp.fun_Ho31865764_state) (Fa tptp.fun_fu700438391_state)) (let ((_let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.minus_1060678561e_bool A) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state X_1) tptp.bot_bo39439654e_bool)))) (let ((_let_2 (tptp.hAPP_f1242401993_state Fa A))) (let ((_let_3 (= _let_1 tptp.bot_bo39439654e_bool))) (=> (tptp.hBOOL (tptp.finite269920017_state F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state A)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state X_1) A)) (and (=> _let_3 (= _let_2 X_1)) (=> (not _let_3) (= _let_2 (tptp.hAPP_H1982017439_state (tptp.hAPP_H230141040_state F X_1) (tptp.hAPP_f1242401993_state Fa _let_1)))))))))))) (forall ((X_1 tptp.fun_pname_bool) (A tptp.fun_fu1430349052l_bool) (F tptp.fun_fu2101097872e_bool) (Fa tptp.fun_fu608906319e_bool)) (let ((_let_1 (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.minus_1290075917l_bool A) (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool X_1) tptp.bot_bo1649642514l_bool)))) (let ((_let_2 (tptp.hAPP_f674760225e_bool Fa A))) (let ((_let_3 (= _let_1 tptp.bot_bo1649642514l_bool))) (=> (tptp.hBOOL (tptp.finite1626890877e_bool F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool X_1) A)) (and (=> _let_3 (= _let_2 X_1)) (=> (not _let_3) (= _let_2 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool F X_1) (tptp.hAPP_f674760225e_bool Fa _let_1)))))))))))) (forall ((X_1 tptp.fun_Ho320143120e_bool) (A tptp.fun_fu1996308102l_bool) (F tptp.fun_fu531943146e_bool) (Fa tptp.fun_fu1671561851e_bool)) (let ((_let_1 (tptp.hAPP_f85652879l_bool (tptp.hAPP_f1175211816l_bool tptp.minus_1119384757l_bool A) (tptp.hAPP_f85652879l_bool (tptp.hAPP_f1941218614l_bool tptp.insert975831690e_bool X_1) tptp.bot_bo133096688l_bool)))) (let ((_let_2 (tptp.hAPP_f1180969799e_bool Fa A))) (let ((_let_3 (= _let_1 tptp.bot_bo133096688l_bool))) (=> (tptp.hBOOL (tptp.finite1264277005e_bool F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool (tptp.hAPP_f1610329741l_bool tptp.member1534059107e_bool X_1) A)) (and (=> _let_3 (= _let_2 X_1)) (=> (not _let_3) (= _let_2 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool F X_1) (tptp.hAPP_f1180969799e_bool Fa _let_1)))))))))))) (forall ((X_3 tptp.pname)) (not (tptp.hBOOL (tptp.is_none_pname (tptp.hAPP_p1252095976_pname tptp.some_pname X_3))))) (forall ((X_3 tptp.hoare_363350478_state)) (not (tptp.hBOOL (tptp.is_non965104584_state (tptp.hAPP_H1942146718_state tptp.some_H629028223_state X_3))))) (forall ((X_3 tptp.com)) (not (tptp.hBOOL (tptp.is_none_com (tptp.hAPP_com_option_com tptp.some_com X_3))))) (forall ((Q_1 tptp.fun_st1506752259e_bool) (G_2 tptp.fun_Ho320143120e_bool) (C tptp.com) (P_1 tptp.fun_st1506752259e_bool)) (=> (forall ((Z_2 tptp.state) (S_1 tptp.state)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool P_1 Z_2) S_1)) (exists ((P_2 tptp.fun_st1506752259e_bool) (Q_2 tptp.fun_st1506752259e_bool)) (and (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hoare_95103338_state G_2) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state (tptp.hAPP_f83715540_state (tptp.hAPP_c1279058753_state (tptp.hAPP_f960042659_state tptp.hoare_608330478_state P_2) C) Q_2)) tptp.bot_bo39439654e_bool))) (forall ((S_2 tptp.state)) (=> (forall ((Z_3 tptp.state)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool P_2 Z_3) S_1)) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool Q_2 Z_3) S_2)))) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool Q_1 Z_2) S_2)))))))) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hoare_95103338_state G_2) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state (tptp.hAPP_f83715540_state (tptp.hAPP_c1279058753_state (tptp.hAPP_f960042659_state tptp.hoare_608330478_state P_1) C) Q_1)) tptp.bot_bo39439654e_bool))))) (forall ((C tptp.com) (A tptp.fun_com_bool) (B tptp.fun_com_bool)) (let ((_let_1 (tptp.hAPP_c667411853l_bool tptp.member_com C))) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila980496562m_bool A) B))) (not (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 A)) (not (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 B)))))))) (forall ((C tptp.pname) (A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname C))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A) B))) (not (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B)))))))) (forall ((C tptp.hoare_363350478_state) (A tptp.fun_Ho320143120e_bool) (B tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_H40373975l_bool tptp.member1253905979_state C))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool A) B))) (not (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 A)) (not (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 B)))))))) (forall ((B tptp.fun_com_bool) (C tptp.com) (A tptp.fun_com_bool)) (let ((_let_1 (tptp.hAPP_c667411853l_bool tptp.member_com C))) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 A)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 B)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila980496562m_bool A) B))))))) (forall ((B tptp.fun_pname_bool) (C tptp.pname) (A tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname C))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A) B))))))) (forall ((B tptp.fun_Ho320143120e_bool) (C tptp.hoare_363350478_state) (A tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_H40373975l_bool tptp.member1253905979_state C))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 A)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 B)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool A) B))))))) (forall ((C tptp.com) (A tptp.fun_com_bool) (B tptp.fun_com_bool)) (let ((_let_1 (tptp.hAPP_c667411853l_bool tptp.member_com C))) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.minus_59609839m_bool A) B))) (not (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 B))))))) (forall ((C tptp.pname) (A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname C))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A) B))) (not (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B))))))) (forall ((C tptp.hoare_363350478_state) (A tptp.fun_Ho320143120e_bool) (B tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_H40373975l_bool tptp.member1253905979_state C))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.minus_1060678561e_bool A) B))) (not (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 B))))))) (forall ((B tptp.fun_com_bool) (C tptp.com) (A tptp.fun_com_bool)) (let ((_let_1 (tptp.hAPP_c667411853l_bool tptp.member_com C))) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 A)) (=> (not (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 B))) (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.minus_59609839m_bool A) B))))))) (forall ((B tptp.fun_pname_bool) (C tptp.pname) (A tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname C))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A)) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A) B))))))) (forall ((B tptp.fun_Ho320143120e_bool) (C tptp.hoare_363350478_state) (A tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_H40373975l_bool tptp.member1253905979_state C))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 A)) (=> (not (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 B))) (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.minus_1060678561e_bool A) B))))))) (forall ((G_2 tptp.fun_fu1430349052l_bool) (Fa tptp.fun_fu1430349052l_bool)) (=> (or (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool Fa)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool G_2))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.semila1130628874l_bool Fa) G_2))))) (forall ((G_2 tptp.fun_fu1996308102l_bool) (Fa tptp.fun_fu1996308102l_bool)) (=> (or (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool Fa)) (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool G_2))) (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool (tptp.hAPP_f85652879l_bool (tptp.hAPP_f1175211816l_bool tptp.semila218417144l_bool Fa) G_2))))) (forall ((G_2 tptp.fun_pname_bool) (Fa tptp.fun_pname_bool)) (=> (or (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname Fa)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname G_2))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool Fa) G_2))))) (forall ((G_2 tptp.fun_Ho320143120e_bool) (Fa tptp.fun_Ho320143120e_bool)) (=> (or (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state Fa)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state G_2))) (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool Fa) G_2))))) (forall ((B tptp.fun_fu1430349052l_bool) (A tptp.fun_fu1430349052l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.minus_1290075917l_bool A) B))))) (forall ((B tptp.fun_fu1996308102l_bool) (A tptp.fun_fu1996308102l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool A)) (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool (tptp.hAPP_f85652879l_bool (tptp.hAPP_f1175211816l_bool tptp.minus_1119384757l_bool A) B))))) (forall ((B tptp.fun_pname_bool) (A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A) B))))) (forall ((B tptp.fun_Ho320143120e_bool) (A tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state A)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.minus_1060678561e_bool A) B))))) (forall ((R_1 tptp.fun_com_bool) (S tptp.fun_com_bool) (X_2 tptp.com)) (let ((_let_1 (tptp.hAPP_f578650245m_bool tptp.cOMBC_1904837336l_bool tptp.member_com))) (= (tptp.hBOOL (tptp.hAPP_com_bool (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila980496562m_bool (tptp.hAPP_f1682609283m_bool _let_1 R_1)) (tptp.hAPP_f1682609283m_bool _let_1 S)) X_2)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_2) (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila980496562m_bool R_1) S)))))) (forall ((R_1 tptp.fun_pname_bool) (S tptp.fun_pname_bool) (X_2 tptp.pname)) (let ((_let_1 (tptp.hAPP_f661147897e_bool tptp.cOMBC_1058051404l_bool tptp.member_pname))) (= (tptp.hBOOL (tptp.hAPP_pname_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool (tptp.hAPP_f759274231e_bool _let_1 R_1)) (tptp.hAPP_f759274231e_bool _let_1 S)) X_2)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool R_1) S)))))) (forall ((R_1 tptp.fun_Ho320143120e_bool) (S tptp.fun_Ho320143120e_bool) (X_2 tptp.hoare_363350478_state)) (let ((_let_1 (tptp.hAPP_f1072682137e_bool tptp.cOMBC_1415895650l_bool tptp.member1253905979_state))) (= (tptp.hBOOL (tptp.hAPP_H1645464494e_bool (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool (tptp.hAPP_f1749453397e_bool _let_1 R_1)) (tptp.hAPP_f1749453397e_bool _let_1 S)) X_2)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state X_2) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool R_1) S)))))) (forall ((A tptp.fun_com_bool) (B tptp.fun_com_bool)) (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila980496562m_bool A) (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.minus_59609839m_bool B) A)) tptp.bot_bot_fun_com_bool)) (forall ((A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool B) A)) tptp.bot_bo844097828e_bool)) (forall ((A tptp.fun_Ho320143120e_bool) (B tptp.fun_Ho320143120e_bool)) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool A) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.minus_1060678561e_bool B) A)) tptp.bot_bo39439654e_bool)) (forall ((A tptp.fun_com_bool) (B tptp.fun_com_bool)) (=> (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila980496562m_bool A) B) tptp.bot_bot_fun_com_bool) (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.minus_59609839m_bool A) B) A))) (forall ((A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (=> (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A) B) tptp.bot_bo844097828e_bool) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A) B) A))) (forall ((A tptp.fun_Ho320143120e_bool) (B tptp.fun_Ho320143120e_bool)) (=> (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool A) B) tptp.bot_bo39439654e_bool) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.minus_1060678561e_bool A) B) A))) (forall ((C tptp.com) (A tptp.fun_com_bool) (B tptp.fun_com_bool)) (let ((_let_1 (tptp.hAPP_c667411853l_bool tptp.member_com C))) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.minus_59609839m_bool A) B))) (not (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 B)))))) (forall ((C tptp.pname) (A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname C))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A) B))) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B)))))) (forall ((C tptp.hoare_363350478_state) (A tptp.fun_Ho320143120e_bool) (B tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_H40373975l_bool tptp.member1253905979_state C))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.minus_1060678561e_bool A) B))) (not (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 B)))))) (forall ((C tptp.com) (A tptp.fun_com_bool) (B tptp.fun_com_bool)) (let ((_let_1 (tptp.hAPP_c667411853l_bool tptp.member_com C))) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila980496562m_bool A) B))) (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 B))))) (forall ((C tptp.pname) (A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname C))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A) B))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B))))) (forall ((C tptp.hoare_363350478_state) (A tptp.fun_Ho320143120e_bool) (B tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_H40373975l_bool tptp.member1253905979_state C))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool A) B))) (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 B))))) (forall ((C tptp.com) (A tptp.fun_com_bool) (B tptp.fun_com_bool)) (let ((_let_1 (tptp.hAPP_c667411853l_bool tptp.member_com C))) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila980496562m_bool A) B))) (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 A))))) (forall ((C tptp.pname) (A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname C))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A) B))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A))))) (forall ((C tptp.hoare_363350478_state) (A tptp.fun_Ho320143120e_bool) (B tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_H40373975l_bool tptp.member1253905979_state C))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool A) B))) (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 A))))) (forall ((C tptp.com) (A tptp.fun_com_bool) (B tptp.fun_com_bool)) (let ((_let_1 (tptp.hAPP_c667411853l_bool tptp.member_com C))) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.minus_59609839m_bool A) B))) (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 A))))) (forall ((C tptp.pname) (A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname C))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A) B))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A))))) (forall ((C tptp.hoare_363350478_state) (A tptp.fun_Ho320143120e_bool) (B tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_H40373975l_bool tptp.member1253905979_state C))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.minus_1060678561e_bool A) B))) (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 A))))) (forall ((C tptp.com) (A tptp.fun_com_bool) (B tptp.fun_com_bool)) (let ((_let_1 (tptp.hAPP_c667411853l_bool tptp.member_com C))) (= (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila980496562m_bool A) B))) (and (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 B)))))) (forall ((C tptp.pname) (A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname C))) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A) B))) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B)))))) (forall ((C tptp.hoare_363350478_state) (A tptp.fun_Ho320143120e_bool) (B tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_H40373975l_bool tptp.member1253905979_state C))) (= (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool A) B))) (and (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 B)))))) (forall ((C tptp.com) (A tptp.fun_com_bool) (B tptp.fun_com_bool)) (let ((_let_1 (tptp.hAPP_c667411853l_bool tptp.member_com C))) (= (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.minus_59609839m_bool A) B))) (and (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 A)) (not (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 B))))))) (forall ((C tptp.pname) (A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname C))) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A) B))) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B))))))) (forall ((C tptp.hoare_363350478_state) (A tptp.fun_Ho320143120e_bool) (B tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_H40373975l_bool tptp.member1253905979_state C))) (= (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.minus_1060678561e_bool A) B))) (and (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 A)) (not (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 B))))))) (forall ((A tptp.fun_com_bool) (B tptp.fun_com_bool)) (let ((_let_1 (tptp.hAPP_f578650245m_bool tptp.cOMBC_1904837336l_bool tptp.member_com))) (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila980496562m_bool A) B) (tptp.hAPP_f1682609283m_bool tptp.collect_com (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f328772264m_bool tptp.cOMBS_com_bool_bool (tptp.hAPP_f954469007l_bool (tptp.cOMBB_886968260ol_com tptp.fconj) (tptp.hAPP_f1682609283m_bool _let_1 A))) (tptp.hAPP_f1682609283m_bool _let_1 B)))))) (forall ((A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f661147897e_bool tptp.cOMBC_1058051404l_bool tptp.member_pname))) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A) B) (tptp.hAPP_f759274231e_bool tptp.collect_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_f649174806e_bool tptp.cOMBS_568398431l_bool (tptp.hAPP_f1402196763l_bool (tptp.cOMBB_675860798_pname tptp.fconj) (tptp.hAPP_f759274231e_bool _let_1 A))) (tptp.hAPP_f759274231e_bool _let_1 B)))))) (forall ((A tptp.fun_Ho320143120e_bool) (B tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_f1072682137e_bool tptp.cOMBC_1415895650l_bool tptp.member1253905979_state))) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool A) B) (tptp.hAPP_f1749453397e_bool tptp.collec223185785_state (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1612626488e_bool tptp.cOMBS_56025283l_bool (tptp.hAPP_f1422032445l_bool (tptp.cOMBB_877416532_state tptp.fconj) (tptp.hAPP_f1749453397e_bool _let_1 A))) (tptp.hAPP_f1749453397e_bool _let_1 B)))))) (forall ((A tptp.fun_fu1430349052l_bool) (B tptp.fun_fu1430349052l_bool)) (let ((_let_1 (tptp.hAPP_f1145991873l_bool tptp.cOMBC_1988546018l_bool tptp.member799430823e_bool))) (= (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.semila1130628874l_bool A) B) (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f624840228l_bool tptp.cOMBS_350070575l_bool (tptp.hAPP_f143162813l_bool (tptp.cOMBB_2095475776e_bool tptp.fconj) (tptp.hAPP_f559147733l_bool _let_1 A))) (tptp.hAPP_f559147733l_bool _let_1 B)))))) (forall ((A tptp.fun_fu1996308102l_bool) (B tptp.fun_fu1996308102l_bool)) (let ((_let_1 (tptp.hAPP_f1854331281l_bool tptp.cOMBC_1522409444l_bool tptp.member1534059107e_bool))) (= (tptp.hAPP_f85652879l_bool (tptp.hAPP_f1175211816l_bool tptp.semila218417144l_bool A) B) (tptp.hAPP_f85652879l_bool tptp.collec1243131813e_bool (tptp.hAPP_f85652879l_bool (tptp.hAPP_f927797370l_bool tptp.cOMBS_1039407915l_bool (tptp.hAPP_f945781379l_bool (tptp.cOMBB_1004232970e_bool tptp.fconj) (tptp.hAPP_f85652879l_bool _let_1 A))) (tptp.hAPP_f85652879l_bool _let_1 B)))))) (forall ((A tptp.fun_com_bool) (B tptp.fun_com_bool)) (let ((_let_1 (tptp.hAPP_f578650245m_bool tptp.cOMBC_1904837336l_bool tptp.member_com))) (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.minus_59609839m_bool A) B) (tptp.hAPP_f1682609283m_bool tptp.collect_com (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f328772264m_bool tptp.cOMBS_com_bool_bool (tptp.hAPP_f954469007l_bool (tptp.cOMBB_886968260ol_com tptp.fconj) (tptp.hAPP_f1682609283m_bool _let_1 A))) (tptp.hAPP_f1682609283m_bool (tptp.cOMBB_bool_bool_com tptp.fNot) (tptp.hAPP_f1682609283m_bool _let_1 B))))))) (forall ((A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f661147897e_bool tptp.cOMBC_1058051404l_bool tptp.member_pname))) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A) B) (tptp.hAPP_f759274231e_bool tptp.collect_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_f649174806e_bool tptp.cOMBS_568398431l_bool (tptp.hAPP_f1402196763l_bool (tptp.cOMBB_675860798_pname tptp.fconj) (tptp.hAPP_f759274231e_bool _let_1 A))) (tptp.hAPP_f759274231e_bool (tptp.cOMBB_647938656_pname tptp.fNot) (tptp.hAPP_f759274231e_bool _let_1 B))))))) (forall ((A tptp.fun_Ho320143120e_bool) (B tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_f1072682137e_bool tptp.cOMBC_1415895650l_bool tptp.member1253905979_state))) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.minus_1060678561e_bool A) B) (tptp.hAPP_f1749453397e_bool tptp.collec223185785_state (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1612626488e_bool tptp.cOMBS_56025283l_bool (tptp.hAPP_f1422032445l_bool (tptp.cOMBB_877416532_state tptp.fconj) (tptp.hAPP_f1749453397e_bool _let_1 A))) (tptp.hAPP_f1749453397e_bool (tptp.cOMBB_2059354034_state tptp.fNot) (tptp.hAPP_f1749453397e_bool _let_1 B))))))) (forall ((A tptp.fun_fu1430349052l_bool) (B tptp.fun_fu1430349052l_bool)) (let ((_let_1 (tptp.hAPP_f1145991873l_bool tptp.cOMBC_1988546018l_bool tptp.member799430823e_bool))) (= (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.minus_1290075917l_bool A) B) (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f624840228l_bool tptp.cOMBS_350070575l_bool (tptp.hAPP_f143162813l_bool (tptp.cOMBB_2095475776e_bool tptp.fconj) (tptp.hAPP_f559147733l_bool _let_1 A))) (tptp.hAPP_f559147733l_bool (tptp.cOMBB_307249310e_bool tptp.fNot) (tptp.hAPP_f559147733l_bool _let_1 