TSTP Solution File: SWW473_3 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWW473_3 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n003.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 00:21:06 EDT 2023
% Result : Theorem 3.59s 3.85s
% Output : Proof 3.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.32 % Problem : SWW473_3 : TPTP v8.1.2. Released v5.3.0.
% 0.11/0.33 % Command : do_cvc5 %s %d
% 0.32/0.54 % Computer : n003.cluster.edu
% 0.32/0.54 % Model : x86_64 x86_64
% 0.32/0.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.32/0.54 % Memory : 8042.1875MB
% 0.32/0.54 % OS : Linux 3.10.0-693.el7.x86_64
% 0.32/0.54 % CPULimit : 300
% 0.32/0.54 % WCLimit : 300
% 0.32/0.54 % DateTime : Sun Aug 27 19:51:10 EDT 2023
% 0.32/0.54 % CPUTime :
% 0.52/0.88 %----Proving TF0_NAR, FOF, or CNF
% 3.59/3.85 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.3AmjMsMH3l/cvc5---1.0.5_10862.p...
% 3.59/3.85 ------- get file name : TPTP file name is SWW473_3
% 3.59/3.85 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_10862.smt2...
% 3.59/3.85 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 3.59/3.85 % SZS status Theorem for SWW473_3
% 3.59/3.85 % SZS output start Proof for SWW473_3
% 3.59/3.85 (
% 3.59/3.85 (let ((_let_1 (tptp.image_pname_a tptp.mgt_call tptp.u))) (let ((_let_2 (tptp.hAPP_pname_a tptp.mgt_call tptp.pn))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool (tptp.hAPP_f2050579477a_bool (tptp.hAPP_a1206381875a_bool tptp.insert_a _let_2) tptp.g)) _let_1)))) (let ((_let_4 (not _let_3))) (let ((_let_5 (tptp.hAPP_a85458249l_bool tptp.member_a _let_2))) (let ((_let_6 (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname tptp.pn) tptp.u)))) (let ((_let_7 (tptp.hAPP_nat_nat tptp.suc tptp.na))) (let ((_let_8 (tptp.hAPP_fun_a_bool_nat tptp.finite_card_a _let_1))) (let ((_let_9 (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool tptp.g) _let_1)))) (let ((_let_10 (tptp.bit1 tptp.pls))) (let ((_let_11 (tptp.bit1 _let_10))) (let ((_let_12 (tptp.number_number_of_int _let_11))) (let ((_let_13 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_14 (tptp.number_number_of_nat tptp.pls))) (let ((_let_15 (tptp.number_number_of_int tptp.pls))) (let ((_let_16 (tptp.number_number_of_nat _let_10))) (let ((_let_17 (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat))) (let ((_let_18 (tptp.number_number_of_nat _let_11))) (let ((_let_19 (tptp.hAPP_nat_int tptp.semiri1621563631at_int tptp.zero_zero_nat))) (let ((_let_20 (tptp.hAPP_nat_int tptp.semiri1621563631at_int tptp.one_one_nat))) (let ((_let_21 (forall ((X_1 tptp.x_a) (A tptp.fun_a_bool) (B tptp.fun_a_bool)) (= (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool (tptp.hAPP_f2050579477a_bool (tptp.hAPP_a1206381875a_bool tptp.insert_a X_1) A)) B)) (and (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a X_1) B)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool A) B))))))) (let ((_let_22 (forall ((A tptp.fun_pname_bool) (B_3 tptp.x_a) (F tptp.fun_pname_a) (X_1 tptp.pname)) (=> (= B_3 (tptp.hAPP_pname_a F X_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a B_3) (tptp.image_pname_a F A)))))))) (let ((_let_23 (forall ((A tptp.fun_pname_bool) (F tptp.fun_pname_a) (X_1 tptp.pname)) (or (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A))) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a (tptp.hAPP_pname_a F X_1)) (tptp.image_pname_a F A))))))) (let ((_let_24 (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_5 _let_1)))) (let ((_let_25 (not _let_6))) (let ((_let_26 (or _let_25 _let_24))) (let ((_let_27 (EQ_RESOLVE (ASSUME :args (_let_22)) (MACRO_SR_EQ_INTRO :args (_let_22 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_28 (not _let_26))) (let ((_let_29 (and _let_24 _let_9))) (let ((_let_30 (not _let_24))) (let ((_let_31 (= _let_3 _let_29))) (let ((_let_32 (not _let_29))) (let ((_let_33 (_let_21))) (let ((_let_34 (ASSUME :args _let_33))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_27 :args (tptp.u tptp.mgt_call tptp.pn QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a (tptp.hAPP_pname_a F X_1)) (tptp.image_pname_a F A))))) :args (_let_23))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_26)) :args ((or _let_25 _let_24 _let_28))) (ASSUME :args (_let_6)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_29)) :args ((or (not _let_9) _let_29 _let_30))) (ASSUME :args (_let_9)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_31)) :args ((or _let_3 _let_32 (not _let_31)))) (ASSUME :args (_let_4)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_34 :args (_let_2 tptp.g _let_1 QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool (tptp.hAPP_f2050579477a_bool (tptp.hAPP_a1206381875a_bool tptp.insert_a X_1) A)) B)))) :args _let_33)) _let_34 :args (_let_31 false _let_21)) :args (_let_32 true _let_3 false _let_31)) :args (_let_30 false _let_9 true _let_29)) :args (_let_28 false _let_6 true _let_24)) _let_27 :args (false true _let_26 false _let_23)) :args ((forall ((Ts tptp.fun_a_bool) (G tptp.fun_a_bool)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool Ts) G)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.p G) Ts)))) (forall ((A tptp.fun_fu819804446l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f215623910l_bool tptp.finite1395289673t_bool A)) (tptp.hBOOL (tptp.hAPP_f1593524852l_bool tptp.finite2095298929l_bool (tptp.collec1409689523l_bool (tptp.hAPP_f317860125l_bool (tptp.cOMBC_348868698l_bool tptp.ord_le1848167016l_bool) A)))))) (forall ((A tptp.fun_fu425979586l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool A)) (tptp.hBOOL (tptp.hAPP_f937997336l_bool tptp.finite1701474069l_bool (tptp.collec1015864663l_bool (tptp.hAPP_f1772781669l_bool (tptp.cOMBC_595898202l_bool tptp.ord_le1454342156l_bool) A)))))) (forall ((A tptp.fun_fu1430349052l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)) (tptp.hBOOL (tptp.hAPP_f389811538l_bool tptp.finite786885583l_bool (tptp.collec1613912337l_bool (tptp.hAPP_f510955609l_bool (tptp.cOMBC_7971162l_bool tptp.ord_le675606854l_bool) A)))))) (forall ((A tptp.fun_fun_a_bool_bool)) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool A)) (tptp.hBOOL (tptp.hAPP_f292226953l_bool tptp.finite1381704300l_bool (tptp.collec707592106l_bool (tptp.hAPP_f1434722111l_bool (tptp.cOMBC_331553030l_bool tptp.ord_le1375614389l_bool) A)))))) (forall ((A tptp.fun_a_bool)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a A)) (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool (tptp.collect_fun_a_bool (tptp.hAPP_f1631501043l_bool (tptp.cOMBC_1732670874l_bool tptp.ord_le1311769555a_bool) A)))))) (forall ((A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.collec1974731493e_bool (tptp.hAPP_f434788991l_bool (tptp.cOMBC_1284144636l_bool tptp.ord_le313189616e_bool) A)))))) (forall ((A tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool (tptp.collect_fun_nat_bool (tptp.hAPP_f103356543l_bool (tptp.cOMBC_1693257480l_bool tptp.ord_le1568362934t_bool) A)))))) (forall ((A tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (tptp.hBOOL (tptp.hAPP_f215623910l_bool tptp.finite1395289673t_bool (tptp.collect_fun_int_bool (tptp.hAPP_f284875647l_bool (tptp.cOMBC_605892544l_bool tptp.ord_le951220754t_bool) A)))))) (forall ((H tptp.fun_pn665169337t_bool) (F_1 tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname F_1)) (tptp.hBOOL (tptp.hAPP_f215623910l_bool tptp.finite1395289673t_bool (tptp.image_1512837979t_bool H F_1))))) (forall ((H tptp.fun_pn406123357t_bool) (F_1 tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname F_1)) (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool (tptp.image_2129980159t_bool H F_1))))) (forall ((H tptp.fun_pn800050071e_bool) (F_1 tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname F_1)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.image_47868345e_bool H F_1))))) (forall ((H tptp.fun_pname_fun_a_bool) (F_1 tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname F_1)) (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool (tptp.image_112932426a_bool H F_1))))) (forall ((H tptp.fun_nat_a) (F_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat F_1)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a (tptp.image_nat_a H F_1))))) (forall ((H tptp.fun_nat_fun_int_bool) (F_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat F_1)) (tptp.hBOOL (tptp.hAPP_f215623910l_bool tptp.finite1395289673t_bool (tptp.image_1556378401t_bool H F_1))))) (forall ((H tptp.fun_nat_fun_nat_bool) (F_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat F_1)) (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool (tptp.image_26036933t_bool H F_1))))) (forall ((H tptp.fun_na936072029e_bool) (F_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat F_1)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.image_1655916159e_bool H F_1))))) (forall ((H tptp.fun_nat_fun_a_bool) (F_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat F_1)) (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool (tptp.image_nat_fun_a_bool H F_1))))) (forall ((H tptp.fun_int_a) (F_1 tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int F_1)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a (tptp.image_int_a H F_1))))) (forall ((H tptp.fun_int_fun_int_bool) (F_1 tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int F_1)) (tptp.hBOOL (tptp.hAPP_f215623910l_bool tptp.finite1395289673t_bool (tptp.image_275383677t_bool H F_1))))) (forall ((H tptp.fun_int_fun_nat_bool) (F_1 tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int F_1)) (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool (tptp.image_892525857t_bool H F_1))))) (forall ((H tptp.fun_in2065004473e_bool) (F_1 tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int F_1)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.image_637364955e_bool H F_1))))) (forall ((H tptp.fun_int_fun_a_bool) (F_1 tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int F_1)) (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool (tptp.image_int_fun_a_bool H F_1))))) (forall ((H tptp.fun_a_pname) (F_1 tptp.fun_a_bool)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a F_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.image_a_pname H F_1))))) (forall ((H tptp.fun_fu953875929_pname) (F_1 tptp.fun_fu819804446l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f215623910l_bool tptp.finite1395289673t_bool F_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.image_62782965_pname H F_1))))) (forall ((H tptp.fun_fu665170229_pname) (F_1 tptp.fun_fu425979586l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool F_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.image_1921560913_pname H F_1))))) (forall ((H tptp.fun_fu1499449723_pname) (F_1 tptp.fun_fu1430349052l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool F_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.image_1283814551_pname H F_1))))) (forall ((H tptp.fun_fun_a_bool_pname) (F_1 tptp.fun_fun_a_bool_bool)) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool F_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.image_1854862208_pname H F_1))))) (forall ((H tptp.fun_a_nat) (F_1 tptp.fun_a_bool)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a F_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.image_a_nat H F_1))))) (forall ((H tptp.fun_fun_int_bool_nat) (F_1 tptp.fun_fu819804446l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f215623910l_bool tptp.finite1395289673t_bool F_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.image_1431733819ol_nat H F_1))))) (forall ((H tptp.fun_fun_nat_bool_nat) (F_1 tptp.fun_fu425979586l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool F_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.image_496248727ol_nat H F_1))))) (forall ((H tptp.fun_fu1668467777ol_nat) (F_1 tptp.fun_fu1430349052l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool F_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.image_1551609309ol_nat H F_1))))) (forall ((H tptp.fun_fun_a_bool_nat) (F_1 tptp.fun_fun_a_bool_bool)) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool F_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.image_fun_a_bool_nat H F_1))))) (forall ((H tptp.fun_a_int) (F_1 tptp.fun_a_bool)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a F_1)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.image_a_int H F_1))))) (forall ((H tptp.fun_fun_int_bool_int) (F_1 tptp.fun_fu819804446l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f215623910l_bool tptp.finite1395289673t_bool F_1)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.image_2069007511ol_int H F_1))))) (forall ((H tptp.fun_fun_nat_bool_int) (F_1 tptp.fun_fu425979586l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool F_1)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.image_1133522419ol_int H F_1))))) (forall ((H tptp.fun_fu1830380701ol_int) (F_1 tptp.fun_fu1430349052l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool F_1)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.image_41399353ol_int H F_1))))) (forall ((H tptp.fun_fun_a_bool_int) (F_1 tptp.fun_fun_a_bool_bool)) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool F_1)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.image_fun_a_bool_int H F_1))))) (forall ((H tptp.fun_pname_a) (F_1 tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname F_1)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a (tptp.image_pname_a H F_1))))) (forall ((H tptp.fun_nat_int) (F_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat F_1)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.image_nat_int H F_1))))) (forall ((A_2 tptp.fun_int_bool) (A tptp.fun_fu819804446l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f215623910l_bool tptp.finite1395289673t_bool A)) (tptp.hBOOL (tptp.hAPP_f215623910l_bool tptp.finite1395289673t_bool (tptp.hAPP_f1948010709l_bool (tptp.hAPP_f587666462l_bool tptp.insert_fun_int_bool A_2) A))))) (forall ((A_2 tptp.fun_nat_bool) (A tptp.fun_fu425979586l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool A)) (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool (tptp.hAPP_f1246832597l_bool (tptp.hAPP_f633452666l_bool tptp.insert_fun_nat_bool A_2) A))))) (forall ((A_2 tptp.fun_pname_bool) (A tptp.fun_fu1430349052l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool A_2) A))))) (forall ((A_2 tptp.fun_a_bool) (A tptp.fun_fun_a_bool_bool)) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool A)) (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool (tptp.hAPP_f2117159681l_bool (tptp.hAPP_f1531278575l_bool tptp.insert_fun_a_bool A_2) A))))) (forall ((A_2 tptp.pname) (A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A_2) A))))) (forall ((A_2 tptp.nat) (A tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_2) A))))) (forall ((A_2 tptp.int) (A tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_2) A))))) (forall ((A_2 tptp.x_a) (A tptp.fun_a_bool)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a A)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a (tptp.hAPP_f2050579477a_bool (tptp.hAPP_a1206381875a_bool tptp.insert_a A_2) A))))) (forall ((F tptp.fun_pname_pname) (A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f921600141ol_nat tptp.finite_card_pname (tptp.image_pname_pname F A))) (tptp.hAPP_f921600141ol_nat tptp.finite_card_pname A))))) (forall ((F tptp.fun_a_a) (A tptp.fun_a_bool)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a A)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_fun_a_bool_nat tptp.finite_card_a (tptp.image_a_a F A))) (tptp.hAPP_fun_a_bool_nat tptp.finite_card_a A))))) (forall ((F tptp.fun_fun_int_bool_a) (A tptp.fun_fu819804446l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f215623910l_bool tptp.finite1395289673t_bool A)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_fun_a_bool_nat tptp.finite_card_a (tptp.image_fun_int_bool_a F A))) (tptp.hAPP_f521865025ol_nat tptp.finite1876863882t_bool A))))) (forall ((F tptp.fun_fun_nat_bool_a) (A tptp.fun_fu425979586l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool A)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_fun_a_bool_nat tptp.finite_card_a (tptp.image_fun_nat_bool_a F A))) (tptp.hAPP_f696928925ol_nat tptp.finite346522414t_bool A))))) (forall ((F tptp.fun_fun_pname_bool_a) (A tptp.fun_fu1430349052l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_fun_a_bool_nat tptp.finite_card_a (tptp.image_876012084bool_a F A))) (tptp.hAPP_f55526627ol_nat tptp.finite1340463720e_bool A))))) (forall ((F tptp.fun_fun_a_bool_a) (A tptp.fun_fun_a_bool_bool)) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool A)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_fun_a_bool_nat tptp.finite_card_a (tptp.image_fun_a_bool_a F A))) (tptp.hAPP_f2009550088ol_nat tptp.finite1306199131a_bool A))))) (forall ((F tptp.fun_pname_nat) (A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat (tptp.image_pname_nat F A))) (tptp.hAPP_f921600141ol_nat tptp.finite_card_pname A))))) (forall ((F tptp.fun_a_nat) (A tptp.fun_a_bool)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a A)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat (tptp.image_a_nat F A))) (tptp.hAPP_fun_a_bool_nat tptp.finite_card_a A))))) (forall ((F tptp.fun_fun_int_bool_nat) (A tptp.fun_fu819804446l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f215623910l_bool