%------------------------------------------------------------------------------
% 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 : n019.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 00:21:11 EDT 2023

% Result   : Theorem 2.77s 2.99s
% Output   : Proof 2.77s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.28  % Problem    : SWW474+3 : TPTP v8.1.2. Released v5.3.0.
% 0.11/0.29  % Command    : do_cvc5 %s %d
% 0.29/0.50  % Computer : n019.cluster.edu
% 0.29/0.50  % Model    : x86_64 x86_64
% 0.29/0.50  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.29/0.50  % Memory   : 8042.1875MB
% 0.29/0.50  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.29/0.50  % CPULimit   : 300
% 0.29/0.50  % WCLimit    : 300
% 0.29/0.50  % DateTime   : Sun Aug 27 18:20:28 EDT 2023
% 0.29/0.51  % CPUTime    : 
% 0.36/0.80  %----Proving TF0_NAR, FOF, or CNF
% 2.77/2.99  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.ZpLCPymHq5/cvc5---1.0.5_1613.p...
% 2.77/2.99  ------- get file name : TPTP file name is SWW474+3
% 2.77/2.99  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_1613.smt2...
% 2.77/2.99  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 2.77/2.99  % SZS status Theorem for SWW474+3
% 2.77/2.99  % SZS output start Proof for SWW474+3
% 2.77/2.99  (
% 2.77/2.99  (let ((_let_1 (tptp.hAPP_c1455475371_state tptp.hoare_Mirabelle_MGT tptp.y))) (let ((_let_2 (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state _let_1) tptp.bot_bo784226126e_bool))) (let ((_let_3 (tptp.dom_pname_com tptp.body))) (let ((_let_4 (tptp.cOMBB_271860050_pname tptp.hoare_Mirabelle_MGT))) (let ((_let_5 (tptp.hAPP_f360545851e_bool (tptp.image_185131637_state (tptp.hAPP_f1377420673_state _let_4 tptp.body_1)) _let_3))) (let ((_let_6 (tptp.hoare_512830354_state _let_5))) (let ((_let_7 (tptp.hBOOL (tptp.hAPP_f1378282496l_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_1795711768gleton))) (let ((_let_12 (forall ((Pn $$unsorted) (B_4 $$unsorted)) (=> (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 $$unsorted)) (=> (tptp.hBOOL tptp.hoare_1795711768gleton) (=> (tptp.hBOOL tptp.wT_bodies) (=> (tptp.hBOOL (tptp.hAPP_com_bool tptp.wt C)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hoare_512830354_state tptp.bot_bo784226126e_bool) (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state (tptp.hAPP_c1455475371_state tptp.hoare_Mirabelle_MGT C)) tptp.bot_bo784226126e_bool))))))))) (let ((_let_14 (forall ((G_2 $$unsorted) (G_3 $$unsorted) (Ts $$unsorted)) (let ((_let_1 (tptp.hoare_512830354_state G_2))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hoare_512830354_state G_3) Ts)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 G_3)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 Ts)))))))) (let ((_let_15 (forall ((G_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hoare_512830354_state G_2) tptp.bot_bo784226126e_bool))))) (let ((_let_16 (tptp.fun tptp.pname tptp.bool))) (let ((_let_17 (forall ((G_2 $$unsorted) (G_3 $$unsorted) (Ts $$unsorted)) (let ((_let_1 (tptp.hoare_512830354_state G_2))) (or (not (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hoare_512830354_state G_3) Ts))) (not (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 G_3))) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 Ts))))))) (let ((_let_18 (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_6 tptp.bot_bo784226126e_bool)))) (let ((_let_19 (not _let_18))) (let ((_let_20 (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hoare_512830354_state tptp.bot_bo784226126e_bool) _let_2)))) (let ((_let_21 (not _let_20))) (let ((_let_22 (or _let_21 _let_19 _let_7))) (let ((_let_23 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_24 (not _let_22))) (let ((_let_25 (tptp.hBOOL (tptp.hAPP_com_bool tptp.wt tptp.y)))) (let ((_let_26 (not _let_25))) (let ((_let_27 (or _let_26 _let_20))) (let ((_let_28 (forall ((C $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP_com_bool tptp.wt C))) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hoare_512830354_state tptp.bot_bo784226126e_bool) (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state (tptp.hAPP_c1455475371_state tptp.hoare_Mirabelle_MGT C)) tptp.bot_bo784226126e_bool))))))) (let ((_let_29 (ASSUME :args (_let_10)))) (let ((_let_30 (_let_28))) (let ((_let_31 (not _let_9))) (let ((_let_32 (or _let_31 _let_25))) (let ((_let_33 (forall ((Pn $$unsorted) (B_4 $$unsorted)) (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_34 (_let_33))) (let ((_let_35 (_let_15))) (let ((_let_36 (ASSUME :args _let_35))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_23 :args (_let_5 tptp.bot_bo784226126e_bool _let_2 QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP_f1378282496l_bool (tptp.hoare_512830354_state G_3) Ts) (tptp.hoare_512830354_state G_2)))) :args (_let_17))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_22)) :args ((or _let_7 _let_19 _let_21 _let_24))) (ASSUME :args (_let_8)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_36 :args (_let_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.hoare_512830354_state G_2)))) :args _let_35)) _let_36 :args (_let_18 false _let_15)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_27)) :args ((or _let_26 _let_20 (not _let_27)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_32)) :args ((or _let_31 _let_25 (not _let_32)))) (ASSUME :args (_let_9)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_34) :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_34)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))) _let_29 :args (_let_33 false _let_10)) :args (_let_32 false _let_33)) :args (_let_25 false _let_9 false _let_32)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_30) :args (tptp.y QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.hAPP_c1455475371_state tptp.hoare_Mirabelle_MGT C)))) :args _let_30)) (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_29 :args (_let_28 false _let_11 false _let_10)) :args (_let_27 false _let_28)) :args (_let_20 false _let_25 false _let_27)) :args (_let_24 true _let_7 false _let_18 false _let_20)) _let_23 :args (false true _let_22 false _let_17)) :args ((tptp.is_bool tptp.wT_bodies) (forall ((B_1_1 $$unsorted)) (tptp.is_bool (tptp.finite1653727294m_bool B_1_1))) (forall ((B_1_1 $$unsorted)) (tptp.is_bool (tptp.finite2017903282e_bool B_1_1))) (forall ((B_1_1 $$unsorted)) (tptp.is_bool (tptp.finite318301748l_bool B_1_1))) (forall ((B_1_1 $$unsorted)) (tptp.is_bool (tptp.finite2036162504e_bool B_1_1))) (forall ((B_1_1 $$unsorted)) (tptp.is_bool (tptp.finite367769966e_bool B_1_1))) (forall ((B_1_1 $$unsorted)) (tptp.is_bool (tptp.finite1765632844e_bool B_1_1))) (tptp.is_fun1661590463l_bool tptp.finite_finite_pname) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.finite860057415ne_com B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.finite1282449217_pname B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.finite683959609_state B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.finite1626890877e_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.finite2009063477e_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.finite666746948em_com B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.finite89670078_pname B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.finite416071164_state B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.finite1268145088e_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.finite688249778e_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted)) (tptp.is_fun1661590463l_bool (tptp.inj_on_pname_pname B_1_1))) (forall ((B_1_1 $$unsorted)) (tptp.is_fun1661590463l_bool (tptp.inj_on621632009_state B_1_1))) (forall ((B_1_1 $$unsorted)) (tptp.is_fun1661590463l_bool (tptp.inj_on737724108_pname B_1_1))) (tptp.is_pname (tptp.undefined_pname tptp.pname)) (tptp.is_bool (tptp.undefined_bool tptp.bool)) (tptp.is_fun_pname_bool (tptp.undefi17486888e_bool _let_16)) (tptp.is_fun1661590463l_bool (tptp.undefi64961550l_bool (tptp.fun _let_16 tptp.bool))) (tptp.is_bool tptp.hoare_1795711768gleton) (forall ((B_1_1 $$unsorted)) (tptp.is_fun_pname_bool (tptp.dom_pname_com B_1_1))) (forall ((B_1_1 $$unsorted)) (tptp.is_fun_pname_bool (tptp.dom_pname_pname B_1_1))) (forall ((B_1_1 $$unsorted)) (tptp.is_fun_pname_bool (tptp.dom_pn480909800_state B_1_1))) (forall ((B_1_1 $$unsorted)) (tptp.is_bool (tptp.is_none_com B_1_1))) (forall ((B_1_1 $$unsorted)) (=> (tptp.is_option_pname B_1_1) (tptp.is_bool (tptp.is_none_pname B_1_1)))) (forall ((B_1_1 $$unsorted)) (tptp.is_bool (tptp.is_non1379144176_state B_1_1))) (tptp.is_option_pname tptp.none_pname) (forall ((B_1_1 $$unsorted)) (=> (tptp.is_option_pname B_1_1) (tptp.is_fun_pname_bool (tptp.set_pname B_1_1)))) (tptp.is_bool tptp.bot_bot_bool) (tptp.is_fun_pname_bool tptp.bot_bo844097828e_bool) (tptp.is_fun1661590463l_bool tptp.bot_bo1649642514l_bool) (tptp.is_fun_pname_bool tptp.top_to2127735616e_bool) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_fun_pname_bool (tptp.vimage1011814463_state B_1_1 B_2_1))) (tptp.is_bool tptp.fFalse) (tptp.is_bool tptp.fTrue) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_pname (tptp.hAPP_com_pname B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.hAPP_com_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_fun_pname_bool (tptp.hAPP_c1967741679e_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_pname B_2_1) (tptp.is_pname (tptp.hAPP_pname_pname B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (and (tptp.is_fun_pname_bool B_1_1) (tptp.is_pname B_2_1)) (tptp.is_bool (tptp.hAPP_pname_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_pname B_2_1) (tptp.is_option_pname (tptp.hAPP_p1252095976_pname B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_pname B_2_1) (tptp.is_fun_pname_bool (tptp.hAPP_p61793385e_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_pname B_2_1) (tptp.is_fun1661590463l_bool (tptp.hAPP_p338031245l_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.hAPP_state_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_bool B_2_1) (tptp.is_bool (tptp.hAPP_bool_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_bool B_2_1) (tptp.is_fun_pname_bool (tptp.hAPP_b76515610e_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_bool B_2_1) (tptp.is_fun1661590463l_bool (tptp.hAPP_b357632156l_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_pname (tptp.hAPP_H1193503499_pname B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.hAPP_H242767318e_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_option_pname (tptp.hAPP_H1671063474_pname B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_fun_pname_bool (tptp.hAPP_H1776011827e_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_fun1661590463l_bool (tptp.hAPP_H358531139l_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.hAPP_option_com_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_fun_pname_bool (tptp.hAPP_o1092643708e_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_option_pname B_2_1) (tptp.is_pname (tptp.hAPP_o593586696_pname B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.hAPP_f990396704l_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_fun_pname_bool (tptp.hAPP_f1438183293e_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_fun_pname_bool B_2_1) (tptp.is_pname (tptp.hAPP_f1297739591_pname B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (and (tptp.is_fun1661590463l_bool B_1_1) (tptp.is_fun_pname_bool B_2_1)) (tptp.is_bool (tptp.hAPP_f1664156314l_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_fun_pname_bool B_2_1) (tptp.is_fun_pname_bool (tptp.hAPP_f759274231e_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_fun_pname_bool B_2_1) (tptp.is_fun1661590463l_bool (tptp.hAPP_f434788991l_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_fun_pname_bool (tptp.hAPP_f42430548e_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.hAPP_f327114704l_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.hAPP_f387058535l_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_pname (tptp.hAPP_f88366945_pname B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.hAPP_f1378282496l_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_fun_pname_bool (tptp.hAPP_f1083669085e_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_fun1661590463l_bool (tptp.hAPP_f1709493145l_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_fun1661590463l_bool B_2_1) (tptp.is_bool (tptp.hAPP_f1935102916l_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_fun1661590463l_bool B_2_1) (tptp.is_fun_pname_bool (tptp.hAPP_f674760225e_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_fun1661590463l_bool B_2_1) (tptp.is_fun1661590463l_bool (tptp.hAPP_f559147733l_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.hAPP_f1410040974l_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_fun_pname_bool (tptp.hAPP_f306376939e_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.hAPP_f389811538l_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.hAPP_f1178960312l_bool B_1_1 B_2_1))) (tptp.is_pname tptp.pn) _let_15 (forall ((Ts $$unsorted) (G_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool Ts) G_2)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hoare_512830354_state G_2) Ts)))) (forall ((Ts $$unsorted) (G_2 $$unsorted) (Ts_1 $$unsorted)) (let ((_let_1 (tptp.hoare_512830354_state G_2))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 Ts_1)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool Ts) Ts_1)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 Ts)))))) (forall ((G_2 $$unsorted) (G_3 $$unsorted) (Ts $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hoare_512830354_state G_3) Ts)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool G_3) G_2)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hoare_512830354_state G_2) Ts))))) _let_14 (forall ((Ts $$unsorted) (G_2 $$unsorted) (T $$unsorted)) (let ((_let_1 (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state T))) (let ((_let_2 (tptp.hoare_512830354_state G_2))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_2 (tptp.hAPP_f806699093e_bool _let_1 tptp.bot_bo784226126e_bool))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_2 Ts)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_2 (tptp.hAPP_f806699093e_bool _let_1 Ts)))))))) (forall ((G_2 $$unsorted) (T $$unsorted) (Ts $$unsorted)) (let ((_let_1 (tptp.hoare_512830354_state G_2))) (let ((_let_2 (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state T))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 (tptp.hAPP_f806699093e_bool _let_2 Ts))) (and (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 (tptp.hAPP_f806699093e_bool _let_2 tptp.bot_bo784226126e_bool))) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 Ts))))))) (forall ((Pn_1 $$unsorted) (G_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state (tptp.hAPP_c1455475371_state tptp.hoare_Mirabelle_MGT (tptp.hAPP_pname_com tptp.body_1 Pn_1))))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hoare_512830354_state (tptp.hAPP_f806699093e_bool _let_1 G_2)) (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state (tptp.hAPP_c1455475371_state tptp.hoare_Mirabelle_MGT (tptp.hAPP_option_com_com tptp.the_com (tptp.hAPP_p799580910on_com tptp.body Pn_1)))) tptp.bot_bo784226126e_bool))) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hoare_512830354_state G_2) (tptp.hAPP_f806699093e_bool _let_1 tptp.bot_bo784226126e_bool)))))) (forall ((A $$unsorted)) (=> (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 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool A)) (tptp.hBOOL (tptp.hAPP_f1178960312l_bool tptp.finite1203709595l_bool (tptp.hAPP_f347786453l_bool tptp.collec895295961l_bool (tptp.hAPP_f1516997247l_bool (tptp.hAPP_f1901243753l_bool tptp.cOMBC_991209188l_bool tptp.ord_le694194916l_bool) A)))))) (forall ((A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state A)) (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool (tptp.hAPP_f734420447l_bool tptp.collec1987918285e_bool (tptp.hAPP_f849457489l_bool (tptp.hAPP_f1348212993l_bool tptp.cOMBC_1350613978l_bool tptp.ord_le1449778818e_bool) A)))))) (forall ((A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool (tptp.hAPP_f434788991l_bool (tptp.hAPP_f1297925993l_bool tptp.cOMBC_1284144636l_bool tptp.ord_le313189616e_bool) A)))))) (forall ((H_1 $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state Fa)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.hAPP_f1709493145l_bool (tptp.image_1403607267e_bool H_1) Fa))))) (forall ((H_1 $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state Fa)) (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool (tptp.hAPP_f849457489l_bool (tptp.image_995511119e_bool H_1) Fa))))) (forall ((H_1 $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname Fa)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.hAPP_f434788991l_bool (tptp.image_47868345e_bool H_1) Fa))))) (forall ((H_1 $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname Fa)) (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool (tptp.hAPP_f1492100075l_bool (tptp.image_234387449e_bool H_1) Fa))))) (forall ((H_1 $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool Fa)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state (tptp.hAPP_f509793681e_bool (tptp.image_845802851_state H_1) Fa))))) (forall ((H_1 $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool Fa)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state (tptp.hAPP_f1216288071e_bool (tptp.image_1497401961_state H_1) Fa))))) (forall ((H_1 $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool Fa)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f674760225e_bool (tptp.image_1283814551_pname H_1) Fa))))) (forall ((H_1 $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool Fa)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f306376939e_bool (tptp.image_1863446033_pname H_1) Fa))))) (forall ((H_1 $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname Fa)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state (tptp.hAPP_f360545851e_bool (tptp.image_185131637_state H_1) Fa))))) (forall ((A $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool tptp.bot_bo844097828e_bool) A))) (forall ((A $$unsorted)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_f273696895l_bool tptp.ord_le1708315510m_bool tptp.bot_bot_fun_com_bool) A))) (forall ((A $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool tptp.bot_bo784226126e_bool) A))) (forall ((A_4 $$unsorted) (A $$unsorted)) (=> (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 $$unsorted) (A $$unsorted)) (=> (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 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool A)) (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool (tptp.hAPP_f734420447l_bool (tptp.hAPP_f1472090462l_bool tptp.insert1720618162e_bool A_4) A))))) (forall ((A_4 $$unsorted) (A $$unsorted)) (=> (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 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state A)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state A_4) A))))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool tptp.bot_bo1649642514l_bool)) (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool tptp.bot_bo942947096l_bool)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool tptp.finite_finite_com tptp.bot_bot_fun_com_bool)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state tptp.bot_bo784226126e_bool)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname tptp.bot_bo844097828e_bool)) (forall ((Q_1 $$unsorted) (P_1 $$unsorted)) (=> (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 $$unsorted) (P_1 $$unsorted)) (=> (or (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool (tptp.hAPP_f734420447l_bool tptp.collec1987918285e_bool P_1))) (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool (tptp.hAPP_f734420447l_bool tptp.collec1987918285e_bool Q_1)))) (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool (tptp.hAPP_f734420447l_bool tptp.collec1987918285e_bool (tptp.hAPP_f734420447l_bool (tptp.hAPP_f524831474l_bool tptp.cOMBS_1162100051l_bool (tptp.hAPP_f118042163l_bool (tptp.cOMBB_1749019442e_bool tptp.fconj) P_1)) Q_1)))))) (forall ((Q_1 $$unsorted) (P_1 $$unsorted)) (=> (or (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state (tptp.hAPP_f806699093e_bool tptp.collec637225377_state P_1))) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state (tptp.hAPP_f806699093e_bool tptp.collec637225377_state Q_1)))) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state (tptp.hAPP_f806699093e_bool tptp.collec637225377_state (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1702629984e_bool tptp.cOMBS_865875691l_bool (tptp.hAPP_f832587837l_bool (tptp.cOMBB_1291456124_state tptp.fconj) P_1)) Q_1)))))) (forall ((Q_1 $$unsorted) (P_1 $$unsorted)) (=> (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 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f1083669085e_bool (tptp.image_1774499931_pname (tptp.hAPP_p1227118702_pname tptp.cOMBK_497473068_state C)) A))) (let ((_let_2 (= A tptp.bot_bo784226126e_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 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f1815646051m_bool (tptp.image_741143905te_com (tptp.hAPP_c57939194te_com tptp.cOMBK_131063602_state C)) A))) (let ((_let_2 (= A tptp.bot_bo784226126e_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 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f457085749e_bool (tptp.image_2605051_state (tptp.hAPP_H275587026_state tptp.cOMBK_869602456te_com C)) A))) (let ((_let_2 (= A tptp.bot_bot_fun_com_bool))) (and (=> _let_2 (= _let_1 tptp.bot_bo784226126e_bool)) (=> (not _let_2) (= _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state C) tptp.bot_bo784226126e_bool))))))) (forall ((C $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f360545851e_bool (tptp.image_185131637_state (tptp.hAPP_H1938877132_state tptp.cOMBK_2086841362_pname C)) A))) (let ((_let_2 (= A tptp.bot_bo844097828e_bool))) (=> (tptp.is_fun_pname_bool A) (and (=> _let_2 (= _let_1 tptp.bot_bo784226126e_bool)) (=> (not _let_2) (= _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state C) tptp.bot_bo784226126e_bool)))))))) (forall ((C $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state X_1) A)) (= (tptp.hAPP_f1083669085e_bool (tptp.image_1774499931_pname (tptp.hAPP_p1227118702_pname tptp.cOMBK_497473068_state C)) A) (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname C) tptp.bot_bo844097828e_bool)))) (forall ((C $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state X_1) A)) (= (tptp.hAPP_f1815646051m_bool (tptp.image_741143905te_com (tptp.hAPP_c57939194te_com tptp.cOMBK_131063602_state C)) A) (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com C) tptp.bot_bot_fun_com_bool)))) (forall ((C $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A)) (= (tptp.hAPP_f759274231e_bool (tptp.image_pname_pname (tptp.hAPP_p1170154830_pname tptp.cOMBK_pname_pname C)) A) (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname C) tptp.bot_bo844097828e_bool)))) (forall ((C $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (=> (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 $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_1) A)) (= (tptp.hAPP_f457085749e_bool (tptp.image_2605051_state (tptp.hAPP_H275587026_state tptp.cOMBK_869602456te_com C)) A) (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state C) tptp.bot_bo784226126e_bool)))) (forall ((C $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A)) (= (tptp.hAPP_f360545851e_bool (tptp.image_185131637_state (tptp.hAPP_H1938877132_state tptp.cOMBK_2086841362_pname C)) A) (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state C) tptp.bot_bo784226126e_bool)))) (forall ((F $$unsorted) (X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.dom_com_com F))) (=> (= (tptp.hAPP_com_option_com F X_1) (tptp.hAPP_com_option_com tptp.some_com Y_2)) (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com X_1) _let_1) _let_1)))) (forall ((F $$unsorted) (X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.dom_Ho2070278094_pname F))) (=> (= (tptp.hAPP_H1671063474_pname F X_1) (tptp.hAPP_p1252095976_pname tptp.some_pname Y_2)) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state X_1) _let_1) _let_1)))) (forall ((F $$unsorted) (X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.dom_Ho1607160812_state F))) (=> (= (tptp.hAPP_H1633077406_state F X_1) (tptp.hAPP_H1633077406_state tptp.some_H1043067815_state Y_2)) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state X_1) _let_1) _let_1)))) (forall ((F $$unsorted) (X_1 $$unsorted) (Y_2 $$unsorted)) (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 $$unsorted) (F $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state A)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool B) (tptp.hAPP_f1709493145l_bool (tptp.image_1403607267e_bool F) A))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool B))))) (forall ((B $$unsorted) (F $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state A)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool (tptp.hAPP_f1516997247l_bool tptp.ord_le694194916l_bool B) (tptp.hAPP_f849457489l_bool (tptp.image_995511119e_bool F) A))) (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool B))))) (forall ((B $$unsorted) (F $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state A)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) (tptp.hAPP_f1083669085e_bool (tptp.image_1774499931_pname F) A))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B))))) (forall ((B $$unsorted) (F $$unsorted) (A $$unsorted)) (=> (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 $$unsorted) (F $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool (tptp.hAPP_f1516997247l_bool tptp.ord_le694194916l_bool B) (tptp.hAPP_f1492100075l_bool (tptp.image_234387449e_bool F) A))) (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool B))))) (forall ((B $$unsorted) (F $$unsorted) (A $$unsorted)) (=> (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 $$unsorted) (F $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool B) (tptp.hAPP_f509793681e_bool (tptp.image_845802851_state F) A))) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state B))))) (forall ((B $$unsorted) (F $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool B) (tptp.hAPP_f1216288071e_bool (tptp.image_1497401961_state F) A))) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state B))))) (forall ((B $$unsorted) (F $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) (tptp.hAPP_f674760225e_bool (tptp.image_1283814551_pname F) A))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B))))) (forall ((B $$unsorted) (F $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) (tptp.hAPP_f306376939e_bool (tptp.image_1863446033_pname F) A))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B))))) (forall ((B $$unsorted) (F $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool B) (tptp.hAPP_f360545851e_bool (tptp.image_185131637_state F) A))) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state B))))) (forall ((A $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1) tptp.bot_bo844097828e_bool))) (=> (tptp.is_fun_pname_bool A) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) _let_1)) (or (= A tptp.bot_bo844097828e_bool) (= A _let_1)))))) (forall ((A $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com X_1) tptp.bot_bot_fun_com_bool))) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_f273696895l_bool tptp.ord_le1708315510m_bool A) _let_1)) (or (= A tptp.bot_bot_fun_com_bool) (= A _let_1))))) (forall ((A $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state X_1) tptp.bot_bo784226126e_bool))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool A) _let_1)) (or (= A tptp.bot_bo784226126e_bool) (= A _let_1))))) _let_13 (forall ((A_4 $$unsorted)) (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 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state A_4) tptp.bot_bo784226126e_bool)))) (forall ((A_4 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A_4) tptp.bot_bo844097828e_bool)))) (forall ((B_1 $$unsorted) (A_4 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_c667411853l_bool tptp.member_com A_4))) (=> (=> (not (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 B))) (= A_4 B_1)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com B_1) B)))))) (forall ((B_1 $$unsorted) (A_4 $$unsorted) (B $$unsorted)) (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 $$unsorted) (A_4 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state A_4))) (=> (=> (not (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 B))) (= A_4 B_1)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state B_1) B)))))) (forall ((A_4 $$unsorted) (B_1 $$unsorted) (A $$unsorted)) (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 $$unsorted) (B_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname A_4))) (=> (and (tptp.is_pname A_4) (tptp.is_pname B_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname B_1) A))) (=> (not (= A_4 B_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A))))))) (forall ((A_4 $$unsorted) (B_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state A_4))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state B_1) A))) (=> (not (= A_4 B_1)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 A)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.is_fun_pname_bool A) (tptp.is_fun_pname_bool B)) (=> (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 $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool B) A)) (= A B)))) (forall ((C $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_c667411853l_bool tptp.member_com C))) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_f273696895l_bool tptp.ord_le1708315510m_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 B)))))) (forall ((C $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state C))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 B)))))) (forall ((C $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname C))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B)))))) (forall ((A $$unsorted) (B_1 $$unsorted) (F $$unsorted) (X_1 $$unsorted)) (=> (= B_1 (tptp.hAPP_H46530577te_com F X_1)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state X_1) A)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com B_1) (tptp.hAPP_f1815646051m_bool (tptp.image_741143905te_com F) A)))))) (forall ((A $$unsorted) (B_1 $$unsorted) (F $$unsorted) (X_1 $$unsorted)) (=> (= B_1 (tptp.hAPP_pname_com F X_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com B_1) (tptp.hAPP_f1206115581m_bool (tptp.image_pname_com F) A)))))) (forall ((A $$unsorted) (B_1 $$unsorted) (F $$unsorted) (X_1 $$unsorted)) (=> (= B_1 (tptp.hAPP_c1455475371_state F X_1)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_1) A)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state B_1) (tptp.hAPP_f457085749e_bool (tptp.image_2605051_state F) A)))))) (forall ((A $$unsorted) (B_1 $$unsorted) (F $$unsorted) (X_1 $$unsorted)) (=> (= B_1 (tptp.hAPP_com_pname F X_1)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_1) A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname B_1) (tptp.hAPP_f1438183293e_bool (tptp.image_com_pname F) A)))))) (forall ((A $$unsorted) (B_1 $$unsorted) (F $$unsorted) (X_1 $$unsorted)) (=> (= B_1 (tptp.hAPP_p1751618853_state F X_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state B_1) (tptp.hAPP_f360545851e_bool (tptp.image_185131637_state F) A)))))) (forall ((A_4 $$unsorted) (A $$unsorted)) (=> (= A tptp.bot_bot_fun_com_bool) (not (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com A_4) A))))) (forall ((A_4 $$unsorted) (A $$unsorted)) (=> (= A tptp.bot_bo784226126e_bool) (not (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state A_4) A))))) (forall ((A_4 $$unsorted) (A $$unsorted)) (=> (= A tptp.bot_bo844097828e_bool) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A_4) A))))) (forall ((P_1 $$unsorted)) (= (= (tptp.hAPP_f759274231e_bool tptp.collect_pname P_1) tptp.bot_bo844097828e_bool) (forall ((X_2 $$unsorted)) (=> (tptp.is_pname X_2) (not (tptp.hBOOL (tptp.hAPP_pname_bool P_1 X_2))))))) (forall ((P_1 $$unsorted)) (= (= (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool P_1) tptp.bot_bo1649642514l_bool) (forall ((X_2 $$unsorted)) (=> (tptp.is_fun_pname_bool X_2) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 X_2))))))) (forall ((P_1 $$unsorted)) (= (= (tptp.hAPP_f734420447l_bool tptp.collec1987918285e_bool P_1) tptp.bot_bo942947096l_bool) (forall ((X_2 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f1378282496l_bool P_1 X_2)))))) (forall ((P_1 $$unsorted)) (= (= (tptp.hAPP_f1682609283m_bool tptp.collect_com P_1) tptp.bot_bot_fun_com_bool) (forall ((X_2 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_com_bool P_1 X_2)))))) (forall ((P_1 $$unsorted)) (= (= (tptp.hAPP_f806699093e_bool tptp.collec637225377_state P_1) tptp.bot_bo784226126e_bool) (forall ((X_2 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_H242767318e_bool P_1 X_2)))))) (forall ((C $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com C) tptp.bot_bot_fun_com_bool)))) (forall ((C $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state C) tptp.bot_bo784226126e_bool)))) (forall ((C $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname C) tptp.bot_bo844097828e_bool)))) (forall ((P_1 $$unsorted)) (= (= tptp.bot_bo844097828e_bool (tptp.hAPP_f759274231e_bool tptp.collect_pname P_1)) (forall ((X_2 $$unsorted)) (=> (tptp.is_pname X_2) (not (tptp.hBOOL (tptp.hAPP_pname_bool P_1 X_2))))))) (forall ((P_1 $$unsorted)) (= (= tptp.bot_bo1649642514l_bool (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool P_1)) (forall ((X_2 $$unsorted)) (=> (tptp.is_fun_pname_bool X_2) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 X_2))))))) (forall ((P_1 $$unsorted)) (= (= tptp.bot_bo942947096l_bool (tptp.hAPP_f734420447l_bool tptp.collec1987918285e_bool P_1)) (forall ((X_2 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f1378282496l_bool P_1 X_2)))))) (forall ((P_1 $$unsorted)) (= (= tptp.bot_bot_fun_com_bool (tptp.hAPP_f1682609283m_bool tptp.collect_com P_1)) (forall ((X_2 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_com_bool P_1 X_2)))))) (forall ((P_1 $$unsorted)) (= (= tptp.bot_bo784226126e_bool (tptp.hAPP_f806699093e_bool tptp.collec637225377_state P_1)) (forall ((X_2 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_H242767318e_bool P_1 X_2)))))) (forall ((A $$unsorted)) (= (exists ((X_2 $$unsorted)) (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 $$unsorted)) (= (exists ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state X_2) A))) (not (= A tptp.bot_bo784226126e_bool)))) (forall ((A $$unsorted)) (=> (tptp.is_fun_pname_bool A) (= (exists ((X_2 $$unsorted)) (and (tptp.is_pname X_2) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A)))) (not (= A tptp.bot_bo844097828e_bool))))) (forall ((A $$unsorted)) (= (forall ((X_2 $$unsorted)) (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 $$unsorted)) (= (forall ((X_2 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state X_2) A)))) (= A tptp.bot_bo784226126e_bool))) (forall ((A $$unsorted)) (=> (tptp.is_fun_pname_bool A) (= (forall ((X_2 $$unsorted)) (=> (tptp.is_pname X_2) (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_bo942947096l_bool (tptp.hAPP_f734420447l_bool tptp.collec1987918285e_bool (tptp.hAPP_b167205134l_bool tptp.cOMBK_293339231e_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_bo784226126e_bool (tptp.hAPP_f806699093e_bool tptp.collec637225377_state (tptp.hAPP_b974863576e_bool tptp.cOMBK_988866959_state tptp.fFalse))) (forall ((A_4 $$unsorted) (A $$unsorted)) (=> (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 $$unsorted) (A $$unsorted)) (=> (tptp.is_fun_pname_bool A) (=> (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 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state A_4) A)) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state A_4) A) A))) (forall ((B_1 $$unsorted) (A_4 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_c667411853l_bool tptp.member_com A_4))) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 B)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com B_1) B)))))) (forall ((B_1 $$unsorted) (A_4 $$unsorted) (B $$unsorted)) (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 $$unsorted) (A_4 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state A_4))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 B)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state B_1) B)))))) (forall ((B $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (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 $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1))) (let ((_let_2 (tptp.hAPP_p338031245l_bool tptp.member_pname X_1))) (=> (and (tptp.is_fun_pname_bool B) (tptp.is_fun_pname_bool A)) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_2 A))) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_2 B))) (= (= (tptp.hAPP_f759274231e_bool _let_1 A) (tptp.hAPP_f759274231e_bool _let_1 B)) (= A B)))))))) (forall ((B $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state X_1))) (let ((_let_2 (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state X_1))) (=> (not (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_2 A))) (=> (not (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_2 B))) (= (= (tptp.hAPP_f806699093e_bool _let_1 A) (tptp.hAPP_f806699093e_bool _let_1 B)) (= A B))))))) (forall ((Y_2 $$unsorted) (A $$unsorted) (X_1 $$unsorted)) (=> (and (tptp.is_pname Y_2) (tptp.is_pname X_1)) (= (tptp.hBOOL (tptp.hAPP_pname_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname Y_2) A) X_1)) (or (= Y_2 X_1) (tptp.hBOOL (tptp.hAPP_pname_bool A X_1)))))) (forall ((Y_2 $$unsorted) (A $$unsorted) (X_1 $$unsorted)) (= (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 $$unsorted) (A $$unsorted) (X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_H242767318e_bool (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state Y_2) A) X_1)) (or (= Y_2 X_1) (tptp.hBOOL (tptp.hAPP_H242767318e_bool A X_1))))) (forall ((A_4 $$unsorted) (B_1 $$unsorted) (A $$unsorted)) (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 $$unsorted) (B_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname A_4))) (=> (and (tptp.is_pname A_4) (tptp.is_pname B_1)) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname B_1) A))) (or (= A_4 B_1) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A))))))) (forall ((A_4 $$unsorted) (B_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state A_4))) (= (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state B_1) A))) (or (= A_4 B_1) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 A)))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1))) (let ((_let_2 (tptp.hAPP_p905327722e_bool tptp.insert_pname Y_2))) (= (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool _let_2 A)) (tptp.hAPP_f759274231e_bool _let_2 (tptp.hAPP_f759274231e_bool _let_1 A)))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted) (A $$unsorted)) (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 $$unsorted) (Y_2 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state X_1))) (let ((_let_2 (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state Y_2))) (= (tptp.hAPP_f806699093e_bool _let_1 (tptp.hAPP_f806699093e_bool _let_2 A)) (tptp.hAPP_f806699093e_bool _let_2 (tptp.hAPP_f806699093e_bool _let_1 A)))))) (forall ((X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1))) (let ((_let_2 (tptp.hAPP_f759274231e_bool _let_1 A))) (= (tptp.hAPP_f759274231e_bool _let_1 _let_2) _let_2)))) (forall ((X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_c566651504m_bool tptp.insert_com X_1))) (let ((_let_2 (tptp.hAPP_f1682609283m_bool _let_1 A))) (= (tptp.hAPP_f1682609283m_bool _let_1 _let_2) _let_2)))) (forall ((X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state X_1))) (let ((_let_2 (tptp.hAPP_f806699093e_bool _let_1 A))) (= (tptp.hAPP_f806699093e_bool _let_1 _let_2) _let_2)))) (forall ((A_4 $$unsorted) (P_1 $$unsorted)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A_4) (tptp.hAPP_f759274231e_bool tptp.collect_pname P_1)) (tptp.hAPP_f759274231e_bool tptp.collect_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_f649174806e_bool tptp.cOMBS_568398431l_bool (tptp.hAPP_f1402196763l_bool (tptp.cOMBB_675860798_pname tptp.fimplies) (tptp.hAPP_f759274231e_bool (tptp.cOMBB_647938656_pname tptp.fNot) (tptp.hAPP_p61793385e_bool (tptp.hAPP_f22061361e_bool tptp.cOMBC_1149511130e_bool tptp.fequal_pname) A_4)))) P_1)))) (forall ((A_4 $$unsorted) (P_1 $$unsorted)) (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com A_4) (tptp.hAPP_f1682609283m_bool tptp.collect_com P_1)) (tptp.hAPP_f1682609283m_bool tptp.collect_com (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f328772264m_bool tptp.cOMBS_com_bool_bool (tptp.hAPP_f954469007l_bool (tptp.cOMBB_886968260ol_com tptp.fimplies) (tptp.hAPP_f1682609283m_bool (tptp.cOMBB_bool_bool_com tptp.fNot) (tptp.hAPP_c1396316405m_bool (tptp.hAPP_f908845385m_bool tptp.cOMBC_com_com_bool tptp.fequal_com) A_4)))) P_1)))) (forall ((A_4 $$unsorted) (P_1 $$unsorted)) (= (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool A_4) (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool P_1)) (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f624840228l_bool tptp.cOMBS_350070575l_bool (tptp.hAPP_f143162813l_bool (tptp.cOMBB_2095475776e_bool tptp.fimplies) (tptp.hAPP_f559147733l_bool (tptp.cOMBB_307249310e_bool tptp.fNot) (tptp.hAPP_f434788991l_bool (tptp.hAPP_f1297925993l_bool tptp.cOMBC_1284144636l_bool tptp.fequal533582459e_bool) A_4)))) P_1)))) (forall ((A_4 $$unsorted) (P_1 $$unsorted)) (= (tptp.hAPP_f734420447l_bool (tptp.hAPP_f1472090462l_bool tptp.insert1720618162e_bool A_4) (tptp.hAPP_f734420447l_bool tptp.collec1987918285e_bool P_1)) (tptp.hAPP_f734420447l_bool tptp.collec1987918285e_bool (tptp.hAPP_f734420447l_bool (tptp.hAPP_f524831474l_bool tptp.cOMBS_1162100051l_bool (tptp.hAPP_f118042163l_bool (tptp.cOMBB_1749019442e_bool tptp.fimplies) (tptp.hAPP_f734420447l_bool (tptp.cOMBB_1686148692e_bool tptp.fNot) (tptp.hAPP_f849457489l_bool (tptp.hAPP_f1348212993l_bool tptp.cOMBC_1350613978l_bool tptp.fequal1475827639e_bool) A_4)))) P_1)))) (forall ((A_4 $$unsorted) (P_1 $$unsorted)) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state A_4) (tptp.hAPP_f806699093e_bool tptp.collec637225377_state P_1)) (tptp.hAPP_f806699093e_bool tptp.collec637225377_state (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1702629984e_bool tptp.cOMBS_865875691l_bool (tptp.hAPP_f832587837l_bool (tptp.cOMBB_1291456124_state tptp.fimplies) (tptp.hAPP_f806699093e_bool (tptp.cOMBB_325909978_state tptp.fNot) (tptp.hAPP_H216526335e_bool (tptp.hAPP_f1902016361e_bool tptp.cOMBC_1967329268e_bool tptp.fequal1440809015_state) A_4)))) P_1)))) (forall ((A_4 $$unsorted) (B $$unsorted)) (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com A_4) B) (tptp.hAPP_f1682609283m_bool tptp.collect_com (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f328772264m_bool tptp.cOMBS_com_bool_bool (tptp.hAPP_f954469007l_bool (tptp.cOMBB_886968260ol_com tptp.fdisj) (tptp.hAPP_c1396316405m_bool (tptp.hAPP_f908845385m_bool tptp.cOMBC_com_com_bool tptp.fequal_com) A_4))) (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f578650245m_bool tptp.cOMBC_1904837336l_bool tptp.member_com) B))))) (forall ((A_4 $$unsorted) (B $$unsorted)) (= (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool A_4) B) (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f624840228l_bool tptp.cOMBS_350070575l_bool (tptp.hAPP_f143162813l_bool (tptp.cOMBB_2095475776e_bool tptp.fdisj) (tptp.hAPP_f434788991l_bool (tptp.hAPP_f1297925993l_bool tptp.cOMBC_1284144636l_bool tptp.fequal533582459e_bool) A_4))) (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1145991873l_bool tptp.cOMBC_1988546018l_bool tptp.member799430823e_bool) B))))) (forall ((A_4 $$unsorted) (B $$unsorted)) (= (tptp.hAPP_f734420447l_bool (tptp.hAPP_f1472090462l_bool tptp.insert1720618162e_bool A_4) B) (tptp.hAPP_f734420447l_bool tptp.collec1987918285e_bool (tptp.hAPP_f734420447l_bool (tptp.hAPP_f524831474l_bool tptp.cOMBS_1162100051l_bool (tptp.hAPP_f118042163l_bool (tptp.cOMBB_1749019442e_bool tptp.fdisj) (tptp.hAPP_f849457489l_bool (tptp.hAPP_f1348212993l_bool tptp.cOMBC_1350613978l_bool tptp.fequal1475827639e_bool) A_4))) (tptp.hAPP_f734420447l_bool (tptp.hAPP_f1236719585l_bool tptp.cOMBC_1484018740l_bool tptp.member131361931e_bool) B))))) (forall ((A_4 $$unsorted) (B $$unsorted)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A_4) B) (tptp.hAPP_f759274231e_bool tptp.collect_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_f649174806e_bool tptp.cOMBS_568398431l_bool (tptp.hAPP_f1402196763l_bool (tptp.cOMBB_675860798_pname tptp.fdisj) (tptp.hAPP_p61793385e_bool (tptp.hAPP_f22061361e_bool tptp.cOMBC_1149511130e_bool