B))))))) (forall ((A tptp.fun_fu1996308102l_bool) (B tptp.fun_fu1996308102l_bool)) (let ((_let_1 (tptp.hAPP_f1854331281l_bool tptp.cOMBC_1522409444l_bool tptp.member1534059107e_bool))) (= (tptp.hAPP_f85652879l_bool (tptp.hAPP_f1175211816l_bool tptp.minus_1119384757l_bool A) B) (tptp.hAPP_f85652879l_bool tptp.collec1243131813e_bool (tptp.hAPP_f85652879l_bool (tptp.hAPP_f927797370l_bool tptp.cOMBS_1039407915l_bool (tptp.hAPP_f945781379l_bool (tptp.cOMBB_1004232970e_bool tptp.fconj) (tptp.hAPP_f85652879l_bool _let_1 A))) (tptp.hAPP_f85652879l_bool (tptp.cOMBB_941362220e_bool tptp.fNot) (tptp.hAPP_f85652879l_bool _let_1 B))))))) (forall ((X_1 tptp.com) (A tptp.fun_com_bool) (P_1 tptp.fun_com_bool)) (let ((_let_1 (tptp.hAPP_c667411853l_bool tptp.member_com X_1))) (= (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila980496562m_bool A) (tptp.hAPP_f1682609283m_bool tptp.collect_com P_1)))) (and (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_com_bool P_1 X_1)))))) (forall ((X_1 tptp.pname) (A tptp.fun_pname_bool) (P_1 tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname X_1))) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A) (tptp.hAPP_f759274231e_bool tptp.collect_pname P_1)))) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_pname_bool P_1 X_1)))))) (forall ((X_1 tptp.hoare_363350478_state) (A tptp.fun_Ho320143120e_bool) (P_1 tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_H40373975l_bool tptp.member1253905979_state X_1))) (= (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool A) (tptp.hAPP_f1749453397e_bool tptp.collec223185785_state P_1)))) (and (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_H1645464494e_bool P_1 X_1)))))) (forall ((X_1 tptp.fun_pname_bool) (A tptp.fun_fu1430349052l_bool) (P_1 tptp.fun_fu1430349052l_bool)) (let ((_let_1 (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool X_1))) (= (tptp.hBOOL (tptp.hAPP_f1935102916l_bool _let_1 (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.semila1130628874l_bool A) (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool P_1)))) (and (tptp.hBOOL (tptp.hAPP_f1935102916l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 X_1)))))) (forall ((X_1 tptp.fun_Ho320143120e_bool) (A tptp.fun_fu1996308102l_bool) (P_1 tptp.fun_fu1996308102l_bool)) (let ((_let_1 (tptp.hAPP_f1610329741l_bool tptp.member1534059107e_bool X_1))) (= (tptp.hBOOL (tptp.hAPP_f1287348838l_bool _let_1 (tptp.hAPP_f85652879l_bool (tptp.hAPP_f1175211816l_bool tptp.semila218417144l_bool A) (tptp.hAPP_f85652879l_bool tptp.collec1243131813e_bool P_1)))) (and (tptp.hBOOL (tptp.hAPP_f1287348838l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool P_1 X_1)))))) (forall ((P_1 tptp.fun_Ho320143120e_bool) (Q_1 tptp.fun_Ho320143120e_bool)) (= (tptp.hAPP_f1749453397e_bool tptp.collec223185785_state (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1612626488e_bool tptp.cOMBS_56025283l_bool (tptp.hAPP_f1422032445l_bool (tptp.cOMBB_877416532_state tptp.fconj) P_1)) Q_1)) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool (tptp.hAPP_f1749453397e_bool tptp.collec223185785_state P_1)) (tptp.hAPP_f1749453397e_bool tptp.collec223185785_state Q_1)))) (forall ((P_1 tptp.fun_pname_bool) (Q_1 tptp.fun_pname_bool)) (= (tptp.hAPP_f759274231e_bool tptp.collect_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_f649174806e_bool tptp.cOMBS_568398431l_bool (tptp.hAPP_f1402196763l_bool (tptp.cOMBB_675860798_pname tptp.fconj) P_1)) Q_1)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool (tptp.hAPP_f759274231e_bool tptp.collect_pname P_1)) (tptp.hAPP_f759274231e_bool tptp.collect_pname Q_1)))) (forall ((P_1 tptp.fun_fu1430349052l_bool) (Q_1 tptp.fun_fu1430349052l_bool)) (= (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f624840228l_bool tptp.cOMBS_350070575l_bool (tptp.hAPP_f143162813l_bool (tptp.cOMBB_2095475776e_bool tptp.fconj) P_1)) Q_1)) (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.semila1130628874l_bool (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool P_1)) (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool Q_1)))) (forall ((P_1 tptp.fun_fu1996308102l_bool) (Q_1 tptp.fun_fu1996308102l_bool)) (= (tptp.hAPP_f85652879l_bool tptp.collec1243131813e_bool (tptp.hAPP_f85652879l_bool (tptp.hAPP_f927797370l_bool tptp.cOMBS_1039407915l_bool (tptp.hAPP_f945781379l_bool (tptp.cOMBB_1004232970e_bool tptp.fconj) P_1)) Q_1)) (tptp.hAPP_f85652879l_bool (tptp.hAPP_f1175211816l_bool tptp.semila218417144l_bool (tptp.hAPP_f85652879l_bool tptp.collec1243131813e_bool P_1)) (tptp.hAPP_f85652879l_bool tptp.collec1243131813e_bool Q_1)))) (forall ((A tptp.fun_pname_bool) (B tptp.fun_pname_bool) (C_1 tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A))) (= (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool B) C_1)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool (tptp.hAPP_f759274231e_bool _let_1 B)) (tptp.hAPP_f759274231e_bool _let_1 C_1))))) (forall ((A tptp.fun_Ho320143120e_bool) (B tptp.fun_Ho320143120e_bool) (C_1 tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_f1043393922e_bool tptp.minus_1060678561e_bool A))) (= (tptp.hAPP_f1749453397e_bool _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool B) C_1)) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool (tptp.hAPP_f1749453397e_bool _let_1 B)) (tptp.hAPP_f1749453397e_bool _let_1 C_1))))) (forall ((A tptp.fun_pname_bool) (B tptp.fun_pname_bool) (C_1 tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A))) (= (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool B) C_1)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool (tptp.hAPP_f759274231e_bool _let_1 B)) (tptp.hAPP_f759274231e_bool _let_1 C_1))))) (forall ((A tptp.fun_Ho320143120e_bool) (B tptp.fun_Ho320143120e_bool) (C_1 tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_f1043393922e_bool tptp.minus_1060678561e_bool A))) (= (tptp.hAPP_f1749453397e_bool _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool B) C_1)) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool (tptp.hAPP_f1749453397e_bool _let_1 B)) (tptp.hAPP_f1749453397e_bool _let_1 C_1))))) (forall ((A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A) B)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A) B)) A)) (forall ((A tptp.fun_Ho320143120e_bool) (B tptp.fun_Ho320143120e_bool)) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.minus_1060678561e_bool A) B)) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool A) B)) A)) (forall ((X_1 tptp.bool) (Y_2 tptp.bool)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila310582991f_bool X_1) Y_2)) X_1))) (forall ((X_1 tptp.fun_pname_bool) (Y_2 tptp.fun_pname_bool)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool X_1) Y_2)) X_1))) (forall ((X_1 tptp.fun_Ho320143120e_bool) (Y_2 tptp.fun_Ho320143120e_bool)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool X_1) Y_2)) X_1))) (forall ((X_1 tptp.bool) (Y_2 tptp.bool)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila310582991f_bool X_1) Y_2)) X_1))) (forall ((X_1 tptp.fun_pname_bool) (Y_2 tptp.fun_pname_bool)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool X_1) Y_2)) X_1))) (forall ((X_1 tptp.fun_Ho320143120e_bool) (Y_2 tptp.fun_Ho320143120e_bool)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool X_1) Y_2)) X_1))) (forall ((X_1 tptp.bool) (Y_2 tptp.bool)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila310582991f_bool X_1) Y_2)) Y_2))) (forall ((X_1 tptp.fun_pname_bool) (Y_2 tptp.fun_pname_bool)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool X_1) Y_2)) Y_2))) (forall ((X_1 tptp.fun_Ho320143120e_bool) (Y_2 tptp.fun_Ho320143120e_bool)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool X_1) Y_2)) Y_2))) (forall ((X_1 tptp.bool) (Y_2 tptp.bool)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila310582991f_bool X_1) Y_2)) Y_2))) (forall ((X_1 tptp.fun_pname_bool) (Y_2 tptp.fun_pname_bool)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool X_1) Y_2)) Y_2))) (forall ((X_1 tptp.fun_Ho320143120e_bool) (Y_2 tptp.fun_Ho320143120e_bool)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool X_1) Y_2)) Y_2))) (forall ((X_1 tptp.bool) (Y_2 tptp.bool)) (= (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool X_1) Y_2)) (= (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila310582991f_bool X_1) Y_2)) (tptp.hBOOL X_1)))) (forall ((X_1 tptp.fun_pname_bool) (Y_2 tptp.fun_pname_bool)) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool X_1) Y_2)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool X_1) Y_2) X_1))) (forall ((X_1 tptp.fun_Ho320143120e_bool) (Y_2 tptp.fun_Ho320143120e_bool)) (= (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool X_1) Y_2)) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool X_1) Y_2) X_1))) (forall ((X_1 tptp.bool) (Y_2 tptp.bool) (Z tptp.bool)) (let ((_let_1 (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool X_1))) (= (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila310582991f_bool Y_2) Z))) (and (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 Y_2)) (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 Z)))))) (forall ((X_1 tptp.fun_pname_bool) (Y_2 tptp.fun_pname_bool) (Z tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool X_1))) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool Y_2) Z))) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 Y_2)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 Z)))))) (forall ((X_1 tptp.fun_Ho320143120e_bool) (Y_2 tptp.fun_Ho320143120e_bool) (Z tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool X_1))) (= (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool Y_2) Z))) (and (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 Y_2)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 Z)))))) (forall ((B_1 tptp.bool) (A_4 tptp.bool) (X_1 tptp.bool)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool A_4) X_1)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila310582991f_bool A_4) B_1)) X_1)))) (forall ((B_1 tptp.fun_pname_bool) (A_4 tptp.fun_pname_bool) (X_1 tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_4) X_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A_4) B_1)) X_1)))) (forall ((B_1 tptp.fun_Ho320143120e_bool) (A_4 tptp.fun_Ho320143120e_bool) (X_1 tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool A_4) X_1)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool A_4) B_1)) X_1)))) (forall ((A_4 tptp.bool) (B_1 tptp.bool) (X_1 tptp.bool)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool B_1) X_1)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila310582991f_bool A_4) B_1)) X_1)))) (forall ((A_4 tptp.fun_pname_bool) (B_1 tptp.fun_pname_bool) (X_1 tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B_1) X_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A_4) B_1)) X_1)))) (forall ((A_4 tptp.fun_Ho320143120e_bool) (B_1 tptp.fun_Ho320143120e_bool) (X_1 tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool B_1) X_1)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool A_4) B_1)) X_1)))) (forall ((X_1 tptp.bool) (Y_2 tptp.bool)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool X_1) Y_2)) (= (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila310582991f_bool X_1) Y_2)) (tptp.hBOOL X_1)))) (forall ((X_1 tptp.fun_pname_bool) (Y_2 tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool X_1) Y_2)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool X_1) Y_2) X_1))) (forall ((X_1 tptp.fun_Ho320143120e_bool) (Y_2 tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool X_1) Y_2)) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool X_1) Y_2) X_1))) (forall ((Y_2 tptp.bool) (X_1 tptp.bool)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Y_2) X_1)) (= (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila310582991f_bool X_1) Y_2)) (tptp.hBOOL Y_2)))) (forall ((Y_2 tptp.fun_pname_bool) (X_1 tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool Y_2) X_1)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool X_1) Y_2) Y_2))) (forall ((Y_2 tptp.fun_Ho320143120e_bool) (X_1 tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool Y_2) X_1)) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool X_1) Y_2) Y_2))) (forall ((B_1 tptp.bool) (X_1 tptp.bool) (A_4 tptp.bool)) (let ((_let_1 (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool X_1))) (=> (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 A_4)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 B_1)) (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila310582991f_bool A_4) B_1))))))) (forall ((B_1 tptp.fun_pname_bool) (X_1 tptp.fun_pname_bool) (A_4 tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool X_1))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A_4)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A_4) B_1))))))) (forall ((B_1 tptp.fun_Ho320143120e_bool) (X_1 tptp.fun_Ho320143120e_bool) (A_4 tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool X_1))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 A_4)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 B_1)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool A_4) B_1))))))) (forall ((Z tptp.bool) (X_1 tptp.bool) (Y_2 tptp.bool)) (let ((_let_1 (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool X_1))) (=> (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 Y_2)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 Z)) (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila310582991f_bool Y_2) Z))))))) (forall ((Z tptp.fun_pname_bool) (X_1 tptp.fun_pname_bool) (Y_2 tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool X_1))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 Y_2)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 Z)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool Y_2) Z))))))) (forall ((Z tptp.fun_Ho320143120e_bool) (X_1 tptp.fun_Ho320143120e_bool) (Y_2 tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool X_1))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 Y_2)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 Z)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool Y_2) Z))))))) (forall ((B_1 tptp.bool) (D_1 tptp.bool) (A_4 tptp.bool) (C tptp.bool)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool A_4) C)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool B_1) D_1)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila310582991f_bool A_4) B_1)) (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila310582991f_bool C) D_1)))))) (forall ((B_1 tptp.fun_pname_bool) (D_1 tptp.fun_pname_bool) (A_4 tptp.fun_pname_bool) (C tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_4) C)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B_1) D_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A_4) B_1)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool C) D_1)))))) (forall ((B_1 tptp.fun_Ho320143120e_bool) (D_1 tptp.fun_Ho320143120e_bool) (A_4 tptp.fun_Ho320143120e_bool) (C tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool A_4) C)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool B_1) D_1)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool A_4) B_1)) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool C) D_1)))))) (forall ((X_1 tptp.bool) (A_4 tptp.bool) (B_1 tptp.bool)) (let ((_let_1 (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool X_1))) (=> (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila310582991f_bool A_4) B_1))) (not (=> (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 A_4)) (not (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 B_1)))))))) (forall ((X_1 tptp.fun_pname_bool) (A_4 tptp.fun_pname_bool) (B_1 tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool X_1))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A_4) B_1))) (not (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A_4)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B_1)))))))) (forall ((X_1 tptp.fun_Ho320143120e_bool) (A_4 tptp.fun_Ho320143120e_bool) (B_1 tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool X_1))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool A_4) B_1))) (not (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 A_4)) (not (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 B_1)))))))) (forall ((X_1 tptp.fun_com_bool)) (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila980496562m_bool X_1) tptp.bot_bot_fun_com_bool) tptp.bot_bot_fun_com_bool)) (forall ((X_1 tptp.bool)) (= (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 tptp.fun_pname_bool)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool X_1) tptp.bot_bo844097828e_bool) tptp.bot_bo844097828e_bool)) (forall ((X_1 tptp.fun_Ho320143120e_bool)) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool X_1) tptp.bot_bo39439654e_bool) tptp.bot_bo39439654e_bool)) (forall ((X_1 tptp.fun_com_bool)) (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila980496562m_bool tptp.bot_bot_fun_com_bool) X_1) tptp.bot_bot_fun_com_bool)) (forall ((X_1 tptp.bool)) (= (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 tptp.fun_pname_bool)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool tptp.bot_bo844097828e_bool) X_1) tptp.bot_bo844097828e_bool)) (forall ((X_1 tptp.fun_Ho320143120e_bool)) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool tptp.bot_bo39439654e_bool) X_1) tptp.bot_bo39439654e_bool)) (forall ((X_1 tptp.bool) (Y_2 tptp.bool)) (= (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila310582991f_bool X_1) (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool X_1) Y_2))) (tptp.hBOOL X_1))) (forall ((X_1 tptp.fun_pname_bool) (Y_2 tptp.fun_pname_bool)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool X_1) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool X_1) Y_2)) X_1)) (forall ((X_1 tptp.fun_Ho320143120e_bool) (Y_2 tptp.fun_Ho320143120e_bool)) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool X_1) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool X_1) Y_2)) X_1)) (forall ((X_1 tptp.bool) (Y_2 tptp.bool)) (= (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool X_1) (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila310582991f_bool X_1) Y_2))) (tptp.hBOOL X_1))) (forall ((X_1 tptp.fun_pname_bool) (Y_2 tptp.fun_pname_bool)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool X_1) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool X_1) Y_2)) X_1)) (forall ((X_1 tptp.fun_Ho320143120e_bool) (Y_2 tptp.fun_Ho320143120e_bool)) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool X_1) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool X_1) Y_2)) X_1)) (forall ((X_1 tptp.bool) (Y_2 tptp.bool) (Z tptp.bool)) (let ((_let_1 (tptp.hAPP_b589554111l_bool tptp.semila310582991f_bool X_1))) (= (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool Y_2) Z))) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool (tptp.hAPP_bool_bool _let_1 Y_2)) (tptp.hAPP_bool_bool _let_1 Z)))))) (forall ((X_1 tptp.fun_pname_bool) (Y_2 tptp.fun_pname_bool) (Z tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool X_1))) (= (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool Y_2) Z)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool (tptp.hAPP_f759274231e_bool _let_1 Y_2)) (tptp.hAPP_f759274231e_bool _let_1 Z))))) (forall ((X_1 tptp.fun_Ho320143120e_bool) (Y_2 tptp.fun_Ho320143120e_bool) (Z tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool X_1))) (= (tptp.hAPP_f1749453397e_bool _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool Y_2) Z)) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool (tptp.hAPP_f1749453397e_bool _let_1 Y_2)) (tptp.hAPP_f1749453397e_bool _let_1 Z))))) (forall ((X_1 tptp.bool) (Y_2 tptp.bool) (Z tptp.bool)) (let ((_let_1 (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool X_1))) (= (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila310582991f_bool Y_2) Z))) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila310582991f_bool (tptp.hAPP_bool_bool _let_1 Y_2)) (tptp.hAPP_bool_bool _let_1 Z)))))) (forall ((X_1 tptp.fun_pname_bool) (Y_2 tptp.fun_pname_bool) (Z tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool X_1))) (= (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool Y_2) Z)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool (tptp.hAPP_f759274231e_bool _let_1 Y_2)) (tptp.hAPP_f759274231e_bool _let_1 Z))))) (forall ((X_1 tptp.fun_Ho320143120e_bool) (Y_2 tptp.fun_Ho320143120e_bool) (Z tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool X_1))) (= (tptp.hAPP_f1749453397e_bool _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool Y_2) Z)) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool (tptp.hAPP_f1749453397e_bool _let_1 Y_2)) (tptp.hAPP_f1749453397e_bool _let_1 Z))))) (forall ((Y_2 tptp.bool) (Z tptp.bool) (X_1 tptp.bool)) (= (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila310582991f_bool (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool Y_2) Z)) X_1)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila310582991f_bool Y_2) X_1)) (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila310582991f_bool Z) X_1))))) (forall ((Y_2 tptp.fun_pname_bool) (Z tptp.fun_pname_bool) (X_1 tptp.fun_pname_bool)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool Y_2) Z)) X_1) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool Y_2) X_1)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool Z) X_1)))) (forall ((Y_2 tptp.fun_Ho320143120e_bool) (Z tptp.fun_Ho320143120e_bool) (X_1 tptp.fun_Ho320143120e_bool)) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool Y_2) Z)) X_1) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool Y_2) X_1)) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool Z) X_1)))) (forall ((Y_2 tptp.bool) (Z tptp.bool) (X_1 tptp.bool)) (= (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila310582991f_bool Y_2) Z)) X_1)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila310582991f_bool (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool Y_2) X_1)) (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool Z) X_1))))) (forall ((Y_2 tptp.fun_pname_bool) (Z tptp.fun_pname_bool) (X_1 tptp.fun_pname_bool)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool Y_2) Z)) X_1) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool Y_2) X_1)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool Z) X_1)))) (forall ((Y_2 tptp.fun_Ho320143120e_bool) (Z tptp.fun_Ho320143120e_bool) (X_1 tptp.fun_Ho320143120e_bool)) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool Y_2) Z)) X_1) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool Y_2) X_1)) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool Z) X_1)))) (forall ((A tptp.fun_com_bool)) (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.minus_59609839m_bool A) A) tptp.bot_bot_fun_com_bool)) (forall ((A tptp.fun_pname_bool)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A) A) tptp.bot_bo844097828e_bool)) (forall ((A tptp.fun_Ho320143120e_bool)) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.minus_1060678561e_bool A) A) tptp.bot_bo39439654e_bool)) (forall ((A tptp.fun_com_bool)) (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.minus_59609839m_bool A) tptp.bot_bot_fun_com_bool) A)) (forall ((A tptp.fun_pname_bool)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A) tptp.bot_bo844097828e_bool) A)) (forall ((A tptp.fun_Ho320143120e_bool)) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.minus_1060678561e_bool A) tptp.bot_bo39439654e_bool) A)) (forall ((A tptp.fun_com_bool)) (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.minus_59609839m_bool tptp.bot_bot_fun_com_bool) A) tptp.bot_bot_fun_com_bool)) (forall ((A tptp.fun_pname_bool)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool tptp.bot_bo844097828e_bool) A) tptp.bot_bo844097828e_bool)) (forall ((A tptp.fun_Ho320143120e_bool)) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.minus_1060678561e_bool tptp.bot_bo39439654e_bool) A) tptp.bot_bo39439654e_bool)) (forall ((A tptp.fun_fu1430349052l_bool) (B tptp.fun_fu1430349052l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool B)) (= (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.minus_1290075917l_bool A) B))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A))))) (forall ((A tptp.fun_fu1996308102l_bool) (B tptp.fun_fu1996308102l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool B)) (= (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool (tptp.hAPP_f85652879l_bool (tptp.hAPP_f1175211816l_bool tptp.minus_1119384757l_bool A) B))) (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool A))))) (forall ((A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B)) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A) B))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A))))) (forall ((A tptp.fun_Ho320143120e_bool) (B tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state B)) (= (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.minus_1060678561e_bool A) B))) (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state A))))) (forall ((A tptp.fun_com_bool) (X_1 tptp.com) (B tptp.fun_com_bool)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_1) B)) (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.minus_59609839m_bool (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com X_1) A)) B) (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.minus_59609839m_bool A) B)))) (forall ((A tptp.fun_pname_bool) (X_1 tptp.pname) (B tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) B)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1) A)) B) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A) B)))) (forall ((A tptp.fun_Ho320143120e_bool) (X_1 tptp.hoare_363350478_state) (B tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state X_1) B)) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.minus_1060678561e_bool (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state X_1) A)) B) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.minus_1060678561e_bool A) B)))) (forall ((A tptp.fun_com_bool) (X_1 tptp.com) (B tptp.fun_com_bool)) (let ((_let_1 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.minus_59609839m_bool A) B))) (let ((_let_2 (tptp.hAPP_c566651504m_bool tptp.insert_com X_1))) (let ((_let_3 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.minus_59609839m_bool (tptp.hAPP_f1682609283m_bool _let_2 A)) B))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_1) B)))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (tptp.hAPP_f1682609283m_bool _let_2 _let_1))))))))) (forall ((A tptp.fun_pname_bool) (X_1 tptp.pname) (B tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A) B))) (let ((_let_2 (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1))) (let ((_let_3 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool (tptp.hAPP_f759274231e_bool _let_2 A)) B))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) B)))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (tptp.hAPP_f759274231e_bool _let_2 _let_1))))))))) (forall ((A tptp.fun_Ho320143120e_bool) (X_1 tptp.hoare_363350478_state) (B tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.minus_1060678561e_bool A) B))) (let ((_let_2 (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state X_1))) (let ((_let_3 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.minus_1060678561e_bool (tptp.hAPP_f1749453397e_bool _let_2 A)) B))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state X_1) B)))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (tptp.hAPP_f1749453397e_bool _let_2 _let_1))))))))) (forall ((A tptp.fun_com_bool) (B tptp.fun_com_bool)) (= (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila980496562m_bool A) B) tptp.bot_bot_fun_com_bool) (forall ((X_2 tptp.com)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_2) A)) (forall ((Xa tptp.com)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com Xa) B)) (not (= X_2 Xa)))))))) (forall ((A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (= (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A) B) tptp.bot_bo844097828e_bool) (forall ((X_2 tptp.pname)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A)) (forall ((Xa tptp.pname)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname Xa) B)) (not (= X_2 Xa)))))))) (forall ((A tptp.fun_Ho320143120e_bool) (B tptp.fun_Ho320143120e_bool)) (= (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool A) B) tptp.bot_bo39439654e_bool) (forall ((X_2 tptp.hoare_363350478_state)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state X_2) A)) (forall ((Xa tptp.hoare_363350478_state)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state Xa) B)) (not (= X_2 Xa)))))))) (forall ((A tptp.fun_com_bool)) (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila980496562m_bool A) tptp.bot_bot_fun_com_bool) tptp.bot_bot_fun_com_bool)) (forall ((A tptp.fun_pname_bool)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A) tptp.bot_bo844097828e_bool) tptp.bot_bo844097828e_bool)) (forall ((A tptp.fun_Ho320143120e_bool)) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool A) tptp.bot_bo39439654e_bool) tptp.bot_bo39439654e_bool)) (forall ((B tptp.fun_com_bool)) (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila980496562m_bool tptp.bot_bot_fun_com_bool) B) tptp.bot_bot_fun_com_bool)) (forall ((B tptp.fun_pname_bool)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool tptp.bot_bo844097828e_bool) B) tptp.bot_bo844097828e_bool)) (forall ((B tptp.fun_Ho320143120e_bool)) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool tptp.bot_bo39439654e_bool) B) tptp.bot_bo39439654e_bool)) (forall ((C_1 tptp.fun_pname_bool) (A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) C_1)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool B) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool C_1) A)) A)))) (forall ((C_1 tptp.fun_Ho320143120e_bool) (A tptp.fun_Ho320143120e_bool) (B tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool B) C_1)) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.minus_1060678561e_bool B) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.minus_1060678561e_bool C_1) A)) A)))) (forall ((D tptp.fun_pname_bool) (B tptp.fun_pname_bool) (A tptp.fun_pname_bool) (C_1 tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) C_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool D) B)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A) B)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool C_1) D)))))) (forall ((D tptp.fun_Ho320143120e_bool) (B tptp.fun_Ho320143120e_bool) (A tptp.fun_Ho320143120e_bool) (C_1 tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool A) C_1)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool D) B)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.minus_1060678561e_bool A) B)) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.minus_1060678561e_bool C_1) D)))))) (forall ((A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A) B)) A))) (forall ((A tptp.fun_Ho320143120e_bool) (B tptp.fun_Ho320143120e_bool)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.minus_1060678561e_bool A) B)) A))) (forall ((A tptp.fun_pname_bool) (B tptp.fun_pname_bool) (C_1 tptp.fun_pname_bool)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A) B)) C_1) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A) C_1)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool B) C_1)))) (forall ((A tptp.fun_Ho320143120e_bool) (B tptp.fun_Ho320143120e_bool) (C_1 tptp.fun_Ho320143120e_bool)) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.minus_1060678561e_bool (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool A) B)) C_1) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.minus_1060678561e_bool A) C_1)) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.minus_1060678561e_bool B) C_1)))) (forall ((B tptp.fun_pname_bool) (A tptp.fun_pname_bool)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool B) A)) A) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool B) A))) (forall ((B tptp.fun_Ho320143120e_bool) (A tptp.fun_Ho320143120e_bool)) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.minus_1060678561e_bool B) A)) A) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool B) A))) (forall ((A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A))) (= (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool B) A)) (tptp.hAPP_f759274231e_bool _let_1 B)))) (forall ((A tptp.fun_Ho320143120e_bool) (B tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool A))) (= (tptp.hAPP_f1749453397e_bool _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.minus_1060678561e_bool B) A)) (tptp.hAPP_f1749453397e_bool _let_1 B)))) (forall ((B tptp.fun_com_bool) (A_4 tptp.com) (C_1 tptp.fun_com_bool)) (let ((_let_1 (tptp.hAPP_c566651504m_bool tptp.insert_com A_4))) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com A_4) C_1)) (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila980496562m_bool (tptp.hAPP_f1682609283m_bool _let_1 B)) C_1) (tptp.hAPP_f1682609283m_bool _let_1 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila980496562m_bool B) C_1)))))) (forall ((B tptp.fun_pname_bool) (A_4 tptp.pname) (C_1 tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p905327722e_bool tptp.insert_pname A_4))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A_4) C_1)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool (tptp.hAPP_f759274231e_bool _let_1 B)) C_1) (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool B) C_1)))))) (forall ((B tptp.fun_Ho320143120e_bool) (A_4 tptp.hoare_363350478_state) (C_1 tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state A_4))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state A_4) C_1)) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool (tptp.hAPP_f1749453397e_bool _let_1 B)) C_1) (tptp.hAPP_f1749453397e_bool _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool B) C_1)))))) (forall ((B tptp.fun_com_bool) (A_4 tptp.com) (A tptp.fun_com_bool)) (let ((_let_1 (tptp.hAPP_f1120618594m_bool tptp.semila980496562m_bool A))) (let ((_let_2 (tptp.hAPP_c566651504m_bool tptp.insert_com A_4))) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com A_4) A)) (= (tptp.hAPP_f1682609283m_bool _let_1 (tptp.hAPP_f1682609283m_bool _let_2 B)) (tptp.hAPP_f1682609283m_bool _let_2 (tptp.hAPP_f1682609283m_bool _let_1 B))))))) (forall ((B tptp.fun_pname_bool) (A_4 tptp.pname) (A tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A))) (let ((_let_2 (tptp.hAPP_p905327722e_bool tptp.insert_pname A_4))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A_4) A)) (= (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool _let_2 B)) (tptp.hAPP_f759274231e_bool _let_2 (tptp.hAPP_f759274231e_bool _let_1 B))))))) (forall ((B tptp.fun_Ho320143120e_bool) (A_4 tptp.hoare_363350478_state) (A tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool A))) (let ((_let_2 (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state A_4))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state A_4) A)) (= (tptp.hAPP_f1749453397e_bool _let_1 (tptp.hAPP_f1749453397e_bool _let_2 B)) (tptp.hAPP_f1749453397e_bool _let_2 (tptp.hAPP_f1749453397e_bool _let_1 B))))))) (forall ((B tptp.fun_com_bool) (A_4 tptp.com) (C_1 tptp.fun_com_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com A_4) C_1))) (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila980496562m_bool (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com A_4) B)) C_1) (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila980496562m_bool B) C_1)))) (forall ((B tptp.fun_pname_bool) (A_4 tptp.pname) (C_1 tptp.fun_pname_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A_4) C_1))) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A_4) B)) C_1) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool B) C_1)))) (forall ((B tptp.fun_Ho320143120e_bool) (A_4 tptp.hoare_363350478_state) (C_1 tptp.fun_Ho320143120e_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state A_4) C_1))) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state A_4) B)) C_1) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool B) C_1)))) (forall ((B tptp.fun_com_bool) (A_4 tptp.com) (A tptp.fun_com_bool)) (let ((_let_1 (tptp.hAPP_f1120618594m_bool tptp.semila980496562m_bool A))) (=> (not (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com A_4) A))) (= (tptp.hAPP_f1682609283m_bool _let_1 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com A_4) B)) (tptp.hAPP_f1682609283m_bool _let_1 B))))) (forall ((B tptp.fun_pname_bool) (A_4 tptp.pname) (A tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A))) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A_4) A))) (= (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A_4) B)) (tptp.hAPP_f759274231e_bool _let_1 B))))) (forall ((B tptp.fun_Ho320143120e_bool) (A_4 tptp.hoare_363350478_state) (A tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool A))) (=> (not (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state A_4) A))) (= (tptp.hAPP_f1749453397e_bool _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state A_4) B)) (tptp.hAPP_f1749453397e_bool _let_1 B))))) (forall ((A_4 tptp.com) (A tptp.fun_com_bool) (B tptp.fun_com_bool)) (let ((_let_1 (tptp.hAPP_c566651504m_bool tptp.insert_com A_4))) (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila980496562m_bool (tptp.hAPP_f1682609283m_bool _let_1 A)) (tptp.hAPP_f1682609283m_bool _let_1 B)) (tptp.hAPP_f1682609283m_bool _let_1 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila980496562m_bool A) B))))) (forall ((A_4 tptp.pname) (A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p905327722e_bool tptp.insert_pname A_4))) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool (tptp.hAPP_f759274231e_bool _let_1 A)) (tptp.hAPP_f759274231e_bool _let_1 B)) (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A) B))))) (forall ((A_4 tptp.hoare_363350478_state) (A tptp.fun_Ho320143120e_bool) (B tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state A_4))) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool (tptp.hAPP_f1749453397e_bool _let_1 A)) (tptp.hAPP_f1749453397e_bool _let_1 B)) (tptp.hAPP_f1749453397e_bool _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool A) B))))) (forall ((B tptp.fun_com_bool) (A_4 tptp.com) (C_1 tptp.fun_com_bool)) (let ((_let_1 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila980496562m_bool B) C_1))) (let ((_let_2 (tptp.hAPP_c566651504m_bool tptp.insert_com A_4))) (let ((_let_3 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila980496562m_bool (tptp.hAPP_f1682609283m_bool _let_2 B)) C_1))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com A_4) C_1)))) (and (=> _let_4 (= _let_3 (tptp.hAPP_f1682609283m_bool _let_2 _let_1))) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((B tptp.fun_pname_bool) (A_4 tptp.pname) (C_1 tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool B) C_1))) (let ((_let_2 (tptp.hAPP_p905327722e_bool tptp.insert_pname A_4))) (let ((_let_3 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool (tptp.hAPP_f759274231e_bool _let_2 B)) C_1))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A_4) C_1)))) (and (=> _let_4 (= _let_3 (tptp.hAPP_f759274231e_bool _let_2 _let_1))) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((B tptp.fun_Ho320143120e_bool) (A_4 tptp.hoare_363350478_state) (C_1 tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool B) C_1))) (let ((_let_2 (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state A_4))) (let ((_let_3 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool (tptp.hAPP_f1749453397e_bool _let_2 B)) C_1))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state A_4) C_1)))) (and (=> _let_4 (= _let_3 (tptp.hAPP_f1749453397e_bool _let_2 _let_1))) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((B tptp.fun_com_bool) (A_4 tptp.com) (A tptp.fun_com_bool)) (let ((_let_1 (tptp.hAPP_f1120618594m_bool tptp.semila980496562m_bool A))) (let ((_let_2 (tptp.hAPP_f1682609283m_bool _let_1 B))) (let ((_let_3 (tptp.hAPP_c566651504m_bool tptp.insert_com A_4))) (let ((_let_4 (tptp.hAPP_f1682609283m_bool _let_1 (tptp.hAPP_f1682609283m_bool _let_3 B)))) (let ((_let_5 (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com A_4) A)))) (and (=> _let_5 (= _let_4 (tptp.hAPP_f1682609283m_bool _let_3 _let_2))) (=> (not _let_5) (= _let_4 _let_2))))))))) (forall ((B tptp.fun_pname_bool) (A_4 tptp.pname) (A tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A))) (let ((_let_2 (tptp.hAPP_f759274231e_bool _let_1 B))) (let ((_let_3 (tptp.hAPP_p905327722e_bool tptp.insert_pname A_4))) (let ((_let_4 (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool _let_3 B)))) (let ((_let_5 (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A_4) A)))) (and (=> _let_5 (= _let_4 (tptp.hAPP_f759274231e_bool _let_3 _let_2))) (=> (not _let_5) (= _let_4 _let_2))))))))) (forall ((B tptp.fun_Ho320143120e_bool) (A_4 tptp.hoare_363350478_state) (A tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool A))) (let ((_let_2 (tptp.hAPP_f1749453397e_bool _let_1 B))) (let ((_let_3 (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state A_4))) (let ((_let_4 (tptp.hAPP_f1749453397e_bool _let_1 (tptp.hAPP_f1749453397e_bool _let_3 B)))) (let ((_let_5 (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state A_4) A)))) (and (=> _let_5 (= _let_4 (tptp.hAPP_f1749453397e_bool _let_3 _let_2))) (=> (not _let_5) (= _let_4 _let_2))))))))) (forall ((B tptp.fun_pname_bool) (D tptp.fun_pname_bool) (A tptp.fun_pname_bool) (C_1 tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) C_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) D)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A) B)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool C_1) D)))))) (forall ((B tptp.fun_Ho320143120e_bool) (D tptp.fun_Ho320143120e_bool) (A tptp.fun_Ho320143120e_bool) (C_1 tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool A) C_1)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool B) D)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool A) B)) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool C_1) D)))))) (forall ((B tptp.fun_pname_bool) (C_1 tptp.fun_pname_bool) (A tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool C_1))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A) B))))))) (forall ((B tptp.fun_Ho320143120e_bool) (C_1 tptp.fun_Ho320143120e_bool) (A tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool C_1))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 A)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 B)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool A) B))))))) (forall ((B tptp.fun_pname_bool) (A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) A)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A) B) B))) (forall ((B tptp.fun_Ho320143120e_bool) (A tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool B) A)) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool A) B) B))) (forall ((A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) B)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A) B) A))) (forall ((A tptp.fun_Ho320143120e_bool) (B tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool A) B)) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool A) B) A))) (forall ((A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A) B)) B))) (forall ((A tptp.fun_Ho320143120e_bool) (B tptp.fun_Ho320143120e_bool)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool A) B)) B))) (forall ((A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A) B)) A))) (forall ((A tptp.fun_Ho320143120e_bool) (B tptp.fun_Ho320143120e_bool)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool A) B)) A))) (forall ((A tptp.fun_pname_bool) (B tptp.fun_pname_bool) (C_1 tptp.fun_pname_bool)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A) B)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool B) C_1))) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool C_1) A)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A) B)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool B) C_1))) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool C_1) A)))) (forall ((A tptp.fun_Ho320143120e_bool) (B tptp.fun_Ho320143120e_bool) (C_1 tptp.fun_Ho320143120e_bool)) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool A) B)) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool B) C_1))) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool C_1) A)) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool A) B)) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool B) C_1))) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool C_1) A)))) (forall ((B tptp.fun_pname_bool) (C_1 tptp.fun_pname_bool) (A tptp.fun_pname_bool)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool B) C_1)) A) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool B) A)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool C_1) A)))) (forall ((B tptp.fun_Ho320143120e_bool) (C_1 tptp.fun_Ho320143120e_bool) (A tptp.fun_Ho320143120e_bool)) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool B) C_1)) A) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool B) A)) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool C_1) A)))) (forall ((B tptp.fun_pname_bool) (C_1 tptp.fun_pname_bool) (A tptp.fun_pname_bool)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool B) C_1)) A) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool B) A)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool C_1) A)))) (forall ((B tptp.fun_Ho320143120e_bool) (C_1 tptp.fun_Ho320143120e_bool) (A tptp.fun_Ho320143120e_bool)) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool B) C_1)) A) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool B) A)) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool C_1) A)))) (forall ((A tptp.fun_pname_bool) (B tptp.fun_pname_bool) (C_1 tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A))) (= (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool B) C_1)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool (tptp.hAPP_f759274231e_bool _let_1 B)) (tptp.hAPP_f759274231e_bool _let_1 C_1))))) (forall ((A tptp.fun_Ho320143120e_bool) (B tptp.fun_Ho320143120e_bool) (C_1 tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool A))) (= (tptp.hAPP_f1749453397e_bool _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool B) C_1)) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool (tptp.hAPP_f1749453397e_bool _let_1 B)) (tptp.hAPP_f1749453397e_bool _let_1 C_1))))) (forall ((A tptp.fun_pname_bool) (B tptp.fun_pname_bool) (C_1 tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A))) (= (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool B) C_1)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool (tptp.hAPP_f759274231e_bool _let_1 B)) (tptp.hAPP_f759274231e_bool _let_1 C_1))))) (forall ((A tptp.fun_Ho320143120e_bool) (B tptp.fun_Ho320143120e_bool) (C_1 tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool A))) (= (tptp.hAPP_f1749453397e_bool _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool B) C_1)) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool (tptp.hAPP_f1749453397e_bool _let_1 B)) (tptp.hAPP_f1749453397e_bool _let_1 C_1))))) (forall ((X_1 tptp.bool) (Y_2 tptp.bool) (Z tptp.bool)) (let ((_let_1 (tptp.hAPP_b589554111l_bool tptp.semila310582991f_bool X_1))) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool (tptp.hAPP_bool_bool _let_1 Y_2)) (tptp.hAPP_bool_bool _let_1 Z))) (tptp.hAPP_bool_bool _let_1 (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool Y_2) Z)))))) (forall ((X_1 tptp.fun_pname_bool) (Y_2 tptp.fun_pname_bool) (Z tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool X_1))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool (tptp.hAPP_f759274231e_bool _let_1 Y_2)) (tptp.hAPP_f759274231e_bool _let_1 Z))) (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool Y_2) Z)))))) (forall ((X_1 tptp.fun_Ho320143120e_bool) (Y_2 tptp.fun_Ho320143120e_bool) (Z tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool X_1))) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool (tptp.hAPP_f1749453397e_bool _let_1 Y_2)) (tptp.hAPP_f1749453397e_bool _let_1 Z))) (tptp.hAPP_f1749453397e_bool _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool Y_2) Z)))))) (forall ((X_1 tptp.bool) (Y_2 tptp.bool) (Z tptp.bool)) (let ((_let_1 (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool X_1))) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_bool_bool _let_1 (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila310582991f_bool Y_2) Z))) (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila310582991f_bool (tptp.hAPP_bool_bool _let_1 Y_2)) (tptp.hAPP_bool_bool _let_1 Z)))))) (forall ((X_1 tptp.fun_pname_bool) (Y_2 tptp.fun_pname_bool) (Z tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool X_1))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool Y_2) Z))) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool (tptp.hAPP_f759274231e_bool _let_1 Y_2)) (tptp.hAPP_f759274231e_bool _let_1 Z)))))) (forall ((X_1 tptp.fun_Ho320143120e_bool) (Y_2 tptp.fun_Ho320143120e_bool) (Z tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool X_1))) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool (tptp.hAPP_f1749453397e_bool _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool Y_2) Z))) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool (tptp.hAPP_f1749453397e_bool _let_1 Y_2)) (tptp.hAPP_f1749453397e_bool _let_1 Z)))))) (forall ((A_4 tptp.com) (A tptp.fun_com_bool)) (let ((_let_1 (tptp.hAPP_c566651504m_bool tptp.insert_com A_4))) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com A_4) A)) (= (tptp.hAPP_f1682609283m_bool _let_1 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.minus_59609839m_bool A) (tptp.hAPP_f1682609283m_bool _let_1 tptp.bot_bot_fun_com_bool))) A)))) (forall ((A_4 tptp.pname) (A tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p905327722e_bool tptp.insert_pname A_4))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A_4) A)) (= (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A) (tptp.hAPP_f759274231e_bool _let_1 tptp.bot_bo844097828e_bool))) A)))) (forall ((A_4 tptp.hoare_363350478_state) (A tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state A_4))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state A_4) A)) (= (tptp.hAPP_f1749453397e_bool _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.minus_1060678561e_bool A) (tptp.hAPP_f1749453397e_bool _let_1 tptp.bot_bo39439654e_bool))) A)))) (forall ((X_1 tptp.com) (A tptp.fun_com_bool)) (let ((_let_1 (tptp.hAPP_c566651504m_bool tptp.insert_com X_1))) (=> (not (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_1) A))) (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.minus_59609839m_bool (tptp.hAPP_f1682609283m_bool _let_1 A)) (tptp.hAPP_f1682609283m_bool _let_1 tptp.bot_bot_fun_com_bool)) A)))) (forall ((X_1 tptp.pname) (A tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1))) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A))) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool (tptp.hAPP_f759274231e_bool _let_1 A)) (tptp.hAPP_f759274231e_bool _let_1 tptp.bot_bo844097828e_bool)) A)))) (forall ((X_1 tptp.hoare_363350478_state) (A tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state X_1))) (=> (not (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state X_1) A))) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.minus_1060678561e_bool (tptp.hAPP_f1749453397e_bool _let_1 A)) (tptp.hAPP_f1749453397e_bool _let_1 tptp.bot_bo39439654e_bool)) A)))) (forall ((A_4 tptp.com) (A tptp.fun_com_bool)) (let ((_let_1 (tptp.hAPP_c566651504m_bool tptp.insert_com A_4))) (= (tptp.hAPP_f1682609283m_bool _let_1 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.minus_59609839m_bool A) (tptp.hAPP_f1682609283m_bool _let_1 tptp.bot_bot_fun_com_bool))) (tptp.hAPP_f1682609283m_bool _let_1 A)))) (forall ((A_4 tptp.pname) (A tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p905327722e_bool tptp.insert_pname A_4))) (= (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A) (tptp.hAPP_f759274231e_bool _let_1 tptp.bot_bo844097828e_bool))) (tptp.hAPP_f759274231e_bool _let_1 A)))) (forall ((A_4 tptp.hoare_363350478_state) (A tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state A_4))) (= (tptp.hAPP_f1749453397e_bool _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.minus_1060678561e_bool A) (tptp.hAPP_f1749453397e_bool _let_1 tptp.bot_bo39439654e_bool))) (tptp.hAPP_f1749453397e_bool _let_1 A)))) (forall ((A tptp.fun_com_bool) (A_4 tptp.com) (B tptp.fun_com_bool)) (let ((_let_1 (tptp.hAPP_c566651504m_bool tptp.insert_com A_4))) (let ((_let_2 (tptp.hAPP_f1120618594m_bool tptp.minus_59609839m_bool A))) (= (tptp.hAPP_f1682609283m_bool _let_2 (tptp.hAPP_f1682609283m_bool _let_1 B)) (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.minus_59609839m_bool (tptp.hAPP_f1682609283m_bool _let_2 (tptp.hAPP_f1682609283m_bool _let_1 tptp.bot_bot_fun_com_bool))) B))))) (forall ((A tptp.fun_pname_bool) (A_4 tptp.pname) (B tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p905327722e_bool tptp.insert_pname A_4))) (let ((_let_2 (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A))) (= (tptp.hAPP_f759274231e_bool _let_2 (tptp.hAPP_f759274231e_bool _let_1 B)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool (tptp.hAPP_f759274231e_bool _let_2 (tptp.hAPP_f759274231e_bool _let_1 tptp.bot_bo844097828e_bool))) B))))) (forall ((A tptp.fun_Ho320143120e_bool) (A_4 tptp.hoare_363350478_state) (B tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state A_4))) (let ((_let_2 (tptp.hAPP_f1043393922e_bool tptp.minus_1060678561e_bool A))) (= (tptp.hAPP_f1749453397e_bool _let_2 (tptp.hAPP_f1749453397e_bool _let_1 B)) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.minus_1060678561e_bool (tptp.hAPP_f1749453397e_bool _let_2 (tptp.hAPP_f1749453397e_bool _let_1 tptp.bot_bo39439654e_bool))) B))))) (forall ((A tptp.fun_com_bool) (A_4 tptp.com) (B tptp.fun_com_bool)) (let ((_let_1 (tptp.hAPP_c566651504m_bool tptp.insert_com A_4))) (let ((_let_2 (tptp.hAPP_f1120618594m_bool tptp.minus_59609839m_bool A))) (= (tptp.hAPP_f1682609283m_bool _let_2 (tptp.hAPP_f1682609283m_bool _let_1 B)) (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.minus_59609839m_bool (tptp.hAPP_f1682609283m_bool _let_2 B)) (tptp.hAPP_f1682609283m_bool _let_1 tptp.bot_bot_fun_com_bool)))))) (forall ((A tptp.fun_pname_bool) (A_4 tptp.pname) (B tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p905327722e_bool tptp.insert_pname A_4))) (let ((_let_2 (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A))) (= (tptp.hAPP_f759274231e_bool _let_2 (tptp.hAPP_f759274231e_bool _let_1 B)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool (tptp.hAPP_f759274231e_bool _let_2 B)) (tptp.hAPP_f759274231e_bool _let_1 tptp.bot_bo844097828e_bool)))))) (forall ((A tptp.fun_Ho320143120e_bool) (A_4 tptp.hoare_363350478_state) (B tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state A_4))) (let ((_let_2 (tptp.hAPP_f1043393922e_bool tptp.minus_1060678561e_bool A))) (= (tptp.hAPP_f1749453397e_bool _let_2 (tptp.hAPP_f1749453397e_bool _let_1 B)) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.minus_1060678561e_bool (tptp.hAPP_f1749453397e_bool _let_2 B)) (tptp.hAPP_f1749453397e_bool _let_1 tptp.bot_bo39439654e_bool)))))) (forall ((A tptp.fun_com_bool) (A_4 tptp.com) (B tptp.fun_com_bool)) (let ((_let_1 (tptp.hAPP_f1120618594m_bool tptp.minus_59609839m_bool A))) (= (tptp.hBOOL (tptp.hAPP_f990396704l_bool tptp.finite_finite_com (tptp.hAPP_f1682609283m_bool _let_1 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com A_4) B)))) (tptp.hBOOL (tptp.hAPP_f990396704l_bool tptp.finite_finite_com (tptp.hAPP_f1682609283m_bool _let_1 B)))))) (forall ((A tptp.fun_pname_bool) (A_4 tptp.pname) (B tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A))) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A_4) B)))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f759274231e_bool _let_1 B)))))) (forall ((A tptp.fun_Ho320143120e_bool) (A_4 tptp.hoare_363350478_state) (B tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_f1043393922e_bool tptp.minus_1060678561e_bool A))) (= (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state (tptp.hAPP_f1749453397e_bool _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state A_4) B)))) (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state (tptp.hAPP_f1749453397e_bool _let_1 B)))))) (forall ((A tptp.fun_fu1430349052l_bool) (A_4 tptp.fun_pname_bool) (B tptp.fun_fu1430349052l_bool)) (let ((_let_1 (tptp.hAPP_f230953622l_bool tptp.minus_1290075917l_bool A))) (= (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.hAPP_f559147733l_bool _let_1 (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool A_4) B)))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.hAPP_f559147733l_bool _let_1 B)))))) (forall ((A tptp.fun_fu1996308102l_bool) (A_4 tptp.fun_Ho320143120e_bool) (B tptp.fun_fu1996308102l_bool)) (let ((_let_1 (tptp.hAPP_f1175211816l_bool tptp.minus_1119384757l_bool A))) (= (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool (tptp.hAPP_f85652879l_bool _let_1 (tptp.hAPP_f85652879l_bool (tptp.hAPP_f1941218614l_bool tptp.insert975831690e_bool A_4) B)))) (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool (tptp.hAPP_f85652879l_bool _let_1 B)))))) (forall ((F tptp.fun_pn1262351275_state) (A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (let ((_let_1 (tptp.image_1918575693_state F))) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.minus_1060678561e_bool (tptp.hAPP_f1763243027e_bool _let_1 A)) (tptp.hAPP_f1763243027e_bool _let_1 B))) (tptp.hAPP_f1763243027e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A) B)))))) (forall ((A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) B)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool B) A)) B))) (forall ((A tptp.fun_Ho320143120e_bool) (B tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool A) B)) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool A) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.minus_1060678561e_bool B) A)) B))) (forall ((A tptp.fun_pname_bool) (B tptp.fun_pname_bool) (C_1 tptp.fun_pname_bool)) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A) B)) C_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool B) C_1))))) (forall ((A tptp.fun_Ho320143120e_bool) (B tptp.fun_Ho320143120e_bool) (C_1 tptp.fun_Ho320143120e_bool)) (= (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.minus_1060678561e_bool A) B)) C_1)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool A) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool B) C_1))))) (forall ((F tptp.fun_pn1262351275_state) (A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (let ((_let_1 (tptp.image_1918575693_state F))) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool (tptp.hAPP_f1763243027e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A) B))) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool (tptp.hAPP_f1763243027e_bool _let_1 A)) (tptp.hAPP_f1763243027e_bool _let_1 B)))))) (forall ((A tptp.fun_pname_bool) (B tptp.fun_pname_bool) (C_1 tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A))) (= (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool (tptp.hAPP_f759274231e_bool _let_1 B)) C_1) (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool B) C_1))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool C_1) A))))) (forall ((A tptp.fun_Ho320143120e_bool) (B tptp.fun_Ho320143120e_bool) (C_1 tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool A))) (= (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool (tptp.hAPP_f1749453397e_bool _let_1 B)) C_1) (tptp.hAPP_f1749453397e_bool _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool B) C_1))) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool C_1) A))))) (forall ((P_1 tptp.fun_pname_bool) (F tptp.fun_pn1262351275_state) (G tptp.fun_pn1262351275_state) (S tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool S))) (= (tptp.hAPP_f1763243027e_bool (tptp.image_1918575693_state (tptp.hAPP_f901668953_state (tptp.hAPP_f1521026326_state tptp.cOMBS_113846849_state (tptp.hAPP_f1180972108_state (tptp.hAPP_f1993951364_state tptp.cOMBS_89825358_state (tptp.hAPP_f1418159294_state (tptp.cOMBB_1777678681_pname tptp.if_Hoa29189214_state) P_1)) F)) G)) S) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool (tptp.hAPP_f1763243027e_bool (tptp.image_1918575693_state F) (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool tptp.collect_pname P_1)))) (tptp.hAPP_f1763243027e_bool (tptp.image_1918575693_state G) (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool tptp.collect_pname (tptp.hAPP_f759274231e_bool (tptp.cOMBB_647938656_pname tptp.fNot) P_1)))))))) (forall ((P_1 tptp.fun_pname_bool) (F tptp.fun_pname_option_com) (G tptp.fun_pname_option_com)) (= (tptp.dom_pname_com (tptp.hAPP_f2123220539on_com (tptp.hAPP_f1673966486on_com tptp.cOMBS_904531235on_com (tptp.hAPP_f648377725on_com (tptp.hAPP_f2093196134on_com tptp.cOMBS_1529518335on_com (tptp.hAPP_f755519727on_com (tptp.cOMBB_1394247784_pname tptp.if_option_com) P_1)) F)) G)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool (tptp.dom_pname_com F)) (tptp.hAPP_f759274231e_bool tptp.collect_pname P_1))) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool (tptp.dom_pname_com G)) (tptp.hAPP_f759274231e_bool tptp.collect_pname (tptp.hAPP_f759274231e_bool (tptp.cOMBB_647938656_pname tptp.fNot) P_1)))))) (forall ((A tptp.fun_com_bool) (X_1 tptp.com) (B tptp.fun_com_bool)) (let ((_let_1 (tptp.hAPP_c566651504m_bool tptp.insert_com X_1))) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_f273696895l_bool tptp.ord_le1708315510m_bool (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.minus_59609839m_bool A) (tptp.hAPP_f1682609283m_bool _let_1 tptp.bot_bot_fun_com_bool))) B)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_1) A)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_f273696895l_bool tptp.ord_le1708315510m_bool A) (tptp.hAPP_f1682609283m_bool _let_1 B))))))) (forall ((A tptp.fun_pname_bool) (X_1 tptp.pname) (B tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A) (tptp.hAPP_f759274231e_bool _let_1 tptp.bot_bo844097828e_bool))) B)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) (tptp.hAPP_f759274231e_bool _let_1 B))))))) (forall ((A tptp.fun_Ho320143120e_bool) (X_1 tptp.hoare_363350478_state) (B tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state X_1))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.minus_1060678561e_bool A) (tptp.hAPP_f1749453397e_bool _let_1 tptp.bot_bo39439654e_bool))) B)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state X_1) A)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool A) (tptp.hAPP_f1749453397e_bool _let_1 B))))))) (forall ((A tptp.fun_com_bool) (X_1 tptp.com) (B tptp.fun_com_bool)) (let ((_let_1 (tptp.hAPP_f273696895l_bool tptp.ord_le1708315510m_bool A))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_1) A)))) (let ((_let_3 (tptp.hAPP_c566651504m_bool tptp.insert_com X_1))) (= (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 (tptp.hAPP_f1682609283m_bool _let_3 B))) (and (=> _let_2 (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_f273696895l_bool tptp.ord_le1708315510m_bool (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.minus_59609839m_bool A) (tptp.hAPP_f1682609283m_bool _let_3 tptp.bot_bot_fun_com_bool))) B))) (=> (not _let_2) (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 B))))))))) (forall ((A tptp.fun_pname_bool) (X_1 tptp.pname) (B tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A)))) (let ((_let_3 (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1))) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool _let_3 B))) (and (=> _let_2 (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A) (tptp.hAPP_f759274231e_bool _let_3 tptp.bot_bo844097828e_bool))) B))) (=> (not _let_2) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B))))))))) (forall ((A tptp.fun_Ho320143120e_bool) (X_1 tptp.hoare_363350478_state) (B tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool A))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state X_1) A)))) (let ((_let_3 (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state X_1))) (= (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 (tptp.hAPP_f1749453397e_bool _let_3 B))) (and (=> _let_2 (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.minus_1060678561e_bool A) (tptp.hAPP_f1749453397e_bool _let_3 tptp.bot_bo39439654e_bool))) B))) (=> (not _let_2) (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 B))))))))) (forall ((P_1 tptp.fun_fu1362071682l_bool) (A tptp.fun_com_bool)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool tptp.finite_finite_com A)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool P_1 A)) (=> (forall ((A_2 tptp.com) (A_7 tptp.fun_com_bool)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool tptp.finite_finite_com A_7)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com A_2) A_7)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool P_1 A_7)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool P_1 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.minus_59609839m_bool A_7) (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com A_2) tptp.bot_bot_fun_com_bool)))))))) (tptp.hBOOL (tptp.hAPP_f990396704l_bool P_1 tptp.bot_bot_fun_com_bool)))))) (forall ((P_1 tptp.fun_fu1430349052l_bool) (A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 A)) (=> (forall ((A_2 tptp.pname) (A_7 tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A_7)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A_2) A_7)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 