tptp.finite1395289673t_bool A)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat (tptp.image_1431733819ol_nat F A))) (tptp.hAPP_f521865025ol_nat tptp.finite1876863882t_bool A))))) (forall ((F tptp.fun_fun_nat_bool_nat) (A tptp.fun_fu425979586l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool A)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat (tptp.image_496248727ol_nat F A))) (tptp.hAPP_f696928925ol_nat tptp.finite346522414t_bool A))))) (forall ((F tptp.fun_fu1668467777ol_nat) (A tptp.fun_fu1430349052l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat (tptp.image_1551609309ol_nat F A))) (tptp.hAPP_f55526627ol_nat tptp.finite1340463720e_bool A))))) (forall ((F tptp.fun_fun_a_bool_nat) (A tptp.fun_fun_a_bool_bool)) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool A)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat (tptp.image_fun_a_bool_nat F A))) (tptp.hAPP_f2009550088ol_nat tptp.finite1306199131a_bool A))))) (forall ((F tptp.fun_pname_int) (A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f957591787ol_nat tptp.finite_card_int (tptp.image_pname_int F A))) (tptp.hAPP_f921600141ol_nat tptp.finite_card_pname A))))) (forall ((F tptp.fun_a_int) (A tptp.fun_a_bool)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a A)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f957591787ol_nat tptp.finite_card_int (tptp.image_a_int F A))) (tptp.hAPP_fun_a_bool_nat tptp.finite_card_a A))))) (forall ((F tptp.fun_fun_int_bool_int) (A tptp.fun_fu819804446l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f215623910l_bool tptp.finite1395289673t_bool A)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f957591787ol_nat tptp.finite_card_int (tptp.image_2069007511ol_int F A))) (tptp.hAPP_f521865025ol_nat tptp.finite1876863882t_bool A))))) (forall ((F tptp.fun_fun_nat_bool_int) (A tptp.fun_fu425979586l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool A)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f957591787ol_nat tptp.finite_card_int (tptp.image_1133522419ol_int F A))) (tptp.hAPP_f696928925ol_nat tptp.finite346522414t_bool A))))) (forall ((F tptp.fun_fu1830380701ol_int) (A tptp.fun_fu1430349052l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f957591787ol_nat tptp.finite_card_int (tptp.image_41399353ol_int F A))) (tptp.hAPP_f55526627ol_nat tptp.finite1340463720e_bool A))))) (forall ((F tptp.fun_fun_a_bool_int) (A tptp.fun_fun_a_bool_bool)) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool A)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f957591787ol_nat tptp.finite_card_int (tptp.image_fun_a_bool_int F A))) (tptp.hAPP_f2009550088ol_nat tptp.finite1306199131a_bool A))))) (forall ((F tptp.fun_a_pname) (A tptp.fun_a_bool)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a A)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f921600141ol_nat tptp.finite_card_pname (tptp.image_a_pname F A))) (tptp.hAPP_fun_a_bool_nat tptp.finite_card_a A))))) (forall ((F tptp.fun_nat_pname) (A tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f921600141ol_nat tptp.finite_card_pname (tptp.image_nat_pname F A))) (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat A))))) (forall ((F tptp.fun_int_pname) (A tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f921600141ol_nat tptp.finite_card_pname (tptp.image_int_pname F A))) (tptp.hAPP_f957591787ol_nat tptp.finite_card_int A))))) (forall ((F tptp.fun_pname_a) (A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_fun_a_bool_nat tptp.finite_card_a (tptp.image_pname_a F A))) (tptp.hAPP_f921600141ol_nat tptp.finite_card_pname A))))) (forall ((F tptp.fun_nat_int) (A tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f957591787ol_nat tptp.finite_card_int (tptp.image_nat_int F A))) (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat A))))) (forall ((A tptp.fun_fu819804446l_bool) (B tptp.fun_fu819804446l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f215623910l_bool tptp.finite1395289673t_bool B)) (=> (tptp.hBOOL (tptp.hAPP_f215623910l_bool (tptp.hAPP_f317860125l_bool tptp.ord_le1848167016l_bool A) B)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f521865025ol_nat tptp.finite1876863882t_bool A)) (tptp.hAPP_f521865025ol_nat tptp.finite1876863882t_bool B)))))) (forall ((A tptp.fun_fu425979586l_bool) (B tptp.fun_fu425979586l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool B)) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool (tptp.hAPP_f1772781669l_bool tptp.ord_le1454342156l_bool A) B)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f696928925ol_nat tptp.finite346522414t_bool A)) (tptp.hAPP_f696928925ol_nat tptp.finite346522414t_bool B)))))) (forall ((A tptp.fun_fu1430349052l_bool) (B tptp.fun_fu1430349052l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool B)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool A) B)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f55526627ol_nat tptp.finite1340463720e_bool A)) (tptp.hAPP_f55526627ol_nat tptp.finite1340463720e_bool B)))))) (forall ((A tptp.fun_fun_a_bool_bool) (B tptp.fun_fun_a_bool_bool)) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool B)) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool (tptp.hAPP_f1434722111l_bool tptp.ord_le1375614389l_bool A) B)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f2009550088ol_nat tptp.finite1306199131a_bool A)) (tptp.hAPP_f2009550088ol_nat tptp.finite1306199131a_bool B)))))) (forall ((A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) B)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f921600141ol_nat tptp.finite_card_pname A)) (tptp.hAPP_f921600141ol_nat tptp.finite_card_pname B)))))) (forall ((A tptp.fun_a_bool) (B tptp.fun_a_bool)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a B)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool A) B)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_fun_a_bool_nat tptp.finite_card_a A)) (tptp.hAPP_fun_a_bool_nat tptp.finite_card_a B)))))) (forall ((A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat B)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) B)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat A)) (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat B)))))) (forall ((A tptp.fun_int_bool) (B tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int B)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A) B)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f957591787ol_nat tptp.finite_card_int A)) (tptp.hAPP_f957591787ol_nat tptp.finite_card_int B)))))) (forall ((A tptp.fun_fu819804446l_bool) (B tptp.fun_fu819804446l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f215623910l_bool tptp.finite1395289673t_bool B)) (=> (tptp.hBOOL (tptp.hAPP_f215623910l_bool (tptp.hAPP_f317860125l_bool tptp.ord_le1848167016l_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f521865025ol_nat tptp.finite1876863882t_bool B)) (tptp.hAPP_f521865025ol_nat tptp.finite1876863882t_bool A))) (= A B))))) (forall ((A tptp.fun_fu425979586l_bool) (B tptp.fun_fu425979586l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool B)) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool (tptp.hAPP_f1772781669l_bool tptp.ord_le1454342156l_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f696928925ol_nat tptp.finite346522414t_bool B)) (tptp.hAPP_f696928925ol_nat tptp.finite346522414t_bool A))) (= A B))))) (forall ((A tptp.fun_fu1430349052l_bool) (B tptp.fun_fu1430349052l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool B)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f55526627ol_nat tptp.finite1340463720e_bool B)) (tptp.hAPP_f55526627ol_nat tptp.finite1340463720e_bool A))) (= A B))))) (forall ((A tptp.fun_fun_a_bool_bool) (B tptp.fun_fun_a_bool_bool)) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool B)) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool (tptp.hAPP_f1434722111l_bool tptp.ord_le1375614389l_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f2009550088ol_nat tptp.finite1306199131a_bool B)) (tptp.hAPP_f2009550088ol_nat tptp.finite1306199131a_bool A))) (= A B))))) (forall ((A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f921600141ol_nat tptp.finite_card_pname B)) (tptp.hAPP_f921600141ol_nat tptp.finite_card_pname A))) (= A B))))) (forall ((A tptp.fun_a_bool) (B tptp.fun_a_bool)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a B)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_fun_a_bool_nat tptp.finite_card_a B)) (tptp.hAPP_fun_a_bool_nat tptp.finite_card_a A))) (= A B))))) (forall ((A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat B)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat B)) (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat A))) (= A B))))) (forall ((A tptp.fun_int_bool) (B tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int B)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f957591787ol_nat tptp.finite_card_int B)) (tptp.hAPP_f957591787ol_nat tptp.finite_card_int A))) (= A B))))) (forall ((X_1 tptp.fun_int_bool) (A tptp.fun_fu819804446l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f215623910l_bool tptp.finite1395289673t_bool A)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f521865025ol_nat tptp.finite1876863882t_bool A)) (tptp.hAPP_f521865025ol_nat tptp.finite1876863882t_bool (tptp.hAPP_f1948010709l_bool (tptp.hAPP_f587666462l_bool tptp.insert_fun_int_bool X_1) A)))))) (forall ((X_1 tptp.fun_nat_bool) (A tptp.fun_fu425979586l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool A)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f696928925ol_nat tptp.finite346522414t_bool A)) (tptp.hAPP_f696928925ol_nat tptp.finite346522414t_bool (tptp.hAPP_f1246832597l_bool (tptp.hAPP_f633452666l_bool tptp.insert_fun_nat_bool X_1) A)))))) (forall ((X_1 tptp.fun_pname_bool) (A tptp.fun_fu1430349052l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f55526627ol_nat tptp.finite1340463720e_bool A)) (tptp.hAPP_f55526627ol_nat tptp.finite1340463720e_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool X_1) A)))))) (forall ((X_1 tptp.fun_a_bool) (A tptp.fun_fun_a_bool_bool)) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool A)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f2009550088ol_nat tptp.finite1306199131a_bool A)) (tptp.hAPP_f2009550088ol_nat tptp.finite1306199131a_bool (tptp.hAPP_f2117159681l_bool (tptp.hAPP_f1531278575l_bool tptp.insert_fun_a_bool X_1) A)))))) (forall ((X_1 tptp.pname) (A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f921600141ol_nat tptp.finite_card_pname A)) (tptp.hAPP_f921600141ol_nat tptp.finite_card_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1) A)))))) (forall ((X_1 tptp.nat) (A tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat A)) (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) A)))))) (forall ((X_1 tptp.int) (A tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f957591787ol_nat tptp.finite_card_int A)) (tptp.hAPP_f957591787ol_nat tptp.finite_card_int (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1) A)))))) (forall ((X_1 tptp.x_a) (A tptp.fun_a_bool)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a A)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_fun_a_bool_nat tptp.finite_card_a A)) (tptp.hAPP_fun_a_bool_nat tptp.finite_card_a (tptp.hAPP_f2050579477a_bool (tptp.hAPP_a1206381875a_bool tptp.insert_a X_1) A)))))) (forall ((X_1 tptp.fun_int_bool) (A tptp.fun_fu819804446l_bool)) (let ((_let_1 (tptp.hAPP_f521865025ol_nat tptp.finite1876863882t_bool A))) (let ((_let_2 (tptp.hAPP_f521865025ol_nat tptp.finite1876863882t_bool (tptp.hAPP_f1948010709l_bool (tptp.hAPP_f587666462l_bool tptp.insert_fun_int_bool X_1) A)))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP_f215623910l_bool (tptp.hAPP_f628503027l_bool tptp.member_fun_int_bool X_1) A)))) (=> (tptp.hBOOL (tptp.hAPP_f215623910l_bool tptp.finite1395289673t_bool A)) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (tptp.hAPP_nat_nat tptp.suc _let_1))))))))) (forall ((X_1 tptp.fun_nat_bool) (A tptp.fun_fu425979586l_bool)) (let ((_let_1 (tptp.hAPP_f696928925ol_nat tptp.finite346522414t_bool A))) (let ((_let_2 (tptp.hAPP_f696928925ol_nat tptp.finite346522414t_bool (tptp.hAPP_f1246832597l_bool (tptp.hAPP_f633452666l_bool tptp.insert_fun_nat_bool X_1) A)))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP_f1637334154l_bool (tptp.hAPP_f1951378235l_bool tptp.member_fun_nat_bool X_1) A)))) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool A)) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (tptp.hAPP_nat_nat tptp.suc _let_1))))))))) (forall ((X_1 tptp.fun_pname_bool) (A tptp.fun_fu1430349052l_bool)) (let ((_let_1 (tptp.hAPP_f55526627ol_nat tptp.finite1340463720e_bool A))) (let ((_let_2 (tptp.hAPP_f55526627ol_nat tptp.finite1340463720e_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool X_1) A)))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool X_1) A)))) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (tptp.hAPP_nat_nat tptp.suc _let_1))))))))) (forall ((X_1 tptp.fun_a_bool) (A tptp.fun_fun_a_bool_bool)) (let ((_let_1 (tptp.hAPP_f2009550088ol_nat tptp.finite1306199131a_bool A))) (let ((_let_2 (tptp.hAPP_f2009550088ol_nat tptp.finite1306199131a_bool (tptp.hAPP_f2117159681l_bool (tptp.hAPP_f1531278575l_bool tptp.insert_fun_a_bool X_1) A)))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP_f621171935l_bool (tptp.hAPP_f285962445l_bool tptp.member_fun_a_bool X_1) A)))) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool A)) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (tptp.hAPP_nat_nat tptp.suc _let_1))))))))) (forall ((X_1 tptp.pname) (A tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f921600141ol_nat tptp.finite_card_pname A))) (let ((_let_2 (tptp.hAPP_f921600141ol_nat tptp.finite_card_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1) A)))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A)))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (tptp.hAPP_nat_nat tptp.suc _let_1))))))))) (forall ((X_1 tptp.nat) (A tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat A))) (let ((_let_2 (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) A)))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (tptp.hAPP_nat_nat tptp.suc _let_1))))))))) (forall ((X_1 tptp.int) (A tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_f957591787ol_nat tptp.finite_card_int A))) (let ((_let_2 (tptp.hAPP_f957591787ol_nat tptp.finite_card_int (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1) A)))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A)))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (tptp.hAPP_nat_nat tptp.suc _let_1))))))))) (forall ((X_1 tptp.x_a) (A tptp.fun_a_bool)) (let ((_let_1 (tptp.hAPP_fun_a_bool_nat tptp.finite_card_a A))) (let ((_let_2 (tptp.hAPP_fun_a_bool_nat tptp.finite_card_a (tptp.hAPP_f2050579477a_bool (tptp.hAPP_a1206381875a_bool tptp.insert_a X_1) A)))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a X_1) A)))) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a A)) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (tptp.hAPP_nat_nat tptp.suc _let_1))))))))) (forall ((X_1 tptp.fun_int_bool) (A tptp.fun_fu819804446l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f215623910l_bool tptp.finite1395289673t_bool A)) (=> (not (tptp.hBOOL (tptp.hAPP_f215623910l_bool (tptp.hAPP_f628503027l_bool tptp.member_fun_int_bool X_1) A))) (= (tptp.hAPP_f521865025ol_nat tptp.finite1876863882t_bool (tptp.hAPP_f1948010709l_bool (tptp.hAPP_f587666462l_bool tptp.insert_fun_int_bool X_1) A)) (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_f521865025ol_nat tptp.finite1876863882t_bool A)))))) (forall ((X_1 tptp.fun_nat_bool) (A tptp.fun_fu425979586l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool A)) (=> (not (tptp.hBOOL (tptp.hAPP_f1637334154l_bool (tptp.hAPP_f1951378235l_bool tptp.member_fun_nat_bool X_1) A))) (= (tptp.hAPP_f696928925ol_nat tptp.finite346522414t_bool (tptp.hAPP_f1246832597l_bool (tptp.hAPP_f633452666l_bool tptp.insert_fun_nat_bool X_1) A)) (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_f696928925ol_nat tptp.finite346522414t_bool A)))))) (forall ((X_1 tptp.fun_pname_bool) (A tptp.fun_fu1430349052l_bool)) (=> (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_f55526627ol_nat tptp.finite1340463720e_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool X_1) A)) (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_f55526627ol_nat tptp.finite1340463720e_bool A)))))) (forall ((X_1 tptp.fun_a_bool) (A tptp.fun_fun_a_bool_bool)) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool A)) (=> (not (tptp.hBOOL (tptp.hAPP_f621171935l_bool (tptp.hAPP_f285962445l_bool tptp.member_fun_a_bool X_1) A))) (= (tptp.hAPP_f2009550088ol_nat tptp.finite1306199131a_bool (tptp.hAPP_f2117159681l_bool (tptp.hAPP_f1531278575l_bool tptp.insert_fun_a_bool X_1) A)) (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_f2009550088ol_nat tptp.finite1306199131a_bool A)))))) (forall ((X_1 tptp.pname) (A tptp.fun_pname_bool)) (=> (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_f921600141ol_nat tptp.finite_card_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1) A)) (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_f921600141ol_nat tptp.finite_card_pname A)))))) (forall ((X_1 tptp.nat) (A tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A))) (= (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) A)) (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat A)))))) (forall ((X_1 tptp.int) (A tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (=> (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A))) (= (tptp.hAPP_f957591787ol_nat tptp.finite_card_int (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1) A)) (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_f957591787ol_nat tptp.finite_card_int A)))))) (forall ((X_1 tptp.x_a) (A tptp.fun_a_bool)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a A)) (=> (not (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a X_1) A))) (= (tptp.hAPP_fun_a_bool_nat tptp.finite_card_a (tptp.hAPP_f2050579477a_bool (tptp.hAPP_a1206381875a_bool tptp.insert_a X_1) A)) (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_fun_a_bool_nat tptp.finite_card_a A)))))) (forall ((Q_3 tptp.fun_a_bool) (Pa tptp.fun_a_bool)) (=> (or (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a (tptp.collect_a Pa))) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a (tptp.collect_a Q_3)))) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a (tptp.collect_a (tptp.cOMBS_a_bool_bool (tptp.cOMBB_1972296269bool_a tptp.fconj Pa) Q_3)))))) (forall ((Q_3 tptp.fun_fu819804446l_bool) (Pa tptp.fun_fu819804446l_bool)) (=> (or (tptp.hBOOL (tptp.hAPP_f215623910l_bool tptp.finite1395289673t_bool (tptp.collect_fun_int_bool Pa))) (tptp.hBOOL (tptp.hAPP_f215623910l_bool tptp.finite1395289673t_bool (tptp.collect_fun_int_bool Q_3)))) (tptp.hBOOL (tptp.hAPP_f215623910l_bool tptp.finite1395289673t_bool (tptp.collect_fun_int_bool (tptp.cOMBS_1912792529l_bool (tptp.cOMBB_1974511970t_bool tptp.fconj Pa) Q_3)))))) (forall ((Q_3 tptp.fun_fu425979586l_bool) (Pa tptp.fun_fu425979586l_bool)) (=> (or (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool (tptp.collect_fun_nat_bool Pa))) (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool (tptp.collect_fun_nat_bool Q_3)))) (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool (tptp.collect_fun_nat_bool (tptp.cOMBS_1187019125l_bool (tptp.cOMBB_444170502t_bool tptp.fconj Pa) Q_3)))))) (forall ((Q_3 tptp.fun_fu1430349052l_bool) (Pa tptp.fun_fu1430349052l_bool)) (=> (or (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.collec1974731493e_bool Pa))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.collec1974731493e_bool Q_3)))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.collec1974731493e_bool (tptp.cOMBS_350070575l_bool (tptp.cOMBB_2095475776e_bool tptp.fconj Pa) Q_3)))))) (forall ((Q_3 tptp.fun_fun_a_bool_bool) (Pa tptp.fun_fun_a_bool_bool)) (=> (or (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool (tptp.collect_fun_a_bool Pa))) (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool (tptp.collect_fun_a_bool Q_3)))) (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool (tptp.collect_fun_a_bool (tptp.cOMBS_1035972772l_bool (tptp.cOMBB_338059395a_bool tptp.fconj Pa) Q_3)))))) (forall ((Q_3 tptp.fun_pname_bool) (Pa tptp.fun_pname_bool)) (=> (or (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.collect_pname Pa))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.collect_pname Q_3)))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.collect_pname (tptp.cOMBS_568398431l_bool (tptp.cOMBB_675860798_pname tptp.fconj Pa) Q_3)))))) (forall ((Q_3 tptp.fun_nat_bool) (Pa tptp.fun_nat_bool)) (=> (or (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.collect_nat Pa))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.collect_nat Q_3)))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.cOMBS_nat_bool_bool (tptp.cOMBB_1015721476ol_nat tptp.fconj Pa) Q_3)))))) (forall ((Q_3 tptp.fun_int_bool) (Pa tptp.fun_int_bool)) (=> (or (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.collect_int Pa))) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.collect_int Q_3)))) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.collect_int (tptp.cOMBS_int_bool_bool (tptp.cOMBB_1652995168ol_int tptp.fconj Pa) Q_3)))))) (forall ((N tptp.nat) (M_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N) M_1)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat tptp.suc M_1)) N) (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M_1) N))))) (forall ((K tptp.nat)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.hAPP_n1699378549t_bool (tptp.cOMBC_nat_nat_bool tptp.ord_less_eq_nat) K))))) (forall ((Na tptp.nat)) (= (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat (tptp.collect_nat (tptp.hAPP_n1699378549t_bool (tptp.cOMBC_nat_nat_bool tptp.ord_less_eq_nat) Na))) (tptp.hAPP_nat_nat tptp.suc Na))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (= (tptp.hAPP_nat_nat tptp.suc X) (tptp.hAPP_nat_nat tptp.suc Y)) (= X Y))) (forall ((Nat_3 tptp.nat) (Nat_4 tptp.nat)) (= (= (tptp.hAPP_nat_nat tptp.suc Nat_3) (tptp.hAPP_nat_nat tptp.suc Nat_4)) (= Nat_3 Nat_4))) (forall ((N tptp.nat)) (not (= (tptp.hAPP_nat_nat tptp.suc N) N))) (forall ((N tptp.nat)) (not (= N (tptp.hAPP_nat_nat tptp.suc N)))) (forall ((M_1 tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_1) N)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N) M_1)) (= M_1 N)))) (forall ((K_1 tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 J)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat J) K_1)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 K_1)))))) (forall ((M_1 tptp.nat) (N tptp.nat)) (=> (= M_1 N) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_1) N)))) (forall ((M_1 tptp.nat) (N tptp.nat)) (or (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_1) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N) M_1)))) (forall ((N tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N) N))) (forall ((I_1 tptp.nat) (J tptp.nat) (K_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat I_1))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat _let_1 J)) K_1) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat _let_1 K_1)) J)))) (forall ((Pa tptp.fun_a_bool) (Q_3 tptp.fun_a_bool)) (= (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a (tptp.collect_a (tptp.cOMBS_a_bool_bool (tptp.cOMBB_1972296269bool_a tptp.fdisj Pa) Q_3)))) (and (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a (tptp.collect_a Pa))) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a (tptp.collect_a Q_3)))))) (forall ((Pa tptp.fun_fu819804446l_bool) (Q_3 tptp.fun_fu819804446l_bool)) (= (tptp.hBOOL (tptp.hAPP_f215623910l_bool tptp.finite1395289673t_bool (tptp.collect_fun_int_bool (tptp.cOMBS_1912792529l_bool (tptp.cOMBB_1974511970t_bool tptp.fdisj Pa) Q_3)))) (and (tptp.hBOOL (tptp.hAPP_f215623910l_bool tptp.finite1395289673t_bool (tptp.collect_fun_int_bool Pa))) (tptp.hBOOL (tptp.hAPP_f215623910l_bool tptp.finite1395289673t_bool (tptp.collect_fun_int_bool Q_3)))))) (forall ((Pa tptp.fun_fu425979586l_bool) (Q_3 tptp.fun_fu425979586l_bool)) (= (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool (tptp.collect_fun_nat_bool (tptp.cOMBS_1187019125l_bool (tptp.cOMBB_444170502t_bool tptp.fdisj Pa) Q_3)))) (and (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool (tptp.collect_fun_nat_bool Pa))) (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool (tptp.collect_fun_nat_bool Q_3)))))) (forall ((Pa tptp.fun_fu1430349052l_bool) (Q_3 tptp.fun_fu1430349052l_bool)) (= (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.collec1974731493e_bool (tptp.cOMBS_350070575l_bool (tptp.cOMBB_2095475776e_bool tptp.fdisj Pa) Q_3)))) (and (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.collec1974731493e_bool Pa))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.collec1974731493e_bool Q_3)))))) (forall ((Pa tptp.fun_fun_a_bool_bool) (Q_3 tptp.fun_fun_a_bool_bool)) (= (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool (tptp.collect_fun_a_bool (tptp.cOMBS_1035972772l_bool (tptp.cOMBB_338059395a_bool tptp.fdisj Pa) Q_3)))) (and (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool (tptp.collect_fun_a_bool Pa))) (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool (tptp.collect_fun_a_bool Q_3)))))) (forall ((Pa tptp.fun_pname_bool) (Q_3 tptp.fun_pname_bool)) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.collect_pname (tptp.cOMBS_568398431l_bool (tptp.cOMBB_675860798_pname tptp.fdisj Pa) Q_3)))) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.collect_pname Pa))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.collect_pname Q_3)))))) (forall ((Pa tptp.fun_nat_bool) (Q_3 tptp.fun_nat_bool)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.cOMBS_nat_bool_bool (tptp.cOMBB_1015721476ol_nat tptp.fdisj Pa) Q_3)))) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.collect_nat Pa))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.collect_nat Q_3)))))) (forall ((Pa tptp.fun_int_bool) (Q_3 tptp.fun_int_bool)) (= (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.collect_int (tptp.cOMBS_int_bool_bool (tptp.cOMBB_1652995168ol_int tptp.fdisj Pa) Q_3)))) (and (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.collect_int Pa))) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.collect_int Q_3)))))) (forall ((A_2 tptp.fun_int_bool) (A tptp.fun_fu819804446l_bool)) (= (tptp.hBOOL (tptp.hAPP_f215623910l_bool tptp.finite1395289673t_bool (tptp.hAPP_f1948010709l_bool (tptp.hAPP_f587666462l_bool tptp.insert_fun_int_bool A_2) A))) (tptp.hBOOL (tptp.hAPP_f215623910l_bool tptp.finite1395289673t_bool A)))) (forall ((A_2 tptp.fun_nat_bool) (A tptp.fun_fu425979586l_bool)) (= (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool (tptp.hAPP_f1246832597l_bool (tptp.hAPP_f633452666l_bool tptp.insert_fun_nat_bool A_2) A))) (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool A)))) (forall ((A_2 tptp.fun_pname_bool) (A tptp.fun_fu1430349052l_bool)) (= (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool A_2) A))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)))) (forall ((A_2 tptp.fun_a_bool) (A tptp.fun_fun_a_bool_bool)) (= (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool (tptp.hAPP_f2117159681l_bool (tptp.hAPP_f1531278575l_bool tptp.insert_fun_a_bool A_2) A))) (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool A)))) (forall ((A_2 tptp.pname) (A tptp.fun_pname_bool)) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A_2) A))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)))) (forall ((A_2 tptp.nat) (A tptp.fun_nat_bool)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_2) A))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)))) (forall ((A_2 tptp.int) (A tptp.fun_int_bool)) (= (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_2) A))) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)))) (forall ((A_2 tptp.x_a) (A tptp.fun_a_bool)) (= (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a (tptp.hAPP_f2050579477a_bool (tptp.hAPP_a1206381875a_bool tptp.insert_a A_2) A))) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a A)))) (forall ((A tptp.fun_fu819804446l_bool) (B tptp.fun_fu819804446l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f215623910l_bool (tptp.hAPP_f317860125l_bool tptp.ord_le1848167016l_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f215623910l_bool tptp.finite1395289673t_bool B)) (tptp.hBOOL (tptp.hAPP_f215623910l_bool tptp.finite1395289673t_bool A))))) (forall ((A tptp.fun_fu425979586l_bool) (B tptp.fun_fu425979586l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool (tptp.hAPP_f1772781669l_bool tptp.ord_le1454342156l_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool B)) (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool A))))) (forall ((A tptp.fun_fu1430349052l_bool) (B tptp.fun_fu1430349052l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool B)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A))))) (forall ((A tptp.fun_fun_a_bool_bool) (B tptp.fun_fun_a_bool_bool)) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool (tptp.hAPP_f1434722111l_bool tptp.ord_le1375614389l_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool B)) (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool A))))) (forall ((A tptp.fun_a_bool) (B tptp.fun_a_bool)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a B)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a A))))) (forall ((A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A))))) (forall ((A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat B)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A))))) (forall ((A tptp.fun_int_bool) (B tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int B)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A))))) (forall ((A tptp.fun_fu819804446l_bool) (B tptp.fun_fu819804446l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f215623910l_bool tptp.finite1395289673t_bool B)) (=> (tptp.hBOOL (tptp.hAPP_f215623910l_bool (tptp.hAPP_f317860125l_bool tptp.ord_le1848167016l_bool A) B)) (tptp.hBOOL (tptp.hAPP_f215623910l_bool tptp.finite1395289673t_bool A))))) (forall ((A tptp.fun_fu425979586l_bool) (B tptp.fun_fu425979586l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool B)) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool (tptp.hAPP_f1772781669l_bool tptp.ord_le1454342156l_bool A) B)) (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool A))))) (forall ((A tptp.fun_fu1430349052l_bool) (B tptp.fun_fu1430349052l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool B)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool A) B)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A))))) (forall ((A tptp.fun_fun_a_bool_bool) (B tptp.fun_fun_a_bool_bool)) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool B)) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool (tptp.hAPP_f1434722111l_bool tptp.ord_le1375614389l_bool A) B)) (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool A))))) (forall ((A tptp.fun_a_bool) (B tptp.fun_a_bool)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a B)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool A) B)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a A))))) (forall ((A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) B)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A))))) (forall ((A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat B)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) B)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A))))) (forall ((A tptp.fun_int_bool) (B tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int B)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A) B)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A))))) (forall ((M_1 tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat tptp.suc M_1)) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_1) N)))) (forall ((M_1 tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat tptp.suc N))) (let ((_let_2 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 _let_1)) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 N))) (= M_1 _let_1)))))) (forall ((M_1 tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat tptp.suc N)))))) (forall ((Na tptp.nat) (M tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat tptp.suc Na)) (tptp.hAPP_nat_nat tptp.suc M))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Na) M)))) (forall ((M tptp.nat) (Na tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat tptp.suc Na))) (let ((_let_2 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M))) (= (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 _let_1)) (or (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 Na)) (= M _let_1)))))) (forall ((M tptp.nat) (Na tptp.nat)) (= (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) Na))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat tptp.suc Na)) M)))) (forall ((N tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat tptp.suc N)) N)))) (forall ((M_1 tptp.nat) (N tptp.nat) (K_1 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat tptp.suc M_1)) N)) (tptp.hAPP_nat_nat tptp.suc K_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M_1) N)) K_1))) (forall ((M_1 tptp.nat) (N tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat tptp.suc M_1)) (tptp.hAPP_nat_nat tptp.suc N)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M_1) N))) (forall ((Na tptp.nat) (K tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Na)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M) K)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat Na) K))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) Na))))))) (forall ((N tptp.nat) (K_1 tptp.nat) (M_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M_1))) (let ((_let_2 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 M_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 N)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat _let_1 K_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N) K_1)) (tptp.hAPP_nat_nat _let_1 N))))))) (forall ((Na tptp.nat) (K tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Na)) (= (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M) K) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat Na) K)) (= M Na)))))) (forall ((I_1 tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_1) N)) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat _let_1 I_1)) I_1)))) (forall ((L_1 tptp.nat) (M_1 tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_1) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M_1) L_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N) L_1))))) (forall ((L_1 tptp.nat) (M_1 tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat L_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_1) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 N)) (tptp.hAPP_nat_nat _let_1 M_1)))))) (forall ((M_1 tptp.nat) (N tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M_1) N)) M_1))) (forall ((B tptp.fun_a_bool) (F tptp.fun_a_a) (A tptp.fun_a_bool)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a A)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool B) (tptp.image_a_a F A))) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a B))))) (forall ((B tptp.fun_a_bool) (F tptp.fun_fun_int_bool_a) (A tptp.fun_fu819804446l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f215623910l_bool tptp.finite1395289673t_bool A)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool B) (tptp.image_fun_int_bool_a F A))) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a B))))) (forall ((B tptp.fun_a_bool) (F tptp.fun_fun_nat_bool_a) (A tptp.fun_fu425979586l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool A)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool B) (tptp.image_fun_nat_bool_a F A))) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a B))))) (forall ((B tptp.fun_a_bool) (F tptp.fun_fun_pname_bool_a) (A tptp.fun_fu1430349052l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool B) (tptp.image_876012084bool_a F A))) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a B))))) (forall ((B tptp.fun_a_bool) (F tptp.fun_fun_a_bool_a) (A tptp.fun_fun_a_bool_bool)) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool A)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool B) (tptp.image_fun_a_bool_a F A))) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a B))))) (forall ((B tptp.fun_fu819804446l_bool) (F tptp.fun_pn665169337t_bool) (A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (=> (tptp.hBOOL (tptp.hAPP_f215623910l_bool (tptp.hAPP_f317860125l_bool tptp.ord_le1848167016l_bool B) (tptp.image_1512837979t_bool F A))) (tptp.hBOOL (tptp.hAPP_f215623910l_bool tptp.finite1395289673t_bool B))))) (forall ((B tptp.fun_fu425979586l_bool) (F tptp.fun_pn406123357t_bool) (A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool (tptp.hAPP_f1772781669l_bool tptp.ord_le1454342156l_bool B) (tptp.image_2129980159t_bool F A))) (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool B))))) (forall ((B tptp.fun_fu1430349052l_bool) (F tptp.fun_pn800050071e_bool) (A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool B) (tptp.image_47868345e_bool F A))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool B))))) (forall ((B tptp.fun_fun_a_bool_bool) (F tptp.fun_pname_fun_a_bool) (A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool (tptp.hAPP_f1434722111l_bool tptp.ord_le1375614389l_bool B) (tptp.image_112932426a_bool F A))) (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool B))))) (forall ((B tptp.fun_pname_bool) (F tptp.fun_pname_pname) (A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) (tptp.image_pname_pname F A))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B))))) (forall ((B tptp.fun_a_bool) (F tptp.fun_nat_a) (A tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool B) (tptp.image_nat_a F A))) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a B))))) (forall ((B tptp.fun_fu819804446l_bool) (F tptp.fun_nat_fun_int_bool) (A tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (tptp.hBOOL (tptp.hAPP_f215623910l_bool (tptp.hAPP_f317860125l_bool tptp.ord_le1848167016l_bool B) (tptp.image_1556378401t_bool F A))) (tptp.hBOOL (tptp.hAPP_f215623910l_bool tptp.finite1395289673t_bool B))))) (forall ((B tptp.fun_fu425979586l_bool) (F tptp.fun_nat_fun_nat_bool) (A tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool (tptp.hAPP_f1772781669l_bool tptp.ord_le1454342156l_bool B) (tptp.image_26036933t_bool F A))) (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool B))))) (forall ((B tptp.fun_fu1430349052l_bool) (F tptp.fun_na936072029e_bool) (A tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool B) (tptp.image_1655916159e_bool F A))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool B))))) (forall ((B tptp.fun_fun_a_bool_bool) (F tptp.fun_nat_fun_a_bool) (A tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool (tptp.hAPP_f1434722111l_bool tptp.ord_le1375614389l_bool B) (tptp.image_nat_fun_a_bool F A))) (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool B))))) (forall ((B tptp.fun_pname_bool) (F tptp.fun_nat_pname) (A tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) (tptp.image_nat_pname F A))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B))))) (forall ((B tptp.fun_a_bool) (F tptp.fun_int_a) (A tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool B) (tptp.image_int_a F A))) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a B))))) (forall ((B tptp.fun_fu819804446l_bool) (F tptp.fun_int_fun_int_bool) (A tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (=> (tptp.hBOOL (tptp.hAPP_f215623910l_bool (tptp.hAPP_f317860125l_bool tptp.ord_le1848167016l_bool B) (tptp.image_275383677t_bool F A))) (tptp.hBOOL (tptp.hAPP_f215623910l_bool tptp.finite1395289673t_bool B))))) (forall ((B tptp.fun_fu425979586l_bool) (F tptp.fun_int_fun_nat_bool) (A tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool (tptp.hAPP_f1772781669l_bool tptp.ord_le1454342156l_bool B) (tptp.image_892525857t_bool F A))) (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool B))))) (forall ((B tptp.fun_fu1430349052l_bool) (F tptp.fun_in2065004473e_bool) (A tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool B) (tptp.image_637364955e_bool F A))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool B))))) (forall ((B tptp.fun_fun_a_bool_bool) (F tptp.fun_int_fun_a_bool) (A tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool (tptp.hAPP_f1434722111l_bool tptp.ord_le1375614389l_bool B) (tptp.image_int_fun_a_bool F A))) (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool B))))) (forall ((B tptp.fun_pname_bool) (F tptp.fun_int_pname) (A tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) (tptp.image_int_pname F A))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B))))) (forall ((B tptp.fun_pname_bool) (F tptp.fun_a_pname) (A tptp.fun_a_bool)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a A)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) (tptp.image_a_pname F A))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B))))) (forall ((B tptp.fun_pname_bool) (F tptp.fun_fu953875929_pname) (A tptp.fun_fu819804446l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f215623910l_bool tptp.finite1395289673t_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) (tptp.image_62782965_pname F A))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B))))) (forall ((B tptp.fun_pname_bool) (F tptp.fun_fu665170229_pname) (A tptp.fun_fu425979586l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) (tptp.image_1921560913_pname F A))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B))))) (forall ((B tptp.fun_pname_bool) (F tptp.fun_fu1499449723_pname) (A tptp.fun_fu1430349052l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) (tptp.image_1283814551_pname F A))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B))))) (forall ((B tptp.fun_pname_bool) (F tptp.fun_fun_a_bool_pname) (A tptp.fun_fun_a_bool_bool)) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) (tptp.image_1854862208_pname F A))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B))))) (forall ((B tptp.fun_nat_bool) (F tptp.fun_a_nat) (A tptp.fun_a_bool)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a A)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool B) (tptp.image_a_nat F A))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat B))))) (forall ((B tptp.fun_nat_bool) (F tptp.fun_fun_int_bool_nat) (A tptp.fun_fu819804446l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f215623910l_bool tptp.finite1395289673t_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool B) (tptp.image_1431733819ol_nat F A))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat B))))) (forall ((B tptp.fun_nat_bool) (F tptp.fun_fun_nat_bool_nat) (A tptp.fun_fu425979586l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool B) (tptp.image_496248727ol_nat F A))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat B))))) (forall ((B tptp.fun_nat_bool) (F tptp.fun_fu1668467777ol_nat) (A tptp.fun_fu1430349052l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool B) (tptp.image_1551609309ol_nat F A))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat B))))) (forall ((B tptp.fun_nat_bool) (F tptp.fun_fun_a_bool_nat) (A tptp.fun_fun_a_bool_bool)) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool B) (tptp.image_fun_a_bool_nat F A))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat B))))) (forall ((B tptp.fun_int_bool) (F tptp.fun_a_int) (A tptp.fun_a_bool)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a A)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool B) (tptp.image_a_int F A))) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int B))))) (forall ((B tptp.fun_int_bool) (F tptp.fun_fun_int_bool_int) (A tptp.fun_fu819804446l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f215623910l_bool tptp.finite1395289673t_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool B) (tptp.image_2069007511ol_int F A))) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int B))))) (forall ((B tptp.fun_int_bool) (F tptp.fun_fun_nat_bool_int) (A tptp.fun_fu425979586l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool B) (tptp.image_1133522419ol_int F A))) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int B))))) (forall ((B tptp.fun_int_bool) (F tptp.fun_fu1830380701ol_int) (A tptp.fun_fu1430349052l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool B) (tptp.image_41399353ol_int F A))) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int B))))) (forall ((B tptp.fun_int_bool) (F tptp.fun_fun_a_bool_int) (A tptp.fun_fun_a_bool_bool)) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool B) (tptp.image_fun_a_bool_int F A))) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int B))))) (forall ((B tptp.fun_a_bool) (F tptp.fun_pname_a) (A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool B) (tptp.image_pname_a F A))) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a B))))) (forall ((B tptp.fun_int_bool) (F tptp.fun_nat_int) (A tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool B) (tptp.image_nat_int F A))) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int B))))) (forall ((F tptp.fun_fun_int_bool_a) (A tptp.fun_fu819804446l_bool) (B tptp.fun_a_bool)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a B)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool B) (tptp.image_fun_int_bool_a F A))) (exists ((C_16 tptp.fun_fu819804446l_bool)) (and (tptp.hBOOL (tptp.hAPP_f215623910l_bool (tptp.hAPP_f317860125l_bool tptp.ord_le1848167016l_bool C_16) A)) (tptp.hBOOL (tptp.hAPP_f215623910l_bool tptp.finite1395289673t_bool C_16)) (= B (tptp.image_fun_int_bool_a F C_16))))))) (forall ((F tptp.fun_fun_nat_bool_a) (A tptp.fun_fu425979586l_bool) (B tptp.fun_a_bool)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a B)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool B) (tptp.image_fun_nat_bool_a F A))) (exists ((C_16 tptp.fun_fu425979586l_bool)) (and (tptp.hBOOL (tptp.hAPP_f1637334154l_bool (tptp.hAPP_f1772781669l_bool tptp.ord_le1454342156l_bool C_16) A)) (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool C_16)) (= B (tptp.image_fun_nat_bool_a F C_16))))))) (forall ((F tptp.fun_fun_pname_bool_a) (A tptp.fun_fu1430349052l_bool) (B tptp.fun_a_bool)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a B)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool B) (tptp.image_876012084bool_a F A))) (exists ((C_16 tptp.fun_fu1430349052l_bool)) (and (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool C_16) A)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool C_16)) (= B (tptp.image_876012084bool_a F C_16))))))) (forall ((F tptp.fun_fun_a_bool_a) (A tptp.fun_fun_a_bool_bool) (B tptp.fun_a_bool)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a B)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool B) (tptp.image_fun_a_bool_a F A))) (exists ((C_16 tptp.fun_fun_a_bool_bool)) (and (tptp.hBOOL (tptp.hAPP_f621171935l_bool (tptp.hAPP_f1434722111l_bool tptp.ord_le1375614389l_bool C_16) A)) (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool C_16)) (= B (tptp.image_fun_a_bool_a F C_16))))))) (forall ((F tptp.fun_a_a) (A tptp.fun_a_bool) (B tptp.fun_a_bool)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a B)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool B) (tptp.image_a_a F A))) (exists ((C_16 tptp.fun_a_bool)) (and (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool C_16) A)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a C_16)) (= B (tptp.image_a_a F C_16))))))) (forall ((F tptp.fun_a_fun_int_bool) (A tptp.fun_a_bool) (B tptp.fun_fu819804446l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f215623910l_bool tptp.finite1395289673t_bool B)) (=> (tptp.hBOOL (tptp.hAPP_f215623910l_bool (tptp.hAPP_f317860125l_bool tptp.ord_le1848167016l_bool B) (tptp.image_a_fun_int_bool F A))) (exists ((C_16 tptp.fun_a_bool)) (and (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool C_16) A)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a C_16)) (= B (tptp.image_a_fun_int_bool F C_16))))))) (forall ((F tptp.fun_a_fun_nat_bool) (A tptp.fun_a_bool) (B tptp.fun_fu425979586l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool B)) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool (tptp.hAPP_f1772781669l_bool tptp.ord_le1454342156l_bool B) (tptp.image_a_fun_nat_bool F A))) (exists ((C_16 tptp.fun_a_bool)) (and (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool C_16) A)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a C_16)) (= B (tptp.image_a_fun_nat_bool F C_16))))))) (forall ((F tptp.fun_a_fun_pname_bool) (A tptp.fun_a_bool) (B tptp.fun_fu1430349052l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool B)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool B) (tptp.image_819518260e_bool F A))) (exists ((C_16 tptp.fun_a_bool)) (and (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool C_16) A)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a C_16)) (= B (tptp.image_819518260e_bool F C_16))))))) (forall ((F tptp.fun_a_fun_a_bool) (A tptp.fun_a_bool) (B tptp.fun_fun_a_bool_bool)) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool B)) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool (tptp.hAPP_f1434722111l_bool tptp.ord_le1375614389l_bool B) (tptp.image_a_fun_a_bool F A))) (exists ((C_16 tptp.fun_a_bool)) (and (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool C_16) A)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a C_16)) (= B (tptp.image_a_fun_a_bool F C_16))))))) (forall ((F tptp.fun_a_pname) (A tptp.fun_a_bool) (B tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) (tptp.image_a_pname F A))) (exists ((C_16 tptp.fun_a_bool)) (and (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool C_16) A)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a C_16)) (= B (tptp.image_a_pname F C_16))))))) (forall ((F tptp.fun_fu953875929_pname) (A tptp.fun_fu819804446l_bool) (B tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) (tptp.image_62782965_pname F A))) (exists ((C_16 tptp.fun_fu819804446l_bool)) (and (tptp.hBOOL (tptp.hAPP_f215623910l_bool (tptp.hAPP_f317860125l_bool tptp.ord_le1848167016l_bool C_16) A)) (tptp.hBOOL (tptp.hAPP_f215623910l_bool tptp.finite1395289673t_bool C_16)) (= B (tptp.image_62782965_pname F C_16))))))) (forall ((F tptp.fun_fu665170229_pname) (A tptp.fun_fu425979586l_bool) (B tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) (tptp.image_1921560913_pname F A))) (exists ((C_16 tptp.fun_fu425979586l_bool)) (and (tptp.hBOOL (tptp.hAPP_f1637334154l_bool (tptp.hAPP_f1772781669l_bool tptp.ord_le1454342156l_bool C_16) A)) (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool C_16)) (= B (tptp.image_1921560913_pname F C_16))))))) (forall ((F tptp.fun_fu1499449723_pname) (A tptp.fun_fu1430349052l_bool) (B tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) (tptp.image_1283814551_pname F A))) (exists ((C_16 tptp.fun_fu1430349052l_bool)) (and (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool C_16) A)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool C_16)) (= B (tptp.image_1283814551_pname F C_16))))))) (forall ((F tptp.fun_fun_a_bool_pname) (A tptp.fun_fun_a_bool_bool) (B tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) (tptp.image_1854862208_pname F A))) (exists ((C_16 tptp.fun_fun_a_bool_bool)) (and (tptp.hBOOL (tptp.hAPP_f621171935l_bool (tptp.hAPP_f1434722111l_bool tptp.ord_le1375614389l_bool C_16) A)) (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool C_16)) (= B (tptp.image_1854862208_pname F C_16))))))) (forall ((F tptp.fun_a_nat) (A tptp.fun_a_bool) (B tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat B)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool B) (tptp.image_a_nat F A))) (exists ((C_16 tptp.fun_a_bool)) (and (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool C_16) A)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a C_16)) (= B (tptp.image_a_nat F C_16))))))) (forall ((F tptp.fun_fun_int_bool_nat) (A tptp.fun_fu819804446l_bool) (B tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat B)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool B) (tptp.image_1431733819ol_nat F A))) (exists ((C_16 tptp.fun_fu819804446l_bool)) (and (tptp.hBOOL (tptp.hAPP_f215623910l_bool (tptp.hAPP_f317860125l_bool tptp.ord_le1848167016l_bool C_16) A)) (tptp.hBOOL (tptp.hAPP_f215623910l_bool tptp.finite1395289673t_bool C_16)) (= B (tptp.image_1431733819ol_nat F C_16))))))) (forall ((F tptp.fun_fun_nat_bool_nat) (A tptp.fun_fu425979586l_bool) (B tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat B)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool B) (tptp.image_496248727ol_nat F A))) (exists ((C_16 tptp.fun_fu425979586l_bool)) (and (tptp.hBOOL (tptp.hAPP_f1637334154l_bool (tptp.hAPP_f1772781669l_bool tptp.ord_le1454342156l_bool C_16) A)) (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool C_16)) (= B (tptp.image_496248727ol_nat F C_16))))))) (forall ((F tptp.fun_fu1668467777ol_nat) (A tptp.fun_fu1430349052l_bool) (B tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat B)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool B) (tptp.image_1551609309ol_nat F A))) (exists ((C_16 tptp.fun_fu1430349052l_bool)) (and (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool C_16) A)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool C_16)) (= B (tptp.image_1551609309ol_nat F C_16))))))) (forall ((F tptp.fun_fun_a_bool_nat) (A tptp.fun_fun_a_bool_bool) (B tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat B)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool B) (tptp.image_fun_a_bool_nat F A))) (exists ((C_16 tptp.fun_fun_a_bool_bool)) (and (tptp.hBOOL (tptp.hAPP_f621171935l_bool (tptp.hAPP_f1434722111l_bool tptp.ord_le1375614389l_bool C_16) A)) (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool C_16)) (= B (tptp.image_fun_a_bool_nat F C_16))))))) (forall ((F tptp.fun_pname_nat) (A tptp.fun_pname_bool) (B tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat B)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool B) (tptp.image_pname_nat F A))) (exists ((C_16 tptp.fun_pname_bool)) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool C_16) A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname C_16)) (= B (tptp.image_pname_nat F C_16))))))) (forall ((F tptp.fun_a_int) (A tptp.fun_a_bool) (B tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int B)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool B) (tptp.image_a_int F A))) (exists ((C_16 tptp.fun_a_bool)) (and (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool C_16) A)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a C_16)) (= B (tptp.image_a_int F C_16))))))) (forall ((F tptp.fun_fun_int_bool_int) (A tptp.fun_fu819804446l_bool) (B tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int B)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool B) (tptp.image_2069007511ol_int F A))) (exists ((C_16 tptp.fun_fu819804446l_bool)) (and (tptp.hBOOL (tptp.hAPP_f215623910l_bool (tptp.hAPP_f317860125l_bool tptp.ord_le1848167016l_bool C_16) A)) (tptp.hBOOL (tptp.hAPP_f215623910l_bool tptp.finite1395289673t_bool C_16)) (= B (tptp.image_2069007511ol_int F C_16))))))) (forall ((F tptp.fun_fun_nat_bool_int) (A tptp.fun_fu425979586l_bool) (B tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int B)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool B) (tptp.image_1133522419ol_int F A))) (exists ((C_16 tptp.fun_fu425979586l_bool)) (and (tptp.hBOOL (tptp.hAPP_f1637334154l_bool (tptp.hAPP_f1772781669l_bool tptp.ord_le1454342156l_bool C_16) A)) (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool C_16)) (= B (tptp.image_1133522419ol_int F C_16))))))) (forall ((F tptp.fun_fu1830380701ol_int) (A tptp.fun_fu1430349052l_bool) (B tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int B)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool B) (tptp.image_41399353ol_int F A))) (exists ((C_16 tptp.fun_fu1430349052l_bool)) (and (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool C_16) A)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool C_16)) (= B (tptp.image_41399353ol_int F C_16))))))) (forall ((F tptp.fun_fun_a_bool_int) (A tptp.fun_fun_a_bool_bool) (B tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int B)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool B) (tptp.image_fun_a_bool_int F A))) (exists ((C_16 tptp.fun_fun_a_bool_bool)) (and (tptp.hBOOL (tptp.hAPP_f621171935l_bool (tptp.hAPP_f1434722111l_bool tptp.ord_le1375614389l_bool C_16) A)) (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool C_16)) (= B (tptp.image_fun_a_bool_int F C_16))))))) (forall ((F tptp.fun_pname_int) (A tptp.fun_pname_bool) (B tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int B)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool B) (tptp.image_pname_int F A))) (exists ((C_16 tptp.fun_pname_bool)) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool C_16) A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname C_16)) (= B (tptp.image_pname_int F C_16))))))) (forall ((F tptp.fun_pn665169337t_bool) (A tptp.fun_pname_bool) (B tptp.fun_fu819804446l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f215623910l_bool tptp.finite1395289673t_bool B)) (=> (tptp.hBOOL (tptp.hAPP_f215623910l_bool (tptp.hAPP_f317860125l_bool tptp.ord_le1848167016l_bool B) (tptp.image_1512837979t_bool F A))) (exists ((C_16 tptp.fun_pname_bool)) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool C_16) A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname C_16)) (= B (tptp.image_1512837979t_bool F C_16))))))) (forall ((F tptp.fun_pn406123357t_bool) (A tptp.fun_pname_bool) (B tptp.fun_fu425979586l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool B)) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool (tptp.hAPP_f1772781669l_bool tptp.ord_le1454342156l_bool B) (tptp.image_2129980159t_bool F A))) (exists ((C_16 tptp.fun_pname_bool)) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool C_16) A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname C_16)) (= B (tptp.image_2129980159t_bool F C_16))))))) (forall ((F tptp.fun_pn800050071e_bool) (A tptp.fun_pname_bool) (B tptp.fun_fu1430349052l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool B)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool B) (tptp.image_47868345e_bool F A))) (exists ((C_16 tptp.fun_pname_bool)) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool C_16) A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname C_16)) (= B (tptp.image_47868345e_bool F C_16))))))) (forall ((F tptp.fun_pname_fun_a_bool) (A tptp.fun_pname_bool) (B tptp.fun_fun_a_bool_bool)) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool B)) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool (tptp.hAPP_f1434722111l_bool tptp.ord_le1375614389l_bool B) (tptp.image_112932426a_bool F A))) (exists ((C_16 tptp.fun_pname_bool)) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool C_16) A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname C_16)) (= B (tptp.image_112932426a_bool F C_16))))))) (forall ((F tptp.fun_pname_pname) (A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) (tptp.image_pname_pname F A))) (exists ((C_16 tptp.fun_pname_bool)) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool C_16) A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname C_16)) (= B (tptp.image_pname_pname F C_16))))))) (forall ((F tptp.fun_nat_a) (A tptp.fun_nat_bool) (B tptp.fun_a_bool)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a B)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool B) (tptp.image_nat_a F A))) (exists ((C_16 tptp.fun_nat_bool)) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool C_16) A)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat C_16)) (= B (tptp.image_nat_a F C_16))))))) (forall ((F tptp.fun_nat_fun_int_bool) (A tptp.fun_nat_bool) (B tptp.fun_fu819804446l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f215623910l_bool tptp.finite1395289673t_bool B)) (=> (tptp.hBOOL (tptp.hAPP_f215623910l_bool (tptp.hAPP_f317860125l_bool tptp.ord_le1848167016l_bool B) (tptp.image_1556378401t_bool F A))) (exists ((C_16 tptp.fun_nat_bool)) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool C_16) A)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat C_16)) (= B (tptp.image_1556378401t_bool F C_16))))))) (forall ((F tptp.fun_nat_fun_nat_bool) (A tptp.fun_nat_bool) (B tptp.fun_fu425979586l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool B)) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool (tptp.hAPP_f1772781669l_bool tptp.ord_le1454342156l_bool B) (tptp.image_26036933t_bool F A))) (exists ((C_16 tptp.fun_nat_bool)) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool C_16) A)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat C_16)) (= B (tptp.image_26036933t_bool F C_16))))))) (forall ((F tptp.fun_na936072029e_bool) (A tptp.fun_nat_bool) (B tptp.fun_fu1430349052l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool B)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool B) (tptp.image_1655916159e_bool F A))) (exists ((C_16 tptp.fun_nat_bool)) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool C_16) A)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat C_16)) (= B (tptp.image_1655916159e_bool F C_16))))))) (forall ((F tptp.fun_nat_fun_a_bool) (A tptp.fun_nat_bool) (B tptp.fun_fun_a_bool_bool)) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool B)) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool (tptp.hAPP_f1434722111l_bool tptp.ord_le1375614389l_bool B) (tptp.image_nat_fun_a_bool F A))) (exists ((C_16 tptp.fun_nat_bool)) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool C_16) A)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat C_16)) (= B (tptp.image_nat_fun_a_bool F C_16))))))) (forall ((F tptp.fun_nat_pname) (A tptp.fun_nat_bool) (B tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) (tptp.image_nat_pname F A))) (exists ((C_16 tptp.fun_nat_bool)) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool C_16) A)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat C_16)) (= B (tptp.image_nat_pname F C_16))))))) (forall ((F tptp.fun_int_a) (A tptp.fun_int_bool) (B tptp.fun_a_bool)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a B)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool B) (tptp.image_int_a F A))) (exists ((C_16 tptp.fun_int_bool)) (and (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool C_16) A)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int C_16)) (= B (tptp.image_int_a F C_16))))))) (forall ((F tptp.fun_int_fun_int_bool) (A tptp.fun_int_bool) (B tptp.fun_fu819804446l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f215623910l_bool tptp.finite1395289673t_bool B)) (=> (tptp.hBOOL (tptp.hAPP_f215623910l_bool (tptp.hAPP_f317860125l_bool tptp.ord_le1848167016l_bool B) (tptp.image_275383677t_bool F A))) (exists ((C_16 tptp.fun_int_bool)) (and (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool C_16) A)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int C_16)) (= B (tptp.image_275383677t_bool F C_16))))))) (forall ((F tptp.fun_int_fun_nat_bool) (A tptp.fun_int_bool) (B tptp.fun_fu425979586l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool B)) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool (tptp.hAPP_f1772781669l_bool tptp.ord_le1454342156l_bool B) (tptp.image_892525857t_bool F A))) (exists ((C_16 tptp.fun_int_bool)) (and (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool C_16) A)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int C_16)) (= B (tptp.image_892525857t_bool F C_16))))))) (forall ((F tptp.fun_in2065004473e_bool) (A tptp.fun_int_bool) (B tptp.fun_fu1430349052l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool B)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool B) (tptp.image_637364955e_bool F A))) (exists ((C_16 tptp.fun_int_bool)) (and (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool C_16) A)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int C_16)) (= B (tptp.image_637364955e_bool F C_16))))))) (forall ((F tptp.fun_int_fun_a_bool) (A tptp.fun_int_bool) (B tptp.fun_fun_a_bool_bool)) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool B)) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool (tptp.hAPP_f1434722111l_bool tptp.ord_le1375614389l_bool B) (tptp.image_int_fun_a_bool F A))) (exists ((C_16 tptp.fun_int_bool)) (and (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool C_16) A)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int C_16)) (= B (tptp.image_int_fun_a_bool F C_16))))))) (forall ((F tptp.fun_int_pname) (A tptp.fun_int_bool) (B tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) (tptp.image_int_pname F A))) (exists ((C_16 tptp.fun_int_bool)) (and (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool C_16) A)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int C_16)) (= B (tptp.image_int_pname F C_16))))))) (forall ((F tptp.fun_pname_a) (A tptp.fun_pname_bool) (B tptp.fun_a_bool)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a B)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool B) (tptp.image_pname_a F A))) (exists ((C_16 tptp.fun_pname_bool)) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool C_16) A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname C_16)) (= B (tptp.image_pname_a F C_16))))))) (forall ((F tptp.fun_nat_int) (A tptp.fun_nat_bool) (B tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int B)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool B) (tptp.image_nat_int F A))) (exists ((C_16 tptp.fun_nat_bool)) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool C_16) A)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat C_16)) (= B (tptp.image_nat_int F C_16))))))) (forall ((Na tptp.nat) (N_3 tptp.nat) (F tptp.fun_na936072029e_bool)) (=> (forall ((N_1 tptp.nat)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_n1025906991e_bool F N_1)) (tptp.hAPP_n1025906991e_bool F (tptp.hAPP_nat_nat tptp.suc N_1))))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Na) N_3)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_n1025906991e_bool F Na)) (tptp.hAPP_n1025906991e_bool F N_3)))))) (forall ((Na tptp.nat) (N_3 tptp.nat) (F tptp.fun_nat_bool)) (=> (forall ((N_1 tptp.nat)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_nat_bool F N_1)) (tptp.hAPP_nat_bool F (tptp.hAPP_nat_nat tptp.suc N_1))))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Na) N_3)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_nat_bool F Na)) (tptp.hAPP_nat_bool F N_3)))))) (forall ((Na tptp.nat) (N_3 tptp.nat) (F tptp.fun_nat_fun_a_bool)) (=> (forall ((N_1 tptp.nat)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool (tptp.hAPP_nat_fun_a_bool F N_1)) (tptp.hAPP_nat_fun_a_bool F (tptp.hAPP_nat_nat tptp.suc N_1))))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Na) N_3)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool (tptp.hAPP_nat_fun_a_bool F Na)) (tptp.hAPP_nat_fun_a_bool F N_3)))))) (forall ((Na tptp.nat) (N_3 tptp.nat) (F tptp.fun_nat_nat)) (=> (forall ((N_1 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat F N_1)) (tptp.hAPP_nat_nat F (tptp.hAPP_nat_nat tptp.suc N_1))))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Na) N_3)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat F Na)) (tptp.hAPP_nat_nat F N_3)))))) (forall ((Na tptp.nat) (N_3 tptp.nat) (F tptp.fun_nat_int)) (=> (forall ((N_1 tptp.nat)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_nat_int F N_1)) (tptp.hAPP_nat_int F (tptp.hAPP_nat_nat tptp.suc N_1))))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Na) N_3)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_nat_int F Na)) (tptp.hAPP_nat_int F N_3)))))) (forall ((Na tptp.nat) (N_3 tptp.nat) (F tptp.fun_nat_fun_nat_bool)) (=> (forall ((N_1 tptp.nat)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_n1699378549t_bool F N_1)) (tptp.hAPP_n1699378549t_bool F (tptp.hAPP_nat_nat tptp.suc N_1))))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Na) N_3)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_n1699378549t_bool F Na)) (tptp.hAPP_n1699378549t_bool F N_3)))))) (forall ((Na tptp.nat) (N_3 tptp.nat) (F tptp.fun_nat_fun_int_bool)) (=> (forall ((N_1 tptp.nat)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool (tptp.hAPP_n1082236369t_bool F N_1)) (tptp.hAPP_n1082236369t_bool F (tptp.hAPP_nat_nat tptp.suc N_1))))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Na) N_3)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool (tptp.hAPP_n1082236369t_bool F Na)) (tptp.hAPP_n1082236369t_bool F N_3)))))) (forall ((F tptp.fun_nat_fun_int_bool) (A tptp.fun_nat_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A))) (=> (tptp.hBOOL (tptp.hAPP_f215623910l_bool tptp.finite1395289673t_bool (tptp.image_1556378401t_bool F A))) (exists ((X_2 tptp.nat)) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) A)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.cOMBS_nat_bool_bool (tptp.cOMBB_1015721476ol_nat tptp.fconj (tptp.hAPP_f800510211t_bool (tptp.cOMBC_226598744l_bool tptp.member_nat) A)) (tptp.hAPP_f274826591t_bool (tptp.cOMBC_620423604l_bool (tptp.cOMBB_1123824708ol_nat