tptp.fequal_pname) A_4))) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f661147897e_bool tptp.cOMBC_1058051404l_bool tptp.member_pname) B))))) (forall ((A_4 $$unsorted) (B $$unsorted)) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state A_4) B) (tptp.hAPP_f806699093e_bool tptp.collec637225377_state (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1702629984e_bool tptp.cOMBS_865875691l_bool (tptp.hAPP_f832587837l_bool (tptp.cOMBB_1291456124_state tptp.fdisj) (tptp.hAPP_H216526335e_bool (tptp.hAPP_f1902016361e_bool tptp.cOMBC_1967329268e_bool tptp.fequal1440809015_state) A_4))) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1184122441e_bool tptp.cOMBC_538205282l_bool tptp.member1667945571_state) B))))) (forall ((A_4 $$unsorted) (B $$unsorted)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com A_4) (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com A_4) B)))) (forall ((A_4 $$unsorted) (B $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A_4) (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A_4) B)))) (forall ((A_4 $$unsorted) (B $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state A_4) (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state A_4) B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (not (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) B)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) A))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (not (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool A) B)) (not (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool B) A))))))) (forall ((C_1 $$unsorted) (A $$unsorted) (B $$unsorted)) (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 $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool A))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 B)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool B) C_1)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 C_1)))))) (forall ((X_1 $$unsorted) (A $$unsorted) (B $$unsorted)) (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 $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state X_1))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 B)))))) (forall ((X_1 $$unsorted) (A $$unsorted) (B $$unsorted)) (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 $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_c667411853l_bool tptp.member_com X_1))) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 A)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_f273696895l_bool tptp.ord_le1708315510m_bool A) B)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 B)))))) (forall ((B $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state X_1))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 A)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool A) B)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 B)))))) (forall ((B $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname X_1))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) B)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B)))))) (forall ((X_1 $$unsorted) (A $$unsorted) (B $$unsorted)) (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 $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state X_1))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 B)))))) (forall ((X_1 $$unsorted) (A $$unsorted) (B $$unsorted)) (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 $$unsorted) (B $$unsorted)) (=> (= A B) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool B) A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool A) B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.is_fun_pname_bool A) (tptp.is_fun_pname_bool B)) (= (= 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 $$unsorted) (B $$unsorted)) (= (= A B) (and (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool A) B)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool B) A))))) (forall ((A $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) A))) (forall ((A $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool A) A))) (forall ((B_1 $$unsorted) (F $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state X_1) A)) (=> (= B_1 (tptp.hAPP_H46530577te_com F X_1)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com B_1) (tptp.hAPP_f1815646051m_bool (tptp.image_741143905te_com F) A)))))) (forall ((B_1 $$unsorted) (F $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (=> (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 $$unsorted) (F $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_1) A)) (=> (= B_1 (tptp.hAPP_c1455475371_state F X_1)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state B_1) (tptp.hAPP_f457085749e_bool (tptp.image_2605051_state F) A)))))) (forall ((B_1 $$unsorted) (F $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (=> (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 $$unsorted) (F $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A)) (=> (= B_1 (tptp.hAPP_p1751618853_state F X_1)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state B_1) (tptp.hAPP_f360545851e_bool (tptp.image_185131637_state F) A)))))) (forall ((F $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state X_1) A)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com (tptp.hAPP_H46530577te_com F X_1)) (tptp.hAPP_f1815646051m_bool (tptp.image_741143905te_com F) A))))) (forall ((F $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (=> (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 $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_1) A)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state (tptp.hAPP_c1455475371_state F X_1)) (tptp.hAPP_f457085749e_bool (tptp.image_2605051_state F) A))))) (forall ((F $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (=> (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 $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state (tptp.hAPP_p1751618853_state F X_1)) (tptp.hAPP_f360545851e_bool (tptp.image_185131637_state F) A))))) (forall ((Z $$unsorted) (F $$unsorted) (A $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state Z) (tptp.hAPP_f360545851e_bool (tptp.image_185131637_state F) A))) (exists ((X_2 $$unsorted)) (and (tptp.is_pname X_2) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A)) (= Z (tptp.hAPP_p1751618853_state F X_2)))))) (forall ((P_1 $$unsorted) (Q_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f624840228l_bool tptp.cOMBS_350070575l_bool (tptp.hAPP_f143162813l_bool (tptp.cOMBB_2095475776e_bool tptp.fdisj) P_1)) Q_1)))) (and (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool P_1))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool Q_1)))))) (forall ((P_1 $$unsorted) (Q_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool (tptp.hAPP_f734420447l_bool tptp.collec1987918285e_bool (tptp.hAPP_f734420447l_bool (tptp.hAPP_f524831474l_bool tptp.cOMBS_1162100051l_bool (tptp.hAPP_f118042163l_bool (tptp.cOMBB_1749019442e_bool tptp.fdisj) P_1)) Q_1)))) (and (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool (tptp.hAPP_f734420447l_bool tptp.collec1987918285e_bool P_1))) (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool (tptp.hAPP_f734420447l_bool tptp.collec1987918285e_bool Q_1)))))) (forall ((P_1 $$unsorted) (Q_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state (tptp.hAPP_f806699093e_bool tptp.collec637225377_state (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1702629984e_bool tptp.cOMBS_865875691l_bool (tptp.hAPP_f832587837l_bool (tptp.cOMBB_1291456124_state tptp.fdisj) P_1)) Q_1)))) (and (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state (tptp.hAPP_f806699093e_bool tptp.collec637225377_state P_1))) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state (tptp.hAPP_f806699093e_bool tptp.collec637225377_state Q_1)))))) (forall ((P_1 $$unsorted) (Q_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f759274231e_bool tptp.collect_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_f649174806e_bool tptp.cOMBS_568398431l_bool (tptp.hAPP_f1402196763l_bool (tptp.cOMBB_675860798_pname tptp.fdisj) P_1)) Q_1)))) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f759274231e_bool tptp.collect_pname P_1))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f759274231e_bool tptp.collect_pname Q_1)))))) (forall ((X_2 $$unsorted) (Xa $$unsorted)) (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com X_2) Xa) (tptp.hAPP_f1682609283m_bool tptp.collect_com (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f328772264m_bool tptp.cOMBS_com_bool_bool (tptp.hAPP_f954469007l_bool (tptp.cOMBB_886968260ol_com tptp.fdisj) (tptp.hAPP_c1396316405m_bool (tptp.hAPP_f908845385m_bool tptp.cOMBC_com_com_bool tptp.fequal_com) X_2))) (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f578650245m_bool tptp.cOMBC_1904837336l_bool tptp.member_com) Xa))))) (forall ((X_2 $$unsorted) (Xa $$unsorted)) (= (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool X_2) Xa) (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f624840228l_bool tptp.cOMBS_350070575l_bool (tptp.hAPP_f143162813l_bool (tptp.cOMBB_2095475776e_bool tptp.fdisj) (tptp.hAPP_f434788991l_bool (tptp.hAPP_f1297925993l_bool tptp.cOMBC_1284144636l_bool tptp.fequal533582459e_bool) X_2))) (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1145991873l_bool tptp.cOMBC_1988546018l_bool tptp.member799430823e_bool) Xa))))) (forall ((X_2 $$unsorted) (Xa $$unsorted)) (= (tptp.hAPP_f734420447l_bool (tptp.hAPP_f1472090462l_bool tptp.insert1720618162e_bool X_2) Xa) (tptp.hAPP_f734420447l_bool tptp.collec1987918285e_bool (tptp.hAPP_f734420447l_bool (tptp.hAPP_f524831474l_bool tptp.cOMBS_1162100051l_bool (tptp.hAPP_f118042163l_bool (tptp.cOMBB_1749019442e_bool tptp.fdisj) (tptp.hAPP_f849457489l_bool (tptp.hAPP_f1348212993l_bool tptp.cOMBC_1350613978l_bool tptp.fequal1475827639e_bool) X_2))) (tptp.hAPP_f734420447l_bool (tptp.hAPP_f1236719585l_bool tptp.cOMBC_1484018740l_bool tptp.member131361931e_bool) Xa))))) (forall ((X_2 $$unsorted) (Xa $$unsorted)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname X_2) Xa) (tptp.hAPP_f759274231e_bool tptp.collect_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_f649174806e_bool tptp.cOMBS_568398431l_bool (tptp.hAPP_f1402196763l_bool (tptp.cOMBB_675860798_pname tptp.fdisj) (tptp.hAPP_p61793385e_bool (tptp.hAPP_f22061361e_bool tptp.cOMBC_1149511130e_bool tptp.fequal_pname) X_2))) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f661147897e_bool tptp.cOMBC_1058051404l_bool tptp.member_pname) Xa))))) (forall ((X_2 $$unsorted) (Xa $$unsorted)) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state X_2) Xa) (tptp.hAPP_f806699093e_bool tptp.collec637225377_state (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1702629984e_bool tptp.cOMBS_865875691l_bool (tptp.hAPP_f832587837l_bool (tptp.cOMBB_1291456124_state tptp.fdisj) (tptp.hAPP_H216526335e_bool (tptp.hAPP_f1902016361e_bool tptp.cOMBC_1967329268e_bool tptp.fequal1440809015_state) X_2))) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1184122441e_bool tptp.cOMBC_538205282l_bool tptp.member1667945571_state) Xa))))) (forall ((A_4 $$unsorted) (B_1 $$unsorted)) (=> (and (tptp.is_pname A_4) (tptp.is_pname B_1)) (=> (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A_4) tptp.bot_bo844097828e_bool) (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname B_1) tptp.bot_bo844097828e_bool)) (= A_4 B_1)))) (forall ((A_4 $$unsorted) (B_1 $$unsorted)) (=> (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com A_4) tptp.bot_bot_fun_com_bool) (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com B_1) tptp.bot_bot_fun_com_bool)) (= A_4 B_1))) (forall ((A_4 $$unsorted) (B_1 $$unsorted)) (=> (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state A_4) tptp.bot_bo784226126e_bool) (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state B_1) tptp.bot_bo784226126e_bool)) (= A_4 B_1))) (forall ((B_1 $$unsorted) (A_4 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com B_1) (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com A_4) tptp.bot_bot_fun_com_bool))) (= B_1 A_4))) (forall ((B_1 $$unsorted) (A_4 $$unsorted)) (=> (and (tptp.is_pname B_1) (tptp.is_pname A_4)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname B_1) (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A_4) tptp.bot_bo844097828e_bool))) (= B_1 A_4)))) (forall ((B_1 $$unsorted) (A_4 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state B_1) (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state A_4) tptp.bot_bo784226126e_bool))) (= B_1 A_4))) (forall ((A_4 $$unsorted) (B_1 $$unsorted) (C $$unsorted) (D_1 $$unsorted)) (=> (and (tptp.is_pname A_4) (tptp.is_pname B_1) (tptp.is_pname C) (tptp.is_pname D_1)) (= (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A_4) (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname B_1) tptp.bot_bo844097828e_bool)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname C) (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname D_1) tptp.bot_bo844097828e_bool))) (or (and (= A_4 C) (= B_1 D_1)) (and (= A_4 D_1) (= B_1 C)))))) (forall ((A_4 $$unsorted) (B_1 $$unsorted) (C $$unsorted) (D_1 $$unsorted)) (= (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com A_4) (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com B_1) tptp.bot_bot_fun_com_bool)) (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com C) (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com D_1) tptp.bot_bot_fun_com_bool))) (or (and (= A_4 C) (= B_1 D_1)) (and (= A_4 D_1) (= B_1 C))))) (forall ((A_4 $$unsorted) (B_1 $$unsorted) (C $$unsorted) (D_1 $$unsorted)) (= (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state A_4) (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state B_1) tptp.bot_bo784226126e_bool)) (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state C) (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state D_1) tptp.bot_bo784226126e_bool))) (or (and (= A_4 C) (= B_1 D_1)) (and (= A_4 D_1) (= B_1 C))))) (forall ((B_1 $$unsorted) (A_4 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com B_1) (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com A_4) tptp.bot_bot_fun_com_bool))) (= B_1 A_4))) (forall ((B_1 $$unsorted) (A_4 $$unsorted)) (=> (and (tptp.is_pname B_1) (tptp.is_pname A_4)) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname B_1) (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A_4) tptp.bot_bo844097828e_bool))) (= B_1 A_4)))) (forall ((B_1 $$unsorted) (A_4 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state B_1) (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state A_4) tptp.bot_bo784226126e_bool))) (= B_1 A_4))) (forall ((A_4 $$unsorted) (A $$unsorted)) (not (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A_4) A) tptp.bot_bo844097828e_bool))) (forall ((A_4 $$unsorted) (A $$unsorted)) (not (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com A_4) A) tptp.bot_bot_fun_com_bool))) (forall ((A_4 $$unsorted) (A $$unsorted)) (not (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state A_4) A) tptp.bot_bo784226126e_bool))) (forall ((A_4 $$unsorted) (A $$unsorted)) (not (= tptp.bot_bo844097828e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A_4) A)))) (forall ((A_4 $$unsorted) (A $$unsorted)) (not (= tptp.bot_bot_fun_com_bool (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com A_4) A)))) (forall ((A_4 $$unsorted) (A $$unsorted)) (not (= tptp.bot_bo784226126e_bool (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state A_4) A)))) (forall ((A_4 $$unsorted) (A $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f990396704l_bool tptp.finite_finite_com (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com A_4) A))) (tptp.hBOOL (tptp.hAPP_f990396704l_bool tptp.finite_finite_com A)))) (forall ((A_4 $$unsorted) (A $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool A_4) A))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)))) (forall ((A_4 $$unsorted) (A $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool (tptp.hAPP_f734420447l_bool (tptp.hAPP_f1472090462l_bool tptp.insert1720618162e_bool A_4) A))) (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool A)))) (forall ((A_4 $$unsorted) (A $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A_4) A))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)))) (forall ((A_4 $$unsorted) (A $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state A_4) A))) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state A)))) (forall ((A $$unsorted)) (=> (tptp.is_fun_pname_bool A) (= (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 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_f273696895l_bool tptp.ord_le1708315510m_bool A) tptp.bot_bot_fun_com_bool)) (= A tptp.bot_bot_fun_com_bool))) (forall ((A $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool A) tptp.bot_bo784226126e_bool)) (= A tptp.bot_bo784226126e_bool))) (forall ((F $$unsorted) (A $$unsorted)) (= (= (tptp.hAPP_f457085749e_bool (tptp.image_2605051_state F) A) tptp.bot_bo784226126e_bool) (= A tptp.bot_bot_fun_com_bool))) (forall ((F $$unsorted) (A $$unsorted)) (= (= (tptp.hAPP_f1083669085e_bool (tptp.image_1774499931_pname F) A) tptp.bot_bo844097828e_bool) (= A tptp.bot_bo784226126e_bool))) (forall ((F $$unsorted) (A $$unsorted)) (= (= (tptp.hAPP_f1815646051m_bool (tptp.image_741143905te_com F) A) tptp.bot_bot_fun_com_bool) (= A tptp.bot_bo784226126e_bool))) (forall ((F $$unsorted) (A $$unsorted)) (=> (tptp.is_fun_pname_bool A) (= (= (tptp.hAPP_f360545851e_bool (tptp.image_185131637_state F) A) tptp.bot_bo784226126e_bool) (= A tptp.bot_bo844097828e_bool)))) (forall ((F $$unsorted)) (= (tptp.hAPP_f1083669085e_bool (tptp.image_1774499931_pname F) tptp.bot_bo784226126e_bool) tptp.bot_bo844097828e_bool)) (forall ((F $$unsorted)) (= (tptp.hAPP_f1815646051m_bool (tptp.image_741143905te_com F) tptp.bot_bo784226126e_bool) tptp.bot_bot_fun_com_bool)) (forall ((F $$unsorted)) (= (tptp.hAPP_f457085749e_bool (tptp.image_2605051_state F) tptp.bot_bot_fun_com_bool) tptp.bot_bo784226126e_bool)) (forall ((F $$unsorted)) (= (tptp.hAPP_f360545851e_bool (tptp.image_185131637_state F) tptp.bot_bo844097828e_bool) tptp.bot_bo784226126e_bool)) (forall ((F $$unsorted) (A $$unsorted)) (= (= tptp.bot_bo784226126e_bool (tptp.hAPP_f457085749e_bool (tptp.image_2605051_state F) A)) (= A tptp.bot_bot_fun_com_bool))) (forall ((F $$unsorted) (A $$unsorted)) (= (= tptp.bot_bo844097828e_bool (tptp.hAPP_f1083669085e_bool (tptp.image_1774499931_pname F) A)) (= A tptp.bot_bo784226126e_bool))) (forall ((F $$unsorted) (A $$unsorted)) (= (= tptp.bot_bot_fun_com_bool (tptp.hAPP_f1815646051m_bool (tptp.image_741143905te_com F) A)) (= A tptp.bot_bo784226126e_bool))) (forall ((F $$unsorted) (A $$unsorted)) (=> (tptp.is_fun_pname_bool A) (= (= tptp.bot_bo784226126e_bool (tptp.hAPP_f360545851e_bool (tptp.image_185131637_state F) A)) (= A tptp.bot_bo844097828e_bool)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (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 $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool (tptp.hAPP_f1516997247l_bool tptp.ord_le694194916l_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool B)) (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool A))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state B)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state A))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (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 $$unsorted) (B $$unsorted)) (=> (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 $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool B)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool (tptp.hAPP_f1516997247l_bool tptp.ord_le694194916l_bool A) B)) (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool A))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state B)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool A) B)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state A))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (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 $$unsorted) (C_1 $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.hAPP_p905327722e_bool tptp.insert_pname A_4))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool C_1) D)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool _let_1 C_1)) (tptp.hAPP_f759274231e_bool _let_1 D)))))) (forall ((A_4 $$unsorted) (C_1 $$unsorted) (D $$unsorted)) (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 $$unsorted) (C_1 $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state A_4))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool C_1) D)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool (tptp.hAPP_f806699093e_bool _let_1 C_1)) (tptp.hAPP_f806699093e_bool _let_1 D)))))) (forall ((X_1 $$unsorted) (A $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_1) A)) (tptp.hBOOL (tptp.hAPP_com_bool A X_1)))) (forall ((X_1 $$unsorted) (A $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state X_1) A)) (tptp.hBOOL (tptp.hAPP_H242767318e_bool A X_1)))) (forall ((X_1 $$unsorted) (A $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A)) (tptp.hBOOL (tptp.hAPP_pname_bool A X_1)))) (forall ((P_1 $$unsorted)) (= (tptp.hAPP_f806699093e_bool tptp.collec637225377_state P_1) P_1)) (forall ((P_1 $$unsorted)) (=> (tptp.is_fun_pname_bool P_1) (= (tptp.hAPP_f759274231e_bool tptp.collect_pname P_1) P_1))) (forall ((P_1 $$unsorted)) (=> (tptp.is_fun1661590463l_bool P_1) (= (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool P_1) P_1))) (forall ((P_1 $$unsorted)) (= (tptp.hAPP_f734420447l_bool tptp.collec1987918285e_bool P_1) P_1)) (forall ((B_1 $$unsorted) (A $$unsorted) (B $$unsorted)) (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 $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f273696895l_bool tptp.ord_le1708315510m_bool A))) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 B)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com B_1) B)))))) (forall ((B_1 $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool A))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 B)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state B_1) B)))))) (forall ((B $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f273696895l_bool tptp.ord_le1708315510m_bool A))) (=> (not (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_1) A))) (= (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com X_1) B))) (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 B)))))) (forall ((B $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (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 $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool A))) (=> (not (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state X_1) A))) (= (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state X_1) B))) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 B)))))) (forall ((X_1 $$unsorted) (A $$unsorted) (B $$unsorted)) (= (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 $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1) A)) B)) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) B)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) B))))) (forall ((X_1 $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state X_1) A)) B)) (and (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state X_1) B)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool A) B))))) (forall ((B $$unsorted) (A_4 $$unsorted)) (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 $$unsorted) (A_4 $$unsorted)) (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 $$unsorted) (A_4 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool B) (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state A_4) B)))) (forall ((F $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f1083669085e_bool (tptp.image_1774499931_pname F) A))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state X_1) A)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname (tptp.hAPP_H1193503499_pname F X_1)) _let_1) _let_1)))) (forall ((F $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f1815646051m_bool (tptp.image_741143905te_com F) A))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state X_1) A)) (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com (tptp.hAPP_H46530577te_com F X_1)) _let_1) _let_1)))) (forall ((F $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f759274231e_bool (tptp.image_pname_pname F) A))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname (tptp.hAPP_pname_pname F X_1)) _let_1) _let_1)))) (forall ((F $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (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 $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f457085749e_bool (tptp.image_2605051_state F) A))) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_1) A)) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state (tptp.hAPP_c1455475371_state F X_1)) _let_1) _let_1)))) (forall ((F $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f360545851e_bool (tptp.image_185131637_state F) A))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A)) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state (tptp.hAPP_p1751618853_state F X_1)) _let_1) _let_1)))) (forall ((F $$unsorted) (A_4 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.image_1774499931_pname F))) (= (tptp.hAPP_f1083669085e_bool _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state A_4) B)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname (tptp.hAPP_H1193503499_pname F A_4)) (tptp.hAPP_f1083669085e_bool _let_1 B))))) (forall ((F $$unsorted) (A_4 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.image_741143905te_com F))) (= (tptp.hAPP_f1815646051m_bool _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state A_4) B)) (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com (tptp.hAPP_H46530577te_com F A_4)) (tptp.hAPP_f1815646051m_bool _let_1 B))))) (forall ((F $$unsorted) (A_4 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.image_2605051_state F))) (= (tptp.hAPP_f457085749e_bool _let_1 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com A_4) B)) (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state (tptp.hAPP_c1455475371_state F A_4)) (tptp.hAPP_f457085749e_bool _let_1 B))))) (forall ((F $$unsorted) (A_4 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.image_185131637_state F))) (= (tptp.hAPP_f360545851e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A_4) B)) (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state (tptp.hAPP_p1751618853_state F A_4)) (tptp.hAPP_f360545851e_bool _let_1 B))))) (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.image_1774499931_pname F))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool A) B)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f1083669085e_bool _let_1 A)) (tptp.hAPP_f1083669085e_bool _let_1 B)))))) (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.image_185131637_state F))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) B)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool (tptp.hAPP_f360545851e_bool _let_1 A)) (tptp.hAPP_f360545851e_bool _let_1 B)))))) (forall ((B $$unsorted) (F $$unsorted) (A $$unsorted)) (=> (tptp.is_fun_pname_bool B) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) (tptp.hAPP_f1083669085e_bool (tptp.image_1774499931_pname F) A))) (exists ((AA $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool AA) A)) (= B (tptp.hAPP_f1083669085e_bool (tptp.image_1774499931_pname F) AA))))))) (forall ((B $$unsorted) (F $$unsorted) (A $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool B) (tptp.hAPP_f360545851e_bool (tptp.image_185131637_state F) A))) (exists ((AA $$unsorted)) (and (tptp.is_fun_pname_bool AA) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool AA) A)) (= B (tptp.hAPP_f360545851e_bool (tptp.image_185131637_state F) AA)))))) (forall ((M $$unsorted) (A_4 $$unsorted) (B_1 $$unsorted)) (=> (= (tptp.hAPP_com_option_com M A_4) (tptp.hAPP_com_option_com tptp.some_com B_1)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com A_4) (tptp.dom_com_com M))))) (forall ((M $$unsorted) (A_4 $$unsorted) (B_1 $$unsorted)) (=> (= (tptp.hAPP_H1671063474_pname M A_4) (tptp.hAPP_p1252095976_pname tptp.some_pname B_1)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state A_4) (tptp.dom_Ho2070278094_pname M))))) (forall ((M $$unsorted) (A_4 $$unsorted) (B_1 $$unsorted)) (=> (= (tptp.hAPP_H1633077406_state M A_4) (tptp.hAPP_H1633077406_state tptp.some_H1043067815_state B_1)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state A_4) (tptp.dom_Ho1607160812_state M))))) (forall ((M $$unsorted) (A_4 $$unsorted) (B_1 $$unsorted)) (=> (= (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 $$unsorted) (A_4 $$unsorted) (B_1 $$unsorted)) (=> (= (tptp.hAPP_p485182952_state M A_4) (tptp.hAPP_H1633077406_state tptp.some_H1043067815_state B_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A_4) (tptp.dom_pn480909800_state M))))) (forall ((M $$unsorted) (A_4 $$unsorted) (B_1 $$unsorted)) (=> (= (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 $$unsorted) (A_4 $$unsorted)) (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 $$unsorted) (A_4 $$unsorted)) (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 $$unsorted) (A_4 $$unsorted)) (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 $$unsorted) (A_4 $$unsorted)) (let ((_let_1 (tptp.hAPP_f734420447l_bool tptp.collec1987918285e_bool (tptp.hAPP_f734420447l_bool (tptp.hAPP_f524831474l_bool tptp.cOMBS_1162100051l_bool (tptp.hAPP_f118042163l_bool (tptp.cOMBB_1749019442e_bool tptp.fconj) (tptp.hAPP_f849457489l_bool (tptp.hAPP_f1348212993l_bool tptp.cOMBC_1350613978l_bool tptp.fequal1475827639e_bool) A_4))) P_1)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_f1378282496l_bool P_1 A_4)))) (and (=> _let_2 (= _let_1 (tptp.hAPP_f734420447l_bool (tptp.hAPP_f1472090462l_bool tptp.insert1720618162e_bool A_4) tptp.bot_bo942947096l_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bo942947096l_bool)))))) (forall ((P_1 $$unsorted) (A_4 $$unsorted)) (let ((_let_1 (tptp.hAPP_f806699093e_bool tptp.collec637225377_state (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1702629984e_bool tptp.cOMBS_865875691l_bool (tptp.hAPP_f832587837l_bool (tptp.cOMBB_1291456124_state tptp.fconj) (tptp.hAPP_H216526335e_bool (tptp.hAPP_f1902016361e_bool tptp.cOMBC_1967329268e_bool tptp.fequal1440809015_state) A_4))) P_1)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_H242767318e_bool P_1 A_4)))) (and (=> _let_2 (= _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state A_4) tptp.bot_bo784226126e_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bo784226126e_bool)))))) (forall ((P_1 $$unsorted) (A_4 $$unsorted)) (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 $$unsorted) (A_4 $$unsorted)) (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 $$unsorted) (A_4 $$unsorted)) (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 $$unsorted) (A_4 $$unsorted)) (let ((_let_1 (tptp.hAPP_f734420447l_bool tptp.collec1987918285e_bool (tptp.hAPP_f734420447l_bool (tptp.hAPP_f524831474l_bool tptp.cOMBS_1162100051l_bool (tptp.hAPP_f118042163l_bool (tptp.cOMBB_1749019442e_bool tptp.fconj) (tptp.hAPP_f849457489l_bool tptp.fequal1475827639e_bool A_4))) P_1)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_f1378282496l_bool P_1 A_4)))) (and (=> _let_2 (= _let_1 (tptp.hAPP_f734420447l_bool (tptp.hAPP_f1472090462l_bool tptp.insert1720618162e_bool A_4) tptp.bot_bo942947096l_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bo942947096l_bool)))))) (forall ((P_1 $$unsorted) (A_4 $$unsorted)) (let ((_let_1 (tptp.hAPP_f806699093e_bool tptp.collec637225377_state (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1702629984e_bool tptp.cOMBS_865875691l_bool (tptp.hAPP_f832587837l_bool (tptp.cOMBB_1291456124_state tptp.fconj) (tptp.hAPP_H216526335e_bool tptp.fequal1440809015_state A_4))) P_1)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_H242767318e_bool P_1 A_4)))) (and (=> _let_2 (= _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state A_4) tptp.bot_bo784226126e_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bo784226126e_bool)))))) (forall ((A_4 $$unsorted)) (= (tptp.hAPP_f759274231e_bool tptp.collect_pname (tptp.hAPP_p61793385e_bool (tptp.hAPP_f22061361e_bool tptp.cOMBC_1149511130e_bool tptp.fequal_pname) A_4)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A_4) tptp.bot_bo844097828e_bool))) (forall ((A_4 $$unsorted)) (= (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 $$unsorted)) (= (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool (tptp.hAPP_f434788991l_bool (tptp.hAPP_f1297925993l_bool tptp.cOMBC_1284144636l_bool tptp.fequal533582459e_bool) A_4)) (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool A_4) tptp.bot_bo1649642514l_bool))) (forall ((A_4 $$unsorted)) (= (tptp.hAPP_f734420447l_bool tptp.collec1987918285e_bool (tptp.hAPP_f849457489l_bool (tptp.hAPP_f1348212993l_bool tptp.cOMBC_1350613978l_bool tptp.fequal1475827639e_bool) A_4)) (tptp.hAPP_f734420447l_bool (tptp.hAPP_f1472090462l_bool tptp.insert1720618162e_bool A_4) tptp.bot_bo942947096l_bool))) (forall ((A_4 $$unsorted)) (= (tptp.hAPP_f806699093e_bool tptp.collec637225377_state (tptp.hAPP_H216526335e_bool (tptp.hAPP_f1902016361e_bool tptp.cOMBC_1967329268e_bool tptp.fequal1440809015_state) A_4)) (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state A_4) tptp.bot_bo784226126e_bool))) (forall ((A_4 $$unsorted)) (= (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 $$unsorted)) (= (tptp.hAPP_f1682609283m_bool tptp.collect_com (tptp.hAPP_c1396316405m_bool tptp.fequal_com A_4)) (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com A_4) tptp.bot_bot_fun_com_bool))) (forall ((A_4 $$unsorted)) (= (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 $$unsorted)) (= (tptp.hAPP_f734420447l_bool tptp.collec1987918285e_bool (tptp.hAPP_f849457489l_bool tptp.fequal1475827639e_bool A_4)) (tptp.hAPP_f734420447l_bool (tptp.hAPP_f1472090462l_bool tptp.insert1720618162e_bool A_4) tptp.bot_bo942947096l_bool))) (forall ((A_4 $$unsorted)) (= (tptp.hAPP_f806699093e_bool tptp.collec637225377_state (tptp.hAPP_H216526335e_bool tptp.fequal1440809015_state A_4)) (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state A_4) tptp.bot_bo784226126e_bool))) (forall ((C $$unsorted) (G_2 $$unsorted)) (=> (tptp.hBOOL tptp.hoare_1795711768gleton) (=> (forall ((X_2 $$unsorted)) (=> (tptp.is_pname X_2) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) (tptp.dom_pname_com tptp.body))) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hoare_512830354_state G_2) (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state (tptp.hAPP_c1455475371_state tptp.hoare_Mirabelle_MGT (tptp.hAPP_pname_com tptp.body_1 X_2))) tptp.bot_bo784226126e_bool)))))) (=> (tptp.hBOOL (tptp.hAPP_com_bool tptp.wt C)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hoare_512830354_state G_2) (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state (tptp.hAPP_c1455475371_state tptp.hoare_Mirabelle_MGT C)) tptp.bot_bo784226126e_bool))))))) _let_12 (forall ((B_1 $$unsorted) (F $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state B_1) (tptp.hAPP_f457085749e_bool (tptp.image_2605051_state F) A))) (not (forall ((X_2 $$unsorted)) (=> (= B_1 (tptp.hAPP_c1455475371_state F X_2)) (not (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_2) A)))))))) (forall ((B_1 $$unsorted) (F $$unsorted) (A $$unsorted)) (=> (tptp.is_pname B_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))) (not (forall ((X_2 $$unsorted)) (=> (= B_1 (tptp.hAPP_com_pname F X_2)) (not (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_2) A))))))))) (forall ((B_1 $$unsorted) (F $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com B_1) (tptp.hAPP_f1815646051m_bool (tptp.image_741143905te_com F) A))) (not (forall ((X_2 $$unsorted)) (=> (= B_1 (tptp.hAPP_H46530577te_com F X_2)) (not (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state X_2) A)))))))) (forall ((B_1 $$unsorted) (F $$unsorted) (A $$unsorted)) (=> (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 $$unsorted)) (=> (tptp.is_pname X_2) (=> (= B_1 (tptp.hAPP_pname_com F X_2)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A))))))))) (forall ((B_1 $$unsorted) (F $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state B_1) (tptp.hAPP_f360545851e_bool (tptp.image_185131637_state F) A))) (not (forall ((X_2 $$unsorted)) (=> (tptp.is_pname X_2) (=> (= B_1 (tptp.hAPP_p1751618853_state F X_2)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A))))))))) (forall ((P_1 $$unsorted) (A $$unsorted) (Fa $$unsorted)) (=> (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 $$unsorted) (F_2 $$unsorted)) (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 $$unsorted) (A $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool Fa) A)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool P_1 tptp.bot_bo1649642514l_bool)) (=> (forall ((A_2 $$unsorted) (F_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool A_2))) (=> (and (tptp.is_fun_pname_bool A_2) (tptp.is_fun1661590463l_bool F_2)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool F_2)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool _let_1 A)) (=> (not (tptp.hBOOL (tptp.hAPP_f1935102916l_bool _let_1 F_2))) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool P_1 F_2)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool P_1 (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool A_2) F_2)))))))))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool P_1 Fa))))))) (forall ((P_1 $$unsorted) (A $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool (tptp.hAPP_f1516997247l_bool tptp.ord_le694194916l_bool Fa) A)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool P_1 tptp.bot_bo942947096l_bool)) (=> (forall ((A_2 $$unsorted) (F_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_f631019661l_bool tptp.member131361931e_bool A_2))) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool F_2)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool _let_1 A)) (=> (not (tptp.hBOOL (tptp.hAPP_f1410040974l_bool _let_1 F_2))) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool P_1 F_2)) (tptp.hBOOL (tptp.hAPP_f1410040974l_bool P_1 (tptp.hAPP_f734420447l_bool (tptp.hAPP_f1472090462l_bool tptp.insert1720618162e_bool A_2) F_2))))))))) (tptp.hBOOL (tptp.hAPP_f1410040974l_bool P_1 Fa))))))) (forall ((P_1 $$unsorted) (A $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool Fa) A)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 tptp.bot_bo844097828e_bool)) (=> (forall ((A_2 $$unsorted) (F_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname A_2))) (=> (and (tptp.is_pname A_2) (tptp.is_fun_pname_bool F_2)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname F_2)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A)) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 F_2))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 F_2)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A_2) F_2)))))))))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 Fa))))))) (forall ((P_1 $$unsorted) (A $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool Fa) A)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool P_1 tptp.bot_bo784226126e_bool)) (=> (forall ((A_2 $$unsorted) (F_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state A_2))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state F_2)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 A)) (=> (not (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 F_2))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool P_1 F_2)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool P_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state A_2) F_2))))))))) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool P_1 Fa))))))) (forall ((P $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_com_bool tptp.wt (tptp.hAPP_pname_com tptp.body_1 P))) (not (forall ((Y_3 $$unsorted)) (not (= (tptp.hAPP_p799580910on_com tptp.body P) (tptp.hAPP_com_option_com tptp.some_com Y_3))))))) (forall ((B $$unsorted) (A $$unsorted)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_c667411853l_bool tptp.member_com X_2))) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 B))))) (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_f273696895l_bool tptp.ord_le1708315510m_bool A) B)))) (forall ((B $$unsorted) (A $$unsorted)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state X_2))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 B))))) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool A) B)))) (forall ((B $$unsorted) (A $$unsorted)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname X_2))) (=> (tptp.is_pname X_2) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B)))))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) B)))) (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state B)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool B) (tptp.hAPP_f509793681e_bool (tptp.image_845802851_state F) A))) (exists ((C_3 $$unsorted)) (and (tptp.is_fun1661590463l_bool C_3) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool C_3) A)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool C_3)) (= B (tptp.hAPP_f509793681e_bool (tptp.image_845802851_state F) C_3))))))) (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state B)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool B) (tptp.hAPP_f1216288071e_bool (tptp.image_1497401961_state F) A))) (exists ((C_3 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f1410040974l_bool (tptp.hAPP_f1516997247l_bool tptp.ord_le694194916l_bool C_3) A)) (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool C_3)) (= B (tptp.hAPP_f1216288071e_bool (tptp.image_1497401961_state F) C_3))))))) (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.is_fun_pname_bool B) (=> (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 $$unsorted)) (and (tptp.is_fun1661590463l_bool C_3) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool C_3) A)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool C_3)) (= B (tptp.hAPP_f674760225e_bool (tptp.image_1283814551_pname F) C_3)))))))) (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.is_fun_pname_bool B) (=> (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_f306376939e_bool (tptp.image_1863446033_pname F) A))) (exists ((C_3 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f1410040974l_bool (tptp.hAPP_f1516997247l_bool tptp.ord_le694194916l_bool C_3) A)) (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool C_3)) (= B (tptp.hAPP_f306376939e_bool (tptp.image_1863446033_pname F) C_3)))))))) (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.is_fun1661590463l_bool B) (=> (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_f1709493145l_bool (tptp.image_1403607267e_bool F) A))) (exists ((C_3 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool C_3) A)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state C_3)) (= B (tptp.hAPP_f1709493145l_bool (tptp.image_1403607267e_bool F) C_3)))))))) (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool B)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool (tptp.hAPP_f1516997247l_bool tptp.ord_le694194916l_bool B) (tptp.hAPP_f849457489l_bool (tptp.image_995511119e_bool F) A))) (exists ((C_3 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool C_3) A)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state C_3)) (= B (tptp.hAPP_f849457489l_bool (tptp.image_995511119e_bool F) C_3))))))) (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.is_fun_pname_bool B) (=> (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_f1083669085e_bool (tptp.image_1774499931_pname F) A))) (exists ((C_3 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool C_3) A)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state C_3)) (= B (tptp.hAPP_f1083669085e_bool (tptp.image_1774499931_pname F) C_3)))))))) (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.is_fun1661590463l_bool B) (=> (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 $$unsorted)) (and (tptp.is_fun_pname_bool C_3) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool C_3) A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname C_3)) (= B (tptp.hAPP_f434788991l_bool (tptp.image_47868345e_bool F) C_3)))))))) (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool B)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool (tptp.hAPP_f1516997247l_bool tptp.ord_le694194916l_bool B) (tptp.hAPP_f1492100075l_bool (tptp.image_234387449e_bool F) A))) (exists ((C_3 $$unsorted)) (and (tptp.is_fun_pname_bool C_3) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool C_3) A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname C_3)) (= B (tptp.hAPP_f1492100075l_bool (tptp.image_234387449e_bool F) C_3))))))) (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.is_fun_pname_bool B) (=> (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 $$unsorted)) (and (tptp.is_fun_pname_bool C_3) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool C_3) A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname C_3)) (= B (tptp.hAPP_f759274231e_bool (tptp.image_pname_pname F) C_3)))))))) (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state B)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool B) (tptp.hAPP_f360545851e_bool (tptp.image_185131637_state F) A))) (exists ((C_3 $$unsorted)) (and (tptp.is_fun_pname_bool C_3) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool C_3) A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname C_3)) (= B (tptp.hAPP_f360545851e_bool (tptp.image_185131637_state F) C_3))))))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname _let_3)) (forall ((P_1 $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool tptp.finite_finite_com Fa)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool P_1 tptp.bot_bot_fun_com_bool)) (=> (forall ((X_2 $$unsorted) (F_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool tptp.finite_finite_com F_2)) (=> (not (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_2) F_2))) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool P_1 F_2)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool P_1 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com X_2) F_2))))))) (tptp.hBOOL (tptp.hAPP_f990396704l_bool P_1 Fa)))))) (forall ((P_1 $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool P_1 tptp.bot_bo1649642514l_bool)) (=> (forall ((X_2 $$unsorted) (F_2 $$unsorted)) (=> (and (tptp.is_fun_pname_bool X_2) (tptp.is_fun1661590463l_bool F_2)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool F_2)) (=> (not (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool X_2) F_2))) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool P_1 F_2)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool P_1 (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool X_2) F_2)))))))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool P_1 Fa)))))) (forall ((P_1 $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool P_1 tptp.bot_bo942947096l_bool)) (=> (forall ((X_2 $$unsorted) (F_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool F_2)) (=> (not (tptp.hBOOL (tptp.hAPP_f1410040974l_bool (tptp.hAPP_f631019661l_bool tptp.member131361931e_bool X_2) F_2))) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool P_1 F_2)) (tptp.hBOOL (tptp.hAPP_f1410040974l_bool P_1 (tptp.hAPP_f734420447l_bool (tptp.hAPP_f1472090462l_bool tptp.insert1720618162e_bool X_2) F_2))))))) (tptp.hBOOL (tptp.hAPP_f1410040974l_bool P_1 Fa)))))) (forall ((P_1 $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 tptp.bot_bo844097828e_bool)) (=> (forall ((X_2 $$unsorted) (F_2 $$unsorted)) (=> (and (tptp.is_pname X_2) (tptp.is_fun_pname_bool F_2)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname F_2)) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) F_2))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 F_2)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname X_2) F_2)))))))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 Fa)))))) (forall ((P_1 $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool P_1 tptp.bot_bo784226126e_bool)) (=> (forall ((X_2 $$unsorted) (F_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state F_2)) (=> (not (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state X_2) F_2))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool P_1 F_2)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool P_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state X_2) F_2))))))) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool P_1 Fa)))))) (forall ((A_4 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f990396704l_bool tptp.finite_finite_com A_4)) (or (= A_4 tptp.bot_bot_fun_com_bool) (exists ((A_7 $$unsorted) (A_2 $$unsorted)) (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 $$unsorted)) (=> (tptp.is_fun1661590463l_bool A_4) (= (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A_4)) (or (= A_4 tptp.bot_bo1649642514l_bool) (exists ((A_7 $$unsorted) (A_2 $$unsorted)) (and (tptp.is_fun1661590463l_bool A_7) (tptp.is_fun_pname_bool A_2) (= A_4 (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool A_2) A_7)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A_7)))))))) (forall ((A_4 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool A_4)) (or (= A_4 tptp.bot_bo942947096l_bool) (exists ((A_7 $$unsorted) (A_2 $$unsorted)) (and (= A_4 (tptp.hAPP_f734420447l_bool (tptp.hAPP_f1472090462l_bool tptp.insert1720618162e_bool A_2) A_7)) (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool A_7))))))) (forall ((A_4 $$unsorted)) (=> (tptp.is_fun_pname_bool A_4) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A_4)) (or (= A_4 tptp.bot_bo844097828e_bool) (exists ((A_7 $$unsorted) (A_2 $$unsorted)) (and (tptp.is_fun_pname_bool A_7) (tptp.is_pname A_2) (= A_4 (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A_2) A_7)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A_7)))))))) (forall ((A_4 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state A_4)) (or (= A_4 tptp.bot_bo784226126e_bool) (exists ((A_7 $$unsorted) (A_2 $$unsorted)) (and (= A_4 (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state A_2) A_7)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state A_7))))))) (forall ((F $$unsorted) (A $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_f990396704l_bool tptp.finite_finite_com A))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state (tptp.hAPP_f457085749e_bool (tptp.image_2605051_state F) A))) (exists ((X_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_2) A)) (not (tptp.hBOOL (tptp.hAPP_f990396704l_bool tptp.finite_finite_com (tptp.hAPP_f1682609283m_bool tptp.collect_com (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f328772264m_bool tptp.cOMBS_com_bool_bool (tptp.hAPP_f954469007l_bool (tptp.cOMBB_886968260ol_com tptp.fconj) (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f578650245m_bool tptp.cOMBC_1904837336l_bool tptp.member_com) A))) (tptp.hAPP_H313059897m_bool (tptp.hAPP_f235185669m_bool tptp.cOMBC_114640782e_bool (tptp.hAPP_f475997903e_bool (tptp.cOMBB_1327031172ol_com tptp.fequal1440809015_state) F)) (tptp.hAPP_c1455475371_state F X_2)))))))))))) (forall ((F $$unsorted) (A $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state A))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state (tptp.hAPP_f806699093e_bool (tptp.image_661047967_state F) A))) (exists ((X_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state X_2) A)) (not (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state (tptp.hAPP_f806699093e_bool tptp.collec637225377_state (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1702629984e_bool tptp.cOMBS_865875691l_bool (tptp.hAPP_f832587837l_bool (tptp.cOMBB_1291456124_state tptp.fconj) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1184122441e_bool tptp.cOMBC_538205282l_bool tptp.member1667945571_state) A))) (tptp.hAPP_H216526335e_bool (tptp.hAPP_f1902016361e_bool tptp.cOMBC_1967329268e_bool (tptp.hAPP_f596278895e_bool (tptp.cOMBB_1563888316_state tptp.fequal1440809015_state) F)) (tptp.hAPP_H574424047_state F X_2)))))))))))) (forall ((F $$unsorted) (A $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state (tptp.hAPP_f509793681e_bool (tptp.image_845802851_state F) A))) (exists ((X_2 $$unsorted)) (and (tptp.is_fun_pname_bool X_2) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool X_2) A)) (not (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f624840228l_bool tptp.cOMBS_350070575l_bool (tptp.hAPP_f143162813l_bool (tptp.cOMBB_2095475776e_bool tptp.fconj) (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1145991873l_bool tptp.cOMBC_1988546018l_bool tptp.member799430823e_bool) A))) (tptp.hAPP_H358531139l_bool (tptp.hAPP_f1186253673l_bool tptp.cOMBC_1836455480e_bool (tptp.hAPP_f2113567599e_bool (tptp.cOMBB_1724041344e_bool tptp.fequal1440809015_state) F)) (tptp.hAPP_f1218207411_state F X_2)))))))))))) (forall ((F $$unsorted) (A $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool A))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state (tptp.hAPP_f1216288071e_bool (tptp.image_1497401961_state F) A))) (exists ((X_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f1410040974l_bool (tptp.hAPP_f631019661l_bool tptp.member131361931e_bool X_2) A)) (not (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool (tptp.hAPP_f734420447l_bool tptp.collec1987918285e_bool (tptp.hAPP_f734420447l_bool (tptp.hAPP_f524831474l_bool tptp.cOMBS_1162100051l_bool (tptp.hAPP_f118042163l_bool (tptp.cOMBB_1749019442e_bool tptp.fconj) (tptp.hAPP_f734420447l_bool (tptp.hAPP_f1236719585l_bool tptp.cOMBC_1484018740l_bool tptp.member131361931e_bool) A))) (tptp.hAPP_H2039996199l_bool (tptp.hAPP_f1463049441l_bool tptp.cOMBC_754402940e_bool (tptp.hAPP_f610934515e_bool (tptp.cOMBB_1840094962e_bool tptp.fequal1440809015_state) F)) (tptp.hAPP_f718417177_state F X_2)))))))))))) (forall ((F $$unsorted) (A $$unsorted)) (=> (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 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_2) A)) (not (tptp.hBOOL (tptp.hAPP_f990396704l_bool tptp.finite_finite_com (tptp.hAPP_f1682609283m_bool tptp.collect_com (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f328772264m_bool tptp.cOMBS_com_bool_bool (tptp.hAPP_f954469007l_bool (tptp.cOMBB_886968260ol_com tptp.fconj) (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f578650245m_bool tptp.cOMBC_1904837336l_bool tptp.member_com) A))) (tptp.hAPP_p1639923567m_bool (tptp.hAPP_f734198589m_bool tptp.cOMBC_com_pname_bool (tptp.hAPP_f835719487e_bool (tptp.cOMBB_1083901850ol_com tptp.fequal_pname) F)) (tptp.hAPP_com_pname F X_2)))))))))))) (forall ((F $$unsorted) (A $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state A))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f1083669085e_bool (tptp.image_1774499931_pname F) A))) (exists ((X_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state X_2) A)) (not (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state (tptp.hAPP_f806699093e_bool tptp.collec637225377_state (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1702629984e_bool tptp.cOMBS_865875691l_bool (tptp.hAPP_f832587837l_bool (tptp.cOMBB_1291456124_state tptp.fconj) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1184122441e_bool tptp.cOMBC_538205282l_bool tptp.member1667945571_state) A))) (tptp.hAPP_p606792009e_bool (tptp.hAPP_f1720171569e_bool tptp.cOMBC_1952686190e_bool (tptp.hAPP_f777604691e_bool (tptp.cOMBB_1365368614_state tptp.fequal_pname) F)) (tptp.hAPP_H1193503499_pname F X_2)))))))))))) (forall ((F $$unsorted) (A $$unsorted)) (=> (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 $$unsorted)) (and (tptp.is_pname X_2) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f759274231e_bool tptp.collect_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_f649174806e_bool tptp.cOMBS_568398431l_bool (tptp.hAPP_f1402196763l_bool (tptp.cOMBB_675860798_pname tptp.fconj) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f661147897e_bool tptp.cOMBC_1058051404l_bool tptp.member_pname) A))) (tptp.hAPP_p61793385e_bool (tptp.hAPP_f22061361e_bool tptp.cOMBC_1149511130e_bool (tptp.hAPP_f1336811455e_bool (tptp.cOMBB_542850580_pname tptp.fequal_pname) F)) (tptp.hAPP_pname_pname F X_2)))))))))))) (forall ((F $$unsorted) (A $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f674760225e_bool (tptp.image_1283814551_pname F) A))) (exists ((X_2 $$unsorted)) (and (tptp.is_fun_pname_bool X_2) (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 $$unsorted) (A $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool A))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f306376939e_bool (tptp.image_1863446033_pname F) A))) (exists ((X_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f1410040974l_bool (tptp.hAPP_f631019661l_bool tptp.member131361931e_bool X_2) A)) (not (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool (tptp.hAPP_f734420447l_bool tptp.collec1987918285e_bool (tptp.hAPP_f734420447l_bool (tptp.hAPP_f524831474l_bool tptp.cOMBS_1162100051l_bool (tptp.hAPP_f118042163l_bool (tptp.cOMBB_1749019442e_bool tptp.fconj) (tptp.hAPP_f734420447l_bool (tptp.hAPP_f1236719585l_bool tptp.cOMBC_1484018740l_bool tptp.member131361931e_bool) A))) (tptp.hAPP_p1235466077l_bool (tptp.hAPP_f780571929l_bool tptp.cOMBC_1558112230e_bool (tptp.hAPP_f700046015e_bool (tptp.cOMBB_1400714760e_bool tptp.fequal_pname) F)) (tptp.hAPP_f88366945_pname F X_2)))))))))))) (forall ((F $$unsorted) (A $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state A))) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.hAPP_f1709493145l_bool (tptp.image_1403607267e_bool F) A))) (exists ((X_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state X_2) A)) (not (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state (tptp.hAPP_f806699093e_bool tptp.collec637225377_state (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1702629984e_bool tptp.cOMBS_865875691l_bool (tptp.hAPP_f832587837l_bool (tptp.cOMBB_1291456124_state tptp.fconj) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1184122441e_bool tptp.cOMBC_538205282l_bool tptp.member1667945571_state) A))) (tptp.hAPP_f360545851e_bool (tptp.hAPP_f591683433e_bool tptp.cOMBC_1984545208l_bool (tptp.hAPP_f381060343l_bool (tptp.cOMBB_1631414076_state tptp.fequal533582459e_bool) F)) (tptp.hAPP_H1776011827e_bool F X_2)))))))))))) (forall ((F $$unsorted) (A $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state A))) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool (tptp.hAPP_f849457489l_bool (tptp.image_995511119e_bool F) A))) (exists ((X_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state X_2) A)) (not (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state (tptp.hAPP_f806699093e_bool tptp.collec637225377_state (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1702629984e_bool tptp.cOMBS_865875691l_bool (tptp.hAPP_f832587837l_bool (tptp.cOMBB_1291456124_state tptp.fconj) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1184122441e_bool tptp.cOMBC_538205282l_bool tptp.member1667945571_state) A))) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1184122441e_bool tptp.cOMBC_538205282l_bool (tptp.hAPP_f1191357267l_bool (tptp.cOMBB_639263758_state tptp.fequal1475827639e_bool) F)) (tptp.hAPP_H216526335e_bool F X_2)))))))))))) (forall ((F $$unsorted) (A $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A))) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.hAPP_f434788991l_bool (tptp.image_47868345e_bool F) A))) (exists ((X_2 $$unsorted)) (and (tptp.is_pname X_2) (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 $$unsorted) (A $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A))) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool (tptp.hAPP_f1492100075l_bool (tptp.image_234387449e_bool F) A))) (exists ((X_2 $$unsorted)) (and (tptp.is_pname X_2) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f759274231e_bool tptp.collect_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_f649174806e_bool tptp.cOMBS_568398431l_bool (tptp.hAPP_f1402196763l_bool (tptp.cOMBB_675860798_pname tptp.fconj) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f661147897e_bool tptp.cOMBC_1058051404l_bool tptp.member_pname) A))) (tptp.hAPP_f1083669085e_bool (tptp.hAPP_f568104217e_bool tptp.cOMBC_1757633998l_bool (tptp.hAPP_f1143533991l_bool (tptp.cOMBB_949755692_pname tptp.fequal1475827639e_bool) F)) (tptp.hAPP_p606792009e_bool F X_2)))))))))))) (forall ((F $$unsorted) (A $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state (tptp.hAPP_f360545851e_bool (tptp.image_185131637_state F) A))) (exists ((X_2 $$unsorted)) (and (tptp.is_pname X_2) (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_H1776011827e_bool (tptp.hAPP_f343137017e_bool tptp.cOMBC_19854728e_bool (tptp.hAPP_f472107739e_bool (tptp.cOMBB_181781758_pname tptp.fequal1440809015_state) F)) (tptp.hAPP_p1751618853_state F X_2)))))))))))) (forall ((Pname_2 $$unsorted) (Pname_1 $$unsorted)) (=> (and (tptp.is_pname Pname_2) (tptp.is_pname Pname_1)) (= (= (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 $$unsorted) (Procs $$unsorted)) (let ((_let_1 (tptp.cOMBB_271860050_pname tptp.hoare_Mirabelle_MGT))) (let ((_let_2 (tptp.hAPP_f360545851e_bool (tptp.image_185131637_state (tptp.hAPP_f1377420673_state _let_1 tptp.body_1)) Procs))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hoare_512830354_state (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool G_2) _let_2)) (tptp.hAPP_f360545851e_bool (tptp.image_185131637_state (tptp.hAPP_f1377420673_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_f1378282496l_bool (tptp.hoare_512830354_state G_2) _let_2))))))) (forall ((A_4 $$unsorted) (M $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com A_4) (tptp.dom_com_com M))) (exists ((B_3 $$unsorted)) (= (tptp.hAPP_com_option_com M A_4) (tptp.hAPP_com_option_com tptp.some_com B_3))))) (forall ((A_4 $$unsorted) (M $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state A_4) (tptp.dom_Ho2070278094_pname M))) (exists ((B_3 $$unsorted)) (and (tptp.is_pname B_3) (= (tptp.hAPP_H1671063474_pname M A_4) (tptp.hAPP_p1252095976_pname tptp.some_pname B_3)))))) (forall ((A_4 $$unsorted) (M $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state A_4) (tptp.dom_Ho1607160812_state M))) (exists ((B_3 $$unsorted)) (= (tptp.hAPP_H1633077406_state M A_4) (tptp.hAPP_H1633077406_state tptp.some_H1043067815_state B_3))))) (forall ((A_4 $$unsorted) (M $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A_4) (tptp.dom_pname_pname M))) (exists ((B_3 $$unsorted)) (and (tptp.is_pname B_3) (= (tptp.hAPP_p1252095976_pname M A_4) (tptp.hAPP_p1252095976_pname tptp.some_pname B_3)))))) (forall ((A_4 $$unsorted) (M $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A_4) (tptp.dom_pn480909800_state M))) (exists ((B_3 $$unsorted)) (= (tptp.hAPP_p485182952_state M A_4) (tptp.hAPP_H1633077406_state tptp.some_H1043067815_state B_3))))) (forall ((A_4 $$unsorted) (M $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A_4) (tptp.dom_pname_com M))) (exists ((B_3 $$unsorted)) (= (tptp.hAPP_p799580910on_com M A_4) (tptp.hAPP_com_option_com tptp.some_com B_3))))) (forall ((X_1 $$unsorted)) (=> (tptp.is_pname X_1) (= (tptp.hAPP_f1297739591_pname tptp.the_elem_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1) tptp.bot_bo844097828e_bool)) X_1))) (forall ((X_1 $$unsorted)) (= (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 $$unsorted)) (= (tptp.hAPP_f718417177_state tptp.the_el2080696983_state (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state X_1) tptp.bot_bo784226126e_bool)) X_1)) (forall ((F $$unsorted) (B $$unsorted) (A $$unsorted)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state X_2) A)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com (tptp.hAPP_H46530577te_com F X_2)) B)))) (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_f273696895l_bool tptp.ord_le1708315510m_bool (tptp.hAPP_f1815646051m_bool (tptp.image_741143905te_com F) A)) B)))) (forall ((F $$unsorted) (B $$unsorted) (A $$unsorted)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state X_2) A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname (tptp.hAPP_H1193503499_pname F X_2)) B)))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f1083669085e_bool (tptp.image_1774499931_pname F) A)) B)))) (forall ((F $$unsorted) (B $$unsorted) (A $$unsorted)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.is_pname X_2) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com (tptp.hAPP_pname_com F X_2)) B))))) (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_f273696895l_bool tptp.ord_le1708315510m_bool (tptp.hAPP_f1206115581m_bool (tptp.image_pname_com F) A)) B)))) (forall ((F $$unsorted) (B $$unsorted) (A $$unsorted)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.is_pname X_2) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname (tptp.hAPP_pname_pname F X_2)) B))))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool (tptp.image_pname_pname F) A)) B)))) (forall ((F $$unsorted) (B $$unsorted) (A $$unsorted)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_2) A)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state (tptp.hAPP_c1455475371_state F X_2)) B)))) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool (tptp.hAPP_f457085749e_bool (tptp.image_2605051_state F) A)) B)))) (forall ((F $$unsorted) (B $$unsorted) (A $$unsorted)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_2) A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname (tptp.hAPP_com_pname F X_2)) B)))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f1438183293e_bool (tptp.image_com_pname F) A)) B)))) (forall ((F $$unsorted) (B $$unsorted) (A $$unsorted)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.is_pname X_2) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state (tptp.hAPP_p1751618853_state F X_2)) B))))) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool (tptp.hAPP_f360545851e_bool (tptp.image_185131637_state F) A)) B)))) (forall ((X_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool X_1) X_1))) (forall ((X_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool X_1) X_1))) (forall ((X_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool X_1) X_1))) (forall ((A $$unsorted)) (= (not (= A tptp.bot_bot_fun_com_bool)) (exists ((X_2 $$unsorted) (B_2 $$unsorted)) (and (= A (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com X_2) B_2)) (not (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_2) B_2))))))) (forall ((A $$unsorted)) (=> (tptp.is_fun_pname_bool A) (= (not (= A tptp.bot_bo844097828e_bool)) (exists ((X_2 $$unsorted) (B_2 $$unsorted)) (and (tptp.is_pname X_2) (tptp.is_fun_pname_bool B_2) (= 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 $$unsorted)) (= (not (= A tptp.bot_bo784226126e_bool)) (exists ((X_2 $$unsorted) (B_2 $$unsorted)) (and (= A (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state X_2) B_2)) (not (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state X_2) B_2))))))) (forall ((X_5 $$unsorted)) (=> (tptp.is_pname X_5) (= (tptp.hAPP_o593586696_pname tptp.the_pname_1 (tptp.hAPP_p1252095976_pname tptp.some_pname X_5)) X_5))) (forall ((X_5 $$unsorted)) (= (tptp.hAPP_o1912464824_state tptp.the_Ho32424093_state (tptp.hAPP_H1633077406_state tptp.some_H1043067815_state X_5)) X_5)) (forall ((X_5 $$unsorted)) (= (tptp.hAPP_option_com_com tptp.the_com (tptp.hAPP_com_option_com tptp.some_com X_5)) X_5)) (forall ((G_2 $$unsorted) (P_1 $$unsorted) (Pn_1 $$unsorted) (Q_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f274181323_state tptp.hoare_1191504582_state P_1))) (let ((_let_2 (tptp.hoare_512830354_state G_2))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_2 (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state (tptp.hAPP_f497755132_state (tptp.hAPP_c27135337_state _let_1 (tptp.hAPP_option_com_com tptp.the_com (tptp.hAPP_p799580910on_com tptp.body Pn_1))) Q_1)) tptp.bot_bo784226126e_bool))) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_2 (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state (tptp.hAPP_f497755132_state (tptp.hAPP_c27135337_state _let_1 (tptp.hAPP_pname_com tptp.body_1 Pn_1)) Q_1)) tptp.bot_bo784226126e_bool))))))) (forall ((P_1 $$unsorted) (Pn_1 $$unsorted) (Q_1 $$unsorted) (G_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_f274181323_state tptp.hoare_1191504582_state P_1))) (let ((_let_2 (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state (tptp.hAPP_f497755132_state (tptp.hAPP_c27135337_state _let_1 (tptp.hAPP_pname_com tptp.body_1 Pn_1)) Q_1)))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hoare_512830354_state (tptp.hAPP_f806699093e_bool _let_2 G_2)) (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state (tptp.hAPP_f497755132_state (tptp.hAPP_c27135337_state _let_1 (tptp.hAPP_option_com_com tptp.the_com (tptp.hAPP_p799580910on_com tptp.body Pn_1))) Q_1)) tptp.bot_bo784226126e_bool))) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hoare_512830354_state G_2) (tptp.hAPP_f806699093e_bool _let_2 tptp.bot_bo784226126e_bool))))))) (= _let_11 (exists ((S_1 $$unsorted) (T_2 $$unsorted)) (not (= S_1 T_2)))) (forall ((A $$unsorted) (C $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_c667411853l_bool tptp.member_com C))) (=> (=> (not (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 B))) (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 A))) (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila605046092m_bool A) B)))))) (forall ((A $$unsorted) (C $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state C))) (=> (=> (not (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 B))) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 A))) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool A) B)))))) (forall ((A $$unsorted) (C $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname C))) (=> (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A) B)))))) (forall ((C $$unsorted) (A $$unsorted) (B $$unsorted)) (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 $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state C))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool A) B))) (=> (not (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 A))) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 B)))))) (forall ((C $$unsorted) (A $$unsorted) (B $$unsorted)) (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 $$unsorted) (Com_1 $$unsorted) (Fun2_2 $$unsorted) (Fun1_1 $$unsorted) (Com_2 $$unsorted) (Fun2_1 $$unsorted)) (= (= (tptp.hAPP_f497755132_state (tptp.hAPP_c27135337_state (tptp.hAPP_f274181323_state tptp.hoare_1191504582_state Fun1_2) Com_1) Fun2_2) (tptp.hAPP_f497755132_state (tptp.hAPP_c27135337_state (tptp.hAPP_f274181323_state tptp.hoare_1191504582_state Fun1_1) Com_2) Fun2_1)) (and (= Fun1_2 Fun1_1) (= Com_1 Com_2) (= Fun2_2 Fun2_1)))) (forall ((A $$unsorted) (C $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_c667411853l_bool tptp.member_com C))) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 B)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila605046092m_bool A) B)))))) (forall ((A $$unsorted) (C $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state C))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 B)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool A) B)))))) (forall ((A $$unsorted) (C $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname C))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A) B)))))) (forall ((B $$unsorted) (C $$unsorted) (A $$unsorted)) (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 $$unsorted) (C $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state C))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool A) B)))))) (forall ((B $$unsorted) (C $$unsorted) (A $$unsorted)) (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 $$unsorted) (A $$unsorted) (B $$unsorted)) (= (forall ((X_2 $$unsorted)) (=> (tptp.is_pname 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 A) B))) (tptp.hBOOL (tptp.hAPP_pname_bool P_1 X_2))))) (and (forall ((X_2 $$unsorted)) (=> (tptp.is_pname X_2) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A)) (tptp.hBOOL (tptp.hAPP_pname_bool P_1 X_2))))) (forall ((X_2 $$unsorted)) (=> (tptp.is_pname X_2) (=> (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 $$unsorted) (A $$unsorted) (B $$unsorted)) (= (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state X_2) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool A) B))) (tptp.hBOOL (tptp.hAPP_H242767318e_bool P_1 X_2)))) (and (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state X_2) A)) (tptp.hBOOL (tptp.hAPP_H242767318e_bool P_1 X_2)))) (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state X_2) B)) (tptp.hBOOL (tptp.hAPP_H242767318e_bool P_1 X_2))))))) (forall ((P_1 $$unsorted) (A $$unsorted) (B $$unsorted)) (= (exists ((X_2 $$unsorted)) (and (tptp.is_pname 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 A) B))) (tptp.hBOOL (tptp.hAPP_pname_bool P_1 X_2)))) (or (exists ((X_2 $$unsorted)) (and (tptp.is_pname X_2) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A)) (tptp.hBOOL (tptp.hAPP_pname_bool P_1 X_2)))) (exists ((X_2 $$unsorted)) (and (tptp.is_pname X_2) (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 $$unsorted) (A $$unsorted) (B $$unsorted)) (= (exists ((X_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state X_2) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool A) B))) (tptp.hBOOL (tptp.hAPP_H242767318e_bool P_1 X_2)))) (or (exists ((X_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state X_2) A)) (tptp.hBOOL (tptp.hAPP_H242767318e_bool P_1 X_2)))) (exists ((X_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state X_2) B)) (tptp.hBOOL (tptp.hAPP_H242767318e_bool P_1 X_2))))))) (forall ((A $$unsorted) (B $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A))) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool (tptp.hAPP_f759274231e_bool _let_1 B)) C_1) (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool B) C_1))))) (forall ((A $$unsorted) (B $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool A))) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool (tptp.hAPP_f806699093e_bool _let_1 B)) C_1) (tptp.hAPP_f806699093e_bool _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool B) C_1))))) (forall ((C $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_c667411853l_bool tptp.member_com C))) (= (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila605046092m_bool A) B))) (or (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 B)))))) (forall ((C $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state C))) (= (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool A) B))) (or (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 B)))))) (forall ((C $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname C))) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A) B))) (or (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B)))))) (forall ((A $$unsorted) (B $$unsorted) (C_1 $$unsorted)) (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 $$unsorted) (B $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool A))) (let ((_let_2 (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool B))) (= (tptp.hAPP_f806699093e_bool _let_1 (tptp.hAPP_f806699093e_bool _let_2 C_1)) (tptp.hAPP_f806699093e_bool _let_2 (tptp.hAPP_f806699093e_bool _let_1 C_1)))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A))) (let ((_let_2 (tptp.hAPP_f759274231e_bool _let_1 B))) (= (tptp.hAPP_f759274231e_bool _let_1 _let_2) _let_2)))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool A))) (let ((_let_2 (tptp.hAPP_f806699093e_bool _let_1 B))) (= (tptp.hAPP_f806699093e_bool _let_1 _let_2) _let_2)))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A) B) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool B) A))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool A) B) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool B) A))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f578650245m_bool tptp.cOMBC_1904837336l_bool tptp.member_com))) (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila605046092m_bool A) B) (tptp.hAPP_f1682609283m_bool tptp.collect_com (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f328772264m_bool tptp.cOMBS_com_bool_bool (tptp.hAPP_f954469007l_bool (tptp.cOMBB_886968260ol_com tptp.fdisj) (tptp.hAPP_f1682609283m_bool _let_1 A))) (tptp.hAPP_f1682609283m_bool _let_1 B)))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f1145991873l_bool tptp.cOMBC_1988546018l_bool tptp.member799430823e_bool))) (= (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.semila1782091504l_bool A) B) (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f624840228l_bool tptp.cOMBS_350070575l_bool (tptp.hAPP_f143162813l_bool (tptp.cOMBB_2095475776e_bool tptp.fdisj) (tptp.hAPP_f559147733l_bool _let_1 A))) (tptp.hAPP_f559147733l_bool _let_1 B)))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f1236719585l_bool tptp.cOMBC_1484018740l_bool tptp.member131361931e_bool))) (= (tptp.hAPP_f734420447l_bool (tptp.hAPP_f1847120l_bool tptp.semila1672697786l_bool A) B) (tptp.hAPP_f734420447l_bool tptp.collec1987918285e_bool (tptp.hAPP_f734420447l_bool (tptp.hAPP_f524831474l_bool tptp.cOMBS_1162100051l_bool (tptp.hAPP_f118042163l_bool (tptp.cOMBB_1749019442e_bool tptp.fdisj) (tptp.hAPP_f734420447l_bool _let_1 A))) (tptp.hAPP_f734420447l_bool _let_1 B)))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f1184122441e_bool tptp.cOMBC_538205282l_bool tptp.member1667945571_state))) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool A) B) (tptp.hAPP_f806699093e_bool tptp.collec637225377_state (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1702629984e_bool tptp.cOMBS_865875691l_bool (tptp.hAPP_f832587837l_bool (tptp.cOMBB_1291456124_state tptp.fdisj) (tptp.hAPP_f806699093e_bool _let_1 A))) (tptp.hAPP_f806699093e_bool _let_1 B)))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f661147897e_bool tptp.cOMBC_1058051404l_bool tptp.member_pname))) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A) B) (tptp.hAPP_f759274231e_bool tptp.collect_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_f649174806e_bool tptp.cOMBS_568398431l_bool (tptp.hAPP_f1402196763l_bool (tptp.cOMBB_675860798_pname tptp.fdisj) (tptp.hAPP_f759274231e_bool _let_1 A))) (tptp.hAPP_f759274231e_bool _let_1 B)))))) (forall ((A $$unsorted)) (=> (tptp.is_fun_pname_bool A) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A) A) A))) (forall ((A $$unsorted)) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool A) A) A)) (forall ((P_1 $$unsorted) (Q_1 $$unsorted)) (= (tptp.hAPP_f759274231e_bool tptp.collect_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_f649174806e_bool tptp.cOMBS_568398431l_bool (tptp.hAPP_f1402196763l_bool (tptp.cOMBB_675860798_pname tptp.fdisj) P_1)) Q_1)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool (tptp.hAPP_f759274231e_bool tptp.collect_pname P_1)) (tptp.hAPP_f759274231e_bool tptp.collect_pname Q_1)))) (forall ((P_1 $$unsorted) (Q_1 $$unsorted)) (= (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f624840228l_bool tptp.cOMBS_350070575l_bool (tptp.hAPP_f143162813l_bool (tptp.cOMBB_2095475776e_bool tptp.fdisj) P_1)) Q_1)) (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.semila1782091504l_bool (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool P_1)) (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool Q_1)))) (forall ((P_1 $$unsorted) (Q_1 $$unsorted)) (= (tptp.hAPP_f734420447l_bool tptp.collec1987918285e_bool (tptp.hAPP_f734420447l_bool (tptp.hAPP_f524831474l_bool tptp.cOMBS_1162100051l_bool (tptp.hAPP_f118042163l_bool (tptp.cOMBB_1749019442e_bool tptp.fdisj) P_1)) Q_1)) (tptp.hAPP_f734420447l_bool (tptp.hAPP_f1847120l_bool tptp.semila1672697786l_bool (tptp.hAPP_f734420447l_bool tptp.collec1987918285e_bool P_1)) (tptp.hAPP_f734420447l_bool tptp.collec1987918285e_bool Q_1)))) (forall ((P_1 $$unsorted) (Q_1 $$unsorted)) (= (tptp.hAPP_f806699093e_bool tptp.collec637225377_state (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1702629984e_bool tptp.cOMBS_865875691l_bool (tptp.hAPP_f832587837l_bool (tptp.cOMBB_1291456124_state tptp.fdisj) P_1)) Q_1)) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool (tptp.hAPP_f806699093e_bool tptp.collec637225377_state P_1)) (tptp.hAPP_f806699093e_bool tptp.collec637225377_state Q_1)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.is_fun_pname_bool A) (tptp.is_fun_pname_bool B)) (= (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A) B) tptp.bot_bo844097828e_bool) (and (= A tptp.bot_bo844097828e_bool) (= B tptp.bot_bo844097828e_bool))))) (forall ((A $$unsorted) (B $$unsorted)) (= (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila605046092m_bool A) B) tptp.bot_bot_fun_com_bool) (and (= A tptp.bot_bot_fun_com_bool) (= B tptp.bot_bot_fun_com_bool)))) (forall ((A $$unsorted) (B $$unsorted)) (= (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool A) B) tptp.bot_bo784226126e_bool) (and (= A tptp.bot_bo784226126e_bool) (= B tptp.bot_bo784226126e_bool)))) (forall ((A $$unsorted)) (=> (tptp.is_fun_pname_bool A) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A) tptp.bot_bo844097828e_bool) A))) (forall ((A $$unsorted)) (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila605046092m_bool A) tptp.bot_bot_fun_com_bool) A)) (forall ((A $$unsorted)) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool A) tptp.bot_bo784226126e_bool) A)) (forall ((B $$unsorted)) (=> (tptp.is_fun_pname_bool B) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool tptp.bot_bo844097828e_bool) B) B))) (forall ((B $$unsorted)) (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila605046092m_bool tptp.bot_bot_fun_com_bool) B) B)) (forall ((B $$unsorted)) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool tptp.bot_bo784226126e_bool) B) B)) (forall ((G_2 $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool G_2)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.semila1782091504l_bool Fa) G_2)))))) (forall ((G_2 $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool G_2)) (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool (tptp.hAPP_f734420447l_bool (tptp.hAPP_f1847120l_bool tptp.semila1672697786l_bool Fa) G_2)))))) (forall ((G_2 $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state G_2)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool Fa) G_2)))))) (forall ((G_2 $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname G_2)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool Fa) G_2)))))) (forall ((Fa $$unsorted) (G_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.semila1782091504l_bool Fa) G_2))) (and (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool Fa)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool G_2))))) (forall ((Fa $$unsorted) (G_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool (tptp.hAPP_f734420447l_bool (tptp.hAPP_f1847120l_bool tptp.semila1672697786l_bool Fa) G_2))) (and (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool Fa)) (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool G_2))))) (forall ((Fa $$unsorted) (G_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool Fa) G_2))) (and (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state Fa)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state G_2))))) (forall ((Fa $$unsorted) (G_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool Fa) G_2))) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname Fa)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname G_2))))) (forall ((A_4 $$unsorted) (B $$unsorted) (C_1 $$unsorted)) (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 $$unsorted) (B $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_c566651504m_bool tptp.insert_com A_4))) (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila605046092m_bool (tptp.hAPP_f1682609283m_bool _let_1 B)) C_1) (tptp.hAPP_f1682609283m_bool _let_1 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila605046092m_bool B) C_1))))) (forall ((A_4 $$unsorted) (B $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state A_4))) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool (tptp.hAPP_f806699093e_bool _let_1 B)) C_1) (tptp.hAPP_f806699093e_bool _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool B) C_1))))) (forall ((A $$unsorted) (A_4 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A))) (let ((_let_2 (tptp.hAPP_p905327722e_bool tptp.insert_pname A_4))) (= (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool _let_2 B)) (tptp.hAPP_f759274231e_bool _let_2 (tptp.hAPP_f759274231e_bool _let_1 B)))))) (forall ((A $$unsorted) (A_4 $$unsorted) (B $$unsorted)) (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 $$unsorted) (A_4 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool A))) (let ((_let_2 (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state A_4))) (= (tptp.hAPP_f806699093e_bool _let_1 (tptp.hAPP_f806699093e_bool _let_2 B)) (tptp.hAPP_f806699093e_bool _let_2 (tptp.hAPP_f806699093e_bool _let_1 B)))))) (forall ((B $$unsorted) (D $$unsorted) (A $$unsorted) (C_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) C_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) D)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A) B)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool C_1) D)))))) (forall ((B $$unsorted) (D $$unsorted) (A $$unsorted) (C_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool A) C_1)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool B) D)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool A) B)) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool C_1) D)))))) (forall ((B $$unsorted) (A $$unsorted) (C_1 $$unsorted)) (=> (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 $$unsorted) (A $$unsorted) (C_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool A) C_1)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool B) C_1)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool A) B)) C_1))))) (forall ((B $$unsorted) (A $$unsorted)) (=> (tptp.is_fun_pname_bool A) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) A)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A) B) A)))) (forall ((B $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool B) A)) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool A) B) A))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.is_fun_pname_bool B) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) B)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A) B) B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool A) B)) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool A) B) B))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.is_fun_pname_bool B) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) B)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A) B) B)))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool A) B)) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool A) B) B))) (forall ((B $$unsorted) (A $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A) B)))) (forall ((B $$unsorted) (A $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool B) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool A) B)))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A) B)))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool A) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool A) B)))) (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.image_1774499931_pname F))) (= (tptp.hAPP_f1083669085e_bool _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool A) B)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool (tptp.hAPP_f1083669085e_bool _let_1 A)) (tptp.hAPP_f1083669085e_bool _let_1 B))))) (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.image_185131637_state F))) (= (tptp.hAPP_f360545851e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A) B)) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool (tptp.hAPP_f360545851e_bool _let_1 A)) (tptp.hAPP_f360545851e_bool _let_1 B))))) (forall ((A_4 $$unsorted) (B $$unsorted)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A_4) B) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool (tptp.hAPP_f759274231e_bool tptp.collect_pname (tptp.hAPP_p61793385e_bool (tptp.hAPP_f22061361e_bool tptp.cOMBC_1149511130e_bool tptp.fequal_pname) A_4))) B))) (forall ((A_4 $$unsorted) (B $$unsorted)) (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com A_4) B) (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila605046092m_bool (tptp.hAPP_f1682609283m_bool tptp.collect_com (tptp.hAPP_c1396316405m_bool (tptp.hAPP_f908845385m_bool tptp.cOMBC_com_com_bool tptp.fequal_com) A_4))) B))) (forall ((A_4 $$unsorted) (B $$unsorted)) (= (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool A_4) B) (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.semila1782091504l_bool (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool (tptp.hAPP_f434788991l_bool (tptp.hAPP_f1297925993l_bool tptp.cOMBC_1284144636l_bool tptp.fequal533582459e_bool) A_4))) B))) (forall ((A_4 $$unsorted) (B $$unsorted)) (= (tptp.hAPP_f734420447l_bool (tptp.hAPP_f1472090462l_bool tptp.insert1720618162e_bool A_4) B) (tptp.hAPP_f734420447l_bool (tptp.hAPP_f1847120l_bool tptp.semila1672697786l_bool (tptp.hAPP_f734420447l_bool tptp.collec1987918285e_bool (tptp.hAPP_f849457489l_bool (tptp.hAPP_f1348212993l_bool tptp.cOMBC_1350613978l_bool tptp.fequal1475827639e_bool) A_4))) B))) (forall ((A_4 $$unsorted) (B $$unsorted)) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state A_4) B) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool (tptp.hAPP_f806699093e_bool tptp.collec637225377_state (tptp.hAPP_H216526335e_bool (tptp.hAPP_f1902016361e_bool tptp.cOMBC_1967329268e_bool tptp.fequal1440809015_state) A_4))) B))) (forall ((A_4 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_p905327722e_bool tptp.insert_pname A_4))) (= (tptp.hAPP_f759274231e_bool _let_1 A) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool (tptp.hAPP_f759274231e_bool _let_1 tptp.bot_bo844097828e_bool)) A)))) (forall ((A_4 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_c566651504m_bool tptp.insert_com A_4))) (= (tptp.hAPP_f1682609283m_bool _let_1 A) (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila605046092m_bool (tptp.hAPP_f1682609283m_bool _let_1 tptp.bot_bot_fun_com_bool)) A)))) (forall ((A_4 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state A_4))) (= (tptp.hAPP_f806699093e_bool _let_1 A) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool (tptp.hAPP_f806699093e_bool _let_1 tptp.bot_bo784226126e_bool)) A)))) (forall ((G_2 $$unsorted) (P_1 $$unsorted) (Q_1 $$unsorted) (Procs $$unsorted)) (let ((_let_1 (tptp.hAPP_f1922754332_state tptp.cOMBS_1020065803_state (tptp.hAPP_f804744487_state (tptp.cOMBB_2084106034_pname tptp.hoare_1191504582_state) P_1)))) (let ((_let_2 (tptp.hAPP_f360545851e_bool (tptp.image_185131637_state (tptp.hAPP_f914896950_state (tptp.hAPP_f1811131990_state tptp.cOMBS_1524960158_state (tptp.hAPP_f460309545_state _let_1 tptp.body_1)) Q_1)) Procs))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hoare_512830354_state (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool G_2) _let_2)) (tptp.hAPP_f360545851e_bool (tptp.image_185131637_state (tptp.hAPP_f914896950_state (tptp.hAPP_f1811131990_state tptp.cOMBS_1524960158_state (tptp.hAPP_f460309545_state _let_1 (tptp.hAPP_f96342628me_com (tptp.cOMBB_923936821_pname tptp.the_com) tptp.body))) Q_1)) Procs))) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hoare_512830354_state G_2) _let_2)))))) (forall ((Z $$unsorted) (Y_2 $$unsorted) (X_1 $$unsorted)) (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 $$unsorted) (Y_2 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Z))) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Y_2) X_1)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 Y_2)) (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 X_1)))))) (forall ((Z $$unsorted) (Y_2 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool Z))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool Y_2) X_1)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 Y_2)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 X_1)))))) (forall ((Y_2 $$unsorted) (X_1 $$unsorted)) (=> (and (tptp.is_fun_pname_bool Y_2) (tptp.is_fun_pname_bool X_1)) (=> (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 $$unsorted) (X_1 $$unsorted)) (=> (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 $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool Y_2) X_1)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool X_1) Y_2)) (= X_1 Y_2)))) (forall ((Z $$unsorted) (X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool X_1))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 Y_2)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool Y_2) Z)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 Z)))))) (forall ((Z $$unsorted) (X_1 $$unsorted) (Y_2 $$unsorted)) (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 $$unsorted) (X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool X_1))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 Y_2)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool Y_2) Z)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 Z)))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (=> (and (tptp.is_fun_pname_bool X_1) (tptp.is_fun_pname_bool Y_2)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool X_1) Y_2)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool Y_2) X_1)) (= X_1 Y_2))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool X_1) Y_2)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Y_2) X_1)) (= (tptp.hBOOL X_1) (tptp.hBOOL Y_2))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool X_1) Y_2)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool Y_2) X_1)) (= X_1 Y_2)))) (forall ((C $$unsorted) (B_1 $$unsorted) (A_4 $$unsorted)) (=> (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 $$unsorted) (B_1 $$unsorted) (A_4 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool B_1) A_4)) (=> (= (tptp.hBOOL B_1) (tptp.hBOOL C)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool C) A_4))))) (forall ((C $$unsorted) (B_1 $$unsorted) (A_4 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool B_1) A_4)) (=> (= B_1 C) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool C) A_4))))) (forall ((C $$unsorted) (A_4 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_4))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B_1)) (=> (= B_1 C) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 C)))))) (forall ((C $$unsorted) (A_4 $$unsorted) (B_1 $$unsorted)) (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 $$unsorted) (A_4 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool A_4))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 B_1)) (=> (= B_1 C) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 C)))))) (forall ((C $$unsorted) (A_4 $$unsorted) (B_1 $$unsorted)) (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 $$unsorted) (B_1 $$unsorted) (A_4 $$unsorted)) (let ((_let_1 (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool C))) (=> (= (tptp.hBOOL A_4) (tptp.hBOOL B_1)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 B_1)) (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 A_4)))))) (forall ((C $$unsorted) (A_4 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool C))) (=> (= A_4 B_1) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 B_1)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 A_4)))))) (forall ((C $$unsorted) (A_4 $$unsorted) (B_1 $$unsorted)) (=> (= A_4 B_1) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B_1) C)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_4) C))))) (forall ((C $$unsorted) (B_1 $$unsorted) (A_4 $$unsorted)) (=> (= (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 $$unsorted) (A_4 $$unsorted) (B_1 $$unsorted)) (=> (= A_4 B_1) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool B_1) C)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool A_4) C))))) (forall ((Y_2 $$unsorted) (X_1 $$unsorted)) (=> (and (tptp.is_fun_pname_bool Y_2) (tptp.is_fun_pname_bool X_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool Y_2) X_1)) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool X_1) Y_2)) (= X_1 Y_2))))) (forall ((Y_2 $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Y_2) X_1)) (= (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool X_1) Y_2)) (= (tptp.hBOOL X_1) (tptp.hBOOL Y_2))))) (forall ((Y_2 $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool Y_2) X_1)) (= (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool X_1) Y_2)) (= X_1 Y_2)))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (=> (= X_1 Y_2) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool X_1) Y_2)))) (forall ((Y_2 $$unsorted) (X_1 $$unsorted)) (=> (= (tptp.hBOOL X_1) (tptp.hBOOL Y_2)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool X_1) Y_2)))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (=> (= X_1 Y_2) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool X_1) Y_2)))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (=> (and (tptp.is_fun_pname_bool X_1) (tptp.is_fun_pname_bool Y_2)) (= (= X_1 Y_2) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool X_1) Y_2)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool Y_2) X_1)))))) (forall ((Y_2 $$unsorted) (X_1 $$unsorted)) (= (= (tptp.hBOOL X_1) (tptp.hBOOL Y_2)) (and (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool X_1) Y_2)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Y_2) X_1))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (= (= X_1 Y_2) (and (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool X_1) Y_2)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool Y_2) X_1))))) (forall ((A_4 $$unsorted) (A_8 $$unsorted)) (=> (and (tptp.is_pname A_4) (tptp.is_pname A_8)) (= (= (tptp.hAPP_p1252095976_pname tptp.some_pname A_4) (tptp.hAPP_p1252095976_pname tptp.some_pname A_8)) (= A_4 A_8)))) (forall ((A_4 $$unsorted) (A_8 $$unsorted)) (= (= (tptp.hAPP_H1633077406_state tptp.some_H1043067815_state A_4) (tptp.hAPP_H1633077406_state tptp.some_H1043067815_state A_8)) (= A_4 A_8))) (forall ((A_4 $$unsorted) (A_8 $$unsorted)) (= (= (tptp.hAPP_com_option_com tptp.some_com A_4) (tptp.hAPP_com_option_com tptp.some_com A_8)) (= A_4 A_8))) (forall ((G_2 $$unsorted) (P_1 $$unsorted) (C $$unsorted) (Q_1 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.hoare_512830354_state G_2))) (=> (=> (tptp.hBOOL C_1) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state (tptp.hAPP_f497755132_state (tptp.hAPP_c27135337_state (tptp.hAPP_f274181323_state tptp.hoare_1191504582_state P_1) C) Q_1)) tptp.bot_bo784226126e_bool)))) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state (tptp.hAPP_f497755132_state (tptp.hAPP_c27135337_state (tptp.hAPP_f274181323_state tptp.hoare_1191504582_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_bo784226126e_bool)))))) (forall ((Pn_1 $$unsorted) (G_2 $$unsorted) (P_1 $$unsorted) (Q_1 $$unsorted) (Procs $$unsorted)) (let ((_let_1 (tptp.hAPP_f1922754332_state tptp.cOMBS_1020065803_state (tptp.hAPP_f804744487_state (tptp.cOMBB_2084106034_pname tptp.hoare_1191504582_state) P_1)))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hoare_512830354_state (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool G_2) (tptp.hAPP_f360545851e_bool (tptp.image_185131637_state (tptp.hAPP_f914896950_state (tptp.hAPP_f1811131990_state tptp.cOMBS_1524960158_state (tptp.hAPP_f460309545_state _let_1 tptp.body_1)) Q_1)) Procs))) (tptp.hAPP_f360545851e_bool (tptp.image_185131637_state (tptp.hAPP_f914896950_state (tptp.hAPP_f1811131990_state tptp.cOMBS_1524960158_state (tptp.hAPP_f460309545_state _let_1 (tptp.hAPP_f96342628me_com (tptp.cOMBB_923936821_pname tptp.the_com) tptp.body))) Q_1)) Procs))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname Pn_1) Procs)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hoare_512830354_state G_2) (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state (tptp.hAPP_f497755132_state (tptp.hAPP_c27135337_state (tptp.hAPP_f274181323_state tptp.hoare_1191504582_state (tptp.hAPP_p1637813682e_bool P_1 Pn_1)) (tptp.hAPP_pname_com tptp.body_1 Pn_1)) (tptp.hAPP_p1637813682e_bool Q_1 Pn_1))) tptp.bot_bo784226126e_bool))))))) (forall ((A_4 $$unsorted)) (=> (tptp.is_fun_pname_bool A_4) (=> (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 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_f273696895l_bool tptp.ord_le1708315510m_bool A_4) tptp.bot_bot_fun_com_bool)) (= A_4 tptp.bot_bot_fun_com_bool))) (forall ((A_4 $$unsorted)) (=> (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 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool A_4) tptp.bot_bo784226126e_bool)) (= A_4 tptp.bot_bo784226126e_bool))) (forall ((A_4 $$unsorted)) (=> (tptp.is_fun_pname_bool A_4) (= (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 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_f273696895l_bool tptp.ord_le1708315510m_bool A_4) tptp.bot_bot_fun_com_bool)) (= A_4 tptp.bot_bot_fun_com_bool))) (forall ((A_4 $$unsorted)) (= (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 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool A_4) tptp.bot_bo784226126e_bool)) (= A_4 tptp.bot_bo784226126e_bool))) (forall ((A_4 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool tptp.bot_bo844097828e_bool) A_4))) (forall ((A_4 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_f273696895l_bool tptp.ord_le1708315510m_bool tptp.bot_bot_fun_com_bool) A_4))) (forall ((A_4 $$unsorted)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool tptp.bot_bot_bool) A_4))) (forall ((A_4 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool tptp.bot_bo784226126e_bool) A_4))) (forall ((X_1 $$unsorted) (F $$unsorted) (G $$unsorted)) (=> (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 $$unsorted) (F $$unsorted) (G $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool F) G)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_H242767318e_bool F X_1)) (tptp.hAPP_H242767318e_bool G X_1))))) (forall ((X_1 $$unsorted) (F $$unsorted) (G $$unsorted)) (=> (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 $$unsorted) (F $$unsorted) (G $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool F) G)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_H242767318e_bool F X_1)) (tptp.hAPP_H242767318e_bool G X_1))))) (forall ((F $$unsorted) (G $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool F) G)) (forall ((X_2 $$unsorted)) (=> (tptp.is_pname X_2) (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 $$unsorted) (G $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool F) G)) (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_H242767318e_bool F X_2)) (tptp.hAPP_H242767318e_bool G X_2)))))) (forall ((X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_pname_bool tptp.bot_bo844097828e_bool X_1)) (tptp.hBOOL tptp.bot_bot_bool))) (forall ((X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_com_bool tptp.bot_bot_fun_com_bool X_1)) (tptp.hBOOL tptp.bot_bot_bool))) (forall ((X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_H242767318e_bool tptp.bot_bo784226126e_bool X_1)) (tptp.hBOOL tptp.bot_bot_bool))) (forall ((X_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_pname_bool tptp.bot_bo844097828e_bool X_2)) (tptp.hBOOL tptp.bot_bot_bool))) (forall ((X_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_com_bool tptp.bot_bot_fun_com_bool X_2)) (tptp.hBOOL tptp.bot_bot_bool))) (forall ((X_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_H242767318e_bool tptp.bot_bo784226126e_bool X_2)) (tptp.hBOOL tptp.bot_bot_bool))) (forall ((P_1 $$unsorted) (Q_1 $$unsorted) (G_2 $$unsorted) (P_3 $$unsorted) (C0_1 $$unsorted) (Q_3 $$unsorted) (U_1 $$unsorted)) (let ((_let_1 (tptp.cOMBB_1794358604e_bool tptp.hoare_1191504582_state))) (let ((_let_2 (tptp.hoare_512830354_state G_2))) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool U_1)) (=> (forall ((P_4 $$unsorted)) (let ((_let_1 (tptp.hAPP_f792846925ol_com C0_1 P_4))) (let ((_let_2 (tptp.hoare_512830354_state G_2))) (=> (tptp.is_fun_pname_bool P_4) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_2 (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state (tptp.hAPP_f497755132_state (tptp.hAPP_c27135337_state (tptp.hAPP_f274181323_state tptp.hoare_1191504582_state (tptp.hAPP_f887530048e_bool P_3 P_4)) _let_1) (tptp.hAPP_f887530048e_bool Q_3 P_4))) tptp.bot_bo784226126e_bool))) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_2 (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state (tptp.hAPP_f497755132_state (tptp.hAPP_c27135337_state (tptp.hAPP_f274181323_state tptp.hoare_1191504582_state (tptp.hAPP_f887530048e_bool P_1 P_4)) _let_1) (tptp.hAPP_f887530048e_bool Q_1 P_4))) tptp.bot_bo784226126e_bool)))))))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_2 (tptp.hAPP_f509793681e_bool (tptp.image_845802851_state (tptp.hAPP_f819036232_state (tptp.hAPP_f815143704_state tptp.cOMBS_858986606_state (tptp.hAPP_f240260249_state (tptp.hAPP_f578932784_state tptp.cOMBS_384351451_state (tptp.hAPP_f1633046421_state _let_1 P_3)) C0_1)) Q_3)) U_1))) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_2 (tptp.hAPP_f509793681e_bool (tptp.image_845802851_state (tptp.hAPP_f819036232_state (tptp.hAPP_f815143704_state tptp.cOMBS_858986606_state (tptp.hAPP_f240260249_state (tptp.hAPP_f578932784_state tptp.cOMBS_384351451_state (tptp.hAPP_f1633046421_state _let_1 P_1)) C0_1)) Q_1)) U_1))))))))) (forall ((P_1 $$unsorted) (Q_1 $$unsorted) (G_2 $$unsorted) (P_3 $$unsorted) (C0_1 $$unsorted) (Q_3 $$unsorted) (U_1 $$unsorted)) (let ((_let_1 (tptp.cOMBB_2049797414e_bool tptp.hoare_1191504582_state))) (let ((_let_2 (tptp.hoare_512830354_state G_2))) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool U_1)) (=> (forall ((P_4 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1547517799ol_com C0_1 P_4))) (let ((_let_2 (tptp.hoare_512830354_state G_2))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_2 (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state (tptp.hAPP_f497755132_state (tptp.hAPP_c27135337_state (tptp.hAPP_f274181323_state tptp.hoare_1191504582_state (tptp.hAPP_f1487042470e_bool P_3 P_4)) _let_1) (tptp.hAPP_f1487042470e_bool Q_3 P_4))) tptp.bot_bo784226126e_bool))) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_2 (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state (tptp.hAPP_f497755132_state (tptp.hAPP_c27135337_state (tptp.hAPP_f274181323_state tptp.hoare_1191504582_state (tptp.hAPP_f1487042470e_bool P_1 P_4)) _let_1) (tptp.hAPP_f1487042470e_bool Q_1 P_4))) tptp.bot_bo784226126e_bool))))))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_2 (tptp.hAPP_f1216288071e_bool (tptp.image_1497401961_state (tptp.hAPP_f578501918_state (tptp.hAPP_f886846002_state tptp.cOMBS_57685138_state (tptp.hAPP_f824259881_state (tptp.hAPP_f37848848_state tptp.cOMBS_1164062463_state (tptp.hAPP_f250550847_state _let_1 P_3)) C0_1)) Q_3)) U_1))) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_2 (tptp.hAPP_f1216288071e_bool (tptp.image_1497401961_state (tptp.hAPP_f578501918_state (tptp.hAPP_f886846002_state tptp.cOMBS_57685138_state (tptp.hAPP_f824259881_state (tptp.hAPP_f37848848_state tptp.cOMBS_1164062463_state (tptp.hAPP_f250550847_state _let_1 P_1)) C0_1)) Q_1)) U_1))))))))) (forall ((P_1 $$unsorted) (Q_1 $$unsorted) (G_2 $$unsorted) (P_3 $$unsorted) (C0_1 $$unsorted) (Q_3 $$unsorted) (U_1 $$unsorted)) (let ((_let_1 (tptp.cOMBB_2084106034_pname tptp.hoare_1191504582_state))) (let ((_let_2 (tptp.hoare_512830354_state G_2))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname U_1)) (=> (forall ((P_4 $$unsorted)) (let ((_let_1 (tptp.hAPP_pname_com C0_1 P_4))) (let ((_let_2 (tptp.hoare_512830354_state G_2))) (=> (tptp.is_pname P_4) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_2 (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state (tptp.hAPP_f497755132_state (tptp.hAPP_c27135337_state (tptp.hAPP_f274181323_state tptp.hoare_1191504582_state (tptp.hAPP_p1637813682e_bool P_3 P_4)) _let_1) (tptp.hAPP_p1637813682e_bool Q_3 P_4))) tptp.bot_bo784226126e_bool))) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_2 (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state (tptp.hAPP_f497755132_state (tptp.hAPP_c27135337_state (tptp.hAPP_f274181323_state tptp.hoare_1191504582_state (tptp.hAPP_p1637813682e_bool P_1 P_4)) _let_1) (tptp.hAPP_p1637813682e_bool Q_1 P_4))) tptp.bot_bo784226126e_bool)))))))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_2 (tptp.hAPP_f360545851e_bool (tptp.image_185131637_state (tptp.hAPP_f914896950_state (tptp.hAPP_f1811131990_state tptp.cOMBS_1524960158_state (tptp.hAPP_f460309545_state (tptp.hAPP_f1922754332_state tptp.cOMBS_1020065803_state (tptp.hAPP_f804744487_state _let_1 P_3)) C0_1)) Q_3)) U_1))) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_2 (tptp.hAPP_f360545851e_bool (tptp.image_185131637_state (tptp.hAPP_f914896950_state (tptp.hAPP_f1811131990_state tptp.cOMBS_1524960158_state (tptp.hAPP_f460309545_state (tptp.hAPP_f1922754332_state tptp.cOMBS_1020065803_state (tptp.hAPP_f804744487_state _let_1 P_1)) C0_1)) Q_1)) U_1))))))))) (forall ((G_2 $$unsorted) (C $$unsorted) (Q_1 $$unsorted) (P_1 $$unsorted)) (=> (forall ((Z_2 $$unsorted) (S_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool P_1 Z_2) S_1)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hoare_512830354_state G_2) (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state (tptp.hAPP_f497755132_state (tptp.hAPP_c27135337_state (tptp.hAPP_f274181323_state tptp.hoare_1191504582_state (tptp.hAPP_f1863945078e_bool tptp.cOMBK_631994958_state (tptp.hAPP_s1806633685e_bool (tptp.hAPP_f817621513e_bool tptp.cOMBC_2027030106e_bool tptp.fequal_state) S_1))) C) (tptp.hAPP_f1863945078e_bool tptp.cOMBK_631994958_state (tptp.hAPP_s1806633685e_bool Q_1 Z_2)))) tptp.bot_bo784226126e_bool))))) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hoare_512830354_state G_2) (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state (tptp.hAPP_f497755132_state (tptp.hAPP_c27135337_state (tptp.hAPP_f274181323_state tptp.hoare_1191504582_state P_1) C) Q_1)) tptp.bot_bo784226126e_bool))))) (forall ((G_2 $$unsorted) (P_1 $$unsorted) (Q_1 $$unsorted) (Procs $$unsorted)) (let ((_let_1 (tptp.hAPP_f1922754332_state tptp.cOMBS_1020065803_state (tptp.hAPP_f804744487_state (tptp.cOMBB_2084106034_pname tptp.hoare_1191504582_state) P_1)))) (let ((_let_2 (tptp.hAPP_f360545851e_bool (tptp.image_185131637_state (tptp.hAPP_f914896950_state (tptp.hAPP_f1811131990_state tptp.cOMBS_1524960158_state (tptp.hAPP_f460309545_state _let_1 tptp.body_1)) Q_1)) Procs))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hoare_919241616_state (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool G_2) _let_2)) (tptp.hAPP_f360545851e_bool (tptp.image_185131637_state (tptp.hAPP_f914896950_state (tptp.hAPP_f1811131990_state tptp.cOMBS_1524960158_state (tptp.hAPP_f460309545_state _let_1 (tptp.hAPP_f96342628me_com (tptp.cOMBB_923936821_pname tptp.the_com) tptp.body))) Q_1)) Procs))) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hoare_919241616_state G_2) _let_2)))))) (forall ((P_1 $$unsorted) (G_2 $$unsorted) (P_3 $$unsorted) (C $$unsorted) (Q_1 $$unsorted)) (let ((_let_1 (tptp.hoare_512830354_state G_2))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state (tptp.hAPP_f497755132_state (tptp.hAPP_c27135337_state (tptp.hAPP_f274181323_state tptp.hoare_1191504582_state P_3) C) Q_1)) tptp.bot_bo784226126e_bool))) (=> (forall ((Z_2 $$unsorted) (S_1 $$unsorted)) (=> (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_f1378282496l_bool _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state (tptp.hAPP_f497755132_state (tptp.hAPP_c27135337_state (tptp.hAPP_f274181323_state tptp.hoare_1191504582_state P_1) C) Q_1)) tptp.bot_bo784226126e_bool))))))) (forall ((Q_1 $$unsorted) (G_2 $$unsorted) (P_1 $$unsorted) (C $$unsorted) (Q_3 $$unsorted)) (let ((_let_1 (tptp.hAPP_c27135337_state (tptp.hAPP_f274181323_state tptp.hoare_1191504582_state P_1) C))) (let ((_let_2 (tptp.hoare_512830354_state G_2))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_2 (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state (tptp.hAPP_f497755132_state _let_1 Q_3)) tptp.bot_bo784226126e_bool))) (=> (forall ((Z_2 $$unsorted) (S_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool Q_3 Z_2) S_1)) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool Q_1 Z_2) S_1)))) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_2 (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state (tptp.hAPP_f497755132_state _let_1 Q_1)) tptp.bot_bo784226126e_bool)))))))) (forall ((P_1 $$unsorted) (Q_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state (tptp.hAPP_f497755132_state (tptp.hAPP_c27135337_state (tptp.hAPP_f274181323_state tptp.hoare_1191504582_state P_1) C) Q_1)) tptp.bot_bo784226126e_bool))) (let ((_let_2 (tptp.hoare_512830354_state tptp.bot_bo784226126e_bool))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_2 (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state (tptp.hAPP_c1455475371_state tptp.hoare_Mirabelle_MGT C)) tptp.bot_bo784226126e_bool))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hoare_919241616_state tptp.bot_bo784226126e_bool) _let_1)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_2 _let_1))))))) (forall ((A $$unsorted) (B $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_pname_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A) B) X_1)) (=> (not (tptp.hBOOL (tptp.hAPP_pname_bool A X_1))) (tptp.hBOOL (tptp.hAPP_pname_bool B X_1))))) (forall ((A $$unsorted) (B $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_H242767318e_bool (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool A) B) X_1)) (=> (not (tptp.hBOOL (tptp.hAPP_H242767318e_bool A X_1))) (tptp.hBOOL (tptp.hAPP_H242767318e_bool B X_1))))) (forall ((A $$unsorted) (B $$unsorted) (X_1 $$unsorted)) (=> (=> (not (tptp.hBOOL (tptp.hAPP_pname_bool B X_1))) (tptp.hBOOL (tptp.hAPP_pname_bool A X_1))) (tptp.hBOOL (tptp.hAPP_pname_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A) B) X_1)))) (forall ((A $$unsorted) (B $$unsorted) (X_1 $$unsorted)) (=> (=> (not (tptp.hBOOL (tptp.hAPP_H242767318e_bool B X_1))) (tptp.hBOOL (tptp.hAPP_H242767318e_bool A X_1))) (tptp.hBOOL (tptp.hAPP_H242767318e_bool (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool A) B) X_1)))) (forall ((Q_1 $$unsorted) (P_1 $$unsorted) (G_2 $$unsorted) (P_3 $$unsorted) (C $$unsorted) (Q_3 $$unsorted)) (let ((_let_1 (tptp.hoare_512830354_state G_2))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state (tptp.hAPP_f497755132_state (tptp.hAPP_c27135337_state (tptp.hAPP_f274181323_state tptp.hoare_1191504582_state P_3) C) Q_3)) tptp.bot_bo784226126e_bool))) (=> (forall ((Z_2 $$unsorted) (S_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool P_1 Z_2) S_1)) (forall ((S_2 $$unsorted)) (=> (forall ((Z_3 $$unsorted)) (=> (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_f1378282496l_bool _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state (tptp.hAPP_f497755132_state (tptp.hAPP_c27135337_state (tptp.hAPP_f274181323_state tptp.hoare_1191504582_state P_1) C) Q_1)) tptp.bot_bo784226126e_bool))))))) (forall ((G_2 $$unsorted) (Ts $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hoare_512830354_state G_2) Ts)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hoare_919241616_state G_2) Ts)))) (forall ((X_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_com_bool tptp.bot_bot_fun_com_bool X_2)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_2) tptp.bot_bot_fun_com_bool)))) (forall ((X_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_H242767318e_bool tptp.bot_bo784226126e_bool X_2)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state X_2) tptp.bot_bo784226126e_bool)))) (forall ((X_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_pname_bool tptp.bot_bo844097828e_bool X_2)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) tptp.bot_bo844097828e_bool)))) (forall ((Q_1 $$unsorted) (P_1 $$unsorted) (X_1 $$unsorted)) (=> (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 $$unsorted) (P_1 $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_H242767318e_bool P_1 X_1)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool P_1) Q_1)) (tptp.hBOOL (tptp.hAPP_H242767318e_bool Q_1 X_1))))) (forall ((X_1 $$unsorted) (P_1 $$unsorted) (Q_1 $$unsorted)) (=> (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 $$unsorted) (P_1 $$unsorted) (Q_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool P_1) Q_1)) (=> (tptp.hBOOL (tptp.hAPP_H242767318e_bool P_1 X_1)) (tptp.hBOOL (tptp.hAPP_H242767318e_bool Q_1 X_1))))) (forall ((A $$unsorted) (B $$unsorted) (X_1 $$unsorted)) (=> (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 $$unsorted) (B $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_H242767318e_bool B X_1)) (tptp.hBOOL (tptp.hAPP_H242767318e_bool (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool A) B) X_1)))) (forall ((B $$unsorted) (A $$unsorted) (X_1 $$unsorted)) (=> (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 $$unsorted) (A $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_H242767318e_bool A X_1)) (tptp.hBOOL (tptp.hAPP_H242767318e_bool (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool A) B) X_1)))) (forall ((R_1 $$unsorted) (S $$unsorted)) (let ((_let_1 (tptp.hAPP_f578650245m_bool tptp.cOMBC_1904837336l_bool tptp.member_com))) (= (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_f273696895l_bool tptp.ord_le1708315510m_bool (tptp.hAPP_f1682609283m_bool _let_1 R_1)) (tptp.hAPP_f1682609283m_bool _let_1 S))) (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_f273696895l_bool tptp.ord_le1708315510m_bool R_1) S))))) (forall ((R_1 $$unsorted) (S $$unsorted)) (let ((_let_1 (tptp.hAPP_f1184122441e_bool tptp.cOMBC_538205282l_bool tptp.member1667945571_state))) (= (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool (tptp.hAPP_f806699093e_bool _let_1 R_1)) (tptp.hAPP_f806699093e_bool _let_1 S))) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool R_1) S))))) (forall ((R_1 $$unsorted) (S $$unsorted)) (let ((_let_1 (tptp.hAPP_f661147897e_bool tptp.cOMBC_1058051404l_bool tptp.member_pname))) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool _let_1 R_1)) (tptp.hAPP_f759274231e_bool _let_1 S))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool R_1) S))))) (forall ((R_1 $$unsorted) (S $$unsorted) (X_2 $$unsorted)) (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 $$unsorted) (S $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1184122441e_bool tptp.cOMBC_538205282l_bool tptp.member1667945571_state))) (= (tptp.hBOOL (tptp.hAPP_H242767318e_bool (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool (tptp.hAPP_f806699093e_bool _let_1 R_1)) (tptp.hAPP_f806699093e_bool _let_1 S)) X_2)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state X_2) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool R_1) S)))))) (forall ((R_1 $$unsorted) (S $$unsorted) (X_2 $$unsorted)) (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 $$unsorted) (G $$unsorted)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.is_pname X_2) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_pname_bool F X_2)) (tptp.hAPP_pname_bool G X_2))))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool F) G)))) (forall ((F $$unsorted) (G $$unsorted)) (=> (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_H242767318e_bool F X_2)) (tptp.hAPP_H242767318e_bool G X_2)))) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool F) G)))) (forall ((X_1 $$unsorted)) (= (tptp.set_pname (tptp.hAPP_p1252095976_pname tptp.some_pname X_1)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1) tptp.bot_bo844097828e_bool))) (forall ((X_1 $$unsorted)) (= (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 $$unsorted)) (= (tptp.set_Ho1741238126_state (tptp.hAPP_H1633077406_state tptp.some_H1043067815_state X_1)) (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state X_1) tptp.bot_bo784226126e_bool))) (forall ((F $$unsorted) (G $$unsorted) (X_1 $$unsorted)) (= (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 $$unsorted) (G $$unsorted) (X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_H242767318e_bool (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool F) G) X_1)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool (tptp.hAPP_H242767318e_bool F X_1)) (tptp.hAPP_H242767318e_bool G X_1))))) (forall ((F $$unsorted) (G $$unsorted) (X_2 $$unsorted)) (= (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 $$unsorted) (G $$unsorted) (X_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_H242767318e_bool (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool F) G) X_2)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool (tptp.hAPP_H242767318e_bool F X_2)) (tptp.hAPP_H242767318e_bool G X_2))))) (=> _let_11 (forall ((T_2 $$unsorted)) (not (forall ((S_1 $$unsorted)) (= S_1 T_2))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (=> (and (tptp.is_fun_pname_bool X_1) (tptp.is_fun_pname_bool Y_2)) (= (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool X_1) Y_2) tptp.bot_bo844097828e_bool) (and (= X_1 tptp.bot_bo844097828e_bool) (= Y_2 tptp.bot_bo844097828e_bool))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (= (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila605046092m_bool X_1) Y_2) tptp.bot_bot_fun_com_bool) (and (= X_1 tptp.bot_bot_fun_com_bool) (= Y_2 tptp.bot_bot_fun_com_bool)))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.hBOOL tptp.bot_bot_bool))) (= (= (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool X_1) Y_2)) _let_1) (and (= (tptp.hBOOL X_1) _let_1) (= (tptp.hBOOL Y_2) _let_1))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (= (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool X_1) Y_2) tptp.bot_bo784226126e_bool) (and (= X_1 tptp.bot_bo784226126e_bool) (= Y_2 tptp.bot_bo784226126e_bool)))) (forall ((X_1 $$unsorted) (Xo $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_1) (tptp.set_com Xo))) (= Xo (tptp.hAPP_com_option_com tptp.some_com X_1)))) (forall ((X_1 $$unsorted) (Xo $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state X_1) (tptp.set_Ho1741238126_state Xo))) (= Xo (tptp.hAPP_H1633077406_state tptp.some_H1043067815_state X_1)))) (forall ((X_1 $$unsorted) (Xo $$unsorted)) (=> (tptp.is_option_pname Xo) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) (tptp.set_pname Xo))) (= Xo (tptp.hAPP_p1252095976_pname tptp.some_pname X_1))))) (forall ((A_4 $$unsorted)) (=> (tptp.is_fun_pname_bool A_4) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A_4) A_4) A_4))) (forall ((A_4 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool A_4) A_4)) (tptp.hBOOL A_4))) (forall ((A_4 $$unsorted)) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool A_4) A_4) A_4)) (forall ((X_1 $$unsorted)) (=> (tptp.is_fun_pname_bool X_1) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool X_1) X_1) X_1))) (forall ((X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool X_1) X_1)) (tptp.hBOOL X_1))) (forall ((X_1 $$unsorted)) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool X_1) X_1) X_1)) (forall ((A_4 $$unsorted) (B_1 $$unsorted)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A_4) B_1) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool B_1) A_4))) (forall ((A_4 $$unsorted) (B_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool A_4) B_1)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool B_1) A_4)))) (forall ((A_4 $$unsorted) (B_1 $$unsorted)) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool A_4) B_1) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool B_1) A_4))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool X_1) Y_2) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool Y_2) X_1))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool X_1) Y_2)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool Y_2) X_1)))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool X_1) Y_2) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool Y_2) X_1))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool X_1) Y_2) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool Y_2) X_1))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool X_1) Y_2)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool Y_2) X_1)))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool X_1) Y_2) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool Y_2) X_1))) (forall ((A_4 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A_4))) (let ((_let_2 (tptp.hAPP_f759274231e_bool _let_1 B_1))) (= (tptp.hAPP_f759274231e_bool _let_1 _let_2) _let_2)))) (forall ((A_4 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool A_4))) (let ((_let_2 (tptp.hAPP_bool_bool _let_1 B_1))) (= (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 _let_2)) (tptp.hBOOL _let_2))))) (forall ((A_4 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool A_4))) (let ((_let_2 (tptp.hAPP_f806699093e_bool _let_1 B_1))) (= (tptp.hAPP_f806699093e_bool _let_1 _let_2) _let_2)))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool X_1))) (let ((_let_2 (tptp.hAPP_f759274231e_bool _let_1 Y_2))) (= (tptp.hAPP_f759274231e_bool _let_1 _let_2) _let_2)))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool X_1))) (let ((_let_2 (tptp.hAPP_bool_bool _let_1 Y_2))) (= (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 _let_2)) (tptp.hBOOL _let_2))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool X_1))) (let ((_let_2 (tptp.hAPP_f806699093e_bool _let_1 Y_2))) (= (tptp.hAPP_f806699093e_bool _let_1 _let_2) _let_2)))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool X_1))) (let ((_let_2 (tptp.hAPP_f759274231e_bool _let_1 Y_2))) (= (tptp.hAPP_f759274231e_bool _let_1 _let_2) _let_2)))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool X_1))) (let ((_let_2 (tptp.hAPP_bool_bool _let_1 Y_2))) (= (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 _let_2)) (tptp.hBOOL _let_2))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool X_1))) (let ((_let_2 (tptp.hAPP_f806699093e_bool _let_1 Y_2))) (= (tptp.hAPP_f806699093e_bool _let_1 _let_2) _let_2)))) (forall ((B_1 $$unsorted) (A_4 $$unsorted) (C $$unsorted)) (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 $$unsorted) (A_4 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool B_1))) (let ((_let_2 (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool A_4))) (= (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 (tptp.hAPP_bool_bool _let_2 C))) (tptp.hBOOL (tptp.hAPP_bool_bool _let_2 (tptp.hAPP_bool_bool _let_1 C))))))) (forall ((B_1 $$unsorted) (A_4 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool B_1))) (let ((_let_2 (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool A_4))) (= (tptp.hAPP_f806699093e_bool _let_1 (tptp.hAPP_f806699093e_bool _let_2 C)) (tptp.hAPP_f806699093e_bool _let_2 (tptp.hAPP_f806699093e_bool _let_1 C)))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool X_1))) (let ((_let_2 (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool Y_2))) (= (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool _let_2 Z)) (tptp.hAPP_f759274231e_bool _let_2 (tptp.hAPP_f759274231e_bool _let_1 Z)))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted) (Z $$unsorted)) (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 $$unsorted) (Y_2 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool X_1))) (let ((_let_2 (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool Y_2))) (= (tptp.hAPP_f806699093e_bool _let_1 (tptp.hAPP_f806699093e_bool _let_2 Z)) (tptp.hAPP_f806699093e_bool _let_2 (tptp.hAPP_f806699093e_bool _let_1 Z)))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted) (Z $$unsorted)) (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 $$unsorted) (Y_2 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool X_1))) (let ((_let_2 (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool Y_2))) (= (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 (tptp.hAPP_bool_bool _let_2 Z))) (tptp.hBOOL (tptp.hAPP_bool_bool _let_2 (tptp.hAPP_bool_bool _let_1 Z))))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool X_1))) (let ((_let_2 (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool Y_2))) (= (tptp.hAPP_f806699093e_bool _let_1 (tptp.hAPP_f806699093e_bool _let_2 Z)) (tptp.hAPP_f806699093e_bool _let_2 (tptp.hAPP_f806699093e_bool _let_1 Z)))))) (forall ((A_4 $$unsorted) (B_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A_4))) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool (tptp.hAPP_f759274231e_bool _let_1 B_1)) C) (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool B_1) C))))) (forall ((A_4 $$unsorted) (B_1 $$unsorted) (C $$unsorted)) (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 $$unsorted) (B_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool A_4))) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool (tptp.hAPP_f806699093e_bool _let_1 B_1)) C) (tptp.hAPP_f806699093e_bool _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool B_1) C))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted) (Z $$unsorted)) (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 $$unsorted) (Y_2 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool X_1))) (= (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool (tptp.hAPP_bool_bool _let_1 Y_2)) Z)) (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool Y_2) Z)))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool X_1))) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool (tptp.hAPP_f806699093e_bool _let_1 Y_2)) Z) (tptp.hAPP_f806699093e_bool _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool Y_2) Z))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool X_1))) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool (tptp.hAPP_f759274231e_bool _let_1 Y_2)) Z) (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool Y_2) Z))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted) (Z $$unsorted)) (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 $$unsorted) (Y_2 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool X_1))) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool (tptp.hAPP_f806699093e_bool _let_1 Y_2)) Z) (tptp.hAPP_f806699093e_bool _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool Y_2) Z))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool X_1) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool X_1) Y_2)))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool X_1) (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool X_1) Y_2)))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool X_1) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool X_1) Y_2)))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool X_1) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool X_1) Y_2)))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool X_1) (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool X_1) Y_2)))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool X_1) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool X_1) Y_2)))) (forall ((Y_2 $$unsorted) (X_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool Y_2) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool X_1) Y_2)))) (forall ((Y_2 $$unsorted) (X_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Y_2) (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool X_1) Y_2)))) (forall ((Y_2 $$unsorted) (X_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool Y_2) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool X_1) Y_2)))) (forall ((Y_2 $$unsorted) (X_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool Y_2) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool X_1) Y_2)))) (forall ((Y_2 $$unsorted) (X_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Y_2) (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool X_1) Y_2)))) (forall ((Y_2 $$unsorted) (X_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool Y_2) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool X_1) Y_2)))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (=> (tptp.is_fun_pname_bool Y_2) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool X_1) Y_2)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool X_1) Y_2) Y_2)))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool X_1) Y_2)) (= (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool X_1) Y_2)) (tptp.hBOOL Y_2)))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool X_1) Y_2)) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool X_1) Y_2) Y_2))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted) (Z $$unsorted)) (= (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 $$unsorted) (Y_2 $$unsorted) (Z $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool X_1) Y_2)) Z)) (and (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool X_1) Z)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Y_2) Z))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted) (Z $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool X_1) Y_2)) Z)) (and (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool X_1) Z)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool Y_2) Z))))) (forall ((B_1 $$unsorted) (X_1 $$unsorted) (A_4 $$unsorted)) (let ((_let_1 (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool X_1))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A_4)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A_4) B_1)))))) (forall ((B_1 $$unsorted) (X_1 $$unsorted) (A_4 $$unsorted)) (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 $$unsorted) (X_1 $$unsorted) (A_4 $$unsorted)) (let ((_let_1 (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool X_1))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 A_4)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool A_4) B_1)))))) (forall ((A_4 $$unsorted) (X_1 $$unsorted) (B_1 $$unsorted)) (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 $$unsorted) (X_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool X_1))) (=> (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 B_1)) (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool A_4) B_1)))))) (forall ((A_4 $$unsorted) (X_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool X_1))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 B_1)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool A_4) B_1)))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (=> (tptp.is_fun_pname_bool Y_2) (=> (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 $$unsorted) (Y_2 $$unsorted)) (=> (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 $$unsorted) (Y_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool X_1) Y_2)) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool X_1) Y_2) Y_2))) (forall ((Y_2 $$unsorted) (X_1 $$unsorted)) (=> (tptp.is_fun_pname_bool X_1) (=> (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 $$unsorted) (X_1 $$unsorted)) (=> (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 $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool Y_2) X_1)) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool X_1) Y_2) X_1))) (forall ((B_1 $$unsorted) (A_4 $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_4) X_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B_1) X_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A_4) B_1)) X_1))))) (forall ((B_1 $$unsorted) (A_4 $$unsorted) (X_1 $$unsorted)) (=> (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 $$unsorted) (A_4 $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool A_4) X_1)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool B_1) X_1)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool A_4) B_1)) X_1))))) (forall ((Z $$unsorted) (Y_2 $$unsorted) (X_1 $$unsorted)) (=> (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 $$unsorted) (Y_2 $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Y_2) X_1)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Z) X_1)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool Y_2) Z)) X_1))))) (forall ((Z $$unsorted) (Y_2 $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool Y_2) X_1)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool Z) X_1)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool Y_2) Z)) X_1))))) (forall ((B_1 $$unsorted) (D_1 $$unsorted) (A_4 $$unsorted) (C $$unsorted)) (=> (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 $$unsorted) (D_1 $$unsorted) (A_4 $$unsorted) (C $$unsorted)) (=> (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 $$unsorted) (D_1 $$unsorted) (A_4 $$unsorted) (C $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool A_4) C)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool B_1) D_1)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool A_4) B_1)) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool C) D_1)))))) (forall ((A_4 $$unsorted) (B_1 $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A_4) B_1)) X_1)) (not (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_4) X_1)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B_1) X_1))))))) (forall ((A_4 $$unsorted) (B_1 $$unsorted) (X_1 $$unsorted)) (=> (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 $$unsorted) (B_1 $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool A_4) B_1)) X_1)) (not (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool A_4) X_1)) (not (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool B_1) X_1))))))) (forall ((X_1 $$unsorted)) (=> (tptp.is_fun_pname_bool X_1) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool tptp.bot_bo844097828e_bool) X_1) X_1))) (forall ((X_1 $$unsorted)) (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila605046092m_bool tptp.bot_bot_fun_com_bool) X_1) X_1)) (forall ((X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool tptp.bot_bot_bool) X_1)) (tptp.hBOOL X_1))) (forall ((X_1 $$unsorted)) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool tptp.bot_bo784226126e_bool) X_1) X_1)) (forall ((X_1 $$unsorted)) (=> (tptp.is_fun_pname_bool X_1) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool X_1) tptp.bot_bo844097828e_bool) X_1))) (forall ((X_1 $$unsorted)) (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila605046092m_bool X_1) tptp.bot_bot_fun_com_bool) X_1)) (forall ((X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool X_1) tptp.bot_bot_bool)) (tptp.hBOOL X_1))) (forall ((X_1 $$unsorted)) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool X_1) tptp.bot_bo784226126e_bool) X_1)) (forall ((X_1 $$unsorted) (P_1 $$unsorted) (A $$unsorted)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.is_pname X_2) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) (tptp.set_pname A))) (tptp.hBOOL (tptp.hAPP_pname_bool P_1 X_2))))) (=> (= A (tptp.hAPP_p1252095976_pname tptp.some_pname X_1)) (tptp.hBOOL (tptp.hAPP_pname_bool P_1 X_1))))) (forall ((X_1 $$unsorted) (P_1 $$unsorted) (A $$unsorted)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state X_2) (tptp.set_Ho1741238126_state A))) (tptp.hBOOL (tptp.hAPP_H242767318e_bool P_1 X_2)))) (=> (= A (tptp.hAPP_H1633077406_state tptp.some_H1043067815_state X_1)) (tptp.hBOOL (tptp.hAPP_H242767318e_bool P_1 X_1))))) (forall ((X_1 $$unsorted) (P_1 $$unsorted) (A $$unsorted)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_2) (tptp.set_com A))) (tptp.hBOOL (tptp.hAPP_com_bool P_1 X_2)))) (=> (= A (tptp.hAPP_com_option_com tptp.some_com X_1)) (tptp.hBOOL (tptp.hAPP_com_bool P_1 X_1))))) (forall ((B $$unsorted) (A $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (and (tptp.is_fun1661590463l_bool B) (tptp.is_fun1661590463l_bool A)) (=> (tptp.hBOOL (tptp.finite1268145088e_bool F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)) (=> (not (= A tptp.bot_bo1649642514l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool B)) (=> (not (= B tptp.bot_bo1649642514l_bool)) (= (tptp.hAPP_f674760225e_bool Fa (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.semila1782091504l_bool A) B)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool F (tptp.hAPP_f674760225e_bool Fa A)) (tptp.hAPP_f674760225e_bool Fa B)))))))))) (forall ((B $$unsorted) (A $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.finite688249778e_bool F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool A)) (=> (not (= A tptp.bot_bo942947096l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool B)) (=> (not (= B tptp.bot_bo942947096l_bool)) (= (tptp.hAPP_f1216288071e_bool Fa (tptp.hAPP_f734420447l_bool (tptp.hAPP_f1847120l_bool tptp.semila1672697786l_bool A) B)) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool F (tptp.hAPP_f1216288071e_bool Fa A)) (tptp.hAPP_f1216288071e_bool Fa B))))))))) (forall ((B $$unsorted) (A $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.finite666746948em_com F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool tptp.finite_finite_com A)) (=> (not (= A tptp.bot_bot_fun_com_bool)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool tptp.finite_finite_com B)) (=> (not (= B tptp.bot_bot_fun_com_bool)) (= (tptp.hAPP_f1276420679ol_com Fa (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila605046092m_bool A) B)) (tptp.hAPP_com_com (tptp.hAPP_com_fun_com_com F (tptp.hAPP_f1276420679ol_com Fa A)) (tptp.hAPP_f1276420679ol_com Fa B))))))))) (forall ((B $$unsorted) (A $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.finite416071164_state F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state A)) (=> (not (= A tptp.bot_bo784226126e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state B)) (=> (not (= B tptp.bot_bo784226126e_bool)) (= (tptp.hAPP_f718417177_state Fa (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool A) B)) (tptp.hAPP_H574424047_state (tptp.hAPP_H280516760_state F (tptp.hAPP_f718417177_state Fa A)) (tptp.hAPP_f718417177_state Fa B))))))))) (forall ((B $$unsorted) (A $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (and (tptp.is_fun_pname_bool B) (tptp.is_fun_pname_bool A)) (=> (tptp.hBOOL (tptp.finite89670078_pname F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (=> (not (= A tptp.bot_bo844097828e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B)) (=> (not (= B tptp.bot_bo844097828e_bool)) (= (tptp.hAPP_f1297739591_pname Fa (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A) B)) (tptp.hAPP_pname_pname (tptp.hAPP_p1170154830_pname F (tptp.hAPP_f1297739591_pname Fa A)) (tptp.hAPP_f1297739591_pname Fa B)))))))))) (forall ((B $$unsorted) (A $$unsorted) (F $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.hAPP_f674760225e_bool Fa A))) (=> (tptp.is_fun1661590463l_bool B) (=> (tptp.hBOOL (tptp.finite1268145088e_bool F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)) (=> (not (= B tptp.bot_bo1649642514l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool B) A)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool F (tptp.hAPP_f674760225e_bool Fa B)) _let_1) _let_1)))))))) (forall ((B $$unsorted) (A $$unsorted) (F $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.hAPP_f1216288071e_bool Fa A))) (=> (tptp.hBOOL (tptp.finite688249778e_bool F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool A)) (=> (not (= B tptp.bot_bo942947096l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool (tptp.hAPP_f1516997247l_bool tptp.ord_le694194916l_bool B) A)) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool F (tptp.hAPP_f1216288071e_bool Fa B)) _let_1) _let_1))))))) (forall ((B $$unsorted) (A $$unsorted) (F $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.hAPP_f1276420679ol_com Fa A))) (=> (tptp.hBOOL (tptp.finite666746948em_com F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool tptp.finite_finite_com A)) (=> (not (= B tptp.bot_bot_fun_com_bool)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_f273696895l_bool tptp.ord_le1708315510m_bool B) A)) (= (tptp.hAPP_com_com (tptp.hAPP_com_fun_com_com F (tptp.hAPP_f1276420679ol_com Fa B)) _let_1) _let_1))))))) (forall ((B $$unsorted) (A $$unsorted) (F $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.hAPP_f718417177_state Fa A))) (=> (tptp.hBOOL (tptp.finite416071164_state F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state A)) (=> (not (= B tptp.bot_bo784226126e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool B) A)) (= (tptp.hAPP_H574424047_state (tptp.hAPP_H280516760_state F (tptp.hAPP_f718417177_state Fa B)) _let_1) _let_1))))))) (forall ((B $$unsorted) (A $$unsorted) (F $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.hAPP_f1297739591_pname Fa A))) (=> (tptp.is_fun_pname_bool B) (=> (tptp.hBOOL (tptp.finite89670078_pname F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (=> (not (= B tptp.bot_bo844097828e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) A)) (= (tptp.hAPP_pname_pname (tptp.hAPP_p1170154830_pname F (tptp.hAPP_f1297739591_pname Fa B)) _let_1) _let_1)))))))) (forall ((G_2 $$unsorted) (P_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hoare_512830354_state G_2) (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state (tptp.hAPP_f497755132_state (tptp.hAPP_c27135337_state (tptp.hAPP_f274181323_state tptp.hoare_1191504582_state P_1) tptp.skip) P_1)) tptp.bot_bo784226126e_bool)))) (forall ((X_1 $$unsorted) (A $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.finite666746948em_com F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool tptp.finite_finite_com A)) (=> (not (= A tptp.bot_bot_fun_com_bool)) (= (tptp.hAPP_f1276420679ol_com Fa (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com X_1) A)) (tptp.hAPP_com_com (tptp.hAPP_com_fun_com_com F X_1) (tptp.hAPP_f1276420679ol_com Fa A))))))) (forall ((X_1 $$unsorted) (A $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (tptp.is_fun1661590463l_bool A) (=> (tptp.hBOOL (tptp.finite1268145088e_bool F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)) (=> (not (= A tptp.bot_bo1649642514l_bool)) (= (tptp.hAPP_f674760225e_bool Fa (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool X_1) A)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool F X_1) (tptp.hAPP_f674760225e_bool Fa A)))))))) (forall ((X_1 $$unsorted) (A $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.finite688249778e_bool F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool A)) (=> (not (= A tptp.bot_bo942947096l_bool)) (= (tptp.hAPP_f1216288071e_bool Fa (tptp.hAPP_f734420447l_bool (tptp.hAPP_f1472090462l_bool tptp.insert1720618162e_bool X_1) A)) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool F X_1) (tptp.hAPP_f1216288071e_bool Fa A))))))) (forall ((X_1 $$unsorted) (A $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (tptp.is_fun_pname_bool A) (=> (tptp.hBOOL (tptp.finite89670078_pname F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (=> (not (= A tptp.bot_bo844097828e_bool)) (= (tptp.hAPP_f1297739591_pname Fa (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1) A)) (tptp.hAPP_pname_pname (tptp.hAPP_p1170154830_pname F X_1) (tptp.hAPP_f1297739591_pname Fa A)))))))) (forall ((X_1 $$unsorted) (A $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.finite416071164_state F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state A)) (=> (not (= A tptp.bot_bo784226126e_bool)) (= (tptp.hAPP_f718417177_state Fa (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state X_1) A)) (tptp.hAPP_H574424047_state (tptp.hAPP_H280516760_state F X_1) (tptp.hAPP_f718417177_state Fa A))))))) (forall ((P_1 $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool tptp.finite_finite_com Fa)) (=> (not (= Fa tptp.bot_bot_fun_com_bool)) (=> (forall ((X_2 $$unsorted)) (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 $$unsorted) (F_2 $$unsorted)) (=> (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 $$unsorted) (Fa $$unsorted)) (=> (tptp.is_fun1661590463l_bool Fa) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool Fa)) (=> (not (= Fa tptp.bot_bo1649642514l_bool)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.is_fun_pname_bool X_2) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool P_1 (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool X_2) tptp.bot_bo1649642514l_bool))))) (=> (forall ((X_2 $$unsorted) (F_2 $$unsorted)) (=> (and (tptp.is_fun_pname_bool X_2) (tptp.is_fun1661590463l_bool F_2)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool F_2)) (=> (not (= F_2 tptp.bot_bo1649642514l_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool X_2) F_2))) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool P_1 F_2)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool P_1 (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool X_2) F_2))))))))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool P_1 Fa)))))))) (forall ((P_1 $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool Fa)) (=> (not (= Fa tptp.bot_bo942947096l_bool)) (=> (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1410040974l_bool P_1 (tptp.hAPP_f734420447l_bool (tptp.hAPP_f1472090462l_bool tptp.insert1720618162e_bool X_2) tptp.bot_bo942947096l_bool)))) (=> (forall ((X_2 $$unsorted) (F_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool F_2)) (=> (not (= F_2 tptp.bot_bo942947096l_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_f1410040974l_bool (tptp.hAPP_f631019661l_bool tptp.member131361931e_bool X_2) F_2))) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool P_1 F_2)) (tptp.hBOOL (tptp.hAPP_f1410040974l_bool P_1 (tptp.hAPP_f734420447l_bool (tptp.hAPP_f1472090462l_bool tptp.insert1720618162e_bool X_2) F_2)))))))) (tptp.hBOOL (tptp.hAPP_f1410040974l_bool P_1 Fa))))))) (forall ((P_1 $$unsorted) (Fa $$unsorted)) (=> (tptp.is_fun_pname_bool Fa) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname Fa)) (=> (not (= Fa tptp.bot_bo844097828e_bool)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.is_pname X_2) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname X_2) tptp.bot_bo844097828e_bool))))) (=> (forall ((X_2 $$unsorted) (F_2 $$unsorted)) (=> (and (tptp.is_pname X_2) (tptp.is_fun_pname_bool F_2)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname F_2)) (=> (not (= F_2 tptp.bot_bo844097828e_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) F_2))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 F_2)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname X_2) F_2))))))))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 Fa)))))))) (forall ((P_1 $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state Fa)) (=> (not (= Fa tptp.bot_bo784226126e_bool)) (=> (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool P_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state X_2) tptp.bot_bo784226126e_bool)))) (=> (forall ((X_2 $$unsorted) (F_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state F_2)) (=> (not (= F_2 tptp.bot_bo784226126e_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state X_2) F_2))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool P_1 F_2)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool P_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state X_2) F_2)))))))) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool P_1 Fa))))))) (forall ((G_2 $$unsorted) (P_1 $$unsorted) (B_1 $$unsorted) (C $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hoare_512830354_state G_2) (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state (tptp.hAPP_f497755132_state (tptp.hAPP_c27135337_state (tptp.hAPP_f274181323_state tptp.hoare_1191504582_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_bo784226126e_bool)))) (forall ((D_1 $$unsorted) (R_1 $$unsorted) (G_2 $$unsorted) (P_1 $$unsorted) (C $$unsorted) (Q_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f274181323_state tptp.hoare_1191504582_state P_1))) (let ((_let_2 (tptp.hoare_512830354_state G_2))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_2 (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state (tptp.hAPP_f497755132_state (tptp.hAPP_c27135337_state _let_1 C) Q_1)) tptp.bot_bo784226126e_bool))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_2 (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state (tptp.hAPP_f497755132_state (tptp.hAPP_c27135337_state (tptp.hAPP_f274181323_state tptp.hoare_1191504582_state Q_1) D_1) R_1)) tptp.bot_bo784226126e_bool))) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_2 (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state (tptp.hAPP_f497755132_state (tptp.hAPP_c27135337_state _let_1 (tptp.hAPP_com_com (tptp.hAPP_com_fun_com_com tptp.semi C) D_1)) R_1)) tptp.bot_bo784226126e_bool)))))))) (forall ((B_1 $$unsorted) (C $$unsorted)) (=> (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 $$unsorted) (C2 $$unsorted)) (=> (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 $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.finite416071164_state F Fa)) (= (tptp.hAPP_H574424047_state (tptp.hAPP_H280516760_state F X_1) X_1) X_1))) (forall ((X_1 $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (tptp.is_pname X_1) (=> (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 $$unsorted) (Com2_3 $$unsorted)) (not (= tptp.skip (tptp.hAPP_com_com (tptp.hAPP_com_fun_com_com tptp.semi Com1_3) Com2_3)))) (forall ((Fun_1 $$unsorted) (Com_2 $$unsorted)) (not (= tptp.skip (tptp.hAPP_com_com (tptp.while Fun_1) Com_2)))) (forall ((Com1_3 $$unsorted) (Com2_3 $$unsorted)) (not (= (tptp.hAPP_com_com (tptp.hAPP_com_fun_com_com tptp.semi Com1_3) Com2_3) tptp.skip))) (forall ((Fun_1 $$unsorted) (Com_2 $$unsorted)) (not (= (tptp.hAPP_com_com (tptp.while Fun_1) Com_2) tptp.skip))) (forall ((Com1_2 $$unsorted) (Com2_2 $$unsorted) (Fun_1 $$unsorted) (Com_2 $$unsorted)) (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 $$unsorted) (Com_2 $$unsorted) (Com1_2 $$unsorted) (Com2_2 $$unsorted)) (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 $$unsorted) (Com2_2 $$unsorted) (Com1_1 $$unsorted) (Com2_1 $$unsorted)) (= (= (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 $$unsorted) (Com_1 $$unsorted) (Fun_1 $$unsorted) (Com_2 $$unsorted)) (= (= (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 $$unsorted) (Fun $$unsorted) (Com_1 $$unsorted)) (not (= (tptp.hAPP_pname_com tptp.body_1 Pname_1) (tptp.hAPP_com_com (tptp.while Fun) Com_1)))) (forall ((Fun $$unsorted) (Com_1 $$unsorted) (Pname_1 $$unsorted)) (not (= (tptp.hAPP_com_com (tptp.while Fun) Com_1) (tptp.hAPP_pname_com tptp.body_1 Pname_1)))) (forall ((B_1 $$unsorted) (C $$unsorted)) (=> (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 $$unsorted) (Com1 $$unsorted) (Com2 $$unsorted)) (not (= (tptp.hAPP_pname_com tptp.body_1 Pname) (tptp.hAPP_com_com (tptp.hAPP_com_fun_com_com tptp.semi Com1) Com2)))) (forall ((Com1 $$unsorted) (Com2 $$unsorted) (Pname $$unsorted)) (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 $$unsorted) (C0 $$unsorted)) (=> (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 $$unsorted)) (not (= tptp.skip (tptp.hAPP_pname_com tptp.body_1 Pname)))) (forall ((Pname $$unsorted)) (not (= (tptp.hAPP_pname_com tptp.body_1 Pname) tptp.skip))) (tptp.hBOOL (tptp.hAPP_com_bool tptp.wt tptp.skip)) (forall ((X_1 $$unsorted) (A $$unsorted) (F $$unsorted) (Fa $$unsorted)) (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 $$unsorted) (A $$unsorted) (F $$unsorted) (Fa $$unsorted)) (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 $$unsorted) (A $$unsorted) (F $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.hAPP_f718417177_state Fa A))) (=> (tptp.hBOOL (tptp.finite416071164_state F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state A)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state X_1) A)) (= (tptp.hAPP_H574424047_state (tptp.hAPP_H280516760_state F X_1) _let_1) _let_1)))))) (forall ((X_1 $$unsorted) (A $$unsorted) (F $$unsorted) (Fa $$unsorted)) (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 $$unsorted) (A $$unsorted) (F $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.hAPP_f1216288071e_bool Fa A))) (=> (tptp.hBOOL (tptp.finite688249778e_bool F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool (tptp.hAPP_f631019661l_bool tptp.member131361931e_bool X_1) A)) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool F X_1) _let_1) _let_1)))))) (forall ((N $$unsorted) (H_1 $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (tptp.is_fun1661590463l_bool N) (=> (tptp.hBOOL (tptp.finite1268145088e_bool F Fa)) (=> (forall ((X_2 $$unsorted) (Y_3 $$unsorted)) (=> (and (tptp.is_fun_pname_bool X_2) (tptp.is_fun_pname_bool Y_3)) (= (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 $$unsorted) (H_1 $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.finite688249778e_bool F Fa)) (=> (forall ((X_2 $$unsorted) (Y_3 $$unsorted)) (= (tptp.hAPP_f806699093e_bool H_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool F X_2) Y_3)) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool F (tptp.hAPP_f806699093e_bool H_1 X_2)) (tptp.hAPP_f806699093e_bool H_1 Y_3)))) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool N)) (=> (not (= N tptp.bot_bo942947096l_bool)) (= (tptp.hAPP_f806699093e_bool H_1 (tptp.hAPP_f1216288071e_bool Fa N)) (tptp.hAPP_f1216288071e_bool Fa (tptp.hAPP_f734420447l_bool (tptp.image_390184709e_bool H_1) N)))))))) (forall ((N $$unsorted) (H_1 $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (tptp.is_fun_pname_bool N) (=> (tptp.hBOOL (tptp.finite89670078_pname F Fa)) (=> (forall ((X_2 $$unsorted) (Y_3 $$unsorted)) (=> (and (tptp.is_pname X_2) (tptp.is_pname Y_3)) (= (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 $$unsorted) (H_1 $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.finite416071164_state F Fa)) (=> (forall ((X_2 $$unsorted) (Y_3 $$unsorted)) (= (tptp.hAPP_H574424047_state H_1 (tptp.hAPP_H574424047_state (tptp.hAPP_H280516760_state F X_2) Y_3)) (tptp.hAPP_H574424047_state (tptp.hAPP_H280516760_state F (tptp.hAPP_H574424047_state H_1 X_2)) (tptp.hAPP_H574424047_state H_1 Y_3)))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state N)) (=> (not (= N tptp.bot_bo784226126e_bool)) (= (tptp.hAPP_H574424047_state H_1 (tptp.hAPP_f718417177_state Fa N)) (tptp.hAPP_f718417177_state Fa (tptp.hAPP_f806699093e_bool (tptp.image_661047967_state H_1) N)))))))) (forall ((N $$unsorted) (H_1 $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.finite666746948em_com F Fa)) (=> (forall ((X_2 $$unsorted) (Y_3 $$unsorted)) (= (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 $$unsorted)) (= (tptp.hAPP_f1276420679ol_com tptp.the_elem_com X_4) (tptp.hAPP_f1276420679ol_com tptp.the_com_1 (tptp.hAPP_f1998868198m_bool (tptp.cOMBB_298914627ol_com (tptp.hAPP_f273696895l_bool tptp.fequal_fun_com_bool X_4)) (tptp.hAPP_f721468006m_bool (tptp.hAPP_f947797701m_bool tptp.cOMBC_1977231931m_bool tptp.insert_com) tptp.bot_bot_fun_com_bool))))) (forall ((X_4 $$unsorted)) (= (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 $$unsorted)) (= (tptp.hAPP_f718417177_state tptp.the_el2080696983_state X_4) (tptp.hAPP_f718417177_state tptp.the_Ho2067184133_state (tptp.hAPP_f1900156034e_bool (tptp.cOMBB_1282391997_state (tptp.hAPP_f849457489l_bool tptp.fequal1475827639e_bool X_4)) (tptp.hAPP_f874203478e_bool (tptp.hAPP_f1802364479e_bool tptp.cOMBC_1229155955e_bool tptp.insert1744391420_state) tptp.bot_bo784226126e_bool))))) (forall ((X_1 $$unsorted) (A $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.finite860057415ne_com F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool tptp.finite_finite_com A)) (=> (not (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_1) A))) (=> (not (= A tptp.bot_bot_fun_com_bool)) (= (tptp.hAPP_f1276420679ol_com Fa (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com X_1) A)) (tptp.hAPP_com_com (tptp.hAPP_com_fun_com_com F X_1) (tptp.hAPP_f1276420679ol_com Fa A)))))))) (forall ((X_1 $$unsorted) (A $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (tptp.is_fun_pname_bool A) (=> (tptp.hBOOL (tptp.finite1282449217_pname F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A))) (=> (not (= A tptp.bot_bo844097828e_bool)) (= (tptp.hAPP_f1297739591_pname Fa (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1) A)) (tptp.hAPP_pname_pname (tptp.hAPP_p1170154830_pname F X_1) (tptp.hAPP_f1297739591_pname Fa A))))))))) (forall ((X_1 $$unsorted) (A $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.finite683959609_state F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state A)) (=> (not (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state X_1) A))) (=> (not (= A tptp.bot_bo784226126e_bool)) (= (tptp.hAPP_f718417177_state Fa (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state X_1) A)) (tptp.hAPP_H574424047_state (tptp.hAPP_H280516760_state F X_1) (tptp.hAPP_f718417177_state Fa A)))))))) (forall ((X_1 $$unsorted) (A $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (tptp.is_fun1661590463l_bool A) (=> (tptp.hBOOL (tptp.finite1626890877e_bool F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)) (=> (not (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool X_1) A))) (=> (not (= A tptp.bot_bo1649642514l_bool)) (= (tptp.hAPP_f674760225e_bool Fa (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool X_1) A)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool F X_1) (tptp.hAPP_f674760225e_bool Fa A))))))))) (forall ((X_1 $$unsorted) (A $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.finite2009063477e_bool F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool A)) (=> (not (tptp.hBOOL (tptp.hAPP_f1410040974l_bool (tptp.hAPP_f631019661l_bool tptp.member131361931e_bool X_1) A))) (=> (not (= A tptp.bot_bo942947096l_bool)) (= (tptp.hAPP_f1216288071e_bool Fa (tptp.hAPP_f734420447l_bool (tptp.hAPP_f1472090462l_bool tptp.insert1720618162e_bool X_1) A)) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool F X_1) (tptp.hAPP_f1216288071e_bool Fa A)))))))) (forall ((Y_2 $$unsorted)) (not (forall ((Fun1 $$unsorted) (Com $$unsorted) (Fun2 $$unsorted)) (not (= Y_2 (tptp.hAPP_f497755132_state (tptp.hAPP_c27135337_state (tptp.hAPP_f274181323_state tptp.hoare_1191504582_state Fun1) Com) Fun2)))))) (forall ((X_1 $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (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 $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (tptp.is_pname X_1) (=> (tptp.hBOOL (tptp.finite1282449217_pname F Fa)) (= (tptp.hAPP_f1297739591_pname Fa (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1) tptp.bot_bo844097828e_bool)) X_1)))) (forall ((X_1 $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.finite683959609_state F Fa)) (= (tptp.hAPP_f718417177_state Fa (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state X_1) tptp.bot_bo784226126e_bool)) X_1))) (forall ((A $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.finite860057415ne_com F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool tptp.finite_finite_com A)) (=> (not (= A tptp.bot_bot_fun_com_bool)) (=> (forall ((X_2 $$unsorted) (Y_3 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com (tptp.hAPP_com_com (tptp.hAPP_com_fun_com_com F X_2) Y_3)) (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com X_2) (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com Y_3) tptp.bot_bot_fun_com_bool))))) (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com (tptp.hAPP_f1276420679ol_com Fa A)) A))))))) (forall ((A $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (tptp.is_fun_pname_bool A) (=> (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 $$unsorted) (Y_3 $$unsorted)) (=> (and (tptp.is_pname X_2) (tptp.is_pname Y_3)) (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 $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.finite683959609_state F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state A)) (=> (not (= A tptp.bot_bo784226126e_bool)) (=> (forall ((X_2 $$unsorted) (Y_3 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state (tptp.hAPP_H574424047_state (tptp.hAPP_H280516760_state F X_2) Y_3)) (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state X_2) (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state Y_3) tptp.bot_bo784226126e_bool))))) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state (tptp.hAPP_f718417177_state Fa A)) A))))))) (forall ((A $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (tptp.is_fun1661590463l_bool A) (=> (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 $$unsorted) (Y_3 $$unsorted)) (=> (and (tptp.is_fun_pname_bool X_2) (tptp.is_fun_pname_bool Y_3)) (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 $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.finite2009063477e_bool F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool A)) (=> (not (= A tptp.bot_bo942947096l_bool)) (=> (forall ((X_2 $$unsorted) (Y_3 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1410040974l_bool (tptp.hAPP_f631019661l_bool tptp.member131361931e_bool (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool F X_2) Y_3)) (tptp.hAPP_f734420447l_bool (tptp.hAPP_f1472090462l_bool tptp.insert1720618162e_bool X_2) (tptp.hAPP_f734420447l_bool (tptp.hAPP_f1472090462l_bool tptp.insert1720618162e_bool Y_3) tptp.bot_bo942947096l_bool))))) (tptp.hBOOL (tptp.hAPP_f1410040974l_bool (tptp.hAPP_f631019661l_bool tptp.member131361931e_bool (tptp.hAPP_f1216288071e_bool Fa A)) A))))))) (forall ((F $$unsorted) (G $$unsorted) (M_1 $$unsorted) (N $$unsorted)) (=> (= M_1 N) (=> (forall ((X_2 $$unsorted)) (=> (tptp.is_pname X_2) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) N)) (= (tptp.hAPP_p1751618853_state F X_2) (tptp.hAPP_p1751618853_state G X_2))))) (= (tptp.hAPP_f360545851e_bool (tptp.image_185131637_state F) M_1) (tptp.hAPP_f360545851e_bool (tptp.image_185131637_state G) N))))) (forall ((Q_1 $$unsorted) (P_1 $$unsorted)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_H242767318e_bool P_1 X_2)) (tptp.hBOOL (tptp.hAPP_H242767318e_bool Q_1 X_2)))) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool (tptp.hAPP_f806699093e_bool tptp.collec637225377_state P_1)) (tptp.hAPP_f806699093e_bool tptp.collec637225377_state Q_1))))) (forall ((Q_1 $$unsorted) (P_1 $$unsorted)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.is_pname X_2) (=> (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 $$unsorted) (P_1 $$unsorted)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.is_fun_pname_bool X_2) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 X_2)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool Q_1 X_2))))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool P_1)) (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool Q_1))))) (forall ((Q_1 $$unsorted) (P_1 $$unsorted)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool P_1 X_2)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool Q_1 X_2)))) (tptp.hBOOL (tptp.hAPP_f1410040974l_bool (tptp.hAPP_f1516997247l_bool tptp.ord_le694194916l_bool (tptp.hAPP_f734420447l_bool tptp.collec1987918285e_bool P_1)) (tptp.hAPP_f734420447l_bool tptp.collec1987918285e_bool Q_1))))) (forall ((Q_1 $$unsorted) (P_1 $$unsorted)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.is_pname X_2) (=> (tptp.hBOOL (tptp.hAPP_pname_bool P_1 X_2)) (tptp.hBOOL (tptp.hAPP_pname_bool Q_1 X_2))))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool P_1) Q_1)))) (forall ((Q_1 $$unsorted) (P_1 $$unsorted)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_H242767318e_bool P_1 X_2)) (tptp.hBOOL (tptp.hAPP_H242767318e_bool Q_1 X_2)))) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool P_1) Q_1)))) (forall ((A_4 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com A_4) A)) (exists ((B_2 $$unsorted)) (and (= A (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com A_4) B_2)) (not (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com A_4) B_2))))))) (forall ((A_4 $$unsorted) (A $$unsorted)) (=> (tptp.is_fun_pname_bool A) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A_4) A)) (exists ((B_2 $$unsorted)) (and (tptp.is_fun_pname_bool B_2) (= 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 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state A_4) A)) (exists ((B_2 $$unsorted)) (and (= A (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state A_4) B_2)) (not (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state A_4) B_2))))))) (forall ((X_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_1) A)) (not (forall ((B_2 $$unsorted)) (=> (= 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 $$unsorted) (A $$unsorted)) (=> (tptp.is_fun_pname_bool A) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A)) (not (forall ((B_2 $$unsorted)) (=> (tptp.is_fun_pname_bool B_2) (=> (= A (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1) B_2)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) B_2))))))))) (forall ((X_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state X_1) A)) (not (forall ((B_2 $$unsorted)) (=> (= A (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state X_1) B_2)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state X_1) B_2))))))) (forall ((A $$unsorted)) (=> (forall ((Y_3 $$unsorted)) (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 $$unsorted)) (=> (tptp.is_fun_pname_bool A) (=> (forall ((Y_3 $$unsorted)) (=> (tptp.is_pname Y_3) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname Y_3) A))))) (= A tptp.bot_bo844097828e_bool)))) (forall ((A $$unsorted)) (=> (forall ((Y_3 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state Y_3) A)))) (= A tptp.bot_bo784226126e_bool))) (forall ((G_2 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.hoare_512830354_state G_2))) (=> (tptp.hBOOL tptp.hoare_1795711768gleton) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state (tptp.hAPP_f497755132_state (tptp.hAPP_c27135337_state (tptp.hAPP_f274181323_state tptp.hoare_1191504582_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_bo784226126e_bool))) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state (tptp.hAPP_c1455475371_state tptp.hoare_Mirabelle_MGT C)) tptp.bot_bo784226126e_bool))))))) (forall ((C $$unsorted) (F $$unsorted) (B_1 $$unsorted) (A_4 $$unsorted)) (=> (= (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 $$unsorted) (Y_3 $$unsorted)) (=> (and (tptp.is_bool X_2) (tptp.is_bool Y_3)) (=> (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 $$unsorted) (A_4 $$unsorted) (F $$unsorted) (B_1 $$unsorted)) (=> (= 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 $$unsorted) (Y_3 $$unsorted)) (=> (and (tptp.is_fun_pname_bool X_2) (tptp.is_fun_pname_bool Y_3)) (=> (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 $$unsorted) (A_4 $$unsorted) (F $$unsorted) (B_1 $$unsorted)) (=> (= A_4 (tptp.hAPP_f806699093e_bool F B_1)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool C) B_1)) (=> (forall ((X_2 $$unsorted) (Y_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool Y_3) X_2)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool (tptp.hAPP_f806699093e_bool F Y_3)) (tptp.hAPP_f806699093e_bool F X_2))))) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool (tptp.hAPP_f806699093e_bool F C)) A_4)))))) (forall ((G_2 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.hoare_512830354_state G_2))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state (tptp.hAPP_c1455475371_state tptp.hoare_Mirabelle_MGT C)) tptp.bot_bo784226126e_bool))) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state (tptp.hAPP_f497755132_state (tptp.hAPP_c27135337_state (tptp.hAPP_f274181323_state tptp.hoare_1191504582_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_bo784226126e_bool)))))) (forall ((C $$unsorted)) (= (tptp.hAPP_c1455475371_state tptp.hoare_Mirabelle_MGT C) (tptp.hAPP_f497755132_state (tptp.hAPP_c27135337_state (tptp.hAPP_f274181323_state tptp.hoare_1191504582_state tptp.fequal_state) C) (tptp.evalc C)))) (forall ((P $$unsorted) (S_4 $$unsorted) (S1_2 $$unsorted)) (=> (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 $$unsorted) (S0_1 $$unsorted) (S1_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool (tptp.evalc (tptp.hAPP_option_com_com tptp.the_com (tptp.hAPP_p799580910on_com tptp.body Pn))) S0_1) S1_2)) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool (tptp.evalc (tptp.hAPP_pname_com tptp.body_1 Pn)) S0_1) S1_2)))) (forall ((S_4 $$unsorted) (T_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool (tptp.evalc tptp.skip) S_4) T_1)) (= T_1 S_4))) (forall ((S_4 $$unsorted)) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool (tptp.evalc tptp.skip) S_4) S_4))) (forall ((C1 $$unsorted) (S2_1 $$unsorted) (C0 $$unsorted) (S0_1 $$unsorted) (S1_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool (tptp.evalc C0) S0_1) S1_2)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool (tptp.evalc C1) S1_2) S2_1)) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool (tptp.evalc (tptp.hAPP_com_com (tptp.hAPP_com_fun_com_com tptp.semi C0) C1)) S0_1) S2_1))))) (forall ((S2 $$unsorted) (C $$unsorted) (S1_1 $$unsorted) (B_1 $$unsorted) (S0 $$unsorted)) (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 $$unsorted) (B_1 $$unsorted) (S_3 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_state_bool B_1 S_3))) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool (tptp.evalc (tptp.hAPP_com_com (tptp.while B_1) C)) S_3) S_3)))) (forall ((U $$unsorted) (C_2 $$unsorted) (S_4 $$unsorted) (T_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_s1806633685e_bool (tptp.evalc C_2) S_4))) (=> (tptp.hBOOL (tptp.hAPP_state_bool _let_1 T_1)) (=> (tptp.hBOOL (tptp.hAPP_state_bool _let_1 U)) (= U T_1))))) (forall ((C1 $$unsorted) (C2 $$unsorted) (S_4 $$unsorted) (T_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool (tptp.evalc (tptp.hAPP_com_com (tptp.hAPP_com_fun_com_com tptp.semi C1) C2)) S_4) T_1)) (not (forall ((S1 $$unsorted)) (=> (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 $$unsorted) (C $$unsorted) (S_3 $$unsorted) (T $$unsorted)) (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 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool (tptp.evalc C) S_3) S1)) (not (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool (tptp.evalc (tptp.hAPP_com_com (tptp.while B_1) C)) S1) T))))))))))) (forall ((C $$unsorted) (F $$unsorted) (B_1 $$unsorted) (A_4 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool B_1) A_4)) (=> (= (tptp.hBOOL (tptp.hAPP_bool_bool F B_1)) (tptp.hBOOL C)) (=> (forall ((X_2 $$unsorted) (Y_3 $$unsorted)) (=> (and (tptp.is_bool X_2) (tptp.is_bool Y_3)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Y_3) X_2)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_bool_bool F Y_3)) (tptp.hAPP_bool_bool F X_2)))))) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool C) (tptp.hAPP_bool_bool F A_4))))))) (forall ((F $$unsorted) (C $$unsorted) (B_1 $$unsorted) (A_4 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B_1) A_4)) (=> (= (tptp.hAPP_f759274231e_bool F B_1) C) (=> (forall ((X_2 $$unsorted) (Y_3 $$unsorted)) (=> (and (tptp.is_fun_pname_bool X_2) (tptp.is_fun_pname_bool Y_3)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool Y_3) X_2)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool F Y_3)) (tptp.hAPP_f759274231e_bool F X_2)))))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool C) (tptp.hAPP_f759274231e_bool F A_4))))))) (forall ((F $$unsorted) (C $$unsorted) (B_1 $$unsorted) (A_4 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool B_1) A_4)) (=> (= (tptp.hAPP_f806699093e_bool F B_1) C) (=> (forall ((X_2 $$unsorted) (Y_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool Y_3) X_2)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool (tptp.hAPP_f806699093e_bool F Y_3)) (tptp.hAPP_f806699093e_bool F X_2))))) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool C) (tptp.hAPP_f806699093e_bool F A_4))))))) (forall ((B $$unsorted) (A $$unsorted) (F $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.semila1130628874l_bool A) B))) (=> (tptp.hBOOL (tptp.finite1626890877e_bool F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool B)) (=> (not (= _let_1 tptp.bot_bo1649642514l_bool)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool F (tptp.hAPP_f674760225e_bool Fa (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.semila1782091504l_bool A) B))) (tptp.hAPP_f674760225e_bool Fa _let_1)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool F (tptp.hAPP_f674760225e_bool Fa A)) (tptp.hAPP_f674760225e_bool Fa B))))))))) (forall ((B $$unsorted) (A $$unsorted) (F $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.hAPP_f734420447l_bool (tptp.hAPP_f1847120l_bool tptp.semila1028267552l_bool A) B))) (=> (tptp.hBOOL (tptp.finite2009063477e_bool F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool B)) (=> (not (= _let_1 tptp.bot_bo942947096l_bool)) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool F (tptp.hAPP_f1216288071e_bool Fa (tptp.hAPP_f734420447l_bool (tptp.hAPP_f1847120l_bool tptp.semila1672697786l_bool A) B))) (tptp.hAPP_f1216288071e_bool Fa _let_1)) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool F (tptp.hAPP_f1216288071e_bool Fa A)) (tptp.hAPP_f1216288071e_bool Fa B))))))))) (forall ((B $$unsorted) (A $$unsorted) (F $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A) B))) (=> (tptp.hBOOL (tptp.finite1282449217_pname F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B)) (=> (not (= _let_1 tptp.bot_bo844097828e_bool)) (= (tptp.hAPP_pname_pname (tptp.hAPP_p1170154830_pname F (tptp.hAPP_f1297739591_pname Fa (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A) B))) (tptp.hAPP_f1297739591_pname Fa _let_1)) (tptp.hAPP_pname_pname (tptp.hAPP_p1170154830_pname F (tptp.hAPP_f1297739591_pname Fa A)) (tptp.hAPP_f1297739591_pname Fa B))))))))) (forall ((B $$unsorted) (A $$unsorted) (F $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool A) B))) (=> (tptp.hBOOL (tptp.finite683959609_state F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state A)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state B)) (=> (not (= _let_1 tptp.bot_bo784226126e_bool)) (= (tptp.hAPP_H574424047_state (tptp.hAPP_H280516760_state F (tptp.hAPP_f718417177_state Fa (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool A) B))) (tptp.hAPP_f718417177_state Fa _let_1)) (tptp.hAPP_H574424047_state (tptp.hAPP_H280516760_state F (tptp.hAPP_f718417177_state Fa A)) (tptp.hAPP_f718417177_state Fa B))))))))) (forall ((B $$unsorted) (A $$unsorted) (F $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila980496562m_bool A) B))) (=> (tptp.hBOOL (tptp.finite860057415ne_com F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool tptp.finite_finite_com A)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool tptp.finite_finite_com B)) (=> (not (= _let_1 tptp.bot_bot_fun_com_bool)) (= (tptp.hAPP_com_com (tptp.hAPP_com_fun_com_com F (tptp.hAPP_f1276420679ol_com Fa (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila605046092m_bool A) B))) (tptp.hAPP_f1276420679ol_com Fa _let_1)) (tptp.hAPP_com_com (tptp.hAPP_com_fun_com_com F (tptp.hAPP_f1276420679ol_com Fa A)) (tptp.hAPP_f1276420679ol_com Fa B))))))))) (forall ((B $$unsorted) (A $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (and (tptp.is_fun1661590463l_bool B) (tptp.is_fun1661590463l_bool A)) (=> (tptp.hBOOL (tptp.finite1626890877e_bool F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)) (=> (not (= A tptp.bot_bo1649642514l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool B)) (=> (not (= B tptp.bot_bo1649642514l_bool)) (=> (= (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.semila1130628874l_bool A) B) tptp.bot_bo1649642514l_bool) (= (tptp.hAPP_f674760225e_bool Fa (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.semila1782091504l_bool A) B)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool F (tptp.hAPP_f674760225e_bool Fa A)) (tptp.hAPP_f674760225e_bool Fa B))))))))))) (forall ((B $$unsorted) (A $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.finite2009063477e_bool F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool A)) (=> (not (= A tptp.bot_bo942947096l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool B)) (=> (not (= B tptp.bot_bo942947096l_bool)) (=> (= (tptp.hAPP_f734420447l_bool (tptp.hAPP_f1847120l_bool tptp.semila1028267552l_bool A) B) tptp.bot_bo942947096l_bool) (= (tptp.hAPP_f1216288071e_bool