A_7)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A_7) (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A_2) tptp.bot_bo844097828e_bool)))))))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 tptp.bot_bo844097828e_bool)))))) (forall ((P_1 tptp.fun_fu1996308102l_bool) (A tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state A)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool P_1 A)) (=> (forall ((A_2 tptp.hoare_363350478_state) (A_7 tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state A_7)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state A_2) A_7)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool P_1 A_7)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool P_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.minus_1060678561e_bool A_7) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state A_2) tptp.bot_bo39439654e_bool)))))))) (tptp.hBOOL (tptp.hAPP_f568432088l_bool P_1 tptp.bot_bo39439654e_bool)))))) (forall ((P_1 tptp.fun_fu399576434l_bool) (A tptp.fun_fu1430349052l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool P_1 A)) (=> (forall ((A_2 tptp.fun_pname_bool) (A_7 tptp.fun_fu1430349052l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A_7)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool A_2) A_7)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool P_1 A_7)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool P_1 (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.minus_1290075917l_bool A_7) (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool A_2) tptp.bot_bo1649642514l_bool)))))))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool P_1 tptp.bot_bo1649642514l_bool)))))) (forall ((P_1 tptp.fun_fu1972704968l_bool) (A tptp.fun_fu1996308102l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool P_1 A)) (=> (forall ((A_2 tptp.fun_Ho320143120e_bool) (A_7 tptp.fun_fu1996308102l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool A_7)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool (tptp.hAPP_f1610329741l_bool tptp.member1534059107e_bool A_2) A_7)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool P_1 A_7)) (tptp.hBOOL (tptp.hAPP_f1287348838l_bool P_1 (tptp.hAPP_f85652879l_bool (tptp.hAPP_f1175211816l_bool tptp.minus_1119384757l_bool A_7) (tptp.hAPP_f85652879l_bool (tptp.hAPP_f1941218614l_bool tptp.insert975831690e_bool A_2) tptp.bot_bo133096688l_bool)))))))) (tptp.hBOOL (tptp.hAPP_f1287348838l_bool P_1 tptp.bot_bo133096688l_bool)))))) (forall ((F tptp.fun_pname_option_com) (G tptp.fun_pname_option_com) (A tptp.fun_pname_bool)) (let ((_let_1 (tptp.dom_pname_com G))) (let ((_let_2 (tptp.hAPP_f661147897e_bool tptp.cOMBC_1058051404l_bool tptp.member_pname))) (= (tptp.dom_pname_com (tptp.overri1496249029on_com F G A)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool (tptp.dom_pname_com F)) (tptp.hAPP_f759274231e_bool tptp.collect_pname (tptp.hAPP_f759274231e_bool _let_2 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A) _let_1))))) (tptp.hAPP_f759274231e_bool tptp.collect_pname (tptp.hAPP_f759274231e_bool _let_2 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A) _let_1)))))))) (forall ((Q_1 tptp.fun_com_bool) (P_1 tptp.fun_com_bool) (A tptp.fun_com_bool) (B tptp.fun_com_bool)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_f273696895l_bool tptp.ord_le1708315510m_bool A) B)) (=> (forall ((X_2 tptp.com)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_2) A)) (=> (tptp.hBOOL (tptp.hAPP_com_bool P_1 X_2)) (tptp.hBOOL (tptp.hAPP_com_bool Q_1 X_2))))) (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_f273696895l_bool tptp.ord_le1708315510m_bool (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila980496562m_bool A) (tptp.hAPP_f1682609283m_bool tptp.collect_com P_1))) (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila980496562m_bool B) (tptp.hAPP_f1682609283m_bool tptp.collect_com Q_1))))))) (forall ((Q_1 tptp.fun_pname_bool) (P_1 tptp.fun_pname_bool) (A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) B)) (=> (forall ((X_2 tptp.pname)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A)) (=> (tptp.hBOOL (tptp.hAPP_pname_bool P_1 X_2)) (tptp.hBOOL (tptp.hAPP_pname_bool Q_1 X_2))))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A) (tptp.hAPP_f759274231e_bool tptp.collect_pname P_1))) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool B) (tptp.hAPP_f759274231e_bool tptp.collect_pname Q_1))))))) (forall ((Q_1 tptp.fun_Ho320143120e_bool) (P_1 tptp.fun_Ho320143120e_bool) (A tptp.fun_Ho320143120e_bool) (B tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool A) B)) (=> (forall ((X_2 tptp.hoare_363350478_state)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state X_2) A)) (=> (tptp.hBOOL (tptp.hAPP_H1645464494e_bool P_1 X_2)) (tptp.hBOOL (tptp.hAPP_H1645464494e_bool Q_1 X_2))))) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool A) (tptp.hAPP_f1749453397e_bool tptp.collec223185785_state P_1))) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool B) (tptp.hAPP_f1749453397e_bool tptp.collec223185785_state Q_1))))))) (forall ((Q_1 tptp.fun_fu1430349052l_bool) (P_1 tptp.fun_fu1430349052l_bool) (A tptp.fun_fu1430349052l_bool) (B tptp.fun_fu1430349052l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool A) B)) (=> (forall ((X_2 tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool X_2) A)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 X_2)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool Q_1 X_2))))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.semila1130628874l_bool A) (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool P_1))) (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.semila1130628874l_bool B) (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool Q_1))))))) (forall ((Q_1 tptp.fun_fu1996308102l_bool) (P_1 tptp.fun_fu1996308102l_bool) (A tptp.fun_fu1996308102l_bool) (B tptp.fun_fu1996308102l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool (tptp.hAPP_f746351743l_bool tptp.ord_le2031828156l_bool A) B)) (=> (forall ((X_2 tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool (tptp.hAPP_f1610329741l_bool tptp.member1534059107e_bool X_2) A)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool P_1 X_2)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool Q_1 X_2))))) (tptp.hBOOL (tptp.hAPP_f1287348838l_bool (tptp.hAPP_f746351743l_bool tptp.ord_le2031828156l_bool (tptp.hAPP_f85652879l_bool (tptp.hAPP_f1175211816l_bool tptp.semila218417144l_bool A) (tptp.hAPP_f85652879l_bool tptp.collec1243131813e_bool P_1))) (tptp.hAPP_f85652879l_bool (tptp.hAPP_f1175211816l_bool tptp.semila218417144l_bool B) (tptp.hAPP_f85652879l_bool tptp.collec1243131813e_bool Q_1))))))) (forall ((X_1 tptp.bool) (Y_2 tptp.bool) (Z tptp.bool)) (let ((_let_1 (tptp.hAPP_b589554111l_bool tptp.semila310582991f_bool X_1))) (=> (forall ((X_2 tptp.bool) (Y_3 tptp.bool) (Z_1 tptp.bool)) (let ((_let_1 (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool X_2))) (= (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila310582991f_bool Y_3) Z_1))) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila310582991f_bool (tptp.hAPP_bool_bool _let_1 Y_3)) (tptp.hAPP_bool_bool _let_1 Z_1)))))) (= (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool Y_2) Z))) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool (tptp.hAPP_bool_bool _let_1 Y_2)) (tptp.hAPP_bool_bool _let_1 Z))))))) (forall ((X_1 tptp.fun_pname_bool) (Y_2 tptp.fun_pname_bool) (Z tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool X_1))) (=> (forall ((X_2 tptp.fun_pname_bool) (Y_3 tptp.fun_pname_bool) (Z_1 tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool X_2))) (= (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool Y_3) Z_1)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool (tptp.hAPP_f759274231e_bool _let_1 Y_3)) (tptp.hAPP_f759274231e_bool _let_1 Z_1))))) (= (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool Y_2) Z)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool (tptp.hAPP_f759274231e_bool _let_1 Y_2)) (tptp.hAPP_f759274231e_bool _let_1 Z)))))) (forall ((X_1 tptp.fun_Ho320143120e_bool) (Y_2 tptp.fun_Ho320143120e_bool) (Z tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool X_1))) (=> (forall ((X_2 tptp.fun_Ho320143120e_bool) (Y_3 tptp.fun_Ho320143120e_bool) (Z_1 tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool X_2))) (= (tptp.hAPP_f1749453397e_bool _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool Y_3) Z_1)) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool (tptp.hAPP_f1749453397e_bool _let_1 Y_3)) (tptp.hAPP_f1749453397e_bool _let_1 Z_1))))) (= (tptp.hAPP_f1749453397e_bool _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool Y_2) Z)) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool (tptp.hAPP_f1749453397e_bool _let_1 Y_2)) (tptp.hAPP_f1749453397e_bool _let_1 Z)))))) (forall ((X_1 tptp.bool) (Y_2 tptp.bool) (Z tptp.bool)) (let ((_let_1 (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool X_1))) (=> (forall ((X_2 tptp.bool) (Y_3 tptp.bool) (Z_1 tptp.bool)) (let ((_let_1 (tptp.hAPP_b589554111l_bool tptp.semila310582991f_bool X_2))) (= (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool Y_3) Z_1))) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool (tptp.hAPP_bool_bool _let_1 Y_3)) (tptp.hAPP_bool_bool _let_1 Z_1)))))) (= (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila310582991f_bool Y_2) Z))) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila310582991f_bool (tptp.hAPP_bool_bool _let_1 Y_2)) (tptp.hAPP_bool_bool _let_1 Z))))))) (forall ((X_1 tptp.fun_pname_bool) (Y_2 tptp.fun_pname_bool) (Z tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool X_1))) (=> (forall ((X_2 tptp.fun_pname_bool) (Y_3 tptp.fun_pname_bool) (Z_1 tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool X_2))) (= (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool Y_3) Z_1)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool (tptp.hAPP_f759274231e_bool _let_1 Y_3)) (tptp.hAPP_f759274231e_bool _let_1 Z_1))))) (= (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool Y_2) Z)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool (tptp.hAPP_f759274231e_bool _let_1 Y_2)) (tptp.hAPP_f759274231e_bool _let_1 Z)))))) (forall ((X_1 tptp.fun_Ho320143120e_bool) (Y_2 tptp.fun_Ho320143120e_bool) (Z tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool X_1))) (=> (forall ((X_2 tptp.fun_Ho320143120e_bool) (Y_3 tptp.fun_Ho320143120e_bool) (Z_1 tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool X_2))) (= (tptp.hAPP_f1749453397e_bool _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool Y_3) Z_1)) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool (tptp.hAPP_f1749453397e_bool _let_1 Y_3)) (tptp.hAPP_f1749453397e_bool _let_1 Z_1))))) (= (tptp.hAPP_f1749453397e_bool _let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool Y_2) Z)) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool (tptp.hAPP_f1749453397e_bool _let_1 Y_2)) (tptp.hAPP_f1749453397e_bool _let_1 Z)))))) (forall ((A tptp.fun_com_bool) (B_1 tptp.com)) (let ((_let_1 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com B_1) tptp.bot_bot_fun_com_bool))) (let ((_let_2 (tptp.hAPP_f1276420679ol_com (tptp.partial_flat_lub_com B_1) A))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_f273696895l_bool tptp.ord_le1708315510m_bool A) _let_1)))) (and (=> _let_3 (= _let_2 B_1)) (=> (not _let_3) (= _let_2 (tptp.hAPP_f1276420679ol_com tptp.the_com_1 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f578650245m_bool tptp.cOMBC_1904837336l_bool tptp.member_com) (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.minus_59609839m_bool A) _let_1)))))))))) (forall ((A tptp.fun_pname_bool) (B_1 tptp.pname)) (let ((_let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname B_1) tptp.bot_bo844097828e_bool))) (let ((_let_2 (tptp.hAPP_f1297739591_pname (tptp.partia752020666_pname B_1) A))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) _let_1)))) (and (=> _let_3 (= _let_2 B_1)) (=> (not _let_3) (= _let_2 (tptp.hAPP_f1297739591_pname tptp.the_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_f661147897e_bool tptp.cOMBC_1058051404l_bool tptp.member_pname) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A) _let_1)))))))))) (forall ((A tptp.fun_Ho320143120e_bool) (B_1 tptp.hoare_363350478_state)) (let ((_let_1 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state B_1) tptp.bot_bo39439654e_bool))) (let ((_let_2 (tptp.hAPP_f1242401993_state (tptp.partia2058675160_state B_1) A))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool A) _let_1)))) (and (=> _let_3 (= _let_2 B_1)) (=> (not _let_3) (= _let_2 (tptp.hAPP_f1242401993_state tptp.the_Ho1653144541_state (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1072682137e_bool tptp.cOMBC_1415895650l_bool tptp.member1253905979_state) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.minus_1060678561e_bool A) _let_1)))))))))) (tptp.hBOOL (tptp.finite1653727294m_bool (tptp.hAPP_f57617970m_bool (tptp.cOMBB_2112550369ol_com (tptp.hAPP_f1898485935m_bool tptp.cOMBC_788185579m_bool tptp.minus_59609839m_bool)) (tptp.hAPP_f721468006m_bool (tptp.hAPP_f947797701m_bool tptp.cOMBC_1977231931m_bool tptp.insert_com) tptp.bot_bot_fun_com_bool)))) (tptp.hBOOL (tptp.finite2017903282e_bool (tptp.hAPP_f647826488e_bool (tptp.cOMBB_1919352417_pname (tptp.hAPP_f182188835e_bool tptp.cOMBC_1880008793e_bool tptp.minus_1015773161e_bool)) (tptp.hAPP_f180827860e_bool (tptp.hAPP_f698292281e_bool tptp.cOMBC_1123258281e_bool tptp.insert_pname) tptp.bot_bo844097828e_bool)))) (tptp.hBOOL (tptp.finite377806280e_bool (tptp.hAPP_f306007574e_bool (tptp.cOMBB_1253415543_state (tptp.hAPP_f1873524693e_bool tptp.cOMBC_1626046675e_bool tptp.minus_1060678561e_bool)) (tptp.hAPP_f596150574e_bool (tptp.hAPP_f961492031e_bool tptp.cOMBC_1774708299e_bool tptp.insert1330351828_state) tptp.bot_bo39439654e_bool)))) (forall ((F tptp.fun_pn1262351275_state) (Y_2 tptp.hoare_363350478_state) (X_1 tptp.pname) (A tptp.fun_pname_bool)) (let ((_let_1 (tptp.image_1918575693_state F))) (let ((_let_2 (tptp.hAPP_f1763243027e_bool (tptp.image_1918575693_state (tptp.fun_up641226197_state F X_1 Y_2)) A))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A)))) (and (=> _let_3 (= _let_2 (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state Y_2) (tptp.hAPP_f1763243027e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A) (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1) tptp.bot_bo844097828e_bool)))))) (=> (not _let_3) (= _let_2 (tptp.hAPP_f1763243027e_bool _let_1 A)))))))) (tptp.hBOOL (tptp.finite1653727294m_bool tptp.insert_com)) (tptp.hBOOL (tptp.finite2017903282e_bool tptp.insert_pname)) (tptp.hBOOL (tptp.finite377806280e_bool tptp.insert1330351828_state)) (tptp.hBOOL (tptp.finite318301748l_bool tptp.semila1168014441p_bool)) (tptp.hBOOL (tptp.finite367769966e_bool tptp.semila278973382e_bool)) (tptp.hBOOL (tptp.finite560903500e_bool tptp.semila1579166468e_bool)) (forall ((F tptp.fun_pn1262351275_state) (A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (let ((_let_1 (tptp.image_1918575693_state F))) (let ((_let_2 (tptp.inj_on207592417_state F))) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_2 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A) B))) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_2 A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_2 B)) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool (tptp.hAPP_f1763243027e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A) B))) (tptp.hAPP_f1763243027e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool B) A))) tptp.bot_bo39439654e_bool)))))) (forall ((F tptp.fun_pname_option_com) (X_1 tptp.pname)) (= (= (tptp.dom_pname_com F) (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1) tptp.bot_bo844097828e_bool)) (exists ((V tptp.com)) (= F (tptp.fun_up879233478on_com (tptp.hAPP_o129566686on_com tptp.cOMBK_413306633_pname tptp.none_com) X_1 (tptp.hAPP_com_option_com tptp.some_com V)))))) (forall ((B tptp.fun_com_bool) (A tptp.fun_com_bool)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool tptp.finite_finite_com A)) (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.minus_59609839m_bool B) A) (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool (tptp.finite1275301314m_bool (tptp.hAPP_f57617970m_bool (tptp.cOMBB_2112550369ol_com (tptp.hAPP_f1898485935m_bool tptp.cOMBC_788185579m_bool tptp.minus_59609839m_bool)) (tptp.hAPP_f721468006m_bool (tptp.hAPP_f947797701m_bool tptp.cOMBC_1977231931m_bool tptp.insert_com) tptp.bot_bot_fun_com_bool))) B) A)))) (forall ((B tptp.fun_pname_bool) (A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool B) A) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool (tptp.finite315386934e_bool (tptp.hAPP_f647826488e_bool (tptp.cOMBB_1919352417_pname (tptp.hAPP_f182188835e_bool tptp.cOMBC_1880008793e_bool tptp.minus_1015773161e_bool)) (tptp.hAPP_f180827860e_bool (tptp.hAPP_f698292281e_bool tptp.cOMBC_1123258281e_bool tptp.insert_pname) tptp.bot_bo844097828e_bool))) B) A)))) (forall ((B tptp.fun_Ho320143120e_bool) (A tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state A)) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.minus_1060678561e_bool B) A) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool (tptp.finite1720034636e_bool (tptp.hAPP_f306007574e_bool (tptp.cOMBB_1253415543_state (tptp.hAPP_f1873524693e_bool tptp.cOMBC_1626046675e_bool tptp.minus_1060678561e_bool)) (tptp.hAPP_f596150574e_bool (tptp.hAPP_f961492031e_bool tptp.cOMBC_1774708299e_bool tptp.insert1330351828_state) tptp.bot_bo39439654e_bool))) B) A)))) (forall ((B tptp.fun_fu1430349052l_bool) (A tptp.fun_fu1430349052l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)) (= (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.minus_1290075917l_bool B) A) (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool (tptp.finite1627341516l_bool (tptp.hAPP_f1149191722l_bool (tptp.cOMBB_631815671e_bool (tptp.hAPP_f1477350485l_bool tptp.cOMBC_694979519l_bool tptp.minus_1290075917l_bool)) (tptp.hAPP_f417341722l_bool (tptp.hAPP_f836143551l_bool tptp.cOMBC_772615479l_bool tptp.insert1325755072e_bool) tptp.bot_bo1649642514l_bool))) B) A)))) (forall ((B tptp.fun_fu1996308102l_bool) (A tptp.fun_fu1996308102l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool A)) (= (tptp.hAPP_f85652879l_bool (tptp.hAPP_f1175211816l_bool tptp.minus_1119384757l_bool B) A) (tptp.hAPP_f85652879l_bool (tptp.hAPP_f1175211816l_bool (tptp.finite1820487374l_bool (tptp.hAPP_f471491948l_bool (tptp.cOMBB_460931425e_bool (tptp.hAPP_f103280059l_bool tptp.cOMBC_646647229l_bool tptp.minus_1119384757l_bool)) (tptp.hAPP_f434845752l_bool (tptp.hAPP_f1793815761l_bool tptp.cOMBC_2079418125l_bool tptp.insert975831690e_bool) tptp.bot_bo133096688l_bool))) B) A)))) (forall ((F tptp.fun_pn1262351275_state) (A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (= (tptp.hAPP_f1763243027e_bool (tptp.image_1918575693_state F) A) (tptp.finite517504007_pname tptp.semila1579166468e_bool (tptp.hAPP_f265219918e_bool (tptp.hAPP_f1853922773e_bool tptp.cOMBC_1001821703e_bool (tptp.hAPP_f43306888e_bool (tptp.cOMBB_1717464465_pname tptp.insert1330351828_state) F)) tptp.bot_bo39439654e_bool) tptp.bot_bo39439654e_bool A)))) (forall ((A tptp.fun_pname_bool)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.inj_on737724108_pname tptp.some_pname) A))) (forall ((A tptp.fun_Ho320143120e_bool)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.inj_on574065538_state tptp.some_H629028223_state) A))) (forall ((A tptp.fun_com_bool)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.inj_on11367768on_com tptp.some_com) A))) (forall ((A_6 tptp.com)) (not (= tptp.none_com (tptp.hAPP_com_option_com tptp.some_com A_6)))) (forall ((A_6 tptp.pname)) (not (= tptp.none_pname (tptp.hAPP_p1252095976_pname tptp.some_pname A_6)))) (forall ((A_6 tptp.hoare_363350478_state)) (not (= tptp.none_H1908530691_state (tptp.hAPP_H1942146718_state tptp.some_H629028223_state A_6)))) (forall ((A_5 tptp.com)) (not (= (tptp.hAPP_com_option_com tptp.some_com A_5) tptp.none_com))) (forall ((A_5 tptp.pname)) (not (= (tptp.hAPP_p1252095976_pname tptp.some_pname A_5) tptp.none_pname))) (forall ((A_5 tptp.hoare_363350478_state)) (not (= (tptp.hAPP_H1942146718_state tptp.some_H629028223_state A_5) tptp.none_H1908530691_state))) (forall ((X_1 tptp.option_com)) (= (forall ((Y_3 tptp.com)) (not (= X_1 (tptp.hAPP_com_option_com tptp.some_com Y_3)))) (= X_1 tptp.none_com))) (forall ((X_1 tptp.option_pname)) (= (forall ((Y_3 tptp.pname)) (not (= X_1 (tptp.hAPP_p1252095976_pname tptp.some_pname Y_3)))) (= X_1 tptp.none_pname))) (forall ((X_1 tptp.option131732143_state)) (= (forall ((Y_3 tptp.hoare_363350478_state)) (not (= X_1 (tptp.hAPP_H1942146718_state tptp.some_H629028223_state Y_3)))) (= X_1 tptp.none_H1908530691_state))) (forall ((X_1 tptp.option_com)) (= (not (= X_1 tptp.none_com)) (exists ((Y_3 tptp.com)) (= X_1 (tptp.hAPP_com_option_com tptp.some_com Y_3))))) (forall ((X_1 tptp.option_pname)) (= (not (= X_1 tptp.none_pname)) (exists ((Y_3 tptp.pname)) (= X_1 (tptp.hAPP_p1252095976_pname tptp.some_pname Y_3))))) (forall ((X_1 tptp.option131732143_state)) (= (not (= X_1 tptp.none_H1908530691_state)) (exists ((Y_3 tptp.hoare_363350478_state)) (= X_1 (tptp.hAPP_H1942146718_state tptp.some_H629028223_state Y_3))))) (forall ((M tptp.fun_pname_option_com)) (= (tptp.dom_pname_com M) (tptp.hAPP_f759274231e_bool tptp.collect_pname (tptp.hAPP_f759274231e_bool (tptp.cOMBB_647938656_pname tptp.fNot) (tptp.hAPP_o1092643708e_bool (tptp.hAPP_f837293113e_bool tptp.cOMBC_1381995473m_bool (tptp.hAPP_f919496731m_bool (tptp.cOMBB_418828222_pname tptp.fequal_option_com) M)) tptp.none_com))))) (forall ((A_4 tptp.pname) (M tptp.fun_pname_option_com)) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A_4) (tptp.dom_pname_com M))) (not (= (tptp.hAPP_p799580910on_com M A_4) tptp.none_com)))) (forall ((F tptp.fun_pn1262351275_state) (A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state (tptp.hAPP_f1763243027e_bool (tptp.image_1918575693_state F) A))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.inj_on207592417_state F) A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A))))) (forall ((F tptp.fun_pn1262351275_state) (A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (let ((_let_1 (tptp.image_1918575693_state F))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.inj_on207592417_state F) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A) B))) (= (= (tptp.hAPP_f1763243027e_bool _let_1 A) (tptp.hAPP_f1763243027e_bool _let_1 B)) (= A B))))) (forall ((X_1 tptp.option_com)) (= (tptp.hBOOL (tptp.is_none_com X_1)) (= X_1 tptp.none_com))) (tptp.hBOOL (tptp.is_none_com tptp.none_com)) (forall ((X_1 tptp.pname) (Y_2 tptp.hoare_363350478_state) (F tptp.fun_pn1262351275_state) (A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.inj_on207592417_state F) A)) (=> (not (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state Y_2) (tptp.hAPP_f1763243027e_bool (tptp.image_1918575693_state F) A)))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.inj_on207592417_state (tptp.fun_up641226197_state F X_1 Y_2)) A))))) (forall ((B_1 tptp.fun_pname_bool) (A_4 tptp.fun_pname_bool) (A tptp.fun_fu1430349052l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool A_4) A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A_4) B_1)) (tptp.hAPP_f674760225e_bool (tptp.hAPP_f246190092e_bool (tptp.finite446335722e_bool tptp.semila278973382e_bool) B_1) A)))))) (forall ((B_1 tptp.fun_Ho320143120e_bool) (A_4 tptp.fun_Ho320143120e_bool) (A tptp.fun_fu1996308102l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool (tptp.hAPP_f1610329741l_bool tptp.member1534059107e_bool A_4) A)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool A_4) B_1)) (tptp.hAPP_f1180969799e_bool (tptp.hAPP_f644061942e_bool (tptp.finite1334634696e_bool tptp.semila1579166468e_bool) B_1) A)))))) (forall ((B_1 tptp.bool) (A_4 tptp.bool) (A tptp.fun_bool_bool)) (=> (tptp.hBOOL (tptp.hAPP_f387058535l_bool tptp.finite_finite_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.hAPP_b1787118453l_bool tptp.member_bool A_4) A)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool A_4) B_1)) (tptp.hAPP_f387058535l_bool (tptp.hAPP_b1787118453l_bool (tptp.finite1909292976l_bool tptp.semila1168014441p_bool) B_1) A)))))) (forall ((B_1 tptp.fun_pname_bool) (A_4 tptp.fun_pname_bool) (A tptp.fun_fu1430349052l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool A_4) A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f674760225e_bool (tptp.hAPP_f246190092e_bool (tptp.finite446335722e_bool tptp.semila1635148844e_bool) B_1) A)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A_4) B_1)))))) (forall ((B_1 tptp.fun_Ho320143120e_bool) (A_4 tptp.fun_Ho320143120e_bool) (A tptp.fun_fu1996308102l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool (tptp.hAPP_f1610329741l_bool tptp.member1534059107e_bool A_4) A)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool (tptp.hAPP_f1180969799e_bool (tptp.hAPP_f644061942e_bool (tptp.finite1334634696e_bool tptp.semila1129477150e_bool) B_1) A)) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool A_4) B_1)))))) (forall ((B_1 tptp.bool) (A_4 tptp.bool) (A tptp.fun_bool_bool)) (=> (tptp.hBOOL (tptp.hAPP_f387058535l_bool tptp.finite_finite_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.hAPP_b1787118453l_bool tptp.member_bool A_4) A)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_f387058535l_bool (tptp.hAPP_b1787118453l_bool (tptp.finite1909292976l_bool tptp.semila310582991f_bool) B_1) A)) (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila310582991f_bool A_4) B_1)))))) (forall ((B_1 tptp.fun_pname_bool) (A_4 tptp.fun_pname_bool) (A tptp.fun_fu1430349052l_bool)) (let ((_let_1 (tptp.hAPP_f246190092e_bool (tptp.finite446335722e_bool tptp.semila278973382e_bool) B_1))) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)) (= (tptp.hAPP_f674760225e_bool _let_1 (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool A_4) A)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A_4) (tptp.hAPP_f674760225e_bool _let_1 A)))))) (forall ((B_1 tptp.fun_Ho320143120e_bool) (A_4 tptp.fun_Ho320143120e_bool) (A tptp.fun_fu1996308102l_bool)) (let ((_let_1 (tptp.hAPP_f644061942e_bool (tptp.finite1334634696e_bool tptp.semila1579166468e_bool) B_1))) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool A)) (= (tptp.hAPP_f1180969799e_bool _let_1 (tptp.hAPP_f85652879l_bool (tptp.hAPP_f1941218614l_bool tptp.insert975831690e_bool A_4) A)) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool A_4) (tptp.hAPP_f1180969799e_bool _let_1 A)))))) (forall ((B_1 tptp.bool) (A_4 tptp.bool) (A tptp.fun_bool_bool)) (let ((_let_1 (tptp.hAPP_b1787118453l_bool (tptp.finite1909292976l_bool tptp.semila1168014441p_bool) B_1))) (=> (tptp.hBOOL (tptp.hAPP_f387058535l_bool tptp.finite_finite_bool A)) (= (tptp.hBOOL (tptp.hAPP_f387058535l_bool _let_1 (tptp.hAPP_f961197973l_bool (tptp.hAPP_b496459037l_bool tptp.insert_bool A_4) A))) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool A_4) (tptp.hAPP_f387058535l_bool _let_1 A))))))) (forall ((B_1 tptp.fun_pname_bool) (A_4 tptp.fun_pname_bool) (A tptp.fun_fu1430349052l_bool)) (let ((_let_1 (tptp.hAPP_f246190092e_bool (tptp.finite446335722e_bool tptp.semila1635148844e_bool) B_1))) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)) (= (tptp.hAPP_f674760225e_bool _let_1 (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool A_4) A)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A_4) (tptp.hAPP_f674760225e_bool _let_1 A)))))) (forall ((B_1 tptp.fun_Ho320143120e_bool) (A_4 tptp.fun_Ho320143120e_bool) (A tptp.fun_fu1996308102l_bool)) (let ((_let_1 (tptp.hAPP_f644061942e_bool (tptp.finite1334634696e_bool tptp.semila1129477150e_bool) B_1))) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool A)) (= (tptp.hAPP_f1180969799e_bool _let_1 (tptp.hAPP_f85652879l_bool (tptp.hAPP_f1941218614l_bool tptp.insert975831690e_bool A_4) A)) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool A_4) (tptp.hAPP_f1180969799e_bool _let_1 A)))))) (forall ((F tptp.fun_pname_option_com)) (= (= (tptp.dom_pname_com F) tptp.bot_bo844097828e_bool) (forall ((X_2 tptp.pname)) (= (tptp.hAPP_p799580910on_com F X_2) tptp.none_com)))) (= (tptp.dom_pname_com (tptp.hAPP_o129566686on_com tptp.cOMBK_413306633_pname tptp.none_com)) tptp.bot_bo844097828e_bool) (= (tptp.set_com tptp.none_com) tptp.bot_bot_fun_com_bool) (= (tptp.set_pname tptp.none_pname) tptp.bot_bo844097828e_bool) (= (tptp.set_Ho1327198534_state tptp.none_H1908530691_state) tptp.bot_bo39439654e_bool) (forall ((Xo tptp.option_com)) (= (= (tptp.set_com Xo) tptp.bot_bot_fun_com_bool) (= Xo tptp.none_com))) (forall ((Xo tptp.option_pname)) (= (= (tptp.set_pname Xo) tptp.bot_bo844097828e_bool) (= Xo tptp.none_pname))) (forall ((Xo tptp.option131732143_state)) (= (= (tptp.set_Ho1327198534_state Xo) tptp.bot_bo39439654e_bool) (= Xo tptp.none_H1908530691_state))) (forall ((F tptp.fun_fu410713561e_bool) (A tptp.fun_fu1430349052l_bool)) (let ((_let_1 (tptp.hAPP_f559147733l_bool (tptp.image_2063528359e_bool F) A))) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool _let_1) A)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.inj_on1490514707e_bool F) A)) (= _let_1 A)))))) (forall ((F tptp.fun_fu1066574909e_bool) (A tptp.fun_fu1996308102l_bool)) (let ((_let_1 (tptp.hAPP_f85652879l_bool (tptp.image_1332939013e_bool F) A))) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool (tptp.hAPP_f746351743l_bool tptp.ord_le2031828156l_bool _let_1) A)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool (tptp.inj_on938701937e_bool F) A)) (= _let_1 A)))))) (forall ((F tptp.fun_pname_pname) (A tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f759274231e_bool (tptp.image_pname_pname F) A))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool _let_1) A)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.inj_on_pname_pname F) A)) (= _let_1 A)))))) (forall ((F tptp.fun_Ho901937921_state) (A tptp.fun_Ho320143120e_bool)) (let ((_let_1 (tptp.hAPP_f1749453397e_bool (tptp.image_2068641359_state F) A))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state A)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool _let_1) A)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.inj_on1943491515_state F) A)) (= _let_1 A)))))) (forall ((F tptp.fun_fu410713561e_bool) (A tptp.fun_fu1430349052l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool A) (tptp.hAPP_f559147733l_bool (tptp.image_2063528359e_bool F) A))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.inj_on1490514707e_bool F) A))))) (forall ((F tptp.fun_fu1066574909e_bool) (A tptp.fun_fu1996308102l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool (tptp.hAPP_f746351743l_bool tptp.ord_le2031828156l_bool A) (tptp.hAPP_f85652879l_bool (tptp.image_1332939013e_bool F) A))) (tptp.hBOOL (tptp.hAPP_f1287348838l_bool (tptp.inj_on938701937e_bool F) A))))) (forall ((F tptp.fun_pname_pname) (A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) (tptp.hAPP_f759274231e_bool (tptp.image_pname_pname F) A))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.inj_on_pname_pname F) A))))) (forall ((F tptp.fun_Ho901937921_state) (A tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state A)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool A) (tptp.hAPP_f1749453397e_bool (tptp.image_2068641359_state F) A))) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.inj_on1943491515_state F) A))))) (forall ((B tptp.fun_pname_bool) (A tptp.fun_pname_bool) (F tptp.fun_pn1262351275_state) (C_1 tptp.fun_pname_bool)) (let ((_let_1 (tptp.image_1918575693_state F))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.inj_on207592417_state F) C_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) C_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) C_1)) (= (tptp.hAPP_f1763243027e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A) B)) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool (tptp.hAPP_f1763243027e_bool _let_1 A)) (tptp.hAPP_f1763243027e_bool _let_1 B)))))))) (forall ((B tptp.fun_pname_bool) (A tptp.fun_pname_bool) (F tptp.fun_pn1262351275_state) (C_1 tptp.fun_pname_bool)) (let ((_let_1 (tptp.image_1918575693_state F))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.inj_on207592417_state F) C_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) C_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) C_1)) (= (tptp.hAPP_f1763243027e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A) B)) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.minus_1060678561e_bool (tptp.hAPP_f1763243027e_bool _let_1 A)) (tptp.hAPP_f1763243027e_bool _let_1 B)))))))) (forall ((B tptp.fun_com_bool) (A tptp.fun_com_bool)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool tptp.finite_finite_com A)) (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila605046092m_bool A) B) (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool (tptp.finite1275301314m_bool tptp.insert_com) B) A)))) (forall ((B tptp.fun_pname_bool) (A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A) B) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool (tptp.finite315386934e_bool tptp.insert_pname) B) A)))) (forall ((B tptp.fun_Ho320143120e_bool) (A tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state A)) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool A) B) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool (tptp.finite1720034636e_bool tptp.insert1330351828_state) B) A)))) (forall ((B tptp.fun_fu1430349052l_bool) (A tptp.fun_fu1430349052l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)) (= (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.semila1782091504l_bool A) B) (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool (tptp.finite1627341516l_bool tptp.insert1325755072e_bool) B) A)))) (forall ((B tptp.fun_fu1996308102l_bool) (A tptp.fun_fu1996308102l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool A)) (= (tptp.hAPP_f85652879l_bool (tptp.hAPP_f1175211816l_bool tptp.semila862847378l_bool A) B) (tptp.hAPP_f85652879l_bool (tptp.hAPP_f1175211816l_bool (tptp.finite1820487374l_bool tptp.insert975831690e_bool) B) A)))) (forall ((A tptp.fun_pname_bool) (F tptp.fun_pname_option_com) (X_1 tptp.pname)) (let ((_let_1 (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool (tptp.dom_pname_com F)))) (=> (= (tptp.hAPP_p799580910on_com F X_1) tptp.none_com) (= (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1) A)) (tptp.hAPP_f759274231e_bool _let_1 A))))) (forall ((X_1 tptp.bool)) (= (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool X_1) X_1)) (tptp.hBOOL X_1))) (forall ((X_1 tptp.fun_pname_bool)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool X_1) X_1) X_1)) (forall ((X_1 tptp.fun_Ho320143120e_bool)) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool X_1) X_1) X_1)) (forall ((X_1 tptp.com) (A tptp.fun_com_bool) (F tptp.fun_com_fun_com_com) (Fa tptp.fun_fun_com_bool_com)) (=> (tptp.hBOOL (tptp.finite860057415ne_com F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool tptp.finite_finite_com A)) (=> (not (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_1) A))) (= (tptp.hAPP_f1276420679ol_com Fa (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com X_1) A)) (tptp.hAPP_f1276420679ol_com (tptp.hAPP_c1546426672ol_com (tptp.finite_fold_com_com F) X_1) A)))))) (forall ((X_1 tptp.pname) (A tptp.fun_pname_bool) (F tptp.fun_pn1208287926_pname) (Fa tptp.fun_fu1499449723_pname)) (=> (tptp.hBOOL (tptp.finite1282449217_pname F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A))) (= (tptp.hAPP_f1297739591_pname Fa (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1) A)) (tptp.hAPP_f1297739591_pname (tptp.hAPP_p1630511146_pname (tptp.finite1657623752_pname F) X_1) A)))))) (forall ((X_1 tptp.hoare_363350478_state) (A tptp.fun_Ho320143120e_bool) (F tptp.fun_Ho31865764_state) (Fa tptp.fun_fu700438391_state)) (=> (tptp.hBOOL (tptp.finite269920017_state F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state A)) (=> (not (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state X_1) A))) (= (tptp.hAPP_f1242401993_state Fa (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state X_1) A)) (tptp.hAPP_f1242401993_state (tptp.hAPP_H2108048200_state (tptp.finite1620577938_state F) X_1) A)))))) (forall ((X_1 tptp.fun_pname_bool) (A tptp.fun_fu1430349052l_bool) (F tptp.fun_fu2101097872e_bool) (Fa tptp.fun_fu608906319e_bool)) (=> (tptp.hBOOL (tptp.finite1626890877e_bool F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)) (=> (not (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool X_1) A))) (= (tptp.hAPP_f674760225e_bool Fa (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool X_1) A)) (tptp.hAPP_f674760225e_bool (tptp.hAPP_f246190092e_bool (tptp.finite446335722e_bool F) X_1) A)))))) (forall ((X_1 tptp.fun_Ho320143120e_bool) (A tptp.fun_fu1996308102l_bool) (F tptp.fun_fu531943146e_bool) (Fa tptp.fun_fu1671561851e_bool)) (=> (tptp.hBOOL (tptp.finite1264277005e_bool F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool A)) (=> (not (tptp.hBOOL (tptp.hAPP_f1287348838l_bool (tptp.hAPP_f1610329741l_bool tptp.member1534059107e_bool X_1) A))) (= (tptp.hAPP_f1180969799e_bool Fa (tptp.hAPP_f85652879l_bool (tptp.hAPP_f1941218614l_bool tptp.insert975831690e_bool X_1) A)) (tptp.hAPP_f1180969799e_bool (tptp.hAPP_f644061942e_bool (tptp.finite1334634696e_bool F) X_1) A)))))) (forall ((A_4 tptp.com) (A tptp.fun_com_bool) (F tptp.fun_com_fun_com_com) (Fa tptp.fun_fun_com_bool_com)) (=> (tptp.hBOOL (tptp.finite666746948em_com F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool tptp.finite_finite_com A)) (= (tptp.hAPP_f1276420679ol_com Fa (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com A_4) A)) (tptp.hAPP_f1276420679ol_com (tptp.hAPP_c1546426672ol_com (tptp.finite_fold_com_com F) A_4) A))))) (forall ((A_4 tptp.pname) (A tptp.fun_pname_bool) (F tptp.fun_pn1208287926_pname) (Fa tptp.fun_fu1499449723_pname)) (=> (tptp.hBOOL (tptp.finite89670078_pname F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (= (tptp.hAPP_f1297739591_pname Fa (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A_4) A)) (tptp.hAPP_f1297739591_pname (tptp.hAPP_p1630511146_pname (tptp.finite1657623752_pname F) A_4) A))))) (forall ((A_4 tptp.hoare_363350478_state) (A tptp.fun_Ho320143120e_bool) (F tptp.fun_Ho31865764_state) (Fa tptp.fun_fu700438391_state)) (=> (tptp.hBOOL (tptp.finite2031572_state F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state A)) (= (tptp.hAPP_f1242401993_state Fa (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool tptp.insert1330351828_state A_4) A)) (tptp.hAPP_f1242401993_state (tptp.hAPP_H2108048200_state (tptp.finite1620577938_state F) A_4) A))))) (forall ((A_4 tptp.fun_pname_bool) (A tptp.fun_fu1430349052l_bool) (F tptp.fun_fu2101097872e_bool) (Fa tptp.fun_fu608906319e_bool)) (=> (tptp.hBOOL (tptp.finite1268145088e_bool F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)) (= (tptp.hAPP_f674760225e_bool Fa (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool A_4) A)) (tptp.hAPP_f674760225e_bool (tptp.hAPP_f246190092e_bool (tptp.finite446335722e_bool F) A_4) A))))) (forall ((A_4 tptp.fun_Ho320143120e_bool) (A tptp.fun_fu1996308102l_bool) (F tptp.fun_fu531943146e_bool) (Fa tptp.fun_fu1671561851e_bool)) (=> (tptp.hBOOL (tptp.finite2090946954e_bool F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool A)) (= (tptp.hAPP_f1180969799e_bool Fa (tptp.hAPP_f85652879l_bool (tptp.hAPP_f1941218614l_bool tptp.insert975831690e_bool A_4) A)) (tptp.hAPP_f1180969799e_bool (tptp.hAPP_f644061942e_bool (tptp.finite1334634696e_bool F) A_4) A))))) (forall ((Pn tptp.pname)) (=> (not (= (tptp.hAPP_p799580910on_com tptp.body Pn) tptp.none_com)) (tptp.hBOOL (tptp.hAPP_com_bool tptp.wt (tptp.hAPP_pname_com tptp.body_1 Pn))))) (forall ((F tptp.fun_pn1262351275_state) (A_4 tptp.pname) (A tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p905327722e_bool tptp.insert_pname A_4))) (let ((_let_2 (tptp.inj_on207592417_state F))) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_2 (tptp.hAPP_f759274231e_bool _let_1 A))) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_2 A)) (not (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state (tptp.hAPP_p1337579261_state F A_4)) (tptp.hAPP_f1763243027e_bool (tptp.image_1918575693_state F) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A) (tptp.hAPP_f759274231e_bool _let_1 tptp.bot_bo844097828e_bool))))))))))) (forall ((F tptp.fun_pname_option_com) (X_1 tptp.pname) (Y_2 tptp.option_com)) (let ((_let_1 (tptp.dom_pname_com F))) (let ((_let_2 (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1))) (let ((_let_3 (tptp.dom_pname_com (tptp.fun_up879233478on_com F X_1 Y_2)))) (let ((_let_4 (= Y_2 tptp.none_com))) (and (=> _let_4 (= _let_3 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool _let_1) (tptp.hAPP_f759274231e_bool _let_2 tptp.bot_bo844097828e_bool)))) (=> (not _let_4) (= _let_3 (tptp.hAPP_f759274231e_bool _let_2 _let_1))))))))) (forall ((C tptp.fun_pname_bool) (B_1 tptp.fun_pname_bool) (A tptp.fun_fu1430349052l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)) (=> (forall ((X_2 tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B_1) X_2)))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool B_1) C)) (tptp.hAPP_f674760225e_bool (tptp.hAPP_f246190092e_bool (tptp.finite446335722e_bool tptp.semila1635148844e_bool) C) A)))))) (forall ((C tptp.fun_Ho320143120e_bool) (B_1 tptp.fun_Ho320143120e_bool) (A tptp.fun_fu1996308102l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool A)) (=> (forall ((X_2 tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool (tptp.hAPP_f1610329741l_bool tptp.member1534059107e_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool B_1) X_2)))) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool B_1) C)) (tptp.hAPP_f1180969799e_bool (tptp.hAPP_f644061942e_bool (tptp.finite1334634696e_bool tptp.semila1129477150e_bool) C) A)))))) (forall ((C tptp.bool) (B_1 tptp.bool) (A tptp.fun_bool_bool)) (=> (tptp.hBOOL (tptp.hAPP_f387058535l_bool tptp.finite_finite_bool A)) (=> (forall ((X_2 tptp.bool)) (=> (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.hAPP_b1787118453l_bool tptp.member_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool B_1) X_2)))) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila310582991f_bool B_1) C)) (tptp.hAPP_f387058535l_bool (tptp.hAPP_b1787118453l_bool (tptp.finite1909292976l_bool tptp.semila310582991f_bool) C) A)))))) (forall ((C tptp.fun_pname_bool) (B_1 tptp.fun_pname_bool) (A tptp.fun_fu1430349052l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)) (=> (forall ((X_2 tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool X_2) B_1)))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f674760225e_bool (tptp.hAPP_f246190092e_bool (tptp.finite446335722e_bool tptp.semila278973382e_bool) C) A)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool B_1) C)))))) (forall ((C tptp.fun_Ho320143120e_bool) (B_1 tptp.fun_Ho320143120e_bool) (A tptp.fun_fu1996308102l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool A)) (=> (forall ((X_2 tptp.fun_Ho320143120e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool (tptp.hAPP_f1610329741l_bool tptp.member1534059107e_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool X_2) B_1)))) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool (tptp.hAPP_f1180969799e_bool (tptp.hAPP_f644061942e_bool (tptp.finite1334634696e_bool tptp.semila1579166468e_bool) C) A)) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1579166468e_bool B_1) C)))))) (forall ((C tptp.bool) (B_1 tptp.bool) (A tptp.fun_bool_bool)) (=> (tptp.hBOOL (tptp.hAPP_f387058535l_bool tptp.finite_finite_bool A)) (=> (forall ((X_2 tptp.bool)) (=> (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.hAPP_b1787118453l_bool tptp.member_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool X_2) B_1)))) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_f387058535l_bool (tptp.hAPP_b1787118453l_bool (tptp.finite1909292976l_bool tptp.semila1168014441p_bool) C) A)) (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool B_1) C)))))) (forall ((A_3 tptp.fun_pname_bool) (A tptp.fun_Ho320143120e_bool)) (=> (not (= A tptp.bot_bo39439654e_bool)) (= (exists ((F_1 tptp.fun_Ho713471079_pname)) (and (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.inj_on216215575_pname F_1) A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f773602357e_bool (tptp.image_1927198851_pname F_1) A)) A_3)))) (exists ((G_1 tptp.fun_pn1262351275_state)) (= (tptp.hAPP_f1763243027e_bool (tptp.image_1918575693_state G_1) A_3) A))))) (forall ((A_3 tptp.fun_Ho320143120e_bool) (A tptp.fun_pname_bool)) (=> (not (= A tptp.bot_bo844097828e_bool)) (= (exists ((F_1 tptp.fun_pn1262351275_state)) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.inj_on207592417_state F_1) A)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool (tptp.hAPP_f1763243027e_bool (tptp.image_1918575693_state F_1) A)) A_3)))) (exists ((G_1 tptp.fun_Ho713471079_pname)) (= (tptp.hAPP_f773602357e_bool (tptp.image_1927198851_pname G_1) A_3) A))))) (forall ((Y_1 tptp.option_com)) (=> (not (= Y_1 tptp.none_com)) (not (forall ((A_2 tptp.com)) (not (= Y_1 (tptp.hAPP_com_option_com tptp.some_com A_2))))))) (forall ((Y_1 tptp.option_pname)) (=> (not (= Y_1 tptp.none_pname)) (not (forall ((A_2 tptp.pname)) (not (= Y_1 (tptp.hAPP_p1252095976_pname tptp.some_pname A_2))))))) (forall ((Y_1 tptp.option131732143_state)) (=> (not (= Y_1 tptp.none_H1908530691_state)) (not (forall ((A_2 tptp.hoare_363350478_state)) (not (= Y_1 (tptp.hAPP_H1942146718_state tptp.some_H629028223_state A_2))))))) (forall ((G tptp.fun_Ho713471079_pname) (B tptp.fun_Ho320143120e_bool) (F tptp.fun_pn1262351275_state) (A tptp.fun_pname_bool)) (exists ((A_1 tptp.fun_pname_bool)) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_1) A)) (forall ((X_2 tptp.pname)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname X_2))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A_1)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f773602357e_bool (tptp.image_1927198851_pname G) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.minus_1060678561e_bool B) (tptp.hAPP_f1763243027e_bool (tptp.image_1918575693_state F) A_1))))))))) (exists ((H tptp.fun_pn1262351275_state)) (and (forall ((X_2 tptp.pname)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A_1)) (= (tptp.hAPP_p1337579261_state H X_2) (tptp.hAPP_p1337579261_state F X_2)))) (forall ((X_2 tptp.pname)) (let ((_let_1 (tptp.hAPP_p1337579261_state H X_2))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A) A_1))) (and (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state _let_1) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.minus_1060678561e_bool B) (tptp.hAPP_f1763243027e_bool (tptp.image_1918575693_state F) A_1)))) (= X_2 (tptp.hAPP_H1346202419_pname G _let_1))))))))))) (forall ((G tptp.fun_pn1262351275_state) (B tptp.fun_pname_bool) (F tptp.fun_Ho713471079_pname) (A tptp.fun_Ho320143120e_bool)) (exists ((A_1 tptp.fun_Ho320143120e_bool)) (and (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool A_1) A)) (forall ((X_2 tptp.hoare_363350478_state)) (let ((_let_1 (tptp.hAPP_H40373975l_bool tptp.member1253905979_state X_2))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 A_1)) (not (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_1 (tptp.hAPP_f1763243027e_bool (tptp.image_1918575693_state G) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool B) (tptp.hAPP_f773602357e_bool (tptp.image_1927198851_pname F) A_1))))))))) (exists ((H tptp.fun_Ho713471079_pname)) (and (forall ((X_2 tptp.hoare_363350478_state)) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state X_2) A_1)) (= (tptp.hAPP_H1346202419_pname H X_2) (tptp.hAPP_H1346202419_pname F X_2)))) (forall ((X_2 tptp.hoare_363350478_state)) (let ((_let_1 (tptp.hAPP_H1346202419_pname H X_2))) (=> (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state X_2) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.minus_1060678561e_bool A) A_1))) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname _let_1) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool B) (tptp.hAPP_f773602357e_bool (tptp.image_1927198851_pname F) A_1)))) (= X_2 (tptp.hAPP_p1337579261_state G _let_1))))))))))) (forall ((F tptp.fun_pn1262351275_state) (A tptp.fun_Ho320143120e_bool)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool (tptp.hAPP_f1763243027e_bool (tptp.image_1918575693_state F) (tptp.vimage597774871_state F A))) A))) (forall ((M tptp.fun_pname_option_com) (A tptp.fun_pname_bool)) (= (tptp.dom_pname_com (tptp.restri1382200118me_com M A)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool (tptp.dom_pname_com M)) A))) (forall ((B tptp.fun_fu1430349052l_bool) (A tptp.fun_fu1430349052l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)) (=> (not (= A tptp.bot_bo1649642514l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool B)) (=> (not (= B tptp.bot_bo1649642514l_bool)) (=> (= (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.semila1130628874l_bool A) B) tptp.bot_bo1649642514l_bool) (= (tptp.hAPP_f674760225e_bool tptp.big_la28065288e_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.semila1782091504l_bool A) B)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool (tptp.hAPP_f674760225e_bool tptp.big_la28065288e_bool A)) (tptp.hAPP_f674760225e_bool tptp.big_la28065288e_bool B))))))))) (forall ((B tptp.fun_fu1996308102l_bool) (A tptp.fun_fu1996308102l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool A)) (=> (not (= A tptp.bot_bo133096688l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool B)) (=> (not (= B tptp.bot_bo133096688l_bool)) (=> (= (tptp.hAPP_f85652879l_bool (tptp.hAPP_f1175211816l_bool tptp.semila218417144l_bool A) B) tptp.bot_bo133096688l_bool) (= (tptp.hAPP_f1180969799e_bool tptp.big_la1639670082e_bool (tptp.hAPP_f85652879l_bool (tptp.hAPP_f1175211816l_bool tptp.semila862847378l_bool A) B)) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool (tptp.hAPP_f1180969799e_bool tptp.big_la1639670082e_bool A)) (tptp.hAPP_f1180969799e_bool tptp.big_la1639670082e_bool B))))))))) (forall ((B tptp.fun_fu1430349052l_bool) (A tptp.fun_fu1430349052l_bool)) (let ((_let_1 (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.semila1130628874l_bool A) B))) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool B)) (=> (not (= _let_1 tptp.bot_bo1649642514l_bool)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool (tptp.hAPP_f674760225e_bool tptp.big_la28065288e_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.semila1782091504l_bool A) B))) (tptp.hAPP_f674760225e_bool tptp.big_la28065288e_bool _let_1)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool (tptp.hAPP_f674760225e_bool tptp.big_la28065288e_bool A)) (tptp.hAPP_f674760225e_bool tptp.big_la28065288e_bool B)))))))) (forall ((B tptp.fun_fu1996308102l_bool) (A tptp.fun_fu1996308102l_bool)) (let ((_let_1 (tptp.hAPP_f85652879l_bool (tptp.hAPP_f1175211816l_bool tptp.semila218417144l_bool A) B))) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f1287348838l_bool tptp.finite2030652771e_bool B)) (=> (not (= _let_1 tptp.bot_bo133096688l_bool)) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool (tptp.hAPP_f1180969799e_bool tptp.big_la1639670082e_bool (tptp.hAPP_f85652879l_bool (tptp.hAPP_f1175211816l_bool tptp.semila862847378l_bool A) B))) (tptp.hAPP_f1180969799e_bool tptp.big_la1639670082e_bool _let_1)) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool tptp.semila1129477150e_bool (tptp.hAPP_f1180969799e_bool tptp.big_la1639670082e_bool A)) (tptp.hAPP_f1180969799e_bool tptp.big_la1639670082e_bool B)))))))) (forall ((X_1 tptp.com)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_1) tptp.top_top_fun_com_bool))) (forall ((X_1 tptp.pname)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) tptp.top_to2127735616e_bool))) (forall ((X_1 tptp.hoare_363350478_state)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state X_1) tptp.top_to1618141706e_bool))) (forall ((F tptp.fun_pn1262351275_state) (X_1 tptp.pname)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state (tptp.hAPP_p1337579261_state F X_1)) (tptp.hAPP_f1763243027e_bool (tptp.image_1918575693_state F) tptp.top_to2127735616e_bool)))) (forall ((P tptp.bool)) (or (not (tptp.hBOOL (tptp.hAPP_bool_bool tptp.fNot P))) (not (tptp.hBOOL P)))) (forall ((P tptp.bool)) (or (tptp.hBOOL P) (tptp.hBOOL (tptp.hAPP_bool_bool tptp.fNot P)))) (forall ((Q tptp.bool) (P tptp.bool)) (or (not (tptp.hBOOL P)) (not (tptp.hBOOL Q)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fconj P) Q)))) (forall ((P tptp.bool) (Q tptp.bool)) (or (not (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fconj P) Q))) (tptp.hBOOL P))) (forall ((P tptp.bool) (Q tptp.bool)) (or (not (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fconj P) Q))) (tptp.hBOOL Q))) (forall ((Q tptp.bool) (P tptp.bool)) (or (not (tptp.hBOOL P)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fdisj P) Q)))) (forall ((P tptp.bool) (Q tptp.bool)) (or (not (tptp.hBOOL Q)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fdisj P) Q)))) (forall ((P tptp.bool) (Q tptp.bool)) (or (not (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fdisj P) Q))) (tptp.hBOOL P) (tptp.hBOOL Q))) (not (tptp.hBOOL tptp.fFalse)) (forall ((P tptp.bool)) (or (= P tptp.fTrue) (= P tptp.fFalse))) (forall ((Q tptp.bool) (P tptp.bool)) (or (tptp.hBOOL P) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fimplies P) Q)))) (forall ((P tptp.bool) (Q tptp.bool)) (or (not (tptp.hBOOL Q)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fimplies P) Q)))) (forall ((P tptp.bool) (Q tptp.bool)) (or (not (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fimplies P) Q))) (not (tptp.hBOOL P)) (tptp.hBOOL Q))) (forall ((X tptp.state) (P tptp.fun_state_bool)) (or (not (tptp.hBOOL (tptp.hAPP_f327114704l_bool tptp.fAll_state P))) (tptp.hBOOL (tptp.hAPP_state_bool P X)))) (forall ((X tptp.com) (Y tptp.com)) (or (not (tptp.hBOOL (tptp.hAPP_com_bool (tptp.hAPP_c1396316405m_bool tptp.fequal_com X) Y))) (= X Y))) (forall ((X tptp.com) (Y tptp.com)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_com_bool (tptp.hAPP_c1396316405m_bool tptp.fequal_com X) Y)))) (forall ((X tptp.pname) (Y tptp.pname)) (or (not (tptp.hBOOL (tptp.hAPP_pname_bool (tptp.hAPP_p61793385e_bool tptp.fequal_pname X) Y))) (= X Y))) (forall ((X tptp.pname) (Y tptp.pname)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_pname_bool (tptp.hAPP_p61793385e_bool tptp.fequal_pname X) Y)))) (forall ((X tptp.state) (Y tptp.state)) (or (not (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool tptp.fequal_state X) Y))) (= X Y))) (forall ((X tptp.state) (Y tptp.state)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool tptp.fequal_state X) Y)))) (forall ((P tptp.bool) (Q tptp.com)) (= (tptp.hAPP_com_bool (tptp.hAPP_b1153789088m_bool tptp.cOMBK_bool_com P) Q) P)) (forall ((P tptp.com) (Q tptp.pname)) (= (tptp.hAPP_pname_com (tptp.hAPP_c1494068046me_com tptp.cOMBK_com_pname P) Q) P)) (forall ((P tptp.bool) (Q tptp.pname)) (= (tptp.hAPP_pname_bool (tptp.hAPP_b76515610e_bool tptp.cOMBK_bool_pname P) Q) P)) (forall ((X tptp.option_com) (Y tptp.option_com)) (= (tptp.hAPP_o356497025on_com (tptp.hAPP_o334540577on_com (tptp.hAPP_b1679505845on_com tptp.if_option_com tptp.fTrue) X) Y) X)) (forall ((X tptp.option_com) (Y tptp.option_com)) (= (tptp.hAPP_o356497025on_com (tptp.hAPP_o334540577on_com (tptp.hAPP_b1679505845on_com tptp.if_option_com tptp.fFalse) X) Y) Y)) (forall ((P tptp.bool)) (or (= P tptp.fTrue) (= P tptp.fFalse))) (forall ((P tptp.pname) (Q tptp.pname)) (= (tptp.hAPP_pname_pname (tptp.hAPP_p1170154830_pname tptp.cOMBK_pname_pname P) Q) P)) (forall ((X tptp.option_com) (Y tptp.option_com)) (or (not (tptp.hBOOL (tptp.hAPP_option_com_bool (tptp.hAPP_o1684370239m_bool tptp.fequal_option_com X) Y))) (= X Y))) (forall ((X tptp.option_com) (Y tptp.option_com)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_option_com_bool (tptp.hAPP_o1684370239m_bool tptp.fequal_option_com X) Y)))) (forall ((X tptp.fun_com_bool) (Y tptp.fun_com_bool)) (or (not (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_f273696895l_bool tptp.fequal_fun_com_bool X) Y))) (= X Y))) (forall ((X tptp.fun_com_bool) (Y tptp.fun_com_bool)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_f273696895l_bool tptp.fequal_fun_com_bool X) Y)))) (forall ((X tptp.fun_pname_bool) (Y tptp.fun_pname_bool)) (or (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.fequal533582459e_bool X) Y))) (= X Y))) (forall ((X tptp.fun_pname_bool) (Y tptp.fun_pname_bool)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.fequal533582459e_bool X) Y)))) (forall ((P tptp.fun_com_fun_com_bool) (Q tptp.com) (R tptp.com)) (= (tptp.hAPP_com_bool (tptp.hAPP_c1396316405m_bool (tptp.hAPP_f908845385m_bool tptp.cOMBC_com_com_bool P) Q) R) (tptp.hAPP_com_bool (tptp.hAPP_c1396316405m_bool P R) Q))) (forall ((P tptp.fun_bool_bool) (Q tptp.fun_com_bool) (R tptp.com)) (= (tptp.hAPP_com_bool (tptp.hAPP_f1682609283m_bool (tptp.cOMBB_bool_bool_com P) Q) R) (tptp.hAPP_bool_bool P (tptp.hAPP_com_bool Q R)))) (forall ((P tptp.fun_co2042843794l_bool) (Q tptp.fun_com_bool) (R tptp.com)) (= (tptp.hAPP_com_bool (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f328772264m_bool tptp.cOMBS_com_bool_bool P) Q) R) (tptp.hAPP_bool_bool (tptp.hAPP_c1580157610l_bool P R) (tptp.hAPP_com_bool Q R)))) (forall ((P tptp.fun_co1877906717e_bool) (Q tptp.pname) (R tptp.com)) (= (tptp.hAPP_com_bool (tptp.hAPP_p1639923567m_bool (tptp.hAPP_f734198589m_bool tptp.cOMBC_com_pname_bool P) Q) R) (tptp.hAPP_pname_bool (tptp.hAPP_c1967741679e_bool P R) Q))) (forall ((P tptp.fun_bool_bool) (Q tptp.fun_pname_bool) (R tptp.pname)) (= (tptp.hAPP_pname_bool (tptp.hAPP_f759274231e_bool (tptp.cOMBB_647938656_pname P) Q) R) (tptp.hAPP_bool_bool P (tptp.hAPP_pname_bool Q R)))) (forall ((P tptp.fun_bool_bool) (Q tptp.fun_state_bool) (R tptp.state)) (= (tptp.hAPP_state_bool (tptp.hAPP_f1759915619e_bool (tptp.cOMBB_160679318_state P) Q) R) (tptp.hAPP_bool_bool P (tptp.hAPP_state_bool Q R)))) (forall ((P tptp.fun_st2063251938l_bool) (Q tptp.bool) (R tptp.state)) (= (tptp.hAPP_state_bool (tptp.hAPP_b2019457360e_bool (tptp.hAPP_f167292325e_bool tptp.cOMBC_231445413l_bool P) Q) R) (tptp.hAPP_bool_bool (tptp.hAPP_s58564346l_bool P R) Q))) (forall ((P tptp.fun_pn250273176l_bool) (Q tptp.fun_pname_bool) (R tptp.pname)) (= (tptp.hAPP_pname_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f649174806e_bool tptp.cOMBS_568398431l_bool P) Q) R) (tptp.hAPP_bool_bool (tptp.hAPP_p393069232l_bool P R) (tptp.hAPP_pname_bool Q R)))) (forall ((P tptp.fun_st2063251938l_bool) (Q tptp.fun_state_bool) (R tptp.state)) (= (tptp.hAPP_state_bool (tptp.hAPP_f1759915619e_bool (tptp.hAPP_f644196280e_bool tptp.cOMBS_1378840469l_bool P) Q) R) (tptp.hAPP_bool_bool (tptp.hAPP_s58564346l_bool P R) (tptp.hAPP_state_bool Q R)))) (forall ((P tptp.fun_pn800050071e_bool) (Q tptp.pname) (R tptp.pname)) (= (tptp.hAPP_pname_bool (tptp.hAPP_p61793385e_bool (tptp.hAPP_f22061361e_bool tptp.cOMBC_1149511130e_bool P) Q) R) (tptp.hAPP_pname_bool (tptp.hAPP_p61793385e_bool P R) Q))) (forall ((P tptp.fun_st1506752259e_bool) (Q tptp.state) (R tptp.state)) (= (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool (tptp.hAPP_f817621513e_bool tptp.cOMBC_2027030106e_bool P) Q) R) (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool P R) Q))) (forall ((P tptp.option_com) (Q tptp.pname)) (= (tptp.hAPP_p799580910on_com (tptp.hAPP_o129566686on_com tptp.cOMBK_413306633_pname P) Q) P)) (forall ((P tptp.bool) (Q tptp.fun_pname_bool)) (= (tptp.hAPP_f1664156314l_bool (tptp.hAPP_b357632156l_bool tptp.cOMBK_1857069011e_bool P) Q) P)) (forall ((P tptp.fun_state_bool) (Q tptp.state)) (= (tptp.hAPP_s1806633685e_bool (tptp.hAPP_f1863945078e_bool tptp.cOMBK_631994958_state P) Q) P)) (forall ((X tptp.hoare_363350478_state) (Y tptp.hoare_363350478_state)) (= (tptp.hAPP_H1982017439_state (tptp.hAPP_H230141040_state (tptp.hAPP_b594649092_state tptp.if_Hoa29189214_state tptp.fTrue) X) Y) X)) (forall ((X tptp.hoare_363350478_state) (Y tptp.hoare_363350478_state)) (= (tptp.hAPP_H1982017439_state (tptp.hAPP_H230141040_state (tptp.hAPP_b594649092_state tptp.if_Hoa29189214_state tptp.fFalse) X) Y) Y)) (forall ((P tptp.bool)) (or (= P tptp.fTrue) (= P tptp.fFalse))) (forall ((X tptp.hoare_363350478_state) (Y tptp.hoare_363350478_state)) (or (not (tptp.hBOOL (tptp.hAPP_H1645464494e_bool (tptp.hAPP_H705653759e_bool tptp.fequal1026769423_state X) Y))) (= X Y))) (forall ((X tptp.hoare_363350478_state) (Y tptp.hoare_363350478_state)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_H1645464494e_bool (tptp.hAPP_H705653759e_bool tptp.fequal1026769423_state X) Y)))) (forall ((P tptp.fun_option_com_com) (Q tptp.fun_pname_option_com) (R tptp.pname)) (= (tptp.hAPP_pname_com (tptp.hAPP_f96342628me_com (tptp.cOMBB_923936821_pname P) Q) R) (tptp.hAPP_option_com_com P (tptp.hAPP_p799580910on_com Q R)))) (forall ((P tptp.fun_pn1824415994m_bool) (Q tptp.option_com) (R tptp.pname)) (= (tptp.hAPP_pname_bool (tptp.hAPP_o1092643708e_bool (tptp.hAPP_f837293113e_bool tptp.cOMBC_1381995473m_bool P) Q) R) (tptp.hAPP_option_com_bool (tptp.hAPP_p558118546m_bool P R) Q))) (forall ((P tptp.fun_fu1362071682l_bool) (Q tptp.fun_com_fun_com_bool) (R tptp.com)) (= (tptp.hAPP_com_bool (tptp.hAPP_f1998868198m_bool (tptp.cOMBB_298914627ol_com P) Q) R) (tptp.hAPP_f990396704l_bool P (tptp.hAPP_c1396316405m_bool Q R)))) (forall ((P tptp.fun_co1633267573l_bool) (Q tptp.fun_com_bool) (R tptp.com)) (= (tptp.hAPP_com_bool (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f578650245m_bool tptp.cOMBC_1904837336l_bool P) Q) R) (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool P R) Q))) (forall ((P tptp.fun_bo1549164019l_bool) (Q tptp.fun_com_bool) (R tptp.com)) (= (tptp.hAPP_c1580157610l_bool (tptp.hAPP_f954469007l_bool (tptp.cOMBB_886968260ol_com P) Q) R) (tptp.hAPP_b589554111l_bool P (tptp.hAPP_com_bool Q R)))) (forall ((P tptp.fun_pn800050071e_bool) (Q tptp.fun_com_pname) (R tptp.com)) (= (tptp.hAPP_c1967741679e_bool (tptp.hAPP_f835719487e_bool (tptp.cOMBB_1083901850ol_com P) Q) R) (tptp.hAPP_p61793385e_bool P (tptp.hAPP_com_pname Q R)))) (forall ((P tptp.fun_bool_bool) (Q tptp.fun_fu1430349052l_bool) (R tptp.fun_pname_bool)) (= (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f559147733l_bool (tptp.cOMBB_307249310e_bool P) Q) R) (tptp.hAPP_bool_bool P (tptp.hAPP_f1664156314l_bool Q R)))) (forall ((P tptp.fun_bo1549164019l_bool) (Q tptp.fun_pname_bool) (R tptp.pname)) (= (tptp.hAPP_p393069232l_bool (tptp.hAPP_f1402196763l_bool (tptp.cOMBB_675860798_pname P) Q) R) (tptp.hAPP_b589554111l_bool P (tptp.hAPP_pname_bool Q R)))) (forall ((P tptp.fun_bo1549164019l_bool) (Q tptp.fun_state_bool) (R tptp.state)) (= (tptp.hAPP_s58564346l_bool (tptp.hAPP_f1259673775l_bool (tptp.cOMBB_188601460_state P) Q) R) (tptp.hAPP_b589554111l_bool P (tptp.hAPP_state_bool Q R)))) (forall ((P tptp.fun_fu31783638l_bool) (Q tptp.fun_fu1430349052l_bool) (R tptp.fun_pname_bool)) (= (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f624840228l_bool tptp.cOMBS_350070575l_bool P) Q) R) (tptp.hAPP_bool_bool (tptp.hAPP_f1476298914l_bool P R) (tptp.hAPP_f1664156314l_bool Q R)))) (forall ((P tptp.fun_fu1430349052l_bool) (Q tptp.fun_pn800050071e_bool) (R tptp.pname)) (= (tptp.hAPP_pname_bool (tptp.hAPP_f42430548e_bool (tptp.cOMBB_530759491_pname P) Q) R) (tptp.hAPP_f1664156314l_bool P (tptp.hAPP_p61793385e_bool Q R)))) (forall ((P tptp.fun_fu93307442l_bool) (Q tptp.fun_st1506752259e_bool) (R tptp.state)) (= (tptp.hAPP_state_bool (tptp.hAPP_f1012183542e_bool (tptp.cOMBB_1911358915_state P) Q) R) (tptp.hAPP_f327114704l_bool P (tptp.hAPP_s1806633685e_bool Q R)))) (forall ((P tptp.fun_pn422929397l_bool) (Q tptp.fun_pname_bool) (R tptp.pname)) (= (tptp.hAPP_pname_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f661147897e_bool tptp.cOMBC_1058051404l_bool P) Q) R) (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool P R) Q))) (forall ((P tptp.fun_st1483075957e_bool) (Q tptp.bool) (R tptp.state)) (= (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 tptp.fun_fu410713561e_bool) (Q tptp.pname) (R tptp.fun_pname_bool)) (= (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool (tptp.hAPP_f2082757169l_bool tptp.cOMBC_1004116266e_bool P) Q) R) (tptp.hAPP_pname_bool (tptp.hAPP_f759274231e_bool P R) Q))) (forall ((P tptp.fun_pn800050071e_bool) (Q tptp.fun_pname_pname) (R tptp.pname)) (= (tptp.hAPP_p61793385e_bool (tptp.hAPP_f1336811455e_bool (tptp.cOMBB_542850580_pname P) Q) R) (tptp.hAPP_p61793385e_bool P (tptp.hAPP_pname_pname Q R)))) (forall ((P tptp.com) (Q tptp.hoare_363350478_state)) (= (tptp.hAPP_H2142737465te_com (tptp.hAPP_c6662434te_com tptp.cOMBK_1864507658_state P) Q) P)) (forall ((P tptp.hoare_363350478_state) (Q tptp.com)) (= (tptp.hAPP_c1041435779_state (tptp.hAPP_H154362754_state tptp.cOMBK_818325696te_com P) Q) P)) (forall ((P tptp.bool) (Q tptp.hoare_363350478_state)) (= (tptp.hAPP_H1645464494e_bool (tptp.hAPP_b230077104e_bool tptp.cOMBK_574827367_state P) Q) P)) (forall ((P tptp.pname) (Q tptp.hoare_363350478_state)) (= (tptp.hAPP_H1346202419_pname (tptp.hAPP_p1379817622_pname tptp.cOMBK_83433476_state P) Q) P)) (forall ((P tptp.hoare_363350478_state) (Q tptp.pname)) (= (tptp.hAPP_p1337579261_state (tptp.hAPP_H1607320188_state tptp.cOMBK_92056634_pname P) Q) P)) (forall ((X tptp.fun_Ho320143120e_bool) (Y tptp.fun_Ho320143120e_bool)) (or (not (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.fequal731041167e_bool X) Y))) (= X Y))) (forall ((X tptp.fun_Ho320143120e_bool) (Y tptp.fun_Ho320143120e_bool)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.fequal731041167e_bool X) Y)))) (forall ((P tptp.fun_pn1580610524on_com) (Q tptp.fun_pname_option_com) (R