tptp.fequal_fun_int_bool F)) (tptp.hAPP_n1082236369t_bool F X_2)))))))))))) (forall ((F tptp.fun_nat_fun_nat_bool) (A tptp.fun_nat_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A))) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool (tptp.image_26036933t_bool F A))) (exists ((X_2 tptp.nat)) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) A)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.cOMBS_nat_bool_bool (tptp.cOMBB_1015721476ol_nat tptp.fconj (tptp.hAPP_f800510211t_bool (tptp.cOMBC_226598744l_bool tptp.member_nat) A)) (tptp.hAPP_f800510211t_bool (tptp.cOMBC_226598744l_bool (tptp.cOMBB_2026977092ol_nat tptp.fequal_fun_nat_bool F)) (tptp.hAPP_n1699378549t_bool F X_2)))))))))))) (forall ((F tptp.fun_na936072029e_bool) (A tptp.fun_nat_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A))) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.image_1655916159e_bool F A))) (exists ((X_2 tptp.nat)) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) A)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.cOMBS_nat_bool_bool (tptp.cOMBB_1015721476ol_nat tptp.fconj (tptp.hAPP_f800510211t_bool (tptp.cOMBC_226598744l_bool tptp.member_nat) A)) (tptp.hAPP_f1066163005t_bool (tptp.cOMBC_386238098l_bool (tptp.cOMBB_2117322052ol_nat tptp.fequal533582459e_bool F)) (tptp.hAPP_n1025906991e_bool F X_2)))))))))))) (forall ((F tptp.fun_nat_fun_a_bool) (A tptp.fun_nat_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A))) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool (tptp.image_nat_fun_a_bool F A))) (exists ((X_2 tptp.nat)) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) A)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.cOMBS_nat_bool_bool (tptp.cOMBB_1015721476ol_nat tptp.fconj (tptp.hAPP_f800510211t_bool (tptp.cOMBC_226598744l_bool tptp.member_nat) A)) (tptp.hAPP_f282463732t_bool (tptp.cOMBC_1928494297l_bool (tptp.cOMBB_1823939024ol_nat tptp.fequal_fun_a_bool F)) (tptp.hAPP_nat_fun_a_bool F X_2)))))))))))) (forall ((F tptp.fun_int_a) (A tptp.fun_int_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A))) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a (tptp.image_int_a F A))) (exists ((X_2 tptp.int)) (and (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_2) A)) (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.collect_int (tptp.cOMBS_int_bool_bool (tptp.cOMBB_1652995168ol_int tptp.fconj (tptp.hAPP_f1805168059t_bool (tptp.cOMBC_94739984l_bool tptp.member_int) A)) (tptp.hAPP_a_fun_int_bool (tptp.cOMBC_int_a_bool (tptp.cOMBB_375279840ol_int tptp.fequal_a F)) (tptp.hAPP_int_a F X_2)))))))))))) (forall ((F tptp.fun_int_fun_int_bool) (A tptp.fun_int_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A))) (=> (tptp.hBOOL (tptp.hAPP_f215623910l_bool tptp.finite1395289673t_bool (tptp.image_275383677t_bool F A))) (exists ((X_2 tptp.int)) (and (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_2) A)) (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.collect_int (tptp.cOMBS_int_bool_bool (tptp.cOMBB_1652995168ol_int tptp.fconj (tptp.hAPP_f1805168059t_bool (tptp.cOMBC_94739984l_bool tptp.member_int) A)) (tptp.hAPP_f1805168059t_bool (tptp.cOMBC_94739984l_bool (tptp.cOMBB_1761098400ol_int tptp.fequal_fun_int_bool F)) (tptp.hAPP_i1948725293t_bool F X_2)))))))))))) (forall ((F tptp.fun_int_fun_nat_bool) (A tptp.fun_int_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A))) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool (tptp.image_892525857t_bool F A))) (exists ((X_2 tptp.int)) (and (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_2) A)) (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.collect_int (tptp.cOMBS_int_bool_bool (tptp.cOMBB_1652995168ol_int tptp.fconj (tptp.hAPP_f1805168059t_bool (tptp.cOMBC_94739984l_bool tptp.member_int) A)) (tptp.hAPP_f183368031t_bool (tptp.cOMBC_1848398772l_bool (tptp.cOMBB_516767136ol_int tptp.fequal_fun_nat_bool F)) (tptp.hAPP_i418383825t_bool F X_2)))))))))))) (forall ((F tptp.fun_in2065004473e_bool) (A tptp.fun_int_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A))) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.image_637364955e_bool F A))) (exists ((X_2 tptp.int)) (and (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_2) A)) (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.collect_int (tptp.cOMBS_int_bool_bool (tptp.cOMBB_1652995168ol_int tptp.fconj (tptp.hAPP_f1805168059t_bool (tptp.cOMBC_94739984l_bool tptp.member_int) A)) (tptp.hAPP_f449020825t_bool (tptp.cOMBC_316919022l_bool (tptp.cOMBB_607112096ol_int tptp.fequal533582459e_bool F)) (tptp.hAPP_i7355787e_bool F X_2)))))))))))) (forall ((F tptp.fun_int_fun_a_bool) (A tptp.fun_int_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A))) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool (tptp.image_int_fun_a_bool F A))) (exists ((X_2 tptp.int)) (and (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_2) A)) (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.collect_int (tptp.cOMBS_int_bool_bool (tptp.cOMBB_1652995168ol_int tptp.fconj (tptp.hAPP_f1805168059t_bool (tptp.cOMBC_94739984l_bool tptp.member_int) A)) (tptp.hAPP_f1812805200t_bool (tptp.cOMBC_1753430397l_bool (tptp.cOMBB_313729068ol_int tptp.fequal_fun_a_bool F)) (tptp.hAPP_int_fun_a_bool F X_2)))))))))))) (forall ((F tptp.fun_pname_a) (A tptp.fun_pname_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A))) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a (tptp.image_pname_a F A))) (exists ((X_2 tptp.pname)) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.collect_pname (tptp.cOMBS_568398431l_bool (tptp.cOMBB_675860798_pname tptp.fconj (tptp.hAPP_f759274231e_bool (tptp.cOMBC_1058051404l_bool tptp.member_pname) A)) (tptp.hAPP_a93125764e_bool (tptp.cOMBC_pname_a_bool (tptp.cOMBB_1897541054_pname tptp.fequal_a F)) (tptp.hAPP_pname_a F X_2)))))))))))) (forall ((F tptp.fun_nat_int) (A tptp.fun_nat_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.image_nat_int F A))) (exists ((X_2 tptp.nat)) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) A)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.cOMBS_nat_bool_bool (tptp.cOMBB_1015721476ol_nat tptp.fconj (tptp.hAPP_f800510211t_bool (tptp.cOMBC_226598744l_bool tptp.member_nat) A)) (tptp.hAPP_i418383825t_bool (tptp.cOMBC_nat_int_bool (tptp.cOMBB_1628441366ol_nat tptp.fequal_int F)) (tptp.hAPP_nat_int F X_2)))))))))))) (forall ((A tptp.fun_nat_bool) (B_3 tptp.int) (F tptp.fun_nat_int) (X_1 tptp.nat)) (=> (= B_3 (tptp.hAPP_nat_int F X_1)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int B_3) (tptp.image_nat_int F A)))))) _let_22 (forall ((A tptp.fun_int_bool) (B tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool B) A)) (= A B)))) (forall ((A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool B) A)) (= A B)))) (forall ((A tptp.fun_a_bool) (B tptp.fun_a_bool)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool B) A)) (= A B)))) (forall ((C_6 tptp.int) (A tptp.fun_int_bool) (B tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_i2112223885l_bool tptp.member_int C_6))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 B)))))) (forall ((C_6 tptp.nat) (A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat C_6))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B)))))) (forall ((C_6 tptp.x_a) (A tptp.fun_a_bool) (B tptp.fun_a_bool)) (let ((_let_1 (tptp.hAPP_a85458249l_bool tptp.member_a C_6))) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 B)))))) (forall ((C_6 tptp.pname) (A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname C_6))) (=> (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_3 tptp.x_a) (A_2 tptp.x_a) (B tptp.fun_a_bool)) (let ((_let_1 (tptp.hAPP_a85458249l_bool tptp.member_a A_2))) (=> (=> (not (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 B))) (= A_2 B_3)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 (tptp.hAPP_f2050579477a_bool (tptp.hAPP_a1206381875a_bool tptp.insert_a B_3) B)))))) (forall ((B_3 tptp.int) (A_2 tptp.int) (B tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_i2112223885l_bool tptp.member_int A_2))) (=> (=> (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 B))) (= A_2 B_3)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int B_3) B)))))) (forall ((B_3 tptp.nat) (A_2 tptp.nat) (B tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat A_2))) (=> (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B))) (= A_2 B_3)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat B_3) B)))))) (forall ((B_3 tptp.pname) (A_2 tptp.pname) (B tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname A_2))) (=> (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B))) (= A_2 B_3)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname B_3) B)))))) (forall ((A_2 tptp.x_a) (B_3 tptp.x_a) (A tptp.fun_a_bool)) (let ((_let_1 (tptp.hAPP_a85458249l_bool tptp.member_a A_2))) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 (tptp.hAPP_f2050579477a_bool (tptp.hAPP_a1206381875a_bool tptp.insert_a B_3) A))) (=> (not (= A_2 B_3)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 A)))))) (forall ((A_2 tptp.int) (B_3 tptp.int) (A tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_i2112223885l_bool tptp.member_int A_2))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int B_3) A))) (=> (not (= A_2 B_3)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 A)))))) (forall ((A_2 tptp.nat) (B_3 tptp.nat) (A tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat A_2))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat B_3) A))) (=> (not (= A_2 B_3)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 A)))))) (forall ((A_2 tptp.pname) (B_3 tptp.pname) (A tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname A_2))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname B_3) A))) (=> (not (= A_2 B_3)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A)))))) (forall ((I_2 tptp.nat) (Pa tptp.fun_nat_bool) (K tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool Pa K)) (=> (forall ((N_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool Pa (tptp.hAPP_nat_nat tptp.suc N_1))) (tptp.hBOOL (tptp.hAPP_nat_bool Pa N_1)))) (tptp.hBOOL (tptp.hAPP_nat_bool Pa (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat K) I_2)))))) (forall ((N tptp.nat) (M_4 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat tptp.suc N)) M_4)) (exists ((M_2 tptp.nat)) (= M_4 (tptp.hAPP_nat_nat tptp.suc M_2))))) (forall ((X_1 tptp.fun_int_bool)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool X_1) X_1))) (forall ((X_1 tptp.fun_nat_bool)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool X_1) X_1))) (forall ((X_11 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_11) X_11))) (forall ((X_11 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_11) X_11))) (forall ((X_1 tptp.fun_a_bool)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool X_1) X_1))) (forall ((X_10 tptp.int) (Y_9 tptp.int)) (or (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_10) Y_9)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Y_9) X_10)))) (forall ((X_10 tptp.nat) (Y_9 tptp.nat)) (or (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_10) Y_9)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_9) X_10)))) (forall ((X_1 tptp.fun_int_bool) (Y_1 tptp.fun_int_bool)) (= (= X_1 Y_1) (and (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool Y_1) X_1))))) (forall ((X_1 tptp.fun_nat_bool) (Y_1 tptp.fun_nat_bool)) (= (= X_1 Y_1) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Y_1) X_1))))) (forall ((X_1 tptp.int) (Y_1 tptp.int)) (= (= X_1 Y_1) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Y_1) X_1))))) (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (= (= X_1 Y_1) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_1) X_1))))) (forall ((X_1 tptp.fun_a_bool) (Y_1 tptp.fun_a_bool)) (= (= X_1 Y_1) (and (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool Y_1) X_1))))) (forall ((X_1 tptp.fun_int_bool) (Y_1 tptp.fun_int_bool)) (=> (= X_1 Y_1) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool X_1) Y_1)))) (forall ((X_1 tptp.fun_nat_bool) (Y_1 tptp.fun_nat_bool)) (=> (= X_1 Y_1) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool X_1) Y_1)))) (forall ((X_9 tptp.int) (Y_8 tptp.int)) (=> (= X_9 Y_8) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_9) Y_8)))) (forall ((X_9 tptp.nat) (Y_8 tptp.nat)) (=> (= X_9 Y_8) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_9) Y_8)))) (forall ((X_1 tptp.fun_a_bool) (Y_1 tptp.fun_a_bool)) (=> (= X_1 Y_1) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool X_1) Y_1)))) (forall ((Y_1 tptp.fun_int_bool) (X_1 tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool Y_1) X_1)) (= (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool X_1) Y_1)) (= X_1 Y_1)))) (forall ((Y_1 tptp.fun_nat_bool) (X_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Y_1) X_1)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool X_1) Y_1)) (= X_1 Y_1)))) (forall ((Y_1 tptp.int) (X_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Y_1) X_1)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_1) Y_1)) (= X_1 Y_1)))) (forall ((Y_1 tptp.nat) (X_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_1) X_1)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_1) Y_1)) (= X_1 Y_1)))) (forall ((Y_1 tptp.fun_a_bool) (X_1 tptp.fun_a_bool)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool Y_1) X_1)) (= (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool X_1) Y_1)) (= X_1 Y_1)))) (forall ((C_6 tptp.fun_int_bool) (A_2 tptp.fun_int_bool) (B_3 tptp.fun_int_bool)) (=> (= A_2 B_3) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool B_3) C_6)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A_2) C_6))))) (forall ((C_6 tptp.fun_nat_bool) (A_2 tptp.fun_nat_bool) (B_3 tptp.fun_nat_bool)) (=> (= A_2 B_3) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool B_3) C_6)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A_2) C_6))))) (forall ((C_15 tptp.int) (A_21 tptp.int) (B_19 tptp.int)) (=> (= A_21 B_19) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_19) C_15)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_21) C_15))))) (forall ((C_15 tptp.nat) (A_21 tptp.nat) (B_19 tptp.nat)) (=> (= A_21 B_19) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat B_19) C_15)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_21) C_15))))) (forall ((C_6 tptp.fun_a_bool) (A_2 tptp.fun_a_bool) (B_3 tptp.fun_a_bool)) (=> (= A_2 B_3) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool B_3) C_6)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool A_2) C_6))))) (forall ((C_6 tptp.fun_int_bool) (A_2 tptp.fun_int_bool) (B_3 tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool C_6))) (=> (= A_2 B_3) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 B_3)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 A_2)))))) (forall ((C_6 tptp.fun_nat_bool) (A_2 tptp.fun_nat_bool) (B_3 tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool C_6))) (=> (= A_2 B_3) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B_3)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 A_2)))))) (forall ((C_14 tptp.int) (A_20 tptp.int) (B_18 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int C_14))) (=> (= A_20 B_18) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_18)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A_20)))))) (forall ((C_14 tptp.nat) (A_20 tptp.nat) (B_18 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat C_14))) (=> (= A_20 B_18) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_18)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A_20)))))) (forall ((C_6 tptp.fun_a_bool) (A_2 tptp.fun_a_bool) (B_3 tptp.fun_a_bool)) (let ((_let_1 (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool C_6))) (=> (= A_2 B_3) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 B_3)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 A_2)))))) (forall ((C_6 tptp.fun_int_bool) (A_2 tptp.fun_int_bool) (B_3 tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A_2))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 B_3)) (=> (= B_3 C_6) (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 C_6)))))) (forall ((C_6 tptp.fun_nat_bool) (A_2 tptp.fun_nat_bool) (B_3 tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A_2))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B_3)) (=> (= B_3 C_6) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 C_6)))))) (forall ((C_13 tptp.int) (A_19 tptp.int) (B_17 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_19))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_17)) (=> (= B_17 C_13) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 C_13)))))) (forall ((C_13 tptp.nat) (A_19 tptp.nat) (B_17 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_19))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_17)) (=> (= B_17 C_13) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 C_13)))))) (forall ((C_6 tptp.fun_a_bool) (A_2 tptp.fun_a_bool) (B_3 tptp.fun_a_bool)) (let ((_let_1 (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool A_2))) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 B_3)) (=> (= B_3 C_6) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 C_6)))))) (forall ((C_6 tptp.fun_int_bool) (B_3 tptp.fun_int_bool) (A_2 tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool B_3) A_2)) (=> (= B_3 