Fa (tptp.hAPP_f734420447l_bool (tptp.hAPP_f1847120l_bool tptp.semila1672697786l_bool A) B)) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool F (tptp.hAPP_f1216288071e_bool Fa A)) (tptp.hAPP_f1216288071e_bool Fa B)))))))))) (forall ((B $$unsorted) (A $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (and (tptp.is_fun_pname_bool B) (tptp.is_fun_pname_bool A)) (=> (tptp.hBOOL (tptp.finite1282449217_pname F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (=> (not (= A tptp.bot_bo844097828e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B)) (=> (not (= B tptp.bot_bo844097828e_bool)) (=> (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A) B) tptp.bot_bo844097828e_bool) (= (tptp.hAPP_f1297739591_pname Fa (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A) B)) (tptp.hAPP_pname_pname (tptp.hAPP_p1170154830_pname F (tptp.hAPP_f1297739591_pname Fa A)) (tptp.hAPP_f1297739591_pname Fa B))))))))))) (forall ((B $$unsorted) (A $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.finite683959609_state F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state A)) (=> (not (= A tptp.bot_bo784226126e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state B)) (=> (not (= B tptp.bot_bo784226126e_bool)) (=> (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool A) B) tptp.bot_bo784226126e_bool) (= (tptp.hAPP_f718417177_state Fa (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool A) B)) (tptp.hAPP_H574424047_state (tptp.hAPP_H280516760_state F (tptp.hAPP_f718417177_state Fa A)) (tptp.hAPP_f718417177_state Fa B)))))))))) (forall ((B $$unsorted) (A $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.finite860057415ne_com F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool tptp.finite_finite_com A)) (=> (not (= A tptp.bot_bot_fun_com_bool)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool tptp.finite_finite_com B)) (=> (not (= B tptp.bot_bot_fun_com_bool)) (=> (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila980496562m_bool A) B) tptp.bot_bot_fun_com_bool) (= (tptp.hAPP_f1276420679ol_com Fa (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila605046092m_bool A) B)) (tptp.hAPP_com_com (tptp.hAPP_com_fun_com_com F (tptp.hAPP_f1276420679ol_com Fa A)) (tptp.hAPP_f1276420679ol_com Fa B)))))))))) (forall ((X_1 $$unsorted) (A $$unsorted) (F $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.hAPP_c566651504m_bool tptp.insert_com X_1))) (let ((_let_2 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.minus_59609839m_bool A) (tptp.hAPP_f1682609283m_bool _let_1 tptp.bot_bot_fun_com_bool)))) (let ((_let_3 (tptp.hAPP_f1276420679ol_com Fa (tptp.hAPP_f1682609283m_bool _let_1 A)))) (let ((_let_4 (= _let_2 tptp.bot_bot_fun_com_bool))) (=> (tptp.hBOOL (tptp.finite860057415ne_com F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool tptp.finite_finite_com A)) (and (=> _let_4 (= _let_3 X_1)) (=> (not _let_4) (= _let_3 (tptp.hAPP_com_com (tptp.hAPP_com_fun_com_com F X_1) (tptp.hAPP_f1276420679ol_com Fa _let_2)))))))))))) (forall ((X_1 $$unsorted) (A $$unsorted) (F $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1))) (let ((_let_2 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A) (tptp.hAPP_f759274231e_bool _let_1 tptp.bot_bo844097828e_bool)))) (let ((_let_3 (tptp.hAPP_f1297739591_pname Fa (tptp.hAPP_f759274231e_bool _let_1 A)))) (let ((_let_4 (= _let_2 tptp.bot_bo844097828e_bool))) (=> (tptp.is_pname X_1) (=> (tptp.hBOOL (tptp.finite1282449217_pname F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (and (=> _let_4 (= _let_3 X_1)) (=> (not _let_4) (= _let_3 (tptp.hAPP_pname_pname (tptp.hAPP_p1170154830_pname F X_1) (tptp.hAPP_f1297739591_pname Fa _let_2))))))))))))) (forall ((X_1 $$unsorted) (A $$unsorted) (F $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state X_1))) (let ((_let_2 (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.minus_1805465033e_bool A) (tptp.hAPP_f806699093e_bool _let_1 tptp.bot_bo784226126e_bool)))) (let ((_let_3 (tptp.hAPP_f718417177_state Fa (tptp.hAPP_f806699093e_bool _let_1 A)))) (let ((_let_4 (= _let_2 tptp.bot_bo784226126e_bool))) (=> (tptp.hBOOL (tptp.finite683959609_state F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state A)) (and (=> _let_4 (= _let_3 X_1)) (=> (not _let_4) (= _let_3 (tptp.hAPP_H574424047_state (tptp.hAPP_H280516760_state F X_1) (tptp.hAPP_f718417177_state Fa _let_2)))))))))))) (forall ((X_1 $$unsorted) (A $$unsorted) (F $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool X_1))) (let ((_let_2 (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.minus_1290075917l_bool A) (tptp.hAPP_f559147733l_bool _let_1 tptp.bot_bo1649642514l_bool)))) (let ((_let_3 (tptp.hAPP_f674760225e_bool Fa (tptp.hAPP_f559147733l_bool _let_1 A)))) (let ((_let_4 (= _let_2 tptp.bot_bo1649642514l_bool))) (=> (tptp.is_fun_pname_bool X_1) (=> (tptp.hBOOL (tptp.finite1626890877e_bool F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)) (and (=> _let_4 (= _let_3 X_1)) (=> (not _let_4) (= _let_3 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool F X_1) (tptp.hAPP_f674760225e_bool Fa _let_2))))))))))))) (forall ((X_1 $$unsorted) (A $$unsorted) (F $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.hAPP_f1472090462l_bool tptp.insert1720618162e_bool X_1))) (let ((_let_2 (tptp.hAPP_f734420447l_bool (tptp.hAPP_f1847120l_bool tptp.minus_1929235165l_bool A) (tptp.hAPP_f734420447l_bool _let_1 tptp.bot_bo942947096l_bool)))) (let ((_let_3 (tptp.hAPP_f1216288071e_bool Fa (tptp.hAPP_f734420447l_bool _let_1 A)))) (let ((_let_4 (= _let_2 tptp.bot_bo942947096l_bool))) (=> (tptp.hBOOL (tptp.finite2009063477e_bool F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool A)) (and (=> _let_4 (= _let_3 X_1)) (=> (not _let_4) (= _let_3 (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool F X_1) (tptp.hAPP_f1216288071e_bool Fa _let_2)))))))))))) (forall ((X_1 $$unsorted) (A $$unsorted) (F $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.minus_59609839m_bool A) (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com X_1) tptp.bot_bot_fun_com_bool)))) (let ((_let_2 (tptp.hAPP_f1276420679ol_com Fa A))) (let ((_let_3 (= _let_1 tptp.bot_bot_fun_com_bool))) (=> (tptp.hBOOL (tptp.finite860057415ne_com F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool tptp.finite_finite_com A)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_1) A)) (and (=> _let_3 (= _let_2 X_1)) (=> (not _let_3) (= _let_2 (tptp.hAPP_com_com (tptp.hAPP_com_fun_com_com F X_1) (tptp.hAPP_f1276420679ol_com Fa _let_1)))))))))))) (forall ((X_1 $$unsorted) (A $$unsorted) (F $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A) (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1) tptp.bot_bo844097828e_bool)))) (let ((_let_2 (tptp.hAPP_f1297739591_pname Fa A))) (let ((_let_3 (= _let_1 tptp.bot_bo844097828e_bool))) (=> (tptp.is_pname X_1) (=> (tptp.hBOOL (tptp.finite1282449217_pname F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A)) (and (=> _let_3 (= _let_2 X_1)) (=> (not _let_3) (= _let_2 (tptp.hAPP_pname_pname (tptp.hAPP_p1170154830_pname F X_1) (tptp.hAPP_f1297739591_pname Fa _let_1))))))))))))) (forall ((X_1 $$unsorted) (A $$unsorted) (F $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.minus_1805465033e_bool A) (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state X_1) tptp.bot_bo784226126e_bool)))) (let ((_let_2 (tptp.hAPP_f718417177_state Fa A))) (let ((_let_3 (= _let_1 tptp.bot_bo784226126e_bool))) (=> (tptp.hBOOL (tptp.finite683959609_state F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state A)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state X_1) A)) (and (=> _let_3 (= _let_2 X_1)) (=> (not _let_3) (= _let_2 (tptp.hAPP_H574424047_state (tptp.hAPP_H280516760_state F X_1) (tptp.hAPP_f718417177_state Fa _let_1)))))))))))) (forall ((X_1 $$unsorted) (A $$unsorted) (F $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.minus_1290075917l_bool A) (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool X_1) tptp.bot_bo1649642514l_bool)))) (let ((_let_2 (tptp.hAPP_f674760225e_bool Fa A))) (let ((_let_3 (= _let_1 tptp.bot_bo1649642514l_bool))) (=> (tptp.is_fun_pname_bool X_1) (=> (tptp.hBOOL (tptp.finite1626890877e_bool F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool X_1) A)) (and (=> _let_3 (= _let_2 X_1)) (=> (not _let_3) (= _let_2 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool F X_1) (tptp.hAPP_f674760225e_bool Fa _let_1))))))))))))) (forall ((X_1 $$unsorted) (A $$unsorted) (F $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.hAPP_f734420447l_bool (tptp.hAPP_f1847120l_bool tptp.minus_1929235165l_bool A) (tptp.hAPP_f734420447l_bool (tptp.hAPP_f1472090462l_bool tptp.insert1720618162e_bool X_1) tptp.bot_bo942947096l_bool)))) (let ((_let_2 (tptp.hAPP_f1216288071e_bool Fa A))) (let ((_let_3 (= _let_1 tptp.bot_bo942947096l_bool))) (=> (tptp.hBOOL (tptp.finite2009063477e_bool F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool (tptp.hAPP_f631019661l_bool tptp.member131361931e_bool X_1) A)) (and (=> _let_3 (= _let_2 X_1)) (=> (not _let_3) (= _let_2 (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool F X_1) (tptp.hAPP_f1216288071e_bool Fa _let_1)))))))))))) (forall ((X_3 $$unsorted)) (not (tptp.hBOOL (tptp.is_none_pname (tptp.hAPP_p1252095976_pname tptp.some_pname X_3))))) (forall ((X_3 $$unsorted)) (not (tptp.hBOOL (tptp.is_non1379144176_state (tptp.hAPP_H1633077406_state tptp.some_H1043067815_state X_3))))) (forall ((X_3 $$unsorted)) (not (tptp.hBOOL (tptp.is_none_com (tptp.hAPP_com_option_com tptp.some_com X_3))))) (forall ((Q_1 $$unsorted) (G_2 $$unsorted) (C $$unsorted) (P_1 $$unsorted)) (=> (forall ((Z_2 $$unsorted) (S_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool P_1 Z_2) S_1)) (exists ((P_2 $$unsorted) (Q_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hoare_512830354_state G_2) (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state (tptp.hAPP_f497755132_state (tptp.hAPP_c27135337_state (tptp.hAPP_f274181323_state tptp.hoare_1191504582_state P_2) C) Q_2)) tptp.bot_bo784226126e_bool))) (forall ((S_2 $$unsorted)) (=> (forall ((Z_3 $$unsorted)) (=> (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_f1378282496l_bool (tptp.hoare_512830354_state G_2) (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state (tptp.hAPP_f497755132_state (tptp.hAPP_c27135337_state (tptp.hAPP_f274181323_state tptp.hoare_1191504582_state P_1) C) Q_1)) tptp.bot_bo784226126e_bool))))) (forall ((C $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_c667411853l_bool tptp.member_com C))) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila980496562m_bool A) B))) (not (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 A)) (not (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 B)))))))) (forall ((C $$unsorted) (A $$unsorted) (B $$unsorted)) (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 $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state C))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool A) B))) (not (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 A)) (not (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 B)))))))) (forall ((B $$unsorted) (C $$unsorted) (A $$unsorted)) (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 $$unsorted) (C $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname C))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A) B))))))) (forall ((B $$unsorted) (C $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state C))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 A)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 B)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool A) B))))))) (forall ((C $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_c667411853l_bool tptp.member_com C))) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.minus_59609839m_bool A) B))) (not (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 B))))))) (forall ((C $$unsorted) (A $$unsorted) (B $$unsorted)) (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 $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state C))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.minus_1805465033e_bool A) B))) (not (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 B))))))) (forall ((B $$unsorted) (C $$unsorted) (A $$unsorted)) (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 $$unsorted) (C $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname C))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A)) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A) B))))))) (forall ((B $$unsorted) (C $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state C))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 A)) (=> (not (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 B))) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.minus_1805465033e_bool A) B))))))) (forall ((G_2 $$unsorted) (Fa $$unsorted)) (=> (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 $$unsorted) (Fa $$unsorted)) (=> (or (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool Fa)) (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool G_2))) (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool (tptp.hAPP_f734420447l_bool (tptp.hAPP_f1847120l_bool tptp.semila1028267552l_bool Fa) G_2))))) (forall ((G_2 $$unsorted) (Fa $$unsorted)) (=> (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 $$unsorted) (Fa $$unsorted)) (=> (or (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state Fa)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state G_2))) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool Fa) G_2))))) (forall ((B $$unsorted) (A $$unsorted)) (=> (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 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool A)) (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool (tptp.hAPP_f734420447l_bool (tptp.hAPP_f1847120l_bool tptp.minus_1929235165l_bool A) B))))) (forall ((B $$unsorted) (A $$unsorted)) (=> (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 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state A)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.minus_1805465033e_bool A) B))))) (forall ((R_1 $$unsorted) (S $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_f578650245m_bool tptp.cOMBC_1904837336l_bool tptp.member_com))) (= (tptp.hBOOL (tptp.hAPP_com_bool (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila980496562m_bool (tptp.hAPP_f1682609283m_bool _let_1 R_1)) (tptp.hAPP_f1682609283m_bool _let_1 S)) X_2)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_2) (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila980496562m_bool R_1) S)))))) (forall ((R_1 $$unsorted) (S $$unsorted) (X_2 $$unsorted)) (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 $$unsorted) (S $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1184122441e_bool tptp.cOMBC_538205282l_bool tptp.member1667945571_state))) (= (tptp.hBOOL (tptp.hAPP_H242767318e_bool (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool (tptp.hAPP_f806699093e_bool _let_1 R_1)) (tptp.hAPP_f806699093e_bool _let_1 S)) X_2)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state X_2) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool R_1) S)))))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila980496562m_bool A) (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.minus_59609839m_bool B) A)) tptp.bot_bot_fun_com_bool)) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool B) A)) tptp.bot_bo844097828e_bool)) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool A) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.minus_1805465033e_bool B) A)) tptp.bot_bo784226126e_bool)) (forall ((A $$unsorted) (B $$unsorted)) (=> (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila980496562m_bool A) B) tptp.bot_bot_fun_com_bool) (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.minus_59609839m_bool A) B) A))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.is_fun_pname_bool A) (=> (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A) B) tptp.bot_bo844097828e_bool) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A) B) A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool A) B) tptp.bot_bo784226126e_bool) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.minus_1805465033e_bool A) B) A))) (forall ((C $$unsorted) (A $$unsorted) (B $$unsorted)) (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 $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname C))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A) B))) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B)))))) (forall ((C $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state C))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.minus_1805465033e_bool A) B))) (not (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 B)))))) (forall ((C $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_c667411853l_bool tptp.member_com C))) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila980496562m_bool A) B))) (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 B))))) (forall ((C $$unsorted) (A $$unsorted) (B $$unsorted)) (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 $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state C))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool A) B))) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 B))))) (forall ((C $$unsorted) (A $$unsorted) (B $$unsorted)) (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 $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname C))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A) B))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A))))) (forall ((C $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state C))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool A) B))) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 A))))) (forall ((C $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_c667411853l_bool tptp.member_com C))) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.minus_59609839m_bool A) B))) (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 A))))) (forall ((C $$unsorted) (A $$unsorted) (B $$unsorted)) (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 $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state C))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.minus_1805465033e_bool A) B))) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 A))))) (forall ((C $$unsorted) (A $$unsorted) (B $$unsorted)) (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 $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname C))) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A) B))) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B)))))) (forall ((C $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state C))) (= (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool A) B))) (and (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 B)))))) (forall ((C $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_c667411853l_bool tptp.member_com C))) (= (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.minus_59609839m_bool A) B))) (and (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 A)) (not (tptp.hBOOL (tptp.hAPP_f990396704l_bool _let_1 B))))))) (forall ((C $$unsorted) (A $$unsorted) (B $$unsorted)) (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 $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state C))) (= (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.minus_1805465033e_bool A) B))) (and (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 A)) (not (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 B))))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f578650245m_bool tptp.cOMBC_1904837336l_bool tptp.member_com))) (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila980496562m_bool A) B) (tptp.hAPP_f1682609283m_bool tptp.collect_com (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f328772264m_bool tptp.cOMBS_com_bool_bool (tptp.hAPP_f954469007l_bool (tptp.cOMBB_886968260ol_com tptp.fconj) (tptp.hAPP_f1682609283m_bool _let_1 A))) (tptp.hAPP_f1682609283m_bool _let_1 B)))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f661147897e_bool tptp.cOMBC_1058051404l_bool tptp.member_pname))) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A) B) (tptp.hAPP_f759274231e_bool tptp.collect_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_f649174806e_bool tptp.cOMBS_568398431l_bool (tptp.hAPP_f1402196763l_bool (tptp.cOMBB_675860798_pname tptp.fconj) (tptp.hAPP_f759274231e_bool _let_1 A))) (tptp.hAPP_f759274231e_bool _let_1 B)))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f1184122441e_bool tptp.cOMBC_538205282l_bool tptp.member1667945571_state))) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool A) B) (tptp.hAPP_f806699093e_bool tptp.collec637225377_state (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1702629984e_bool tptp.cOMBS_865875691l_bool (tptp.hAPP_f832587837l_bool (tptp.cOMBB_1291456124_state tptp.fconj) (tptp.hAPP_f806699093e_bool _let_1 A))) (tptp.hAPP_f806699093e_bool _let_1 B)))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f1145991873l_bool tptp.cOMBC_1988546018l_bool tptp.member799430823e_bool))) (= (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.semila1130628874l_bool A) B) (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f624840228l_bool tptp.cOMBS_350070575l_bool (tptp.hAPP_f143162813l_bool (tptp.cOMBB_2095475776e_bool tptp.fconj) (tptp.hAPP_f559147733l_bool _let_1 A))) (tptp.hAPP_f559147733l_bool _let_1 B)))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f1236719585l_bool tptp.cOMBC_1484018740l_bool tptp.member131361931e_bool))) (= (tptp.hAPP_f734420447l_bool (tptp.hAPP_f1847120l_bool tptp.semila1028267552l_bool A) B) (tptp.hAPP_f734420447l_bool tptp.collec1987918285e_bool (tptp.hAPP_f734420447l_bool (tptp.hAPP_f524831474l_bool tptp.cOMBS_1162100051l_bool (tptp.hAPP_f118042163l_bool (tptp.cOMBB_1749019442e_bool tptp.fconj) (tptp.hAPP_f734420447l_bool _let_1 A))) (tptp.hAPP_f734420447l_bool _let_1 B)))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f578650245m_bool tptp.cOMBC_1904837336l_bool tptp.member_com))) (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.minus_59609839m_bool A) B) (tptp.hAPP_f1682609283m_bool tptp.collect_com (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f328772264m_bool tptp.cOMBS_com_bool_bool (tptp.hAPP_f954469007l_bool (tptp.cOMBB_886968260ol_com tptp.fconj) (tptp.hAPP_f1682609283m_bool _let_1 A))) (tptp.hAPP_f1682609283m_bool (tptp.cOMBB_bool_bool_com tptp.fNot) (tptp.hAPP_f1682609283m_bool _let_1 B))))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f661147897e_bool tptp.cOMBC_1058051404l_bool tptp.member_pname))) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A) B) (tptp.hAPP_f759274231e_bool tptp.collect_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_f649174806e_bool tptp.cOMBS_568398431l_bool (tptp.hAPP_f1402196763l_bool (tptp.cOMBB_675860798_pname tptp.fconj) (tptp.hAPP_f759274231e_bool _let_1 A))) (tptp.hAPP_f759274231e_bool (tptp.cOMBB_647938656_pname tptp.fNot) (tptp.hAPP_f759274231e_bool _let_1 B))))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f1184122441e_bool tptp.cOMBC_538205282l_bool tptp.member1667945571_state))) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.minus_1805465033e_bool A) B) (tptp.hAPP_f806699093e_bool tptp.collec637225377_state (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1702629984e_bool tptp.cOMBS_865875691l_bool (tptp.hAPP_f832587837l_bool (tptp.cOMBB_1291456124_state tptp.fconj) (tptp.hAPP_f806699093e_bool _let_1 A))) (tptp.hAPP_f806699093e_bool (tptp.cOMBB_325909978_state tptp.fNot) (tptp.hAPP_f806699093e_bool _let_1 B))))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f1145991873l_bool tptp.cOMBC_1988546018l_bool tptp.member799430823e_bool))) (= (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.minus_1290075917l_bool A) B) (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f624840228l_bool tptp.cOMBS_350070575l_bool (tptp.hAPP_f143162813l_bool (tptp.cOMBB_2095475776e_bool tptp.fconj) (tptp.hAPP_f559147733l_bool _let_1 A))) (tptp.hAPP_f559147733l_bool (tptp.cOMBB_307249310e_bool tptp.fNot) (tptp.hAPP_f559147733l_bool _let_1 B))))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f1236719585l_bool tptp.cOMBC_1484018740l_bool tptp.member131361931e_bool))) (= (tptp.hAPP_f734420447l_bool (tptp.hAPP_f1847120l_bool tptp.minus_1929235165l_bool A) B) (tptp.hAPP_f734420447l_bool tptp.collec1987918285e_bool (tptp.hAPP_f734420447l_bool (tptp.hAPP_f524831474l_bool tptp.cOMBS_1162100051l_bool (tptp.hAPP_f118042163l_bool (tptp.cOMBB_1749019442e_bool tptp.fconj) (tptp.hAPP_f734420447l_bool _let_1 A))) (tptp.hAPP_f734420447l_bool (tptp.cOMBB_1686148692e_bool tptp.fNot) (tptp.hAPP_f734420447l_bool _let_1 B))))))) (forall ((X_1 $$unsorted) (A $$unsorted) (P_1 $$unsorted)) (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 $$unsorted) (A $$unsorted) (P_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname X_1))) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A) (tptp.hAPP_f759274231e_bool tptp.collect_pname P_1)))) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_pname_bool P_1 X_1)))))) (forall ((X_1 $$unsorted) (A $$unsorted) (P_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state X_1))) (= (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool A) (tptp.hAPP_f806699093e_bool tptp.collec637225377_state P_1)))) (and (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_H242767318e_bool P_1 X_1)))))) (forall ((X_1 $$unsorted) (A $$unsorted) (P_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool X_1))) (= (tptp.hBOOL (tptp.hAPP_f1935102916l_bool _let_1 (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.semila1130628874l_bool A) (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool P_1)))) (and (tptp.hBOOL (tptp.hAPP_f1935102916l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 X_1)))))) (forall ((X_1 $$unsorted) (A $$unsorted) (P_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f631019661l_bool tptp.member131361931e_bool X_1))) (= (tptp.hBOOL (tptp.hAPP_f1410040974l_bool _let_1 (tptp.hAPP_f734420447l_bool (tptp.hAPP_f1847120l_bool tptp.semila1028267552l_bool A) (tptp.hAPP_f734420447l_bool tptp.collec1987918285e_bool P_1)))) (and (tptp.hBOOL (tptp.hAPP_f1410040974l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool P_1 X_1)))))) (forall ((P_1 $$unsorted) (Q_1 $$unsorted)) (= (tptp.hAPP_f806699093e_bool tptp.collec637225377_state (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1702629984e_bool tptp.cOMBS_865875691l_bool (tptp.hAPP_f832587837l_bool (tptp.cOMBB_1291456124_state tptp.fconj) P_1)) Q_1)) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool (tptp.hAPP_f806699093e_bool tptp.collec637225377_state P_1)) (tptp.hAPP_f806699093e_bool tptp.collec637225377_state Q_1)))) (forall ((P_1 $$unsorted) (Q_1 $$unsorted)) (= (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 $$unsorted) (Q_1 $$unsorted)) (= (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 $$unsorted) (Q_1 $$unsorted)) (= (tptp.hAPP_f734420447l_bool tptp.collec1987918285e_bool (tptp.hAPP_f734420447l_bool (tptp.hAPP_f524831474l_bool tptp.cOMBS_1162100051l_bool (tptp.hAPP_f118042163l_bool (tptp.cOMBB_1749019442e_bool tptp.fconj) P_1)) Q_1)) (tptp.hAPP_f734420447l_bool (tptp.hAPP_f1847120l_bool tptp.semila1028267552l_bool (tptp.hAPP_f734420447l_bool tptp.collec1987918285e_bool P_1)) (tptp.hAPP_f734420447l_bool tptp.collec1987918285e_bool Q_1)))) (forall ((A $$unsorted) (B $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A))) (= (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool B) C_1)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool (tptp.hAPP_f759274231e_bool _let_1 B)) (tptp.hAPP_f759274231e_bool _let_1 C_1))))) (forall ((A $$unsorted) (B $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1794460506e_bool tptp.minus_1805465033e_bool A))) (= (tptp.hAPP_f806699093e_bool _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool B) C_1)) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool (tptp.hAPP_f806699093e_bool _let_1 B)) (tptp.hAPP_f806699093e_bool _let_1 C_1))))) (forall ((A $$unsorted) (B $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A))) (= (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool B) C_1)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool (tptp.hAPP_f759274231e_bool _let_1 B)) (tptp.hAPP_f759274231e_bool _let_1 C_1))))) (forall ((A $$unsorted) (B $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1794460506e_bool tptp.minus_1805465033e_bool A))) (= (tptp.hAPP_f806699093e_bool _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool B) C_1)) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool (tptp.hAPP_f806699093e_bool _let_1 B)) (tptp.hAPP_f806699093e_bool _let_1 C_1))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.is_fun_pname_bool A) (= (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 $$unsorted) (B $$unsorted)) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.minus_1805465033e_bool A) B)) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool A) B)) A)) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (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 $$unsorted) (Y_2 $$unsorted)) (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 $$unsorted) (Y_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool X_1) Y_2)) X_1))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (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 $$unsorted) (Y_2 $$unsorted)) (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 $$unsorted) (Y_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool X_1) Y_2)) X_1))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (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 $$unsorted) (Y_2 $$unsorted)) (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 $$unsorted) (Y_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool X_1) Y_2)) Y_2))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (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 $$unsorted) (Y_2 $$unsorted)) (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 $$unsorted) (Y_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool X_1) Y_2)) Y_2))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (= (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 $$unsorted) (Y_2 $$unsorted)) (=> (tptp.is_fun_pname_bool X_1) (= (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 $$unsorted) (Y_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool X_1) Y_2)) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool X_1) Y_2) X_1))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool X_1))) (= (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila310582991f_bool Y_2) Z))) (and (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 Y_2)) (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 Z)))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted) (Z $$unsorted)) (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 $$unsorted) (Y_2 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool X_1))) (= (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool Y_2) Z))) (and (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 Y_2)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 Z)))))) (forall ((B_1 $$unsorted) (A_4 $$unsorted) (X_1 $$unsorted)) (=> (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 $$unsorted) (A_4 $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_4) X_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A_4) B_1)) X_1)))) (forall ((B_1 $$unsorted) (A_4 $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool A_4) X_1)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool A_4) B_1)) X_1)))) (forall ((A_4 $$unsorted) (B_1 $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool B_1) X_1)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila310582991f_bool A_4) B_1)) X_1)))) (forall ((A_4 $$unsorted) (B_1 $$unsorted) (X_1 $$unsorted)) (=> (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 $$unsorted) (B_1 $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool B_1) X_1)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool A_4) B_1)) X_1)))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool X_1) Y_2)) (= (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila310582991f_bool X_1) Y_2)) (tptp.hBOOL X_1)))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (=> (tptp.is_fun_pname_bool X_1) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool X_1) Y_2)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool X_1) Y_2) X_1)))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool X_1) Y_2)) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool X_1) Y_2) X_1))) (forall ((Y_2 $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Y_2) X_1)) (= (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila310582991f_bool X_1) Y_2)) (tptp.hBOOL Y_2)))) (forall ((Y_2 $$unsorted) (X_1 $$unsorted)) (=> (tptp.is_fun_pname_bool Y_2) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool Y_2) X_1)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool X_1) Y_2) Y_2)))) (forall ((Y_2 $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool Y_2) X_1)) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool X_1) Y_2) Y_2))) (forall ((B_1 $$unsorted) (X_1 $$unsorted) (A_4 $$unsorted)) (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 $$unsorted) (X_1 $$unsorted) (A_4 $$unsorted)) (let ((_let_1 (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool X_1))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A_4)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A_4) B_1))))))) (forall ((B_1 $$unsorted) (X_1 $$unsorted) (A_4 $$unsorted)) (let ((_let_1 (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool X_1))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 A_4)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 B_1)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool A_4) B_1))))))) (forall ((Z $$unsorted) (X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool X_1))) (=> (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 Y_2)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 Z)) (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila310582991f_bool Y_2) Z))))))) (forall ((Z $$unsorted) (X_1 $$unsorted) (Y_2 $$unsorted)) (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 $$unsorted) (X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool X_1))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 Y_2)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 Z)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool Y_2) Z))))))) (forall ((B_1 $$unsorted) (D_1 $$unsorted) (A_4 $$unsorted) (C $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool A_4) C)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool B_1) D_1)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila310582991f_bool A_4) B_1)) (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila310582991f_bool C) D_1)))))) (forall ((B_1 $$unsorted) (D_1 $$unsorted) (A_4 $$unsorted) (C $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_4) C)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B_1) D_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A_4) B_1)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool C) D_1)))))) (forall ((B_1 $$unsorted) (D_1 $$unsorted) (A_4 $$unsorted) (C $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool A_4) C)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool B_1) D_1)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool A_4) B_1)) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool C) D_1)))))) (forall ((X_1 $$unsorted) (A_4 $$unsorted) (B_1 $$unsorted)) (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 $$unsorted) (A_4 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool X_1))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A_4) B_1))) (not (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A_4)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B_1)))))))) (forall ((X_1 $$unsorted) (A_4 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool X_1))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool A_4) B_1))) (not (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 A_4)) (not (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 B_1)))))))) (forall ((X_1 $$unsorted)) (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila980496562m_bool X_1) tptp.bot_bot_fun_com_bool) tptp.bot_bot_fun_com_bool)) (forall ((X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila310582991f_bool X_1) tptp.bot_bot_bool)) (tptp.hBOOL tptp.bot_bot_bool))) (forall ((X_1 $$unsorted)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool X_1) tptp.bot_bo844097828e_bool) tptp.bot_bo844097828e_bool)) (forall ((X_1 $$unsorted)) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool X_1) tptp.bot_bo784226126e_bool) tptp.bot_bo784226126e_bool)) (forall ((X_1 $$unsorted)) (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila980496562m_bool tptp.bot_bot_fun_com_bool) X_1) tptp.bot_bot_fun_com_bool)) (forall ((X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila310582991f_bool tptp.bot_bot_bool) X_1)) (tptp.hBOOL tptp.bot_bot_bool))) (forall ((X_1 $$unsorted)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool tptp.bot_bo844097828e_bool) X_1) tptp.bot_bo844097828e_bool)) (forall ((X_1 $$unsorted)) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool tptp.bot_bo784226126e_bool) X_1) tptp.bot_bo784226126e_bool)) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (= (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 $$unsorted) (Y_2 $$unsorted)) (=> (tptp.is_fun_pname_bool X_1) (= (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 $$unsorted) (Y_2 $$unsorted)) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool X_1) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool X_1) Y_2)) X_1)) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (= (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 $$unsorted) (Y_2 $$unsorted)) (=> (tptp.is_fun_pname_bool X_1) (= (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 $$unsorted) (Y_2 $$unsorted)) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool X_1) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool X_1) Y_2)) X_1)) (forall ((X_1 $$unsorted) (Y_2 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.hAPP_b589554111l_bool tptp.semila310582991f_bool X_1))) (= (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool Y_2) Z))) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool (tptp.hAPP_bool_bool _let_1 Y_2)) (tptp.hAPP_bool_bool _let_1 Z)))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted) (Z $$unsorted)) (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 $$unsorted) (Y_2 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool X_1))) (= (tptp.hAPP_f806699093e_bool _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool Y_2) Z)) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool (tptp.hAPP_f806699093e_bool _let_1 Y_2)) (tptp.hAPP_f806699093e_bool _let_1 Z))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted) (Z $$unsorted)) (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 $$unsorted) (Y_2 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool X_1))) (= (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool Y_2) Z)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool (tptp.hAPP_f759274231e_bool _let_1 Y_2)) (tptp.hAPP_f759274231e_bool _let_1 Z))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool X_1))) (= (tptp.hAPP_f806699093e_bool _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool Y_2) Z)) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool (tptp.hAPP_f806699093e_bool _let_1 Y_2)) (tptp.hAPP_f806699093e_bool _let_1 Z))))) (forall ((Y_2 $$unsorted) (Z $$unsorted) (X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila310582991f_bool (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool Y_2) Z)) X_1)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila310582991f_bool Y_2) X_1)) (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila310582991f_bool Z) X_1))))) (forall ((Y_2 $$unsorted) (Z $$unsorted) (X_1 $$unsorted)) (= (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 $$unsorted) (Z $$unsorted) (X_1 $$unsorted)) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool Y_2) Z)) X_1) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool Y_2) X_1)) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool Z) X_1)))) (forall ((Y_2 $$unsorted) (Z $$unsorted) (X_1 $$unsorted)) (= (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 $$unsorted) (Z $$unsorted) (X_1 $$unsorted)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool Y_2) Z)) X_1) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool Y_2) X_1)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool Z) X_1)))) (forall ((Y_2 $$unsorted) (Z $$unsorted) (X_1 $$unsorted)) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool Y_2) Z)) X_1) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool Y_2) X_1)) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool Z) X_1)))) (forall ((A $$unsorted)) (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.minus_59609839m_bool A) A) tptp.bot_bot_fun_com_bool)) (forall ((A $$unsorted)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A) A) tptp.bot_bo844097828e_bool)) (forall ((A $$unsorted)) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.minus_1805465033e_bool A) A) tptp.bot_bo784226126e_bool)) (forall ((A $$unsorted)) (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.minus_59609839m_bool A) tptp.bot_bot_fun_com_bool) A)) (forall ((A $$unsorted)) (=> (tptp.is_fun_pname_bool A) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A) tptp.bot_bo844097828e_bool) A))) (forall ((A $$unsorted)) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.minus_1805465033e_bool A) tptp.bot_bo784226126e_bool) A)) (forall ((A $$unsorted)) (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.minus_59609839m_bool tptp.bot_bot_fun_com_bool) A) tptp.bot_bot_fun_com_bool)) (forall ((A $$unsorted)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool tptp.bot_bo844097828e_bool) A) tptp.bot_bo844097828e_bool)) (forall ((A $$unsorted)) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.minus_1805465033e_bool tptp.bot_bo784226126e_bool) A) tptp.bot_bo784226126e_bool)) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool B)) (= (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.minus_1290075917l_bool A) B))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool B)) (= (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool (tptp.hAPP_f734420447l_bool (tptp.hAPP_f1847120l_bool tptp.minus_1929235165l_bool A) B))) (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool A))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B)) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A) B))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state B)) (= (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.minus_1805465033e_bool A) B))) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state A))))) (forall ((A $$unsorted) (X_1 $$unsorted) (B $$unsorted)) (=> (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 $$unsorted) (X_1 $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) B)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1) A)) B) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A) B)))) (forall ((A $$unsorted) (X_1 $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state X_1) B)) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.minus_1805465033e_bool (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state X_1) A)) B) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.minus_1805465033e_bool A) B)))) (forall ((A $$unsorted) (X_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.minus_59609839m_bool A) B))) (let ((_let_2 (tptp.hAPP_c566651504m_bool tptp.insert_com X_1))) (let ((_let_3 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.minus_59609839m_bool (tptp.hAPP_f1682609283m_bool _let_2 A)) B))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_1) B)))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (tptp.hAPP_f1682609283m_bool _let_2 _let_1))))))))) (forall ((A $$unsorted) (X_1 $$unsorted) (B $$unsorted)) (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 $$unsorted) (X_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.minus_1805465033e_bool A) B))) (let ((_let_2 (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state X_1))) (let ((_let_3 (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.minus_1805465033e_bool (tptp.hAPP_f806699093e_bool _let_2 A)) B))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state X_1) B)))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (tptp.hAPP_f806699093e_bool _let_2 _let_1))))))))) (forall ((A $$unsorted) (B $$unsorted)) (= (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila980496562m_bool A) B) tptp.bot_bot_fun_com_bool) (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_2) A)) (forall ((Xa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com Xa) B)) (not (= X_2 Xa)))))))) (forall ((A $$unsorted) (B $$unsorted)) (= (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A) B) tptp.bot_bo844097828e_bool) (forall ((X_2 $$unsorted)) (=> (tptp.is_pname X_2) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A)) (forall ((Xa $$unsorted)) (=> (tptp.is_pname Xa) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname Xa) B)) (not (= X_2 Xa)))))))))) (forall ((A $$unsorted) (B $$unsorted)) (= (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool A) B) tptp.bot_bo784226126e_bool) (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state X_2) A)) (forall ((Xa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state Xa) B)) (not (= X_2 Xa)))))))) (forall ((A $$unsorted)) (= (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 $$unsorted)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A) tptp.bot_bo844097828e_bool) tptp.bot_bo844097828e_bool)) (forall ((A $$unsorted)) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool A) tptp.bot_bo784226126e_bool) tptp.bot_bo784226126e_bool)) (forall ((B $$unsorted)) (= (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila980496562m_bool tptp.bot_bot_fun_com_bool) B) tptp.bot_bot_fun_com_bool)) (forall ((B $$unsorted)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool tptp.bot_bo844097828e_bool) B) tptp.bot_bo844097828e_bool)) (forall ((B $$unsorted)) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool tptp.bot_bo784226126e_bool) B) tptp.bot_bo784226126e_bool)) (forall ((C_1 $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.is_fun_pname_bool A) (=> (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 $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool B) C_1)) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.minus_1805465033e_bool B) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.minus_1805465033e_bool C_1) A)) A)))) (forall ((D $$unsorted) (B $$unsorted) (A $$unsorted) (C_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) C_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool D) B)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A) B)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool C_1) D)))))) (forall ((D $$unsorted) (B $$unsorted) (A $$unsorted) (C_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool A) C_1)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool D) B)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.minus_1805465033e_bool A) B)) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.minus_1805465033e_bool C_1) D)))))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A) B)) A))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.minus_1805465033e_bool A) B)) A))) (forall ((A $$unsorted) (B $$unsorted) (C_1 $$unsorted)) (= (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 $$unsorted) (B $$unsorted) (C_1 $$unsorted)) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.minus_1805465033e_bool (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool A) B)) C_1) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.minus_1805465033e_bool A) C_1)) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.minus_1805465033e_bool B) C_1)))) (forall ((B $$unsorted) (A $$unsorted)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool B) A)) A) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool B) A))) (forall ((B $$unsorted) (A $$unsorted)) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.minus_1805465033e_bool B) A)) A) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool B) A))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A))) (= (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool B) A)) (tptp.hAPP_f759274231e_bool _let_1 B)))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool A))) (= (tptp.hAPP_f806699093e_bool _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.minus_1805465033e_bool B) A)) (tptp.hAPP_f806699093e_bool _let_1 B)))) (forall ((B $$unsorted) (A_4 $$unsorted) (C_1 $$unsorted)) (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 $$unsorted) (A_4 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_p905327722e_bool tptp.insert_pname A_4))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A_4) C_1)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool (tptp.hAPP_f759274231e_bool _let_1 B)) C_1) (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool B) C_1)))))) (forall ((B $$unsorted) (A_4 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state A_4))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state A_4) C_1)) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool (tptp.hAPP_f806699093e_bool _let_1 B)) C_1) (tptp.hAPP_f806699093e_bool _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool B) C_1)))))) (forall ((B $$unsorted) (A_4 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f1120618594m_bool tptp.semila980496562m_bool A))) (let ((_let_2 (tptp.hAPP_c566651504m_bool tptp.insert_com A_4))) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com A_4) A)) (= (tptp.hAPP_f1682609283m_bool _let_1 (tptp.hAPP_f1682609283m_bool _let_2 B)) (tptp.hAPP_f1682609283m_bool _let_2 (tptp.hAPP_f1682609283m_bool _let_1 B))))))) (forall ((B $$unsorted) (A_4 $$unsorted) (A $$unsorted)) (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 $$unsorted) (A_4 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool A))) (let ((_let_2 (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state A_4))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state A_4) A)) (= (tptp.hAPP_f806699093e_bool _let_1 (tptp.hAPP_f806699093e_bool _let_2 B)) (tptp.hAPP_f806699093e_bool _let_2 (tptp.hAPP_f806699093e_bool _let_1 B))))))) (forall ((B $$unsorted) (A_4 $$unsorted) (C_1 $$unsorted)) (=> (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 $$unsorted) (A_4 $$unsorted) (C_1 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A_4) C_1))) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A_4) B)) C_1) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool B) C_1)))) (forall ((B $$unsorted) (A_4 $$unsorted) (C_1 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state A_4) C_1))) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state A_4) B)) C_1) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool B) C_1)))) (forall ((B $$unsorted) (A_4 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f1120618594m_bool tptp.semila980496562m_bool A))) (=> (not (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com A_4) A))) (= (tptp.hAPP_f1682609283m_bool _let_1 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com A_4) B)) (tptp.hAPP_f1682609283m_bool _let_1 B))))) (forall ((B $$unsorted) (A_4 $$unsorted) (A $$unsorted)) (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 $$unsorted) (A_4 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool A))) (=> (not (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state A_4) A))) (= (tptp.hAPP_f806699093e_bool _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state A_4) B)) (tptp.hAPP_f806699093e_bool _let_1 B))))) (forall ((A_4 $$unsorted) (A $$unsorted) (B $$unsorted)) (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 $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_p905327722e_bool tptp.insert_pname A_4))) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool (tptp.hAPP_f759274231e_bool _let_1 A)) (tptp.hAPP_f759274231e_bool _let_1 B)) (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A) B))))) (forall ((A_4 $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state A_4))) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool (tptp.hAPP_f806699093e_bool _let_1 A)) (tptp.hAPP_f806699093e_bool _let_1 B)) (tptp.hAPP_f806699093e_bool _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool A) B))))) (forall ((B $$unsorted) (A_4 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila980496562m_bool B) C_1))) (let ((_let_2 (tptp.hAPP_c566651504m_bool tptp.insert_com A_4))) (let ((_let_3 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.semila980496562m_bool (tptp.hAPP_f1682609283m_bool _let_2 B)) C_1))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com A_4) C_1)))) (and (=> _let_4 (= _let_3 (tptp.hAPP_f1682609283m_bool _let_2 _let_1))) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((B $$unsorted) (A_4 $$unsorted) (C_1 $$unsorted)) (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 $$unsorted) (A_4 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool B) C_1))) (let ((_let_2 (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state A_4))) (let ((_let_3 (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool (tptp.hAPP_f806699093e_bool _let_2 B)) C_1))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state A_4) C_1)))) (and (=> _let_4 (= _let_3 (tptp.hAPP_f806699093e_bool _let_2 _let_1))) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((B $$unsorted) (A_4 $$unsorted) (A $$unsorted)) (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 $$unsorted) (A_4 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A))) (let ((_let_2 (tptp.hAPP_f759274231e_bool _let_1 B))) (let ((_let_3 (tptp.hAPP_p905327722e_bool tptp.insert_pname A_4))) (let ((_let_4 (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool _let_3 B)))) (let ((_let_5 (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A_4) A)))) (and (=> _let_5 (= _let_4 (tptp.hAPP_f759274231e_bool _let_3 _let_2))) (=> (not _let_5) (= _let_4 _let_2))))))))) (forall ((B $$unsorted) (A_4 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool A))) (let ((_let_2 (tptp.hAPP_f806699093e_bool _let_1 B))) (let ((_let_3 (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state A_4))) (let ((_let_4 (tptp.hAPP_f806699093e_bool _let_1 (tptp.hAPP_f806699093e_bool _let_3 B)))) (let ((_let_5 (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state A_4) A)))) (and (=> _let_5 (= _let_4 (tptp.hAPP_f806699093e_bool _let_3 _let_2))) (=> (not _let_5) (= _let_4 _let_2))))))))) (forall ((B $$unsorted) (D $$unsorted) (A $$unsorted) (C_1 $$unsorted)) (=> (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 $$unsorted) (D $$unsorted) (A $$unsorted) (C_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool A) C_1)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool B) D)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool A) B)) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool C_1) D)))))) (forall ((B $$unsorted) (C_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool C_1))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A) B))))))) (forall ((B $$unsorted) (C_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool C_1))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 A)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 B)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool A) B))))))) (forall ((B $$unsorted) (A $$unsorted)) (=> (tptp.is_fun_pname_bool B) (=> (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 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool B) A)) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool A) B) B))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.is_fun_pname_bool A) (=> (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 $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool A) B)) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool A) B) A))) (forall ((A $$unsorted) (B $$unsorted)) (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 $$unsorted) (B $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool A) B)) B))) (forall ((A $$unsorted) (B $$unsorted)) (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 $$unsorted) (B $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool A) B)) A))) (forall ((A $$unsorted) (B $$unsorted) (C_1 $$unsorted)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A) B)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool B) C_1))) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool C_1) A)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A) B)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool B) C_1))) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool C_1) A)))) (forall ((A $$unsorted) (B $$unsorted) (C_1 $$unsorted)) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool A) B)) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool B) C_1))) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool C_1) A)) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool A) B)) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool B) C_1))) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool C_1) A)))) (forall ((B $$unsorted) (C_1 $$unsorted) (A $$unsorted)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool B) C_1)) A) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool B) A)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool C_1) A)))) (forall ((B $$unsorted) (C_1 $$unsorted) (A $$unsorted)) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool B) C_1)) A) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool B) A)) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool C_1) A)))) (forall ((B $$unsorted) (C_1 $$unsorted) (A $$unsorted)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool B) C_1)) A) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool B) A)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool C_1) A)))) (forall ((B $$unsorted) (C_1 $$unsorted) (A $$unsorted)) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool B) C_1)) A) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool B) A)) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool C_1) A)))) (forall ((A $$unsorted) (B $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A))) (= (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool B) C_1)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool (tptp.hAPP_f759274231e_bool _let_1 B)) (tptp.hAPP_f759274231e_bool _let_1 C_1))))) (forall ((A $$unsorted) (B $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool A))) (= (tptp.hAPP_f806699093e_bool _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool B) C_1)) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool (tptp.hAPP_f806699093e_bool _let_1 B)) (tptp.hAPP_f806699093e_bool _let_1 C_1))))) (forall ((A $$unsorted) (B $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A))) (= (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool B) C_1)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool (tptp.hAPP_f759274231e_bool _let_1 B)) (tptp.hAPP_f759274231e_bool _let_1 C_1))))) (forall ((A $$unsorted) (B $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool A))) (= (tptp.hAPP_f806699093e_bool _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool B) C_1)) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool (tptp.hAPP_f806699093e_bool _let_1 B)) (tptp.hAPP_f806699093e_bool _let_1 C_1))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.hAPP_b589554111l_bool tptp.semila310582991f_bool X_1))) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool (tptp.hAPP_bool_bool _let_1 Y_2)) (tptp.hAPP_bool_bool _let_1 Z))) (tptp.hAPP_bool_bool _let_1 (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool Y_2) Z)))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted) (Z $$unsorted)) (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 $$unsorted) (Y_2 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool X_1))) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool (tptp.hAPP_f806699093e_bool _let_1 Y_2)) (tptp.hAPP_f806699093e_bool _let_1 Z))) (tptp.hAPP_f806699093e_bool _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool Y_2) Z)))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted) (Z $$unsorted)) (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 $$unsorted) (Y_2 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool X_1))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool Y_2) Z))) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool (tptp.hAPP_f759274231e_bool _let_1 Y_2)) (tptp.hAPP_f759274231e_bool _let_1 Z)))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool X_1))) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool (tptp.hAPP_f806699093e_bool _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool Y_2) Z))) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool (tptp.hAPP_f806699093e_bool _let_1 Y_2)) (tptp.hAPP_f806699093e_bool _let_1 Z)))))) (forall ((A_4 $$unsorted) (A $$unsorted)) (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 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_p905327722e_bool tptp.insert_pname A_4))) (=> (tptp.is_fun_pname_bool A) (=> (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 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state A_4))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state A_4) A)) (= (tptp.hAPP_f806699093e_bool _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.minus_1805465033e_bool A) (tptp.hAPP_f806699093e_bool _let_1 tptp.bot_bo784226126e_bool))) A)))) (forall ((X_1 $$unsorted) (A $$unsorted)) (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 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1))) (=> (tptp.is_fun_pname_bool A) (=> (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 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state X_1))) (=> (not (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state X_1) A))) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.minus_1805465033e_bool (tptp.hAPP_f806699093e_bool _let_1 A)) (tptp.hAPP_f806699093e_bool _let_1 tptp.bot_bo784226126e_bool)) A)))) (forall ((A_4 $$unsorted) (A $$unsorted)) (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 $$unsorted) (A $$unsorted)) (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 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state A_4))) (= (tptp.hAPP_f806699093e_bool _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.minus_1805465033e_bool A) (tptp.hAPP_f806699093e_bool _let_1 tptp.bot_bo784226126e_bool))) (tptp.hAPP_f806699093e_bool _let_1 A)))) (forall ((A $$unsorted) (A_4 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_c566651504m_bool tptp.insert_com A_4))) (let ((_let_2 (tptp.hAPP_f1120618594m_bool tptp.minus_59609839m_bool A))) (= (tptp.hAPP_f1682609283m_bool _let_2 (tptp.hAPP_f1682609283m_bool _let_1 B)) (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.minus_59609839m_bool (tptp.hAPP_f1682609283m_bool _let_2 (tptp.hAPP_f1682609283m_bool _let_1 tptp.bot_bot_fun_com_bool))) B))))) (forall ((A $$unsorted) (A_4 $$unsorted) (B $$unsorted)) (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 $$unsorted) (A_4 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state A_4))) (let ((_let_2 (tptp.hAPP_f1794460506e_bool tptp.minus_1805465033e_bool A))) (= (tptp.hAPP_f806699093e_bool _let_2 (tptp.hAPP_f806699093e_bool _let_1 B)) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.minus_1805465033e_bool (tptp.hAPP_f806699093e_bool _let_2 (tptp.hAPP_f806699093e_bool _let_1 tptp.bot_bo784226126e_bool))) B))))) (forall ((A $$unsorted) (A_4 $$unsorted) (B $$unsorted)) (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 $$unsorted) (A_4 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_p905327722e_bool tptp.insert_pname A_4))) (let ((_let_2 (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A))) (= (tptp.hAPP_f759274231e_bool _let_2 (tptp.hAPP_f759274231e_bool _let_1 B)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool (tptp.hAPP_f759274231e_bool _let_2 B)) (tptp.hAPP_f759274231e_bool _let_1 tptp.bot_bo844097828e_bool)))))) (forall ((A $$unsorted) (A_4 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state A_4))) (let ((_let_2 (tptp.hAPP_f1794460506e_bool tptp.minus_1805465033e_bool A))) (= (tptp.hAPP_f806699093e_bool _let_2 (tptp.hAPP_f806699093e_bool _let_1 B)) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.minus_1805465033e_bool (tptp.hAPP_f806699093e_bool _let_2 B)) (tptp.hAPP_f806699093e_bool _let_1 tptp.bot_bo784226126e_bool)))))) (forall ((A $$unsorted) (A_4 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f1120618594m_bool tptp.minus_59609839m_bool A))) (= (tptp.hBOOL (tptp.hAPP_f990396704l_bool tptp.finite_finite_com (tptp.hAPP_f1682609283m_bool _let_1 (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com A_4) B)))) (tptp.hBOOL (tptp.hAPP_f990396704l_bool tptp.finite_finite_com (tptp.hAPP_f1682609283m_bool _let_1 B)))))) (forall ((A $$unsorted) (A_4 $$unsorted) (B $$unsorted)) (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 $$unsorted) (A_4 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f1794460506e_bool tptp.minus_1805465033e_bool A))) (= (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state (tptp.hAPP_f806699093e_bool _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state A_4) B)))) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state (tptp.hAPP_f806699093e_bool _let_1 B)))))) (forall ((A $$unsorted) (A_4 $$unsorted) (B $$unsorted)) (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 $$unsorted) (A_4 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f1847120l_bool tptp.minus_1929235165l_bool A))) (= (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool (tptp.hAPP_f734420447l_bool _let_1 (tptp.hAPP_f734420447l_bool (tptp.hAPP_f1472090462l_bool tptp.insert1720618162e_bool A_4) B)))) (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool (tptp.hAPP_f734420447l_bool _let_1 B)))))) (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.image_185131637_state F))) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.minus_1805465033e_bool (tptp.hAPP_f360545851e_bool _let_1 A)) (tptp.hAPP_f360545851e_bool _let_1 B))) (tptp.hAPP_f360545851e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A) B)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.is_fun_pname_bool B) (=> (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 $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool A) B)) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool A) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.minus_1805465033e_bool B) A)) B))) (forall ((A $$unsorted) (B $$unsorted) (C_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A) B)) C_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool B) C_1))))) (forall ((A $$unsorted) (B $$unsorted) (C_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.minus_1805465033e_bool A) B)) C_1)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool A) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool B) C_1))))) (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.image_185131637_state F))) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool (tptp.hAPP_f360545851e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A) B))) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool (tptp.hAPP_f360545851e_bool _let_1 A)) (tptp.hAPP_f360545851e_bool _let_1 B)))))) (forall ((A $$unsorted) (B $$unsorted) (C_1 $$unsorted)) (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 $$unsorted) (B $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool A))) (= (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool (tptp.hAPP_f806699093e_bool _let_1 B)) C_1) (tptp.hAPP_f806699093e_bool _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool B) C_1))) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool C_1) A))))) (forall ((P_1 $$unsorted) (F $$unsorted) (G $$unsorted) (S $$unsorted)) (let ((_let_1 (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool S))) (= (tptp.hAPP_f360545851e_bool (tptp.image_185131637_state (tptp.hAPP_f1343550633_state (tptp.hAPP_f799842582_state tptp.cOMBS_853737105_state (tptp.hAPP_f1655792756_state (tptp.hAPP_f2119427284_state tptp.cOMBS_140201078_state (tptp.hAPP_f1836930278_state (tptp.cOMBB_143651633_pname tptp.if_Hoa443228806_state) P_1)) F)) G)) S) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool (tptp.hAPP_f360545851e_bool (tptp.image_185131637_state F) (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool tptp.collect_pname P_1)))) (tptp.hAPP_f360545851e_bool (tptp.image_185131637_state G) (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool tptp.collect_pname (tptp.hAPP_f759274231e_bool (tptp.cOMBB_647938656_pname tptp.fNot) P_1)))))))) (forall ((P_1 $$unsorted) (F $$unsorted) (G $$unsorted)) (= (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 $$unsorted) (X_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_c566651504m_bool tptp.insert_com X_1))) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_f273696895l_bool tptp.ord_le1708315510m_bool (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f1120618594m_bool tptp.minus_59609839m_bool A) (tptp.hAPP_f1682609283m_bool _let_1 tptp.bot_bot_fun_com_bool))) B)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_1) A)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_f273696895l_bool tptp.ord_le1708315510m_bool A) (tptp.hAPP_f1682609283m_bool _let_1 B))))))) (forall ((A $$unsorted) (X_1 $$unsorted) (B $$unsorted)) (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 $$unsorted) (X_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state X_1))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.minus_1805465033e_bool A) (tptp.hAPP_f806699093e_bool _let_1 tptp.bot_bo784226126e_bool))) B)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state X_1) A)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool A) (tptp.hAPP_f806699093e_bool _let_1 B))))))) (forall ((A $$unsorted) (X_1 $$unsorted) (B $$unsorted)) (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 $$unsorted) (X_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A)))) (let ((_let_3 (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1))) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool _let_3 B))) (and (=> _let_2 (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A) (tptp.hAPP_f759274231e_bool _let_3 tptp.bot_bo844097828e_bool))) B))) (=> (not _let_2) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B))))))))) (forall ((A $$unsorted) (X_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool A))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state X_1) A)))) (let ((_let_3 (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state X_1))) (= (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 (tptp.hAPP_f806699093e_bool _let_3 B))) (and (=> _let_2 (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.minus_1805465033e_bool A) (tptp.hAPP_f806699093e_bool _let_3 tptp.bot_bo784226126e_bool))) B))) (=> (not _let_2) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 B))))))))) (forall ((P_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool tptp.finite_finite_com A)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool P_1 A)) (=> (forall ((A_2 $$unsorted) (A_7 $$unsorted)) (=> (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 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 A)) (=> (forall ((A_2 $$unsorted) (A_7 $$unsorted)) (=> (and (tptp.is_pname A_2) (tptp.is_fun_pname_bool A_7)) (=> (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 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state A)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool P_1 A)) (=> (forall ((A_2 $$unsorted) (A_7 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state A_7)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state A_2) A_7)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool P_1 A_7)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool P_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.minus_1805465033e_bool A_7) (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state A_2) tptp.bot_bo784226126e_bool)))))))) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool P_1 tptp.bot_bo784226126e_bool)))))) (forall ((P_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool P_1 A)) (=> (forall ((A_2 $$unsorted) (A_7 $$unsorted)) (=> (and (tptp.is_fun_pname_bool A_2) (tptp.is_fun1661590463l_bool A_7)) (=> (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 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool P_1 A)) (=> (forall ((A_2 $$unsorted) (A_7 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool A_7)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool (tptp.hAPP_f631019661l_bool tptp.member131361931e_bool A_2) A_7)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool P_1 A_7)) (tptp.hBOOL (tptp.hAPP_f1410040974l_bool P_1 (tptp.hAPP_f734420447l_bool (tptp.hAPP_f1847120l_bool tptp.minus_1929235165l_bool A_7) (tptp.hAPP_f734420447l_bool (tptp.hAPP_f1472090462l_bool tptp.insert1720618162e_bool A_2) tptp.bot_bo942947096l_bool)))))))) (tptp.hBOOL (tptp.hAPP_f1410040974l_bool P_1 tptp.bot_bo942947096l_bool)))))) (forall ((F $$unsorted) (G $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.dom_pname_com G))) (let ((_let_2 (tptp.hAPP_f661147897e_bool tptp.cOMBC_1058051404l_bool tptp.member_pname))) (= (tptp.dom_pname_com (tptp.overri1496249029on_com F G A)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool (tptp.dom_pname_com F)) (tptp.hAPP_f759274231e_bool tptp.collect_pname (tptp.hAPP_f759274231e_bool _let_2 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A) _let_1))))) (tptp.hAPP_f759274231e_bool tptp.collect_pname (tptp.hAPP_f759274231e_bool _let_2 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A) _let_1)))))))) (forall ((Q_1 $$unsorted) (P_1 $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_f273696895l_bool tptp.ord_le1708315510m_bool A) B)) (=> (forall ((X_2 $$unsorted)) (=> (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 $$unsorted) (P_1 $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) B)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.is_pname X_2) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A)) (=> (tptp.hBOOL (tptp.hAPP_pname_bool P_1 X_2)) (tptp.hBOOL (tptp.hAPP_pname_bool Q_1 X_2)))))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A) (tptp.hAPP_f759274231e_bool tptp.collect_pname P_1))) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool B) (tptp.hAPP_f759274231e_bool tptp.collect_pname Q_1))))))) (forall ((Q_1 $$unsorted) (P_1 $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool A) B)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state X_2) A)) (=> (tptp.hBOOL (tptp.hAPP_H242767318e_bool P_1 X_2)) (tptp.hBOOL (tptp.hAPP_H242767318e_bool Q_1 X_2))))) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool A) (tptp.hAPP_f806699093e_bool tptp.collec637225377_state P_1))) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool B) (tptp.hAPP_f806699093e_bool tptp.collec637225377_state Q_1))))))) (forall ((Q_1 $$unsorted) (P_1 $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool A) B)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.is_fun_pname_bool X_2) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool X_2) A)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 X_2)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool Q_1 X_2)))))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.semila1130628874l_bool A) (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool P_1))) (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.semila1130628874l_bool B) (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool Q_1))))))) (forall ((Q_1 $$unsorted) (P_1 $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool (tptp.hAPP_f1516997247l_bool tptp.ord_le694194916l_bool A) B)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool (tptp.hAPP_f631019661l_bool tptp.member131361931e_bool X_2) A)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool P_1 X_2)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool Q_1 X_2))))) (tptp.hBOOL (tptp.hAPP_f1410040974l_bool (tptp.hAPP_f1516997247l_bool tptp.ord_le694194916l_bool (tptp.hAPP_f734420447l_bool (tptp.hAPP_f1847120l_bool tptp.semila1028267552l_bool A) (tptp.hAPP_f734420447l_bool tptp.collec1987918285e_bool P_1))) (tptp.hAPP_f734420447l_bool (tptp.hAPP_f1847120l_bool tptp.semila1028267552l_bool B) (tptp.hAPP_f734420447l_bool tptp.collec1987918285e_bool Q_1))))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.hAPP_b589554111l_bool tptp.semila310582991f_bool X_1))) (=> (forall ((X_2 $$unsorted) (Y_3 $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool X_2))) (=> (and (tptp.is_bool X_2) (tptp.is_bool Y_3) (tptp.is_bool Z_1)) (= (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 $$unsorted) (Y_2 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool X_1))) (=> (forall ((X_2 $$unsorted) (Y_3 $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool X_2))) (=> (and (tptp.is_fun_pname_bool X_2) (tptp.is_fun_pname_bool Y_3) (tptp.is_fun_pname_bool Z_1)) (= (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 $$unsorted) (Y_2 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool X_1))) (=> (forall ((X_2 $$unsorted) (Y_3 $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool X_2))) (= (tptp.hAPP_f806699093e_bool _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool Y_3) Z_1)) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool (tptp.hAPP_f806699093e_bool _let_1 Y_3)) (tptp.hAPP_f806699093e_bool _let_1 Z_1))))) (= (tptp.hAPP_f806699093e_bool _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool Y_2) Z)) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool (tptp.hAPP_f806699093e_bool _let_1 Y_2)) (tptp.hAPP_f806699093e_bool _let_1 Z)))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool X_1))) (=> (forall ((X_2 $$unsorted) (Y_3 $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_b589554111l_bool tptp.semila310582991f_bool X_2))) (=> (and (tptp.is_bool X_2) (tptp.is_bool Y_3) (tptp.is_bool Z_1)) (= (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 $$unsorted) (Y_2 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool X_1))) (=> (forall ((X_2 $$unsorted) (Y_3 $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool X_2))) (=> (and (tptp.is_fun_pname_bool X_2) (tptp.is_fun_pname_bool Y_3) (tptp.is_fun_pname_bool Z_1)) (= (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 $$unsorted) (Y_2 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool X_1))) (=> (forall ((X_2 $$unsorted) (Y_3 $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool X_2))) (= (tptp.hAPP_f806699093e_bool _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool Y_3) Z_1)) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool (tptp.hAPP_f806699093e_bool _let_1 Y_3)) (tptp.hAPP_f806699093e_bool _let_1 Z_1))))) (= (tptp.hAPP_f806699093e_bool _let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool Y_2) Z)) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool (tptp.hAPP_f806699093e_bool _let_1 Y_2)) (tptp.hAPP_f806699093e_bool _let_1 Z)))))) (forall ((A $$unsorted) (B_1 $$unsorted)) (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 $$unsorted) (B_1 $$unsorted)) (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)))) (=> (tptp.is_pname B_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 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state B_1) tptp.bot_bo784226126e_bool))) (let ((_let_2 (tptp.hAPP_f718417177_state (tptp.partia325231104_state B_1) A))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool A) _let_1)))) (and (=> _let_3 (= _let_2 B_1)) (=> (not _let_3) (= _let_2 (tptp.hAPP_f718417177_state tptp.the_Ho2067184133_state (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1184122441e_bool tptp.cOMBC_538205282l_bool tptp.member1667945571_state) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.minus_1805465033e_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.finite2036162504e_bool (tptp.hAPP_f241329646e_bool (tptp.cOMBB_604855927_state (tptp.hAPP_f2061951445e_bool tptp.cOMBC_528733435e_bool tptp.minus_1805465033e_bool)) (tptp.hAPP_f874203478e_bool (tptp.hAPP_f1802364479e_bool tptp.cOMBC_1229155955e_bool tptp.insert1744391420_state) tptp.bot_bo784226126e_bool)))) (forall ((F $$unsorted) (Y_2 $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.image_185131637_state F))) (let ((_let_2 (tptp.hAPP_f360545851e_bool (tptp.image_185131637_state (tptp.fun_up1055265789_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_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state Y_2) (tptp.hAPP_f360545851e_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_f360545851e_bool _let_1 A)))))))) (tptp.hBOOL (tptp.finite1653727294m_bool tptp.insert_com)) (tptp.hBOOL (tptp.finite2017903282e_bool tptp.insert_pname)) (tptp.hBOOL (tptp.finite2036162504e_bool tptp.insert1744391420_state)) (tptp.hBOOL (tptp.finite318301748l_bool tptp.semila1168014441p_bool)) (tptp.hBOOL (tptp.finite367769966e_bool tptp.semila278973382e_bool)) (tptp.hBOOL (tptp.finite1765632844e_bool tptp.semila176469292e_bool)) (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.image_185131637_state F))) (let ((_let_2 (tptp.inj_on621632009_state F))) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_2 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A) B))) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_2 A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_2 B)) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool (tptp.hAPP_f360545851e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A) B))) (tptp.hAPP_f360545851e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool B) A))) tptp.bot_bo784226126e_bool)))))) (forall ((F $$unsorted) (X_1 $$unsorted)) (= (= (tptp.dom_pname_com F) (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1) tptp.bot_bo844097828e_bool)) (exists ((V $$unsorted)) (= 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 $$unsorted) (A $$unsorted)) (=> (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 $$unsorted) (A $$unsorted)) (=> (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 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state A)) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.minus_1805465033e_bool B) A) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool (tptp.finite1230907212e_bool (tptp.hAPP_f241329646e_bool (tptp.cOMBB_604855927_state (tptp.hAPP_f2061951445e_bool tptp.cOMBC_528733435e_bool tptp.minus_1805465033e_bool)) (tptp.hAPP_f874203478e_bool (tptp.hAPP_f1802364479e_bool tptp.cOMBC_1229155955e_bool tptp.insert1744391420_state) tptp.bot_bo784226126e_bool))) B) A)))) (forall ((B $$unsorted) (A $$unsorted)) (=> (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 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool A)) (= (tptp.hAPP_f734420447l_bool (tptp.hAPP_f1847120l_bool tptp.minus_1929235165l_bool B) A) (tptp.hAPP_f734420447l_bool (tptp.hAPP_f1847120l_bool (tptp.finite1943735070l_bool (tptp.hAPP_f1316144452l_bool (tptp.cOMBB_494346593e_bool (tptp.hAPP_f1573805579l_bool tptp.cOMBC_1377256501l_bool tptp.minus_1929235165l_bool)) (tptp.hAPP_f2059879088l_bool (tptp.hAPP_f476955937l_bool tptp.cOMBC_1639502213l_bool tptp.insert1720618162e_bool) tptp.bot_bo942947096l_bool))) B) A)))) (forall ((F $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (= (tptp.hAPP_f360545851e_bool (tptp.image_185131637_state F) A) (tptp.finite1443934175_pname tptp.semila176469292e_bool (tptp.hAPP_f103229774e_bool (tptp.hAPP_f376349141e_bool tptp.cOMBC_59067399e_bool (tptp.hAPP_f2028971360e_bool (tptp.cOMBB_667059641_pname tptp.insert1744391420_state) F)) tptp.bot_bo784226126e_bool) tptp.bot_bo784226126e_bool A)))) (forall ((A $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.inj_on737724108_pname tptp.some_pname) A))) (forall ((A $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.inj_on264996226_state tptp.some_H1043067815_state) A))) (forall ((A $$unsorted)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.inj_on11367768on_com tptp.some_com) A))) (forall ((A_6 $$unsorted)) (not (= tptp.none_com (tptp.hAPP_com_option_com tptp.some_com A_6)))) (forall ((A_6 $$unsorted)) (not (= tptp.none_pname (tptp.hAPP_p1252095976_pname tptp.some_pname A_6)))) (forall ((A_6 $$unsorted)) (not (= tptp.none_H175086635_state (tptp.hAPP_H1633077406_state tptp.some_H1043067815_state A_6)))) (forall ((A_5 $$unsorted)) (not (= (tptp.hAPP_com_option_com tptp.some_com A_5) tptp.none_com))) (forall ((A_5 $$unsorted)) (not (= (tptp.hAPP_p1252095976_pname tptp.some_pname A_5) tptp.none_pname))) (forall ((A_5 $$unsorted)) (not (= (tptp.hAPP_H1633077406_state tptp.some_H1043067815_state A_5) tptp.none_H175086635_state))) (forall ((X_1 $$unsorted)) (= (forall ((Y_3 $$unsorted)) (not (= X_1 (tptp.hAPP_com_option_com tptp.some_com Y_3)))) (= X_1 tptp.none_com))) (forall ((X_1 $$unsorted)) (=> (tptp.is_option_pname X_1) (= (forall ((Y_3 $$unsorted)) (=> (tptp.is_pname Y_3) (not (= X_1 (tptp.hAPP_p1252095976_pname tptp.some_pname Y_3))))) (= X_1 tptp.none_pname)))) (forall ((X_1 $$unsorted)) (= (forall ((Y_3 $$unsorted)) (not (= X_1 (tptp.hAPP_H1633077406_state tptp.some_H1043067815_state Y_3)))) (= X_1 tptp.none_H175086635_state))) (forall ((X_1 $$unsorted)) (= (not (= X_1 tptp.none_com)) (exists ((Y_3 $$unsorted)) (= X_1 (tptp.hAPP_com_option_com tptp.some_com Y_3))))) (forall ((X_1 $$unsorted)) (=> (tptp.is_option_pname X_1) (= (not (= X_1 tptp.none_pname)) (exists ((Y_3 $$unsorted)) (and (tptp.is_pname Y_3) (= X_1 (tptp.hAPP_p1252095976_pname tptp.some_pname Y_3))))))) (forall ((X_1 $$unsorted)) (= (not (= X_1 tptp.none_H175086635_state)) (exists ((Y_3 $$unsorted)) (= X_1 (tptp.hAPP_H1633077406_state tptp.some_H1043067815_state Y_3))))) (forall ((M $$unsorted)) (= (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 $$unsorted) (M $$unsorted)) (= (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 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state (tptp.hAPP_f360545851e_bool (tptp.image_185131637_state F) A))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.inj_on621632009_state F) A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A))))) (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.image_185131637_state F))) (=> (and (tptp.is_fun_pname_bool A) (tptp.is_fun_pname_bool B)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.inj_on621632009_state F) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A) B))) (= (= (tptp.hAPP_f360545851e_bool _let_1 A) (tptp.hAPP_f360545851e_bool _let_1 B)) (= A B)))))) (forall ((X_1 $$unsorted)) (= (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 $$unsorted) (Y_2 $$unsorted) (F $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.inj_on621632009_state F) A)) (=> (not (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state Y_2) (tptp.hAPP_f360545851e_bool (tptp.image_185131637_state F) A)))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.inj_on621632009_state (tptp.fun_up1055265789_state F X_1 Y_2)) A))))) (forall ((B_1 $$unsorted) (A_4 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool A_4) A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A_4) B_1)) (tptp.hAPP_f674760225e_bool (tptp.hAPP_f246190092e_bool (tptp.finite446335722e_bool tptp.semila278973382e_bool) B_1) A)))))) (forall ((B_1 $$unsorted) (A_4 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool (tptp.hAPP_f631019661l_bool tptp.member131361931e_bool A_4) A)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool A_4) B_1)) (tptp.hAPP_f1216288071e_bool (tptp.hAPP_f1712138014e_bool (tptp.finite391880392e_bool tptp.semila176469292e_bool) B_1) A)))))) (forall ((B_1 $$unsorted) (A_4 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f387058535l_bool tptp.finite_finite_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.hAPP_b1787118453l_bool tptp.member_bool A_4) A)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool A_4) B_1)) (tptp.hAPP_f387058535l_bool (tptp.hAPP_b1787118453l_bool (tptp.finite1909292976l_bool tptp.semila1168014441p_bool) B_1) A)))))) (forall ((B_1 $$unsorted) (A_4 $$unsorted) (A $$unsorted)) (=> (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 $$unsorted) (A_4 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool (tptp.hAPP_f631019661l_bool tptp.member131361931e_bool A_4) A)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool (tptp.hAPP_f1216288071e_bool (tptp.hAPP_f1712138014e_bool (tptp.finite391880392e_bool tptp.semila1874263622e_bool) B_1) A)) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool A_4) B_1)))))) (forall ((B_1 $$unsorted) (A_4 $$unsorted) (A $$unsorted)) (=> (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 $$unsorted) (A_4 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f246190092e_bool (tptp.finite446335722e_bool tptp.semila278973382e_bool) B_1))) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)) (= (tptp.hAPP_f674760225e_bool _let_1 (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool A_4) A)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A_4) (tptp.hAPP_f674760225e_bool _let_1 A)))))) (forall ((B_1 $$unsorted) (A_4 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f1712138014e_bool (tptp.finite391880392e_bool tptp.semila176469292e_bool) B_1))) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool A)) (= (tptp.hAPP_f1216288071e_bool _let_1 (tptp.hAPP_f734420447l_bool (tptp.hAPP_f1472090462l_bool tptp.insert1720618162e_bool A_4) A)) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool A_4) (tptp.hAPP_f1216288071e_bool _let_1 A)))))) (forall ((B_1 $$unsorted) (A_4 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_b1787118453l_bool (tptp.finite1909292976l_bool tptp.semila1168014441p_bool) B_1))) (=> (tptp.hBOOL (tptp.hAPP_f387058535l_bool tptp.finite_finite_bool A)) (= (tptp.hBOOL (tptp.hAPP_f387058535l_bool _let_1 (tptp.hAPP_f961197973l_bool (tptp.hAPP_b496459037l_bool tptp.insert_bool A_4) A))) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool A_4) (tptp.hAPP_f387058535l_bool _let_1 A))))))) (forall ((B_1 $$unsorted) (A_4 $$unsorted) (A $$unsorted)) (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 $$unsorted) (A_4 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f1712138014e_bool (tptp.finite391880392e_bool tptp.semila1874263622e_bool) B_1))) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool A)) (= (tptp.hAPP_f1216288071e_bool _let_1 (tptp.hAPP_f734420447l_bool (tptp.hAPP_f1472090462l_bool tptp.insert1720618162e_bool A_4) A)) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool A_4) (tptp.hAPP_f1216288071e_bool _let_1 A)))))) (forall ((F $$unsorted)) (= (= (tptp.dom_pname_com F) tptp.bot_bo844097828e_bool) (forall ((X_2 $$unsorted)) (=> (tptp.is_pname X_2) (= (tptp.hAPP_p799580910on_com F X_2) tptp.none_com))))) (= (tptp.dom_pname_com (tptp.hAPP_o129566686on_com tptp.cOMBK_413306633_pname tptp.none_com)) tptp.bot_bo844097828e_bool) (= (tptp.set_com tptp.none_com) tptp.bot_bot_fun_com_bool) (= (tptp.set_pname tptp.none_pname) tptp.bot_bo844097828e_bool) (= (tptp.set_Ho1741238126_state tptp.none_H175086635_state) tptp.bot_bo784226126e_bool) (forall ((Xo $$unsorted)) (= (= (tptp.set_com Xo) tptp.bot_bot_fun_com_bool) (= Xo tptp.none_com))) (forall ((Xo $$unsorted)) (=> (tptp.is_option_pname Xo) (= (= (tptp.set_pname Xo) tptp.bot_bo844097828e_bool) (= Xo tptp.none_pname)))) (forall ((Xo $$unsorted)) (= (= (tptp.set_Ho1741238126_state Xo) tptp.bot_bo784226126e_bool) (= Xo tptp.none_H175086635_state))) (forall ((F $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f559147733l_bool (tptp.image_2063528359e_bool F) A))) (=> (tptp.is_fun1661590463l_bool 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 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f734420447l_bool (tptp.image_390184709e_bool F) A))) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool (tptp.hAPP_f1516997247l_bool tptp.ord_le694194916l_bool _let_1) A)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool (tptp.inj_on2143431281e_bool F) A)) (= _let_1 A)))))) (forall ((F $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f759274231e_bool (tptp.image_pname_pname F) A))) (=> (tptp.is_fun_pname_bool 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 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f806699093e_bool (tptp.image_661047967_state F) A))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state A)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool _let_1) A)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.inj_on535898123_state F) A)) (= _let_1 A)))))) (forall ((F $$unsorted) (A $$unsorted)) (=> (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 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool (tptp.hAPP_f1516997247l_bool tptp.ord_le694194916l_bool A) (tptp.hAPP_f734420447l_bool (tptp.image_390184709e_bool F) A))) (tptp.hBOOL (tptp.hAPP_f1410040974l_bool (tptp.inj_on2143431281e_bool F) A))))) (forall ((F $$unsorted) (A $$unsorted)) (=> (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 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state A)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool A) (tptp.hAPP_f806699093e_bool (tptp.image_661047967_state F) A))) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.inj_on535898123_state F) A))))) (forall ((B $$unsorted) (A $$unsorted) (F $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.image_185131637_state F))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.inj_on621632009_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_f360545851e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A) B)) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool (tptp.hAPP_f360545851e_bool _let_1 A)) (tptp.hAPP_f360545851e_bool _let_1 B)))))))) (forall ((B $$unsorted) (A $$unsorted) (F $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.image_185131637_state F))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.inj_on621632009_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_f360545851e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A) B)) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.minus_1805465033e_bool (tptp.hAPP_f360545851e_bool _let_1 A)) (tptp.hAPP_f360545851e_bool _let_1 B)))))))) (forall ((B $$unsorted) (A $$unsorted)) (=> (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 $$unsorted) (A $$unsorted)) (=> (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 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state A)) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool A) B) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool (tptp.finite1230907212e_bool tptp.insert1744391420_state) B) A)))) (forall ((B $$unsorted) (A $$unsorted)) (=> (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 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool A)) (= (tptp.hAPP_f734420447l_bool (tptp.hAPP_f1847120l_bool tptp.semila1672697786l_bool A) B) (tptp.hAPP_f734420447l_bool (tptp.hAPP_f1847120l_bool (tptp.finite1943735070l_bool tptp.insert1720618162e_bool) B) A)))) (forall ((A $$unsorted) (F $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool (tptp.dom_pname_com F)))) (=> (= (tptp.hAPP_p799580910on_com F X_1) tptp.none_com) (= (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1) A)) (tptp.hAPP_f759274231e_bool _let_1 A))))) (forall ((X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool X_1) X_1)) (tptp.hBOOL X_1))) (forall ((X_1 $$unsorted)) (=> (tptp.is_fun_pname_bool X_1) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool X_1) X_1) X_1))) (forall ((X_1 $$unsorted)) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool X_1) X_1) X_1)) (forall ((X_1 $$unsorted) (A $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (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 $$unsorted) (A $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (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 $$unsorted) (A $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.finite683959609_state F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state A)) (=> (not (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state X_1) A))) (= (tptp.hAPP_f718417177_state Fa (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state X_1) A)) (tptp.hAPP_f718417177_state (tptp.hAPP_H1440241088_state (tptp.finite212984546_state F) X_1) A)))))) (forall ((X_1 $$unsorted) (A $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (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 $$unsorted) (A $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.finite2009063477e_bool F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool A)) (=> (not (tptp.hBOOL (tptp.hAPP_f1410040974l_bool (tptp.hAPP_f631019661l_bool tptp.member131361931e_bool X_1) A))) (= (tptp.hAPP_f1216288071e_bool Fa (tptp.hAPP_f734420447l_bool (tptp.hAPP_f1472090462l_bool tptp.insert1720618162e_bool X_1) A)) (tptp.hAPP_f1216288071e_bool (tptp.hAPP_f1712138014e_bool (tptp.finite391880392e_bool F) X_1) A)))))) (forall ((A_4 $$unsorted) (A $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (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 $$unsorted) (A $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (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 $$unsorted) (A $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.finite416071164_state F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state A)) (= (tptp.hAPP_f718417177_state Fa (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool tptp.insert1744391420_state A_4) A)) (tptp.hAPP_f718417177_state (tptp.hAPP_H1440241088_state (tptp.finite212984546_state F) A_4) A))))) (forall ((A_4 $$unsorted) (A $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (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 $$unsorted) (A $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.finite688249778e_bool F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool A)) (= (tptp.hAPP_f1216288071e_bool Fa (tptp.hAPP_f734420447l_bool (tptp.hAPP_f1472090462l_bool tptp.insert1720618162e_bool A_4) A)) (tptp.hAPP_f1216288071e_bool (tptp.hAPP_f1712138014e_bool (tptp.finite391880392e_bool F) A_4) A))))) (forall ((Pn $$unsorted)) (=> (not (= (tptp.hAPP_p799580910on_com tptp.body Pn) tptp.none_com)) (tptp.hBOOL (tptp.hAPP_com_bool tptp.wt (tptp.hAPP_pname_com tptp.body_1 Pn))))) (forall ((F $$unsorted) (A_4 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_p905327722e_bool tptp.insert_pname A_4))) (let ((_let_2 (tptp.inj_on621632009_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_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state (tptp.hAPP_p1751618853_state F A_4)) (tptp.hAPP_f360545851e_bool (tptp.image_185131637_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 $$unsorted) (X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.dom_pname_com F))) (let ((_let_2 (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1))) (let ((_let_3 (tptp.dom_pname_com (tptp.fun_up879233478on_com F X_1 Y_2)))) (let ((_let_4 (= Y_2 tptp.none_com))) (and (=> _let_4 (= _let_3 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool _let_1) (tptp.hAPP_f759274231e_bool _let_2 tptp.bot_bo844097828e_bool)))) (=> (not _let_4) (= _let_3 (tptp.hAPP_f759274231e_bool _let_2 _let_1))))))))) (forall ((C $$unsorted) (B_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.is_fun_pname_bool X_2) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B_1) X_2))))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool B_1) C)) (tptp.hAPP_f674760225e_bool (tptp.hAPP_f246190092e_bool (tptp.finite446335722e_bool tptp.semila1635148844e_bool) C) A)))))) (forall ((C $$unsorted) (B_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool A)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool (tptp.hAPP_f631019661l_bool tptp.member131361931e_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool B_1) X_2)))) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool B_1) C)) (tptp.hAPP_f1216288071e_bool (tptp.hAPP_f1712138014e_bool (tptp.finite391880392e_bool tptp.semila1874263622e_bool) C) A)))))) (forall ((C $$unsorted) (B_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f387058535l_bool tptp.finite_finite_bool A)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.is_bool X_2) (=> (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.hAPP_b1787118453l_bool tptp.member_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool B_1) X_2))))) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila310582991f_bool B_1) C)) (tptp.hAPP_f387058535l_bool (tptp.hAPP_b1787118453l_bool (tptp.finite1909292976l_bool tptp.semila310582991f_bool) C) A)))))) (forall ((C $$unsorted) (B_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.is_fun_pname_bool X_2) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool X_2) B_1))))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f674760225e_bool (tptp.hAPP_f246190092e_bool (tptp.finite446335722e_bool tptp.semila278973382e_bool) C) A)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool B_1) C)))))) (forall ((C $$unsorted) (B_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool A)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool (tptp.hAPP_f631019661l_bool tptp.member131361931e_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool X_2) B_1)))) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool (tptp.hAPP_f1216288071e_bool (tptp.hAPP_f1712138014e_bool (tptp.finite391880392e_bool tptp.semila176469292e_bool) C) A)) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila176469292e_bool B_1) C)))))) (forall ((C $$unsorted) (B_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f387058535l_bool tptp.finite_finite_bool A)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.is_bool X_2) (=> (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.hAPP_b1787118453l_bool tptp.member_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool X_2) B_1))))) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_f387058535l_bool (tptp.hAPP_b1787118453l_bool (tptp.finite1909292976l_bool tptp.semila1168014441p_bool) C) A)) (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool B_1) C)))))) (forall ((A_3 $$unsorted) (A $$unsorted)) (=> (not (= A tptp.bot_bo784226126e_bool)) (= (exists ((F_1 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.inj_on63516655_pname F_1) A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f1083669085e_bool (tptp.image_1774499931_pname F_1) A)) A_3)))) (exists ((G_1 $$unsorted)) (= (tptp.hAPP_f360545851e_bool (tptp.image_185131637_state G_1) A_3) A))))) (forall ((A_3 $$unsorted) (A $$unsorted)) (=> (tptp.is_fun_pname_bool A) (=> (not (= A tptp.bot_bo844097828e_bool)) (= (exists ((F_1 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.inj_on621632009_state F_1) A)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool (tptp.hAPP_f360545851e_bool (tptp.image_185131637_state F_1) A)) A_3)))) (exists ((G_1 $$unsorted)) (= (tptp.hAPP_f1083669085e_bool (tptp.image_1774499931_pname G_1) A_3) A)))))) (forall ((Y_1 $$unsorted)) (=> (not (= Y_1 tptp.none_com)) (not (forall ((A_2 $$unsorted)) (not (= Y_1 (tptp.hAPP_com_option_com tptp.some_com A_2))))))) (forall ((Y_1 $$unsorted)) (=> (tptp.is_option_pname Y_1) (=> (not (= Y_1 tptp.none_pname)) (not (forall ((A_2 $$unsorted)) (=> (tptp.is_pname A_2) (not (= Y_1 (tptp.hAPP_p1252095976_pname tptp.some_pname A_2))))))))) (forall ((Y_1 $$unsorted)) (=> (not (= Y_1 tptp.none_H175086635_state)) (not (forall ((A_2 $$unsorted)) (not (= Y_1 (tptp.hAPP_H1633077406_state tptp.some_H1043067815_state A_2))))))) (forall ((G $$unsorted) (B $$unsorted) (F $$unsorted) (A $$unsorted)) (exists ((A_1 $$unsorted)) (and (tptp.is_fun_pname_bool A_1) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_1) A)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname X_2))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A_1)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f1083669085e_bool (tptp.image_1774499931_pname G) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.minus_1805465033e_bool B) (tptp.hAPP_f360545851e_bool (tptp.image_185131637_state F) A_1))))))))) (exists ((H $$unsorted)) (and (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A_1)) (= (tptp.hAPP_p1751618853_state H X_2) (tptp.hAPP_p1751618853_state F X_2)))) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_p1751618853_state H X_2))) (=> (tptp.is_pname 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_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state _let_1) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.minus_1805465033e_bool B) (tptp.hAPP_f360545851e_bool (tptp.image_185131637_state F) A_1)))) (= X_2 (tptp.hAPP_H1193503499_pname G _let_1)))))))))))) (forall ((G $$unsorted) (B $$unsorted) (F $$unsorted) (A $$unsorted)) (exists ((A_1 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool A_1) A)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state X_2))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 A_1)) (not (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_1 (tptp.hAPP_f360545851e_bool (tptp.image_185131637_state G) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool B) (tptp.hAPP_f1083669085e_bool (tptp.image_1774499931_pname F) A_1))))))))) (exists ((H $$unsorted)) (and (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state X_2) A_1)) (= (tptp.hAPP_H1193503499_pname H X_2) (tptp.hAPP_H1193503499_pname F X_2)))) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_H1193503499_pname H X_2))) (=> (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state X_2) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.minus_1805465033e_bool A) A_1))) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname _let_1) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool B) (tptp.hAPP_f1083669085e_bool (tptp.image_1774499931_pname F) A_1)))) (= X_2 (tptp.hAPP_p1751618853_state G _let_1))))))))))) (forall ((F $$unsorted) (A $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool (tptp.hAPP_f360545851e_bool (tptp.image_185131637_state F) (tptp.vimage1011814463_state F A))) A))) (forall ((M $$unsorted) (A $$unsorted)) (= (tptp.dom_pname_com (tptp.restri1382200118me_com M A)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool (tptp.dom_pname_com M)) A))) (forall ((B $$unsorted) (A $$unsorted)) (=> (and (tptp.is_fun1661590463l_bool B) (tptp.is_fun1661590463l_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)) (=> (not (= A tptp.bot_bo1649642514l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool B)) (=> (not (= B tptp.bot_bo1649642514l_bool)) (=> (= (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.semila1130628874l_bool A) B) tptp.bot_bo1649642514l_bool) (= (tptp.hAPP_f674760225e_bool tptp.big_la28065288e_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.semila1782091504l_bool A) B)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool (tptp.hAPP_f674760225e_bool tptp.big_la28065288e_bool A)) (tptp.hAPP_f674760225e_bool tptp.big_la28065288e_bool B)))))))))) (forall ((B $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool A)) (=> (not (= A tptp.bot_bo942947096l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool B)) (=> (not (= B tptp.bot_bo942947096l_bool)) (=> (= (tptp.hAPP_f734420447l_bool (tptp.hAPP_f1847120l_bool tptp.semila1028267552l_bool A) B) tptp.bot_bo942947096l_bool) (= (tptp.hAPP_f1216288071e_bool tptp.big_la236972906e_bool (tptp.hAPP_f734420447l_bool (tptp.hAPP_f1847120l_bool tptp.semila1672697786l_bool A) B)) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool (tptp.hAPP_f1216288071e_bool tptp.big_la236972906e_bool A)) (tptp.hAPP_f1216288071e_bool tptp.big_la236972906e_bool B))))))))) (forall ((B $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.semila1130628874l_bool A) B))) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool B)) (=> (not (= _let_1 tptp.bot_bo1649642514l_bool)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool (tptp.hAPP_f674760225e_bool tptp.big_la28065288e_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.semila1782091504l_bool A) B))) (tptp.hAPP_f674760225e_bool tptp.big_la28065288e_bool _let_1)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool (tptp.hAPP_f674760225e_bool tptp.big_la28065288e_bool A)) (tptp.hAPP_f674760225e_bool tptp.big_la28065288e_bool B)))))))) (forall ((B $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f734420447l_bool (tptp.hAPP_f1847120l_bool tptp.semila1028267552l_bool A) B))) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f1410040974l_bool tptp.finite627955595e_bool B)) (=> (not (= _let_1 tptp.bot_bo942947096l_bool)) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool (tptp.hAPP_f1216288071e_bool tptp.big_la236972906e_bool (tptp.hAPP_f734420447l_bool (tptp.hAPP_f1847120l_bool tptp.semila1672697786l_bool A) B))) (tptp.hAPP_f1216288071e_bool tptp.big_la236972906e_bool _let_1)) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool tptp.semila1874263622e_bool (tptp.hAPP_f1216288071e_bool tptp.big_la236972906e_bool A)) (tptp.hAPP_f1216288071e_bool tptp.big_la236972906e_bool B)))))))) (forall ((X_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_1) tptp.top_top_fun_com_bool))) (forall ((X_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) tptp.top_to2127735616e_bool))) (forall ((X_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state X_1) tptp.top_to215444530e_bool))) (forall ((F $$unsorted) (X_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state (tptp.hAPP_p1751618853_state F X_1)) (tptp.hAPP_f360545851e_bool (tptp.image_185131637_state F) tptp.top_to2127735616e_bool)))) (forall ((P $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP_bool_bool tptp.fNot P))) (not (tptp.hBOOL P)))) (forall ((P $$unsorted)) (or (tptp.hBOOL P) (tptp.hBOOL (tptp.hAPP_bool_bool tptp.fNot P)))) (forall ((Q $$unsorted) (P $$unsorted)) (or (not (tptp.hBOOL P)) (not (tptp.hBOOL Q)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fconj P) Q)))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fconj P) Q))) (tptp.hBOOL P))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fconj P) Q))) (tptp.hBOOL Q))) (forall ((Q $$unsorted) (P $$unsorted)) (or (not (tptp.hBOOL P)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fdisj P) Q)))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL Q)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fdisj P) Q)))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fdisj P) Q))) (tptp.hBOOL P) (tptp.hBOOL Q))) (not (tptp.hBOOL tptp.fFalse)) (forall ((P $$unsorted)) (=> (tptp.is_bool P) (or (= P tptp.fTrue) (= P tptp.fFalse)))) (forall ((Q $$unsorted) (P $$unsorted)) (or (tptp.hBOOL P) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fimplies P) Q)))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL Q)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fimplies P) Q)))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fimplies P) Q))) (not (tptp.hBOOL P)) (tptp.hBOOL Q))) (forall ((X $$unsorted) (P $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP_f327114704l_bool tptp.fAll_state P))) (tptp.hBOOL (tptp.hAPP_state_bool P X)))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP_com_bool (tptp.hAPP_c1396316405m_bool tptp.fequal_com X) Y))) (= X Y))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_com_bool (tptp.hAPP_c1396316405m_bool tptp.fequal_com X) Y)))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (and (tptp.is_pname X) (tptp.is_pname Y)) (or (not (tptp.hBOOL (tptp.hAPP_pname_bool (tptp.hAPP_p61793385e_bool tptp.fequal_pname X) Y))) (= X Y)))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_pname_bool (tptp.hAPP_p61793385e_bool tptp.fequal_pname X) Y)))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool tptp.fequal_state X) Y))) (= X Y))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool tptp.fequal_state X) Y)))) (forall ((P $$unsorted) (Q $$unsorted)) (=> (tptp.is_bool P) (= (tptp.hAPP_com_bool (tptp.hAPP_b1153789088m_bool tptp.cOMBK_bool_com P) Q) P))) (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.hAPP_pname_com (tptp.hAPP_c1494068046me_com tptp.cOMBK_com_pname P) Q) P)) (forall ((P $$unsorted) (Q $$unsorted)) (=> (tptp.is_bool P) (= (tptp.hAPP_pname_bool (tptp.hAPP_b76515610e_bool tptp.cOMBK_bool_pname P) Q) P))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.hAPP_o356497025on_com (tptp.hAPP_o334540577on_com (tptp.hAPP_b1679505845on_com tptp.if_option_com tptp.fTrue) X) Y) X)) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.hAPP_o356497025on_com (tptp.hAPP_o334540577on_com (tptp.hAPP_b1679505845on_com tptp.if_option_com tptp.fFalse) X) Y) Y)) (forall ((P $$unsorted)) (=> (tptp.is_bool P) (or (= P tptp.fTrue) (= P tptp.fFalse)))) (forall ((P $$unsorted) (Q $$unsorted)) (=> (tptp.is_pname P) (= (tptp.hAPP_pname_pname (tptp.hAPP_p1170154830_pname tptp.cOMBK_pname_pname P) Q) P))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP_option_com_bool (tptp.hAPP_o1684370239m_bool tptp.fequal_option_com X) Y))) (= X Y))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_option_com_bool (tptp.hAPP_o1684370239m_bool tptp.fequal_option_com X) Y)))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_f273696895l_bool tptp.fequal_fun_com_bool X) Y))) (= X Y))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_f273696895l_bool tptp.fequal_fun_com_bool X) Y)))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (and (tptp.is_fun_pname_bool X) (tptp.is_fun_pname_bool Y)) (or (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.fequal533582459e_bool X) Y))) (= X Y)))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.fequal533582459e_bool X) Y)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_com_bool (tptp.hAPP_c1396316405m_bool (tptp.hAPP_f908845385m_bool tptp.cOMBC_com_com_bool P) Q) R) (tptp.hAPP_com_bool (tptp.hAPP_c1396316405m_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (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 $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_com_bool (tptp.hAPP_f1682609283m_bool (tptp.hAPP_f328772264m_bool tptp.cOMBS_com_bool_bool P) Q) R) (tptp.hAPP_bool_bool (tptp.hAPP_c1580157610l_bool P R) (tptp.hAPP_com_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (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 $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_pname_bool (tptp.hAPP_f759274231e_bool (tptp.cOMBB_647938656_pname P) Q) R) (tptp.hAPP_bool_bool P (tptp.hAPP_pname_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (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 $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_state_bool (tptp.hAPP_b2019457360e_bool (tptp.hAPP_f167292325e_bool tptp.cOMBC_231445413l_bool P) Q) R) (tptp.hAPP_bool_bool (tptp.hAPP_s58564346l_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_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 $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_state_bool (tptp.hAPP_f1759915619e_bool (tptp.hAPP_f644196280e_bool tptp.cOMBS_1378840469l_bool P) Q) R) (tptp.hAPP_bool_bool (tptp.hAPP_s58564346l_bool P R) (tptp.hAPP_state_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_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 $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool (tptp.hAPP_f817621513e_bool tptp.cOMBC_2027030106e_bool P) Q) R) (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.hAPP_p799580910on_com (tptp.hAPP_o129566686on_com tptp.cOMBK_413306633_pname P) Q) P)) (forall ((P $$unsorted) (Q $$unsorted)) (=> (tptp.is_bool P) (= (tptp.hAPP_f1664156314l_bool (tptp.hAPP_b357632156l_bool tptp.cOMBK_1857069011e_bool P) Q) P))) (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.hAPP_s1806633685e_bool (tptp.hAPP_f1863945078e_bool tptp.cOMBK_631994958_state P) Q) P)) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.hAPP_H574424047_state (tptp.hAPP_H280516760_state (tptp.hAPP_b993469484_state tptp.if_Hoa443228806_state tptp.fTrue) X) Y) X)) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.hAPP_H574424047_state (tptp.hAPP_H280516760_state (tptp.hAPP_b993469484_state tptp.if_Hoa443228806_state tptp.fFalse) X) Y) Y)) (forall ((P $$unsorted)) (=> (tptp.is_bool P) (or (= P tptp.fTrue) (= P tptp.fFalse)))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP_H242767318e_bool (tptp.hAPP_H216526335e_bool tptp.fequal1440809015_state X) Y))) (= X Y))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_H242767318e_bool (tptp.hAPP_H216526335e_bool tptp.fequal1440809015_state X) Y)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_pname_com (tptp.hAPP_f96342628me_com (tptp.cOMBB_923936821_pname P) Q) R) (tptp.hAPP_option_com_com P (tptp.hAPP_p799580910on_com Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (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 $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_com_bool (tptp.hAPP_f1998868198m_bool (tptp.cOMBB_298914627ol_com P) Q) R) (tptp.hAPP_f990396704l_bool P (tptp.hAPP_c1396316405m_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (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 $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_c1580157610l_bool (tptp.hAPP_f954469007l_bool (tptp.cOMBB_886968260ol_com P) Q) R) (tptp.hAPP_b589554111l_bool P (tptp.hAPP_com_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (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 $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f559147733l_bool (tptp.cOMBB_307249310e_bool P) Q) R) (tptp.hAPP_bool_bool P (tptp.hAPP_f1664156314l_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (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 $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_s58564346l_bool (tptp.hAPP_f1259673775l_bool (tptp.cOMBB_188601460_state P) Q) R) (tptp.hAPP_b589554111l_bool P (tptp.hAPP_state_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (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 $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_pname_bool (tptp.hAPP_f42430548e_bool (tptp.cOMBB_530759491_pname P) Q) R) (tptp.hAPP_f1664156314l_bool P (tptp.hAPP_p61793385e_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (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 $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_pname_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f661147897e_bool tptp.cOMBC_1058051404l_bool P) Q) R) (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_s1806633685e_bool (tptp.hAPP_b1095269219e_bool (tptp.hAPP_f701449317e_bool tptp.cOMBC_471052088e_bool P) Q) R) (tptp.hAPP_b2019457360e_bool (tptp.hAPP_s1874344717e_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool (tptp.hAPP_f2082757169l_bool tptp.cOMBC_1004116266e_bool P) Q) R) (tptp.hAPP_pname_bool (tptp.hAPP_f759274231e_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (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 $$unsorted) (Q $$unsorted)) (= (tptp.hAPP_H46530577te_com (tptp.hAPP_c57939194te_com tptp.cOMBK_131063602_state P) Q) P)) (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.hAPP_c1455475371_state (tptp.hAPP_H275587026_state tptp.cOMBK_869602456te_com P) Q) P)) (forall ((P $$unsorted) (Q $$unsorted)) (=> (tptp.is_bool P) (= (tptp.hAPP_H242767318e_bool (tptp.hAPP_b974863576e_bool tptp.cOMBK_988866959_state P) Q) P))) (forall ((P $$unsorted) (Q $$unsorted)) (=> (tptp.is_pname P) (= (tptp.hAPP_H1193503499_pname (tptp.hAPP_p1227118702_pname tptp.cOMBK_497473068_state P) Q) P))) (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.hAPP_p1751618853_state (tptp.hAPP_H1938877132_state tptp.cOMBK_2086841362_pname P) Q) P)) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.fequal1475827639e_bool X) Y))) (= X Y))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.fequal1475827639e_bool X) Y)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_p799580910on_com (tptp.hAPP_f2123220539on_com (tptp.hAPP_f1673966486on_com tptp.cOMBS_904531235on_com P) Q) R) (tptp.hAPP_o356497025on_com (tptp.hAPP_p1086945780on_com P R) (tptp.hAPP_p799580910on_com Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_com_bool (tptp.hAPP_H313059897m_bool (tptp.hAPP_f235185669m_bool tptp.cOMBC_114640782e_bool P) Q) R) (tptp.hAPP_H242767318e_bool (tptp.hAPP_c1311333443e_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_p1751618853_state (tptp.hAPP_f1377420673_state (tptp.cOMBB_271860050_pname P) Q) R) (tptp.hAPP_c1455475371_state P (tptp.hAPP_pname_com Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H242767318e_bool (tptp.hAPP_f806699093e_bool (tptp.cOMBB_325909978_state P) Q) R) (tptp.hAPP_bool_bool P (tptp.hAPP_H242767318e_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H242767318e_bool (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1702629984e_bool tptp.cOMBS_865875691l_bool P) Q) R) (tptp.hAPP_bool_bool (tptp.hAPP_H1270401638l_bool P R) (tptp.hAPP_H242767318e_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (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 $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_pname_bool (tptp.hAPP_H1776011827e_bool (tptp.hAPP_f343137017e_bool tptp.cOMBC_19854728e_bool P) Q) R) (tptp.hAPP_H242767318e_bool (tptp.hAPP_p606792009e_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H242767318e_bool (tptp.hAPP_p606792009e_bool (tptp.hAPP_f1720171569e_bool tptp.cOMBC_1952686190e_bool P) Q) R) (tptp.hAPP_pname_bool (tptp.hAPP_H1776011827e_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f1476298914l_bool (tptp.hAPP_f143162813l_bool (tptp.cOMBB_2095475776e_bool P) Q) R) (tptp.hAPP_b589554111l_bool P (tptp.hAPP_f1664156314l_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (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 $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1385420507e_bool (tptp.cOMBB_598082538e_bool P) Q) R) (tptp.hAPP_p61793385e_bool P (tptp.hAPP_f1297739591_pname Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (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 $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_s1806633685e_bool (tptp.hAPP_f1863945078e_bool (tptp.hAPP_f915354021e_bool tptp.cOMBC_952831051e_bool P) Q) R) (tptp.hAPP_f1759915619e_bool (tptp.hAPP_s1226857760e_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted)) (=> (tptp.is_bool P) (= (tptp.hAPP_f1378282496l_bool (tptp.hAPP_b167205134l_bool tptp.cOMBK_293339231e_bool P) Q) P))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (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 $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f734420447l_bool (tptp.cOMBB_1686148692e_bool P) Q) R) (tptp.hAPP_bool_bool P (tptp.hAPP_f1378282496l_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H1270401638l_bool (tptp.hAPP_f832587837l_bool (tptp.cOMBB_1291456124_state P) Q) R) (tptp.hAPP_b589554111l_bool P (tptp.hAPP_H242767318e_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f734420447l_bool (tptp.hAPP_f524831474l_bool tptp.cOMBS_1162100051l_bool P) Q) R) (tptp.hAPP_bool_bool (tptp.hAPP_f2067558332l_bool P R) (tptp.hAPP_f1378282496l_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_pname_bool (tptp.hAPP_f1083669085e_bool (tptp.hAPP_f568104217e_bool tptp.cOMBC_1757633998l_bool P) Q) R) (tptp.hAPP_f1378282496l_bool (tptp.hAPP_p1235466077l_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H242767318e_bool (tptp.hAPP_f360545851e_bool (tptp.hAPP_f591683433e_bool tptp.cOMBC_1984545208l_bool P) Q) R) (tptp.hAPP_f1664156314l_bool (tptp.hAPP_H358531139l_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (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 $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f1664156314l_bool (tptp.hAPP_H358531139l_bool (tptp.hAPP_f1186253673l_bool tptp.cOMBC_1836455480e_bool P) Q) R) (tptp.hAPP_H242767318e_bool (tptp.hAPP_f360545851e_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f1378282496l_bool (tptp.hAPP_p1235466077l_bool (tptp.hAPP_f780571929l_bool tptp.cOMBC_1558112230e_bool P) Q) R) (tptp.hAPP_pname_bool (tptp.hAPP_f1083669085e_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H1776011827e_bool (tptp.hAPP_f777604691e_bool (tptp.cOMBB_1365368614_state P) Q) R) (tptp.hAPP_p61793385e_bool P (tptp.hAPP_H1193503499_pname Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (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 $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_p338031245l_bool (tptp.hAPP_f567934427l_bool (tptp.cOMBB_408569982_pname P) Q) R) (tptp.hAPP_f434788991l_bool P (tptp.hAPP_p61793385e_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (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 $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool (tptp.hAPP_f182188835e_bool tptp.cOMBC_1880008793e_bool P) Q) R) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (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 $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_s1806633685e_bool (tptp.hAPP_f1935169308e_bool (tptp.cOMBB_1036740637_state P) Q) R) (tptp.hAPP_f1012183542e_bool P (tptp.hAPP_s336103912e_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (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 $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H242767318e_bool (tptp.hAPP_H216526335e_bool (tptp.hAPP_f1902016361e_bool tptp.cOMBC_1967329268e_bool P) Q) R) (tptp.hAPP_H242767318e_bool (tptp.hAPP_H216526335e_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_p1751618853_state (tptp.hAPP_f1343550633_state (tptp.hAPP_f799842582_state tptp.cOMBS_853737105_state P) Q) R) (tptp.hAPP_H574424047_state (tptp.hAPP_p1947457250_state P R) (tptp.hAPP_p1751618853_state Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f2067558332l_bool (tptp.hAPP_f118042163l_bool (tptp.cOMBB_1749019442e_bool P) Q) R) (tptp.hAPP_b589554111l_bool P (tptp.hAPP_f1378282496l_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (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 $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f1083669085e_bool (tptp.hAPP_f700046015e_bool (tptp.cOMBB_1400714760e_bool P) Q) R) (tptp.hAPP_p61793385e_bool P (tptp.hAPP_f88366945_pname Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_p1751618853_state (tptp.hAPP_f914896950_state (tptp.hAPP_f1811131990_state tptp.cOMBS_1524960158_state P) Q) R) (tptp.hAPP_f497755132_state (tptp.hAPP_p1331349103_state P R) (tptp.hAPP_p1637813682e_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool (tptp.hAPP_f1879335953l_bool tptp.cOMBC_7971162l_bool P) Q) R) (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (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 $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_p905327722e_bool (tptp.hAPP_f647826488e_bool (tptp.cOMBB_1919352417_pname P) Q) R) (tptp.hAPP_f1388330588e_bool P (tptp.hAPP_p61793385e_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (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 $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_c1311333443e_bool (tptp.hAPP_f475997903e_bool (tptp.cOMBB_1327031172ol_com P) Q) R) (tptp.hAPP_H216526335e_bool P (tptp.hAPP_c1455475371_state Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H242767318e_bool (tptp.hAPP_f1900156034e_bool (tptp.cOMBB_1282391997_state P) Q) R) (tptp.hAPP_f1378282496l_bool P (tptp.hAPP_H216526335e_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H242767318e_bool (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1184122441e_bool tptp.cOMBC_538205282l_bool P) Q) R) (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool (tptp.hAPP_f1463049441l_bool tptp.cOMBC_754402940e_bool P) Q) R) (tptp.hAPP_H242767318e_bool (tptp.hAPP_f806699093e_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_p606792009e_bool (tptp.hAPP_f472107739e_bool (tptp.cOMBB_181781758_pname P) Q) R) (tptp.hAPP_H216526335e_bool P (tptp.hAPP_p1751618853_state Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H358531139l_bool (tptp.hAPP_f381060343l_bool (tptp.cOMBB_1631414076_state P) Q) R) (tptp.hAPP_f434788991l_bool P (tptp.hAPP_H1776011827e_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_p1331349103_state (tptp.hAPP_f460309545_state (tptp.hAPP_f1922754332_state tptp.cOMBS_1020065803_state P) Q) R) (tptp.hAPP_c27135337_state (tptp.hAPP_p357103842_state P R) (tptp.hAPP_pname_com Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f1218207411_state (tptp.hAPP_f819036232_state (tptp.hAPP_f815143704_state tptp.cOMBS_858986606_state P) Q) R) (tptp.hAPP_f497755132_state (tptp.hAPP_f1867816801_state P R) (tptp.hAPP_f887530048e_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f434788991l_bool (tptp.hAPP_f417341722l_bool (tptp.hAPP_f836143551l_bool tptp.cOMBC_772615479l_bool P) Q) R) (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (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 $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool (tptp.hAPP_f1348212993l_bool tptp.cOMBC_1350613978l_bool P) Q) R) (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f360545851e_bool (tptp.hAPP_f2113567599e_bool (tptp.cOMBB_1724041344e_bool P) Q) R) (tptp.hAPP_H216526335e_bool P (tptp.hAPP_f1218207411_state Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_p606792009e_bool (tptp.hAPP_f103229774e_bool (tptp.hAPP_f376349141e_bool tptp.cOMBC_59067399e_bool P) Q) R) (tptp.hAPP_f806699093e_bool (tptp.hAPP_p105983054e_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f1867816801_state (tptp.hAPP_f240260249_state (tptp.hAPP_f578932784_state tptp.cOMBS_384351451_state P) Q) R) (tptp.hAPP_c27135337_state (tptp.hAPP_f2099268820_state P R) (tptp.hAPP_f792846925ol_com Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool (tptp.hAPP_f1477350485l_bool tptp.cOMBC_694979519l_bool P) Q) R) (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H216526335e_bool (tptp.hAPP_f596278895e_bool (tptp.cOMBB_1563888316_state P) Q) R) (tptp.hAPP_H216526335e_bool P (tptp.hAPP_H574424047_state Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_p1947457250_state (tptp.hAPP_f1655792756_state (tptp.hAPP_f2119427284_state tptp.cOMBS_140201078_state P) Q) R) (tptp.hAPP_H280516760_state (tptp.hAPP_p1159359355_state P R) (tptp.hAPP_p1751618853_state Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f734420447l_bool (tptp.hAPP_f1236719585l_bool tptp.cOMBC_1484018740l_bool P) Q) R) (tptp.hAPP_f1410040974l_bool (tptp.hAPP_f631019661l_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_p1235466077l_bool (tptp.hAPP_f1143533991l_bool (tptp.cOMBB_949755692_pname P) Q) R) (tptp.hAPP_f849457489l_bool P (tptp.hAPP_p606792009e_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f718417177_state (tptp.hAPP_f578501918_state (tptp.hAPP_f886846002_state tptp.cOMBS_57685138_state P) Q) R) (tptp.hAPP_f497755132_state (tptp.hAPP_f1554347387_state P R) (tptp.hAPP_f1487042470e_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f610934515e_bool (tptp.cOMBB_1840094962e_bool P) Q) R) (tptp.hAPP_H216526335e_bool P (tptp.hAPP_f718417177_state Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H216526335e_bool (tptp.hAPP_f874203478e_bool (tptp.hAPP_f1802364479e_bool tptp.cOMBC_1229155955e_bool P) Q) R) (tptp.hAPP_f806699093e_bool (tptp.hAPP_H1902130436e_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_p1159359355_state (tptp.hAPP_f1836930278_state (tptp.cOMBB_143651633_pname P) Q) R) (tptp.hAPP_b993469484_state P (tptp.hAPP_pname_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f1410040974l_bool (tptp.hAPP_f1516997247l_bool (tptp.hAPP_f1901243753l_bool tptp.cOMBC_991209188l_bool P) Q) R) (tptp.hAPP_f1410040974l_bool (tptp.hAPP_f1516997247l_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f1554347387_state (tptp.hAPP_f824259881_state (tptp.hAPP_f37848848_state tptp.cOMBS_1164062463_state P) Q) R) (tptp.hAPP_c27135337_state (tptp.hAPP_f403544558_state P R) (tptp.hAPP_f1547517799ol_com Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_p357103842_state (tptp.hAPP_f804744487_state (tptp.cOMBB_2084106034_pname P) Q) R) (tptp.hAPP_f274181323_state P (tptp.hAPP_p1637813682e_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f1320879424l_bool (tptp.hAPP_f1149191722l_bool (tptp.cOMBB_631815671e_bool P) Q) R) (tptp.hAPP_f230953622l_bool P (tptp.hAPP_f434788991l_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H2039996199l_bool (tptp.hAPP_f1191357267l_bool (tptp.cOMBB_639263758_state P) Q) R) (tptp.hAPP_f849457489l_bool P (tptp.hAPP_H216526335e_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool (tptp.hAPP_f2061951445e_bool tptp.cOMBC_528733435e_bool P) Q) R) (tptp.hAPP_f806699093e_bool (tptp.hAPP_f1794460506e_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_p105983054e_bool (tptp.hAPP_f2028971360e_bool (tptp.cOMBB_667059641_pname P) Q) R) (tptp.hAPP_H1902130436e_bool P (tptp.hAPP_p1751618853_state Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f2099268820_state (tptp.hAPP_f1633046421_state (tptp.cOMBB_1794358604e_bool P) Q) R) (tptp.hAPP_f274181323_state P (tptp.hAPP_f887530048e_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f849457489l_bool (tptp.hAPP_f2059879088l_bool (tptp.hAPP_f476955937l_bool tptp.cOMBC_1639502213l_bool P) Q) R) (tptp.hAPP_f734420447l_bool (tptp.hAPP_f1472090462l_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f403544558_state (tptp.hAPP_f250550847_state (tptp.cOMBB_2049797414e_bool P) Q) R) (tptp.hAPP_f274181323_state P (tptp.hAPP_f1487042470e_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H1902130436e_bool (tptp.hAPP_f241329646e_bool (tptp.cOMBB_604855927_state P) Q) R) (tptp.hAPP_f1794460506e_bool P (tptp.hAPP_H216526335e_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f734420447l_bool (tptp.hAPP_f1847120l_bool (tptp.hAPP_f1573805579l_bool tptp.cOMBC_1377256501l_bool P) Q) R) (tptp.hAPP_f734420447l_bool (tptp.hAPP_f1847120l_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f1472090462l_bool (tptp.hAPP_f1316144452l_bool (tptp.cOMBB_494346593e_bool P) Q) R) (tptp.hAPP_f1847120l_bool P (tptp.hAPP_f849457489l_bool Q R)))) _let_11 _let_10 (tptp.hBOOL (tptp.hAPP_f1378282496l_bool tptp.finite694102371_state tptp.fa)) (not (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_H2039996199l_bool tptp.member1667945571_state _let_1) tptp.fa))) (tptp.hBOOL (tptp.hAPP_f1378282496l_bool (tptp.hAPP_f849457489l_bool tptp.ord_le1449778818e_bool tptp.fa) (tptp.hAPP_f360545851e_bool (tptp.image_185131637_state (tptp.hAPP_f1377420673_state _let_4 (tptp.hAPP_f96342628me_com (tptp.cOMBB_923936821_pname tptp.the_com) tptp.body))) _let_3))) _let_9 (tptp.hBOOL (tptp.hAPP_f1378282496l_bool _let_6 tptp.fa)) _let_8 true)))))))))))))))))))))))))))))))))))))))
% 2.77/3.00  )
% 2.77/3.00  % SZS output end Proof for SWW474+3
% 2.77/3.00  % cvc5---1.0.5 exiting
% 2.77/3.01  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------