tptp.pname)) (= (tptp.hAPP_p799580910on_com (tptp.hAPP_f2123220539on_com (tptp.hAPP_f1673966486on_com tptp.cOMBS_904531235on_com P) Q) R) (tptp.hAPP_o356497025on_com (tptp.hAPP_p1086945780on_com P R) (tptp.hAPP_p799580910on_com Q R)))) (forall ((P tptp.fun_co1098712835e_bool) (Q tptp.hoare_363350478_state) (R tptp.com)) (= (tptp.hAPP_com_bool (tptp.hAPP_H176808977m_bool (tptp.hAPP_f1375689733m_bool tptp.cOMBC_1517337958e_bool P) Q) R) (tptp.hAPP_H1645464494e_bool (tptp.hAPP_c566546971e_bool P R) Q))) (forall ((P tptp.fun_co482540593_state) (Q tptp.fun_pname_com) (R tptp.pname)) (= (tptp.hAPP_p1337579261_state (tptp.hAPP_f481860441_state (tptp.cOMBB_424558970_pname P) Q) R) (tptp.hAPP_c1041435779_state P (tptp.hAPP_pname_com Q R)))) (forall ((P tptp.fun_bool_bool) (Q tptp.fun_Ho320143120e_bool) (R tptp.hoare_363350478_state)) (= (tptp.hAPP_H1645464494e_bool (tptp.hAPP_f1749453397e_bool (tptp.cOMBB_2059354034_state P) Q) R) (tptp.hAPP_bool_bool P (tptp.hAPP_H1645464494e_bool Q R)))) (forall ((P tptp.fun_Ho544647106l_bool) (Q tptp.fun_Ho320143120e_bool) (R tptp.hoare_363350478_state)) (= (tptp.hAPP_H1645464494e_bool (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1612626488e_bool tptp.cOMBS_56025283l_bool P) Q) R) (tptp.hAPP_bool_bool (tptp.hAPP_H1173243534l_bool P R) (tptp.hAPP_H1645464494e_bool Q R)))) (forall ((P tptp.fun_co2038576728m_bool) (Q tptp.fun_com_bool) (R tptp.com)) (= (tptp.hAPP_c1396316405m_bool (tptp.hAPP_f721468006m_bool (tptp.hAPP_f947797701m_bool tptp.cOMBC_1977231931m_bool P) Q) R) (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool P R) Q))) (forall ((P tptp.fun_pn1521100553e_bool) (Q tptp.hoare_363350478_state) (R tptp.pname)) (= (tptp.hAPP_pname_bool (tptp.hAPP_H2033014795e_bool (tptp.hAPP_f443781369e_bool tptp.cOMBC_1422551904e_bool P) Q) R) (tptp.hAPP_H1645464494e_bool (tptp.hAPP_p2009489185e_bool P R) Q))) (forall ((P tptp.fun_Ho1262521325e_bool) (Q tptp.pname) (R tptp.hoare_363350478_state)) (= (tptp.hAPP_H1645464494e_bool (tptp.hAPP_p2009489185e_bool (tptp.hAPP_f626747953e_bool tptp.cOMBC_1026256022e_bool P) Q) R) (tptp.hAPP_pname_bool (tptp.hAPP_H2033014795e_bool P R) Q))) (forall ((P tptp.fun_bo1549164019l_bool) (Q tptp.fun_fu1430349052l_bool) (R tptp.fun_pname_bool)) (= (tptp.hAPP_f1476298914l_bool (tptp.hAPP_f143162813l_bool (tptp.cOMBB_2095475776e_bool P) Q) R) (tptp.hAPP_b589554111l_bool P (tptp.hAPP_f1664156314l_bool Q R)))) (forall ((P tptp.fun_fu802393907l_bool) (Q tptp.fun_pname_bool) (R tptp.fun_pname_bool)) (= (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool (tptp.hAPP_f1297925993l_bool tptp.cOMBC_1284144636l_bool P) Q) R) (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool P R) Q))) (forall ((P tptp.fun_pn800050071e_bool) (Q tptp.fun_fu1499449723_pname) (R tptp.fun_pname_bool)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1385420507e_bool (tptp.cOMBB_598082538e_bool P) Q) R) (tptp.hAPP_p61793385e_bool P (tptp.hAPP_f1297739591_pname Q R)))) (forall ((P tptp.fun_pn479984722e_bool) (Q tptp.fun_pname_bool) (R tptp.pname)) (= (tptp.hAPP_p61793385e_bool (tptp.hAPP_f180827860e_bool (tptp.hAPP_f698292281e_bool tptp.cOMBC_1123258281e_bool P) Q) R) (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool P R) Q))) (forall ((P tptp.fun_st277393160e_bool) (Q tptp.fun_state_bool) (R tptp.state)) (= (tptp.hAPP_s1806633685e_bool (tptp.hAPP_f1863945078e_bool (tptp.hAPP_f915354021e_bool tptp.cOMBC_952831051e_bool P) Q) R) (tptp.hAPP_f1759915619e_bool (tptp.hAPP_s1226857760e_bool P R) Q))) (forall ((P tptp.bool) (Q tptp.fun_Ho320143120e_bool)) (= (tptp.hAPP_f568432088l_bool (tptp.hAPP_b1504838374l_bool tptp.cOMBK_1696036407e_bool P) Q) P)) (forall ((P tptp.fun_op2091355123m_bool) (Q tptp.fun_pname_option_com) (R tptp.pname)) (= (tptp.hAPP_p558118546m_bool (tptp.hAPP_f919496731m_bool (tptp.cOMBB_418828222_pname P) Q) R) (tptp.hAPP_o1684370239m_bool P (tptp.hAPP_p799580910on_com Q R)))) (forall ((P tptp.fun_bool_bool) (Q tptp.fun_fu1996308102l_bool) (R tptp.fun_Ho320143120e_bool)) (= (tptp.hAPP_f568432088l_bool (tptp.hAPP_f85652879l_bool (tptp.cOMBB_941362220e_bool P) Q) R) (tptp.hAPP_bool_bool P (tptp.hAPP_f568432088l_bool Q R)))) (forall ((P tptp.fun_bo1549164019l_bool) (Q tptp.fun_Ho320143120e_bool) (R tptp.hoare_363350478_state)) (= (tptp.hAPP_H1173243534l_bool (tptp.hAPP_f1422032445l_bool (tptp.cOMBB_877416532_state P) Q) R) (tptp.hAPP_b589554111l_bool P (tptp.hAPP_H1645464494e_bool Q R)))) (forall ((P tptp.fun_fu24650956l_bool) (Q tptp.fun_fu1996308102l_bool) (R tptp.fun_Ho320143120e_bool)) (= (tptp.hAPP_f568432088l_bool (tptp.hAPP_f85652879l_bool (tptp.hAPP_f927797370l_bool tptp.cOMBS_1039407915l_bool P) Q) R) (tptp.hAPP_bool_bool (tptp.hAPP_f1395767268l_bool P R) (tptp.hAPP_f568432088l_bool Q R)))) (forall ((P tptp.fun_pn1419495779l_bool) (Q tptp.fun_Ho320143120e_bool) (R tptp.pname)) (= (tptp.hAPP_pname_bool (tptp.hAPP_f773602357e_bool (tptp.hAPP_f1863577801e_bool tptp.cOMBC_947783590l_bool P) Q) R) (tptp.hAPP_f568432088l_bool (tptp.hAPP_p425615669l_bool P R) Q))) (forall ((P tptp.fun_Ho769804319l_bool) (Q tptp.fun_pname_bool) (R tptp.hoare_363350478_state)) (= (tptp.hAPP_H1645464494e_bool (tptp.hAPP_f1763243027e_bool (tptp.hAPP_f1421439337e_bool tptp.cOMBC_1674478480l_bool P) Q) R) (tptp.hAPP_f1664156314l_bool (tptp.hAPP_H444605547l_bool P R) Q))) (forall ((P tptp.fun_fu1107293590m_bool) (Q tptp.fun_com_bool) (R tptp.fun_com_bool)) (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool (tptp.hAPP_f1898485935m_bool tptp.cOMBC_788185579m_bool P) Q) R) (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool P R) Q))) (forall ((P tptp.fun_fu1937087815e_bool) (Q tptp.hoare_363350478_state) (R tptp.fun_pname_bool)) (= (tptp.hAPP_f1664156314l_bool (tptp.hAPP_H444605547l_bool (tptp.hAPP_f1075942761l_bool tptp.cOMBC_1091669008e_bool P) Q) R) (tptp.hAPP_H1645464494e_bool (tptp.hAPP_f1763243027e_bool P R) Q))) (forall ((P tptp.fun_fu665342307e_bool) (Q tptp.pname) (R tptp.fun_Ho320143120e_bool)) (= (tptp.hAPP_f568432088l_bool (tptp.hAPP_p425615669l_bool (tptp.hAPP_f883421385l_bool tptp.cOMBC_1845395470e_bool P) Q) R) (tptp.hAPP_pname_bool (tptp.hAPP_f773602357e_bool P R) Q))) (forall ((P tptp.fun_pn800050071e_bool) (Q tptp.fun_Ho713471079_pname) (R tptp.hoare_363350478_state)) (= (tptp.hAPP_H2033014795e_bool (tptp.hAPP_f875047427e_bool (tptp.cOMBB_951329022_state P) Q) R) (tptp.hAPP_p61793385e_bool P (tptp.hAPP_H1346202419_pname Q R)))) (forall ((P tptp.fun_fu931343505l_bool) (Q tptp.fun_fu1430349052l_bool) (R tptp.fun_pname_bool)) (= (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1145991873l_bool tptp.cOMBC_1988546018l_bool P) Q) R) (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool P R) Q))) (forall ((P tptp.fun_fu802393907l_bool) (Q tptp.fun_pn800050071e_bool) (R tptp.pname)) (= (tptp.hAPP_p338031245l_bool (tptp.hAPP_f567934427l_bool (tptp.cOMBB_408569982_pname P) Q) R) (tptp.hAPP_f434788991l_bool P (tptp.hAPP_p61793385e_bool Q R)))) (forall ((P tptp.fun_fu1658206819l_bool) (Q tptp.fun_st1506752259e_bool) (R tptp.state)) (= (tptp.hAPP_s2001034685l_bool (tptp.hAPP_f1283379615l_bool (tptp.cOMBB_1759179140_state P) Q) R) (tptp.hAPP_f1259673775l_bool P (tptp.hAPP_s1806633685e_bool Q R)))) (forall ((P tptp.fun_fu2101097872e_bool) (Q tptp.fun_pname_bool) (R tptp.fun_pname_bool)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool (tptp.hAPP_f182188835e_bool tptp.cOMBC_1880008793e_bool P) Q) R) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool P R) Q))) (forall ((P tptp.fun_fu1998731480e_bool) (Q tptp.fun_st1506752259e_bool) (R tptp.state)) (= (tptp.hAPP_s336103912e_bool (tptp.hAPP_f249262236e_bool (tptp.cOMBB_1476898461_state P) Q) R) (tptp.hAPP_f1863945078e_bool P (tptp.hAPP_s1806633685e_bool Q R)))) (forall ((P tptp.fun_fu2104550360e_bool) (Q tptp.fun_st858662806e_bool) (R tptp.state)) (= (tptp.hAPP_s1806633685e_bool (tptp.hAPP_f1935169308e_bool (tptp.cOMBB_1036740637_state P) Q) R) (tptp.hAPP_f1012183542e_bool P (tptp.hAPP_s336103912e_bool Q R)))) (forall ((P tptp.fun_pn1673019570on_com) (Q tptp.fun_pname_option_com) (R tptp.pname)) (= (tptp.hAPP_p1086945780on_com (tptp.hAPP_f648377725on_com (tptp.hAPP_f2093196134on_com tptp.cOMBS_1529518335on_com P) Q) R) (tptp.hAPP_o334540577on_com (tptp.hAPP_p1164893188on_com P R) (tptp.hAPP_p799580910on_com Q R)))) (forall ((P tptp.fun_Ho424838195e_bool) (Q tptp.hoare_363350478_state) (R tptp.hoare_363350478_state)) (= (tptp.hAPP_H1645464494e_bool (tptp.hAPP_H705653759e_bool (tptp.hAPP_f114072425e_bool tptp.cOMBC_13083556e_bool P) Q) R) (tptp.hAPP_H1645464494e_bool (tptp.hAPP_H705653759e_bool P R) Q))) (forall ((P tptp.fun_pn983485306_state) (Q tptp.fun_pn1262351275_state) (R tptp.pname)) (= (tptp.hAPP_p1337579261_state (tptp.hAPP_f901668953_state (tptp.hAPP_f1521026326_state tptp.cOMBS_113846849_state P) Q) R) (tptp.hAPP_H1982017439_state (tptp.hAPP_p726046354_state P R) (tptp.hAPP_p1337579261_state Q R)))) (forall ((P tptp.fun_bo1549164019l_bool) (Q tptp.fun_fu1996308102l_bool) (R tptp.fun_Ho320143120e_bool)) (= (tptp.hAPP_f1395767268l_bool (tptp.hAPP_f945781379l_bool (tptp.cOMBB_1004232970e_bool P) Q) R) (tptp.hAPP_b589554111l_bool P (tptp.hAPP_f568432088l_bool Q R)))) (forall ((P tptp.fun_fu1107293590m_bool) (Q tptp.fun_com_fun_com_bool) (R tptp.com)) (= (tptp.hAPP_c566651504m_bool (tptp.hAPP_f57617970m_bool (tptp.cOMBB_2112550369ol_com P) Q) R) (tptp.hAPP_f1120618594m_bool P (tptp.hAPP_c1396316405m_bool Q R)))) (forall ((P tptp.fun_pn800050071e_bool) (Q tptp.fun_fu2380401_pname) (R tptp.fun_Ho320143120e_bool)) (= (tptp.hAPP_f773602357e_bool (tptp.hAPP_f1544555711e_bool (tptp.cOMBB_655928288e_bool P) Q) R) (tptp.hAPP_p61793385e_bool P (tptp.hAPP_f1309420425_pname Q R)))) (forall ((P tptp.fun_pn640817967_state) (Q tptp.fun_pn12888928e_bool) (R tptp.pname)) (= (tptp.hAPP_p1337579261_state (tptp.hAPP_f19336718_state (tptp.hAPP_f720869462_state tptp.cOMBS_1110920566_state P) Q) R) (tptp.hAPP_f83715540_state (tptp.hAPP_p435788871_state P R) (tptp.hAPP_p1637813682e_bool Q R)))) (forall ((P tptp.fun_fu1911931399l_bool) (Q tptp.fun_fu1430349052l_bool) (R tptp.fun_fu1430349052l_bool)) (= (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool (tptp.hAPP_f1879335953l_bool tptp.cOMBC_7971162l_bool P) Q) R) (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool P R) Q))) (forall ((P tptp.fun_fu1219323149e_bool) (Q tptp.fun_st2116860965l_bool) (R tptp.state)) (= (tptp.hAPP_s1874344717e_bool (tptp.hAPP_f873506917e_bool (tptp.cOMBB_1757942702_state P) Q) R) (tptp.hAPP_f167292325e_bool P (tptp.hAPP_s2001034685l_bool Q R)))) (forall ((P tptp.fun_fu2101097872e_bool) (Q tptp.fun_pn800050071e_bool) (R tptp.pname)) (= (tptp.hAPP_p905327722e_bool (tptp.hAPP_f647826488e_bool (tptp.cOMBB_1919352417_pname P) Q) R) (tptp.hAPP_f1388330588e_bool P (tptp.hAPP_p61793385e_bool Q R)))) (forall ((P tptp.fun_bo79750167on_com) (Q tptp.fun_pname_bool) (R tptp.pname)) (= (tptp.hAPP_p1164893188on_com (tptp.hAPP_f755519727on_com (tptp.cOMBB_1394247784_pname P) Q) R) (tptp.hAPP_b1679505845on_com P (tptp.hAPP_pname_bool Q R)))) (forall ((P tptp.fun_Ho424838195e_bool) (Q tptp.fun_co482540593_state) (R tptp.com)) (= (tptp.hAPP_c566546971e_bool (tptp.hAPP_f1813061839e_bool (tptp.cOMBB_147383684ol_com P) Q) R) (tptp.hAPP_H705653759e_bool P (tptp.hAPP_c1041435779_state Q R)))) (forall ((P tptp.fun_fu1996308102l_bool) (Q tptp.fun_Ho424838195e_bool) (R tptp.hoare_363350478_state)) (= (tptp.hAPP_H1645464494e_bool (tptp.hAPP_f265222234e_bool (tptp.cOMBB_1356223341_state P) Q) R) (tptp.hAPP_f568432088l_bool P (tptp.hAPP_H705653759e_bool Q R)))) (forall ((P tptp.fun_Ho177530809l_bool) (Q tptp.fun_Ho320143120e_bool) (R tptp.hoare_363350478_state)) (= (tptp.hAPP_H1645464494e_bool (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1072682137e_bool tptp.cOMBC_1415895650l_bool P) Q) R) (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool P R) Q))) (forall ((P tptp.fun_fu1066574909e_bool) (Q tptp.hoare_363350478_state) (R tptp.fun_Ho320143120e_bool)) (= (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool (tptp.hAPP_f1585300113l_bool tptp.cOMBC_497487404e_bool P) Q) R) (tptp.hAPP_H1645464494e_bool (tptp.hAPP_f1749453397e_bool P R) Q))) (forall ((P tptp.fun_Ho424838195e_bool) (Q tptp.fun_pn1262351275_state) (R tptp.pname)) (= (tptp.hAPP_p2009489185e_bool (tptp.hAPP_f1284518107e_bool (tptp.cOMBB_1755629310_pname P) Q) R) (tptp.hAPP_H705653759e_bool P (tptp.hAPP_p1337579261_state Q R)))) (forall ((P tptp.fun_fu802393907l_bool) (Q tptp.fun_Ho1262521325e_bool) (R tptp.hoare_363350478_state)) (= (tptp.hAPP_H444605547l_bool (tptp.hAPP_f399561463l_bool (tptp.cOMBB_1217374484_state P) Q) R) (tptp.hAPP_f434788991l_bool P (tptp.hAPP_H2033014795e_bool Q R)))) (forall ((P tptp.fun_pn203430818_state) (Q tptp.fun_pname_com) (R tptp.pname)) (= (tptp.hAPP_p435788871_state (tptp.hAPP_f1146170881_state (tptp.hAPP_f1311198492_state tptp.cOMBS_124505571_state P) Q) R) (tptp.hAPP_c1279058753_state (tptp.hAPP_p1042965178_state P R) (tptp.hAPP_pname_com Q R)))) (forall ((P tptp.fun_fu1476767085_state) (Q tptp.fun_fu1022316450e_bool) (R tptp.fun_pname_bool)) (= (tptp.hAPP_f804167819_state (tptp.hAPP_f2070959648_state (tptp.hAPP_f820078872_state tptp.cOMBS_444947014_state P) Q) R) (tptp.hAPP_f83715540_state (tptp.hAPP_f972256569_state P R) (tptp.hAPP_f887530048e_bool Q R)))) (forall ((P tptp.fun_fu1232732404l_bool) (Q tptp.fun_fu1430349052l_bool) (R tptp.fun_pname_bool)) (= (tptp.hAPP_f434788991l_bool (tptp.hAPP_f417341722l_bool (tptp.hAPP_f836143551l_bool tptp.cOMBC_772615479l_bool P) Q) R) (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool P R) Q))) (forall ((P tptp.fun_fu1047394976e_bool) (Q tptp.fun_st2116860965l_bool) (R tptp.state)) (= (tptp.hAPP_s1226857760e_bool (tptp.hAPP_f1138284024e_bool (tptp.cOMBB_20296667_state P) Q) R) (tptp.hAPP_f644196280e_bool P (tptp.hAPP_s2001034685l_bool Q R)))) (forall ((P tptp.fun_fu2036837167l_bool) (Q tptp.fun_Ho320143120e_bool) (R tptp.fun_Ho320143120e_bool)) (= (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool (tptp.hAPP_f205303905l_bool tptp.cOMBC_1250231770l_bool P) Q) R) (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool P R) Q))) (forall ((P tptp.fun_Ho424838195e_bool) (Q tptp.fun_fu54631149_state) (R tptp.fun_pname_bool)) (= (tptp.hAPP_f1763243027e_bool (tptp.hAPP_f272807711e_bool (tptp.cOMBB_543245952e_bool P) Q) R) (tptp.hAPP_H705653759e_bool P (tptp.hAPP_f804167819_state Q R)))) (forall ((P tptp.fun_pn73701814e_bool) (Q tptp.fun_Ho320143120e_bool) (R tptp.pname)) (= (tptp.hAPP_p2009489185e_bool (tptp.hAPP_f265219918e_bool (tptp.hAPP_f1853922773e_bool tptp.cOMBC_1001821703e_bool P) Q) R) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_p678758990e_bool P R) Q))) (forall ((P tptp.fun_fu121404128_state) (Q tptp.fun_fu78728705ol_com) (R tptp.fun_pname_bool)) (= (tptp.hAPP_f972256569_state (tptp.hAPP_f926121585_state (tptp.hAPP_f907647536_state tptp.cOMBS_1636274867_state P) Q) R) (tptp.hAPP_c1279058753_state (tptp.hAPP_f637646508_state P R) (tptp.hAPP_f792846925ol_com Q R)))) (forall ((P tptp.fun_fu1759027710l_bool) (Q tptp.fun_fu1430349052l_bool) (R tptp.fun_fu1430349052l_bool)) (= (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool (tptp.hAPP_f1477350485l_bool tptp.cOMBC_694979519l_bool P) Q) R) (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool P R) Q))) (forall ((P tptp.fun_Ho424838195e_bool) (Q tptp.fun_Ho901937921_state) (R tptp.hoare_363350478_state)) (= (tptp.hAPP_H705653759e_bool (tptp.hAPP_f355123231e_bool (tptp.cOMBB_496159380_state P) Q) R) (tptp.hAPP_H705653759e_bool P (tptp.hAPP_H1982017439_state Q R)))) (forall ((P tptp.fun_pn1681257857_state) (Q tptp.fun_pn1262351275_state) (R tptp.pname)) (= (tptp.hAPP_p726046354_state (tptp.hAPP_f1180972108_state (tptp.hAPP_f1993951364_state tptp.cOMBS_89825358_state P) Q) R) (tptp.hAPP_H230141040_state (tptp.hAPP_p760538963_state P R) (tptp.hAPP_p1337579261_state Q R)))) (forall ((P tptp.fun_fu1467933941l_bool) (Q tptp.fun_fu1996308102l_bool) (R tptp.fun_Ho320143120e_bool)) (= (tptp.hAPP_f568432088l_bool (tptp.hAPP_f85652879l_bool (tptp.hAPP_f1854331281l_bool tptp.cOMBC_1522409444l_bool P) Q) R) (tptp.hAPP_f1287348838l_bool (tptp.hAPP_f1610329741l_bool P R) Q))) (forall ((P tptp.fun_fu2036837167l_bool) (Q tptp.fun_pn1521100553e_bool) (R tptp.pname)) (= (tptp.hAPP_p425615669l_bool (tptp.hAPP_f1841796439l_bool (tptp.cOMBB_343228284_pname P) Q) R) (tptp.hAPP_f726209793l_bool P (tptp.hAPP_p2009489185e_bool Q R)))) (forall ((P tptp.fun_fu422494307_state) (Q tptp.fun_fu1232608556e_bool) (R tptp.fun_Ho320143120e_bool)) (= (tptp.hAPP_f1242401993_state (tptp.hAPP_f605405862_state (tptp.hAPP_f1593397690_state tptp.cOMBS_1452472386_state P) Q) R) (tptp.hAPP_f83715540_state (tptp.hAPP_f680128379_state P R) (tptp.hAPP_f877220222e_bool Q R)))) (forall ((P tptp.fun_Ho424838195e_bool) (Q tptp.fun_fu700438391_state) (R tptp.fun_Ho320143120e_bool)) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f440040771e_bool (tptp.cOMBB_238163658e_bool P) Q) R) (tptp.hAPP_H705653759e_bool P (tptp.hAPP_f1242401993_state Q R)))) (forall ((P tptp.fun_Ho1500656352e_bool) (Q tptp.fun_Ho320143120e_bool) (R tptp.hoare_363350478_state)) (= (tptp.hAPP_H705653759e_bool (tptp.hAPP_f596150574e_bool (tptp.hAPP_f961492031e_bool tptp.cOMBC_1774708299e_bool P) Q) R) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_H122293036e_bool P R) Q))) (forall ((P tptp.fun_bo1278783462_state) (Q tptp.fun_pname_bool) (R tptp.pname)) (= (tptp.hAPP_p760538963_state (tptp.hAPP_f1418159294_state (tptp.cOMBB_1777678681_pname P) Q) R) (tptp.hAPP_b594649092_state P (tptp.hAPP_pname_bool Q R)))) (forall ((P tptp.fun_fu1575689779l_bool) (Q tptp.fun_fu1996308102l_bool) (R tptp.fun_fu1996308102l_bool)) (= (tptp.hAPP_f1287348838l_bool (tptp.hAPP_f746351743l_bool (tptp.hAPP_f992844137l_bool tptp.cOMBC_736208532l_bool P) Q) R) (tptp.hAPP_f1287348838l_bool (tptp.hAPP_f746351743l_bool P R) Q))) (forall ((P tptp.fun_fu47394518_state) (Q tptp.fun_fu1203007991ol_com) (R tptp.fun_Ho320143120e_bool)) (= (tptp.hAPP_f680128379_state (tptp.hAPP_f153770241_state (tptp.hAPP_f2014973160_state tptp.cOMBS_319359663_state P) Q) R) (tptp.hAPP_c1279058753_state (tptp.hAPP_f1659249646_state P R) (tptp.hAPP_f1577230223ol_com Q R)))) (forall ((P tptp.fun_fu515363031_state) (Q tptp.fun_pn12888928e_bool) (R tptp.pname)) (= (tptp.hAPP_p1042965178_state (tptp.hAPP_f387017471_state (tptp.cOMBB_1212270426_pname P) Q) R) (tptp.hAPP_f960042659_state P (tptp.hAPP_p1637813682e_bool Q R)))) (forall ((P tptp.fun_fu1759027710l_bool) (Q tptp.fun_fu802393907l_bool) (R tptp.fun_pname_bool)) (= (tptp.hAPP_f1320879424l_bool (tptp.hAPP_f1149191722l_bool (tptp.cOMBB_631815671e_bool P) Q) R) (tptp.hAPP_f230953622l_bool P (tptp.hAPP_f434788991l_bool Q R)))) (forall ((P tptp.fun_fu2036837167l_bool) (Q tptp.fun_Ho424838195e_bool) (R tptp.hoare_363350478_state)) (= (tptp.hAPP_H40373975l_bool (tptp.hAPP_f565239043l_bool (tptp.cOMBB_867654038_state P) Q) R) (tptp.hAPP_f726209793l_bool P (tptp.hAPP_H705653759e_bool Q R)))) (forall ((P tptp.fun_fu531943146e_bool) (Q tptp.fun_Ho320143120e_bool) (R tptp.fun_Ho320143120e_bool)) (= (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool (tptp.hAPP_f1873524693e_bool tptp.cOMBC_1626046675e_bool P) Q) R) (tptp.hAPP_f1749453397e_bool (tptp.hAPP_f1043393922e_bool P R) Q))) (forall ((P tptp.fun_Ho1500656352e_bool) (Q tptp.fun_pn1262351275_state) (R tptp.pname)) (= (tptp.hAPP_p678758990e_bool (tptp.hAPP_f43306888e_bool (tptp.cOMBB_1717464465_pname P) Q) R) (tptp.hAPP_H122293036e_bool P (tptp.hAPP_p1337579261_state Q R)))) (forall ((P tptp.fun_fu515363031_state) (Q tptp.fun_fu1022316450e_bool) (R tptp.fun_pname_bool)) (= (tptp.hAPP_f637646508_state (tptp.hAPP_f1215319405_state (tptp.cOMBB_151548708e_bool P) Q) R) (tptp.hAPP_f960042659_state P (tptp.hAPP_f887530048e_bool Q R)))) (forall ((P tptp.fun_fu1997055262l_bool) (Q tptp.fun_fu1996308102l_bool) (R tptp.fun_Ho320143120e_bool)) (= (tptp.hAPP_f726209793l_bool (tptp.hAPP_f434845752l_bool (tptp.hAPP_f1793815761l_bool tptp.cOMBC_2079418125l_bool P) Q) R) (tptp.hAPP_f85652879l_bool (tptp.hAPP_f1941218614l_bool P R) Q))) (forall ((P tptp.fun_fu515363031_state) (Q tptp.fun_fu1232608556e_bool) (R tptp.fun_Ho320143120e_bool)) (= (tptp.hAPP_f1659249646_state (tptp.hAPP_f1323754599_state (tptp.cOMBB_188465958e_bool P) Q) R) (tptp.hAPP_f960042659_state P (tptp.hAPP_f877220222e_bool Q R)))) (forall ((P tptp.fun_fu531943146e_bool) (Q tptp.fun_Ho424838195e_bool) (R tptp.hoare_363350478_state)) (= (tptp.hAPP_H122293036e_bool (tptp.hAPP_f306007574e_bool (tptp.cOMBB_1253415543_state P) Q) R) (tptp.hAPP_f1043393922e_bool P (tptp.hAPP_H705653759e_bool Q R)))) (forall ((P tptp.fun_fu1392972380l_bool) (Q tptp.fun_fu1996308102l_bool) (R tptp.fun_fu1996308102l_bool)) (= (tptp.hAPP_f85652879l_bool (tptp.hAPP_f1175211816l_bool (tptp.hAPP_f103280059l_bool tptp.cOMBC_646647229l_bool P) Q) R) (tptp.hAPP_f85652879l_bool (tptp.hAPP_f1175211816l_bool P R) Q))) (forall ((P tptp.fun_fu1392972380l_bool) (Q tptp.fun_fu2036837167l_bool) (R tptp.fun_Ho320143120e_bool)) (= (tptp.hAPP_f1941218614l_bool (tptp.hAPP_f471491948l_bool (tptp.cOMBB_460931425e_bool P) Q) R) (tptp.hAPP_f1175211816l_bool P (tptp.hAPP_f726209793l_bool Q R)))) _let_11 _let_10 (tptp.hBOOL (tptp.hAPP_f568432088l_bool tptp.finite280062779_state tptp.fa)) (not (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_H40373975l_bool tptp.member1253905979_state _let_1) tptp.fa))) (tptp.hBOOL (tptp.hAPP_f568432088l_bool (tptp.hAPP_f726209793l_bool tptp.ord_le704992346e_bool tptp.fa) (tptp.hAPP_f1763243027e_bool (tptp.image_1918575693_state (tptp.hAPP_f481860441_state _let_4 (tptp.hAPP_f96342628me_com (tptp.cOMBB_923936821_pname tptp.the_com) tptp.body))) _let_3))) _let_9 (tptp.hBOOL (tptp.hAPP_f568432088l_bool _let_6 tptp.fa)) _let_8 true))))))))))))))))))))))))))))))))))))))
% 6.03/6.27  )
% 6.03/6.27  % SZS output end Proof for SWW474_3
% 6.03/6.27  % cvc5---1.0.5 exiting
% 6.03/6.27  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------