C_6) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool C_6) A_2))))) (forall ((C_6 tptp.fun_nat_bool) (B_3 tptp.fun_nat_bool) (A_2 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool B_3) A_2)) (=> (= B_3 C_6) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool C_6) A_2))))) (forall ((C_12 tptp.int) (B_16 tptp.int) (A_18 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_16) A_18)) (=> (= B_16 C_12) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int C_12) A_18))))) (forall ((C_12 tptp.nat) (B_16 tptp.nat) (A_18 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat B_16) A_18)) (=> (= B_16 C_12) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat C_12) A_18))))) (forall ((C_6 tptp.fun_a_bool) (B_3 tptp.fun_a_bool) (A_2 tptp.fun_a_bool)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool B_3) A_2)) (=> (= B_3 C_6) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool C_6) A_2))))) (forall ((X_1 tptp.fun_int_bool) (Y_1 tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool X_1) Y_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool Y_1) X_1)) (= X_1 Y_1)))) (forall ((X_1 tptp.fun_nat_bool) (Y_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool X_1) Y_1)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Y_1) X_1)) (= X_1 Y_1)))) (forall ((X_8 tptp.int) (Y_7 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_8) Y_7)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Y_7) X_8)) (= X_8 Y_7)))) (forall ((X_8 tptp.nat) (Y_7 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_8) Y_7)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_7) X_8)) (= X_8 Y_7)))) (forall ((X_1 tptp.fun_a_bool) (Y_1 tptp.fun_a_bool)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool X_1) Y_1)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool Y_1) X_1)) (= X_1 Y_1)))) (forall ((Z_2 tptp.fun_int_bool) (X_1 tptp.fun_int_bool) (Y_1 tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool X_1))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 Y_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool Y_1) Z_2)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 Z_2)))))) (forall ((Z_2 tptp.fun_nat_bool) (X_1 tptp.fun_nat_bool) (Y_1 tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool X_1))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 Y_1)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Y_1) Z_2)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 Z_2)))))) (forall ((Z_6 tptp.int) (X_7 tptp.int) (Y_6 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_7))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Y_6)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Y_6) Z_6)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Z_6)))))) (forall ((Z_6 tptp.nat) (X_7 tptp.nat) (Y_6 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_7))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Y_6)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_6) Z_6)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Z_6)))))) (forall ((Z_2 tptp.fun_a_bool) (X_1 tptp.fun_a_bool) (Y_1 tptp.fun_a_bool)) (let ((_let_1 (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool X_1))) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 Y_1)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool Y_1) Z_2)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 Z_2)))))) (forall ((Y_1 tptp.fun_int_bool) (X_1 tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool Y_1) X_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool X_1) Y_1)) (= X_1 Y_1)))) (forall ((Y_1 tptp.fun_nat_bool) (X_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Y_1) X_1)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool X_1) Y_1)) (= X_1 Y_1)))) (forall ((Y_5 tptp.int) (X_6 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Y_5) X_6)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_6) Y_5)) (= X_6 Y_5)))) (forall ((Y_5 tptp.nat) (X_6 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_5) X_6)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_6) Y_5)) (= X_6 Y_5)))) (forall ((Y_1 tptp.fun_a_bool) (X_1 tptp.fun_a_bool)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool Y_1) X_1)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool X_1) Y_1)) (= X_1 Y_1)))) (forall ((Z_2 tptp.fun_int_bool) (Y_1 tptp.fun_int_bool) (X_1 tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool Z_2))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool Y_1) X_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 Y_1)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 X_1)))))) (forall ((Z_2 tptp.fun_nat_bool) (Y_1 tptp.fun_nat_bool) (X_1 tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Z_2))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Y_1) X_1)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 Y_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 X_1)))))) (forall ((Z_5 tptp.int) (Y_4 tptp.int) (X_5 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Z_5))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Y_4) X_5)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Y_4)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 X_5)))))) (forall ((Z_5 tptp.nat) (Y_4 tptp.nat) (X_5 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Z_5))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_4) X_5)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Y_4)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 X_5)))))) (forall ((Z_2 tptp.fun_a_bool) (Y_1 tptp.fun_a_bool) (X_1 tptp.fun_a_bool)) (let ((_let_1 (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool Z_2))) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool Y_1) X_1)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 Y_1)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 X_1)))))) (forall ((X_4 tptp.int) (Y_3 tptp.int)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_4) Y_3))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Y_3) X_4)))) (forall ((X_4 tptp.nat) (Y_3 tptp.nat)) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_4) Y_3))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_3) X_4)))) (forall ((A_2 tptp.x_a) (B tptp.fun_a_bool)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a A_2) (tptp.hAPP_f2050579477a_bool (tptp.hAPP_a1206381875a_bool tptp.insert_a A_2) B)))) (forall ((A_2 tptp.int) (B tptp.fun_int_bool)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int A_2) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_2) B)))) (forall ((A_2 tptp.nat) (B tptp.fun_nat_bool)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_2) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_2) B)))) (forall ((A_2 tptp.pname) (B tptp.fun_pname_bool)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A_2) (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A_2) B)))) (forall ((A_2 tptp.x_a) (B tptp.fun_a_bool)) (= (tptp.hAPP_f2050579477a_bool (tptp.hAPP_a1206381875a_bool tptp.insert_a A_2) B) (tptp.collect_a (tptp.cOMBS_a_bool_bool (tptp.cOMBB_1972296269bool_a tptp.fdisj (tptp.hAPP_a_fun_a_bool (tptp.cOMBC_a_a_bool tptp.fequal_a) A_2)) (tptp.hAPP_f2050579477a_bool (tptp.cOMBC_1355376034l_bool tptp.member_a) B))))) (forall ((A_2 tptp.int) (B tptp.fun_int_bool)) (= (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_2) B) (tptp.collect_int (tptp.cOMBS_int_bool_bool (tptp.cOMBB_1652995168ol_int tptp.fdisj (tptp.hAPP_i1948725293t_bool (tptp.cOMBC_int_int_bool tptp.fequal_int) A_2)) (tptp.hAPP_f1805168059t_bool (tptp.cOMBC_94739984l_bool tptp.member_int) B))))) (forall ((A_2 tptp.nat) (B tptp.fun_nat_bool)) (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_2) B) (tptp.collect_nat (tptp.cOMBS_nat_bool_bool (tptp.cOMBB_1015721476ol_nat tptp.fdisj (tptp.hAPP_n1699378549t_bool (tptp.cOMBC_nat_nat_bool tptp.fequal_nat) A_2)) (tptp.hAPP_f800510211t_bool (tptp.cOMBC_226598744l_bool tptp.member_nat) B))))) (forall ((A_2 tptp.pname) (B tptp.fun_pname_bool)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A_2) B) (tptp.collect_pname (tptp.cOMBS_568398431l_bool (tptp.cOMBB_675860798_pname tptp.fdisj (tptp.hAPP_p61793385e_bool (tptp.cOMBC_1149511130e_bool tptp.fequal_pname) A_2)) (tptp.hAPP_f759274231e_bool (tptp.cOMBC_1058051404l_bool tptp.member_pname) B))))) (forall ((A_2 tptp.x_a) (Pa tptp.fun_a_bool)) (= (tptp.hAPP_f2050579477a_bool (tptp.hAPP_a1206381875a_bool tptp.insert_a A_2) (tptp.collect_a Pa)) (tptp.collect_a (tptp.cOMBS_a_bool_bool (tptp.cOMBB_1972296269bool_a tptp.fimplies (tptp.cOMBB_bool_bool_a tptp.fNot (tptp.hAPP_a_fun_a_bool (tptp.cOMBC_a_a_bool tptp.fequal_a) A_2))) Pa)))) (forall ((A_2 tptp.int) (Pa tptp.fun_int_bool)) (= (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_2) (tptp.collect_int Pa)) (tptp.collect_int (tptp.cOMBS_int_bool_bool (tptp.cOMBB_1652995168ol_int tptp.fimplies (tptp.cOMBB_bool_bool_int tptp.fNot (tptp.hAPP_i1948725293t_bool (tptp.cOMBC_int_int_bool tptp.fequal_int) A_2))) Pa)))) (forall ((A_2 tptp.nat) (Pa tptp.fun_nat_bool)) (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_2) (tptp.collect_nat Pa)) (tptp.collect_nat (tptp.cOMBS_nat_bool_bool (tptp.cOMBB_1015721476ol_nat tptp.fimplies (tptp.cOMBB_bool_bool_nat tptp.fNot (tptp.hAPP_n1699378549t_bool (tptp.cOMBC_nat_nat_bool tptp.fequal_nat) A_2))) Pa)))) (forall ((X_1 tptp.int) (A tptp.fun_int_bool)) (= (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A)) (tptp.hBOOL (tptp.hAPP_int_bool A X_1)))) (forall ((X_1 tptp.nat) (A tptp.fun_nat_bool)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)) (tptp.hBOOL (tptp.hAPP_nat_bool A X_1)))) (forall ((X_1 tptp.x_a) (A tptp.fun_a_bool)) (= (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a X_1) A)) (tptp.hBOOL (tptp.hAPP_a_bool A X_1)))) (forall ((X_1 tptp.pname) (A tptp.fun_pname_bool)) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A)) (tptp.hBOOL (tptp.hAPP_pname_bool A X_1)))) (forall ((Pa tptp.fun_int_bool)) (= (tptp.collect_int Pa) Pa)) (forall ((Pa tptp.fun_nat_bool)) (= (tptp.collect_nat Pa) Pa)) (forall ((X_1 tptp.x_a) (A tptp.fun_a_bool)) (let ((_let_1 (tptp.hAPP_a1206381875a_bool tptp.insert_a X_1))) (let ((_let_2 (tptp.hAPP_f2050579477a_bool _let_1 A))) (= (tptp.hAPP_f2050579477a_bool _let_1 _let_2) _let_2)))) (forall ((X_1 tptp.x_a) (Y_1 tptp.x_a) (A tptp.fun_a_bool)) (let ((_let_1 (tptp.hAPP_a1206381875a_bool tptp.insert_a X_1))) (let ((_let_2 (tptp.hAPP_a1206381875a_bool tptp.insert_a Y_1))) (= (tptp.hAPP_f2050579477a_bool _let_1 (tptp.hAPP_f2050579477a_bool _let_2 A)) (tptp.hAPP_f2050579477a_bool _let_2 (tptp.hAPP_f2050579477a_bool _let_1 A)))))) (forall ((A_2 tptp.x_a) (B_3 tptp.x_a) (A tptp.fun_a_bool)) (let ((_let_1 (tptp.hAPP_a85458249l_bool tptp.member_a A_2))) (= (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 (tptp.hAPP_f2050579477a_bool (tptp.hAPP_a1206381875a_bool tptp.insert_a B_3) A))) (or (= A_2 B_3) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 A)))))) (forall ((A_2 tptp.int) (B_3 tptp.int) (A tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_i2112223885l_bool tptp.member_int A_2))) (= (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int B_3) A))) (or (= A_2 B_3) (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 A)))))) (forall ((A_2 tptp.nat) (B_3 tptp.nat) (A tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat A_2))) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat B_3) A))) (or (= A_2 B_3) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 A)))))) (forall ((A_2 tptp.pname) (B_3 tptp.pname) (A tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname A_2))) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname B_3) A))) (or (= A_2 B_3) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A)))))) (forall ((Y_1 tptp.x_a) (A tptp.fun_a_bool) (X_1 tptp.x_a)) (= (tptp.hBOOL (tptp.hAPP_a_bool (tptp.hAPP_f2050579477a_bool (tptp.hAPP_a1206381875a_bool tptp.insert_a Y_1) A) X_1)) (or (= Y_1 X_1) (tptp.hBOOL (tptp.hAPP_a_bool A X_1))))) (forall ((B tptp.fun_a_bool) (X_1 tptp.x_a) (A tptp.fun_a_bool)) (let ((_let_1 (tptp.hAPP_a1206381875a_bool tptp.insert_a X_1))) (let ((_let_2 (tptp.hAPP_a85458249l_bool tptp.member_a X_1))) (=> (not (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_2 A))) (=> (not (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_2 B))) (= (= (tptp.hAPP_f2050579477a_bool _let_1 A) (tptp.hAPP_f2050579477a_bool _let_1 B)) (= A B))))))) (forall ((B tptp.fun_int_bool) (X_1 tptp.int) (A tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1))) (let ((_let_2 (tptp.hAPP_i2112223885l_bool tptp.member_int X_1))) (=> (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_2 A))) (=> (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_2 B))) (= (= (tptp.hAPP_f1805168059t_bool _let_1 A) (tptp.hAPP_f1805168059t_bool _let_1 B)) (= A B))))))) (forall ((B tptp.fun_nat_bool) (X_1 tptp.nat) (A tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1))) (let ((_let_2 (tptp.hAPP_n215258509l_bool tptp.member_nat X_1))) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_2 A))) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_2 B))) (= (= (tptp.hAPP_f800510211t_bool _let_1 A) (tptp.hAPP_f800510211t_bool _let_1 B)) (= A B))))))) (forall ((B tptp.fun_pname_bool) (X_1 tptp.pname) (A tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1))) (let ((_let_2 (tptp.hAPP_p338031245l_bool tptp.member_pname X_1))) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_2 A))) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_2 B))) (= (= (tptp.hAPP_f759274231e_bool _let_1 A) (tptp.hAPP_f759274231e_bool _let_1 B)) (= A B))))))) (forall ((B_3 tptp.x_a) (A_2 tptp.x_a) (B tptp.fun_a_bool)) (let ((_let_1 (tptp.hAPP_a85458249l_bool tptp.member_a A_2))) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 B)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 (tptp.hAPP_f2050579477a_bool (tptp.hAPP_a1206381875a_bool tptp.insert_a B_3) B)))))) (forall ((B_3 tptp.int) (A_2 tptp.int) (B tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_i2112223885l_bool tptp.member_int A_2))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 B)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int B_3) B)))))) (forall ((B_3 tptp.nat) (A_2 tptp.nat) (B tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat A_2))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat B_3) B)))))) (forall ((B_3 tptp.pname) (A_2 tptp.pname) (B tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname A_2))) (=> (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_3) B)))))) (forall ((A_2 tptp.x_a) (A tptp.fun_a_bool)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a A_2) A)) (= (tptp.hAPP_f2050579477a_bool (tptp.hAPP_a1206381875a_bool tptp.insert_a A_2) A) A))) (forall ((A_2 tptp.int) (A tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int A_2) A)) (= (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_2) A) A))) (forall ((A_2 tptp.nat) (A tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_2) A)) (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_2) A) A))) (forall ((A_2 tptp.pname) (A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A_2) A)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A_2) A) A))) (forall ((A tptp.fun_int_bool)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A) A))) (forall ((A tptp.fun_nat_bool)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) A))) (forall ((A tptp.fun_a_bool)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool A) A))) (forall ((A tptp.fun_int_bool) (B tptp.fun_int_bool)) (= (= A B) (and (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A) B)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool B) A))))) (forall ((A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (= (= A B) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) B)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool B) A))))) (forall ((A tptp.fun_a_bool) (B tptp.fun_a_bool)) (= (= A B) (and (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool A) B)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool B) A))))) (forall ((A tptp.fun_int_bool) (B tptp.fun_int_bool)) (=> (= A B) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A) B)))) (forall ((A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (=> (= A B) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) B)))) (forall ((A tptp.fun_a_bool) (B tptp.fun_a_bool)) (=> (= A B) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool A) B)))) (forall ((A tptp.fun_int_bool) (B tptp.fun_int_bool)) (=> (= A B) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool B) A)))) (forall ((A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (=> (= A B) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool B) A)))) (forall ((A tptp.fun_a_bool) (B tptp.fun_a_bool)) (=> (= A B) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool B) A)))) (forall ((X_1 tptp.int) (A tptp.fun_int_bool) (B tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_i2112223885l_bool tptp.member_int X_1))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 B)))))) (forall ((X_1 tptp.nat) (A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat X_1))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B)))))) (forall ((X_1 tptp.x_a) (A tptp.fun_a_bool) (B tptp.fun_a_bool)) (let ((_let_1 (tptp.hAPP_a85458249l_bool tptp.member_a X_1))) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 B)))))) (forall ((X_1 tptp.pname) (A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname X_1))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B)))))) (forall ((B tptp.fun_int_bool) (X_1 tptp.int) (A tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_i2112223885l_bool tptp.member_int X_1))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 A)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A) B)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 B)))))) (forall ((B tptp.fun_nat_bool) (X_1 tptp.nat) (A tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat X_1))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 A)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) B)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B)))))) (forall ((B tptp.fun_a_bool) (X_1 tptp.x_a) (A tptp.fun_a_bool)) (let ((_let_1 (tptp.hAPP_a85458249l_bool tptp.member_a X_1))) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 A)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool A) B)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 B)))))) (forall ((B tptp.fun_pname_bool) (X_1 tptp.pname) (A tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname X_1))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) B)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B)))))) (forall ((X_1 tptp.int) (A tptp.fun_int_bool) (B tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_i2112223885l_bool tptp.member_int X_1))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 B)))))) (forall ((X_1 tptp.nat) (A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat X_1))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B)))))) (forall ((X_1 tptp.x_a) (A tptp.fun_a_bool) (B tptp.fun_a_bool)) (let ((_let_1 (tptp.hAPP_a85458249l_bool tptp.member_a X_1))) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 B)))))) (forall ((X_1 tptp.pname) (A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname X_1))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B)))))) (forall ((C_11 tptp.fun_int_bool) (A tptp.fun_int_bool) (B tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 B)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool B) C_11)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 C_11)))))) (forall ((C_11 tptp.fun_nat_bool) (A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool B) C_11)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 C_11)))))) (forall ((C_11 tptp.fun_a_bool) (A tptp.fun_a_bool) (B tptp.fun_a_bool)) (let ((_let_1 (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool A))) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 B)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool B) C_11)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 C_11)))))) (forall ((A tptp.fun_int_bool) (B tptp.fun_int_bool)) (=> (= A B) (not (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A) B)) (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool B) A))))))) (forall ((A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (=> (= A B) (not (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) B)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool B) A))))))) (forall ((A tptp.fun_a_bool) (B tptp.fun_a_bool)) (=> (= A B) (not (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool A) B)) (not (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool B) A))))))) (forall ((Z_2 tptp.int) (F tptp.fun_nat_int) (A tptp.fun_nat_bool)) (= (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Z_2) (tptp.image_nat_int F A))) (exists ((X_2 tptp.nat)) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) A)) (= Z_2 (tptp.hAPP_nat_int F X_2)))))) (forall ((Z_2 tptp.x_a) (F tptp.fun_pname_a) (A tptp.fun_pname_bool)) (= (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a Z_2) (tptp.image_pname_a F A))) (exists ((X_2 tptp.pname)) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A)) (= Z_2 (tptp.hAPP_pname_a F X_2)))))) (forall ((F tptp.fun_nat_int) (X_1 tptp.nat) (A tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int (tptp.hAPP_nat_int F X_1)) (tptp.image_nat_int F A))))) (forall ((F tptp.fun_pname_a) (X_1 tptp.pname) (A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a (tptp.hAPP_pname_a F X_1)) (tptp.image_pname_a F A))))) (forall ((B_3 tptp.int) (F tptp.fun_nat_int) (X_1 tptp.nat) (A tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)) (=> (= B_3 (tptp.hAPP_nat_int F X_1)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int B_3) (tptp.image_nat_int F A)))))) (forall ((B_3 tptp.x_a) (F tptp.fun_pname_a) (X_1 tptp.pname) (A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A)) (=> (= B_3 (tptp.hAPP_pname_a F X_1)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a B_3) (tptp.image_pname_a F A)))))) (forall ((X_2 tptp.x_a) (Xa tptp.fun_a_bool)) (= (tptp.hAPP_f2050579477a_bool (tptp.hAPP_a1206381875a_bool tptp.insert_a X_2) Xa) (tptp.collect_a (tptp.cOMBS_a_bool_bool (tptp.cOMBB_1972296269bool_a tptp.fdisj (tptp.hAPP_a_fun_a_bool (tptp.cOMBC_a_a_bool tptp.fequal_a) X_2)) (tptp.hAPP_f2050579477a_bool (tptp.cOMBC_1355376034l_bool tptp.member_a) Xa))))) (forall ((X_2 tptp.int) (Xa tptp.fun_int_bool)) (= (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_2) Xa) (tptp.collect_int (tptp.cOMBS_int_bool_bool (tptp.cOMBB_1652995168ol_int tptp.fdisj (tptp.hAPP_i1948725293t_bool (tptp.cOMBC_int_int_bool tptp.fequal_int) X_2)) (tptp.hAPP_f1805168059t_bool (tptp.cOMBC_94739984l_bool tptp.member_int) Xa))))) (forall ((X_2 tptp.nat) (Xa tptp.fun_nat_bool)) (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_2) Xa) (tptp.collect_nat (tptp.cOMBS_nat_bool_bool (tptp.cOMBB_1015721476ol_nat tptp.fdisj (tptp.hAPP_n1699378549t_bool (tptp.cOMBC_nat_nat_bool tptp.fequal_nat) X_2)) (tptp.hAPP_f800510211t_bool (tptp.cOMBC_226598744l_bool tptp.member_nat) Xa))))) (forall ((X_2 tptp.pname) (Xa tptp.fun_pname_bool)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname X_2) Xa) (tptp.collect_pname (tptp.cOMBS_568398431l_bool (tptp.cOMBB_675860798_pname tptp.fdisj (tptp.hAPP_p61793385e_bool (tptp.cOMBC_1149511130e_bool tptp.fequal_pname) X_2)) (tptp.hAPP_f759274231e_bool (tptp.cOMBC_1058051404l_bool tptp.member_pname) Xa))))) (forall ((F tptp.fun_int_bool) (G_1 tptp.fun_int_bool)) (= (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool F) G_1)) (forall ((X_2 tptp.int)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_int_bool F X_2)) (tptp.hAPP_int_bool G_1 X_2)))))) (forall ((F tptp.fun_nat_bool) (G_1 tptp.fun_nat_bool)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool F) G_1)) (forall ((X_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_nat_bool F X_2)) (tptp.hAPP_nat_bool G_1 X_2)))))) (forall ((F tptp.fun_a_bool) (G_1 tptp.fun_a_bool)) (= (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool F) G_1)) (forall ((X_2 tptp.x_a)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_a_bool F X_2)) (tptp.hAPP_a_bool G_1 X_2)))))) (forall ((X_1 tptp.int) (F tptp.fun_int_bool) (G_1 tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool F) G_1)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_int_bool F X_1)) (tptp.hAPP_int_bool G_1 X_1))))) (forall ((X_1 tptp.nat) (F tptp.fun_nat_bool) (G_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool F) G_1)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_nat_bool F X_1)) (tptp.hAPP_nat_bool G_1 X_1))))) (forall ((X_1 tptp.x_a) (F tptp.fun_a_bool) (G_1 tptp.fun_a_bool)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool F) G_1)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_a_bool F X_1)) (tptp.hAPP_a_bool G_1 X_1))))) (forall ((X_1 tptp.int) (F tptp.fun_int_bool) (G_1 tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool F) G_1)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_int_bool F X_1)) (tptp.hAPP_int_bool G_1 X_1))))) (forall ((X_1 tptp.nat) (F tptp.fun_nat_bool) (G_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool F) G_1)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_nat_bool F X_1)) (tptp.hAPP_nat_bool G_1 X_1))))) (forall ((X_1 tptp.x_a) (F tptp.fun_a_bool) (G_1 tptp.fun_a_bool)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool F) G_1)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_a_bool F X_1)) (tptp.hAPP_a_bool G_1 X_1))))) (forall ((B tptp.fun_a_bool) (A_2 tptp.x_a)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool B) (tptp.hAPP_f2050579477a_bool (tptp.hAPP_a1206381875a_bool tptp.insert_a A_2) B)))) (forall ((B tptp.fun_int_bool) (A_2 tptp.int)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool B) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_2) B)))) (forall ((B tptp.fun_nat_bool) (A_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool B) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_2) B)))) _let_21 (forall ((X_1 tptp.int) (A tptp.fun_int_bool) (B tptp.fun_int_bool)) (= (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1) A)) B)) (and (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) B)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A) B))))) (forall ((X_1 tptp.nat) (A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) A)) B)) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) B)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) B))))) (forall ((X_1 tptp.pname) (A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1) A)) B)) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) B)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) B))))) (forall ((B tptp.fun_a_bool) (X_1 tptp.x_a) (A tptp.fun_a_bool)) (let ((_let_1 (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool A))) (=> (not (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a X_1) A))) (= (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 (tptp.hAPP_f2050579477a_bool (tptp.hAPP_a1206381875a_bool tptp.insert_a X_1) B))) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 B)))))) (forall ((B tptp.fun_int_bool) (X_1 tptp.int) (A tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A))) (=> (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A))) (= (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1) B))) (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 B)))))) (forall ((B tptp.fun_nat_bool) (X_1 tptp.nat) (A tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A))) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A))) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) B))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B)))))) (forall ((B tptp.fun_pname_bool) (X_1 tptp.pname) (A tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A))) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A))) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1) B))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B)))))) (forall ((B_3 tptp.x_a) (A tptp.fun_a_bool) (B tptp.fun_a_bool)) (let ((_let_1 (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool A))) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 B)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 (tptp.hAPP_f2050579477a_bool (tptp.hAPP_a1206381875a_bool tptp.insert_a B_3) B)))))) (forall ((B_3 tptp.int) (A tptp.fun_int_bool) (B tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 B)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int B_3) B)))))) (forall ((B_3 tptp.nat) (A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat B_3) B)))))) (forall ((A_2 tptp.x_a) (C_11 tptp.fun_a_bool) (D_4 tptp.fun_a_bool)) (let ((_let_1 (tptp.hAPP_a1206381875a_bool tptp.insert_a A_2))) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool C_11) D_4)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool (tptp.hAPP_f2050579477a_bool _let_1 C_11)) (tptp.hAPP_f2050579477a_bool _let_1 D_4)))))) (forall ((A_2 tptp.int) (C_11 tptp.fun_int_bool) (D_4 tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_i1529485324t_bool tptp.insert_int A_2))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool C_11) D_4)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool (tptp.hAPP_f1805168059t_bool _let_1 C_11)) (tptp.hAPP_f1805168059t_bool _let_1 D_4)))))) (forall ((A_2 tptp.nat) (C_11 tptp.fun_nat_bool) (D_4 tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_2))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool C_11) D_4)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_f800510211t_bool _let_1 C_11)) (tptp.hAPP_f800510211t_bool _let_1 D_4)))))) (forall ((F tptp.fun_nat_int) (A_2 tptp.nat) (B tptp.fun_nat_bool)) (= (tptp.image_nat_int F (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_2) B)) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int (tptp.hAPP_nat_int F A_2)) (tptp.image_nat_int F B)))) (forall ((F tptp.fun_pname_a) (A_2 tptp.pname) (B tptp.fun_pname_bool)) (= (tptp.image_pname_a F (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A_2) B)) (tptp.hAPP_f2050579477a_bool (tptp.hAPP_a1206381875a_bool tptp.insert_a (tptp.hAPP_pname_a F A_2)) (tptp.image_pname_a F B)))) (forall ((F tptp.fun_nat_int) (X_1 tptp.nat) (A tptp.fun_nat_bool)) (let ((_let_1 (tptp.image_nat_int F A))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)) (= (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int (tptp.hAPP_nat_int F X_1)) _let_1) _let_1)))) (forall ((F tptp.fun_pname_a) (X_1 tptp.pname) (A tptp.fun_pname_bool)) (let ((_let_1 (tptp.image_pname_a F A))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A)) (= (tptp.hAPP_f2050579477a_bool (tptp.hAPP_a1206381875a_bool tptp.insert_a (tptp.hAPP_pname_a F X_1)) _let_1) _let_1)))) (forall ((B tptp.fun_int_bool) (F tptp.fun_nat_int) (A tptp.fun_nat_bool)) (= (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool B) (tptp.image_nat_int F A))) (exists ((AA tptp.fun_nat_bool)) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool AA) A)) (= B (tptp.image_nat_int F AA)))))) (forall ((B tptp.fun_a_bool) (F tptp.fun_pname_a) (A tptp.fun_pname_bool)) (= (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool B) (tptp.image_pname_a F A))) (exists ((AA tptp.fun_pname_bool)) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool AA) A)) (= B (tptp.image_pname_a F AA)))))) (forall ((F tptp.fun_nat_int) (A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) B)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool (tptp.image_nat_int F A)) (tptp.image_nat_int F B))))) (forall ((F tptp.fun_pname_a) (A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) B)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool (tptp.image_pname_a F A)) (tptp.image_pname_a F B))))) (forall ((B_3 tptp.int) (F tptp.fun_nat_int) (A tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int B_3) (tptp.image_nat_int F A))) (not (forall ((X_2 tptp.nat)) (=> (= B_3 (tptp.hAPP_nat_int F X_2)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) A)))))))) (forall ((B_3 tptp.x_a) (F tptp.fun_pname_a) (A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a B_3) (tptp.image_pname_a F A))) (not (forall ((X_2 tptp.pname)) (=> (= B_3 (tptp.hAPP_pname_a F X_2)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A)))))))) (forall ((B tptp.fun_int_bool) (A tptp.fun_int_bool)) (=> (forall ((X_2 tptp.int)) (let ((_let_1 (tptp.hAPP_i2112223885l_bool tptp.member_int X_2))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 B))))) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A) B)))) (forall ((B tptp.fun_nat_bool) (A tptp.fun_nat_bool)) (=> (forall ((X_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat X_2))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) B)))) (forall ((B tptp.fun_a_bool) (A tptp.fun_a_bool)) (=> (forall ((X_2 tptp.x_a)) (let ((_let_1 (tptp.hAPP_a85458249l_bool tptp.member_a X_2))) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 B))))) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool A) B)))) (forall ((B tptp.fun_pname_bool) (A tptp.fun_pname_bool)) (=> (forall ((X_2 tptp.pname)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname X_2))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B))))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) B)))) (forall ((F tptp.fun_nat_int) (B tptp.fun_int_bool) (A tptp.fun_nat_bool)) (=> (forall ((X_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) A)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int (tptp.hAPP_nat_int F X_2)) B)))) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool (tptp.image_nat_int F A)) B)))) (forall ((F tptp.fun_pname_a) (B tptp.fun_a_bool) (A tptp.fun_pname_bool)) (=> (forall ((X_2 tptp.pname)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a (tptp.hAPP_pname_a F X_2)) B)))) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool (tptp.image_pname_a F A)) B)))) (forall ((F tptp.fun_int_bool) (G_1 tptp.fun_int_bool)) (=> (forall ((X_2 tptp.int)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_int_bool F X_2)) (tptp.hAPP_int_bool G_1 X_2)))) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool F) G_1)))) (forall ((F tptp.fun_nat_bool) (G_1 tptp.fun_nat_bool)) (=> (forall ((X_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_nat_bool F X_2)) (tptp.hAPP_nat_bool G_1 X_2)))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool F) G_1)))) (forall ((F tptp.fun_a_bool) (G_1 tptp.fun_a_bool)) (=> (forall ((X_2 tptp.x_a)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_a_bool F X_2)) (tptp.hAPP_a_bool G_1 X_2)))) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool F) G_1)))) (forall ((N_2 tptp.fun_nat_bool)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat N_2)) (exists ((M_2 tptp.nat)) (forall ((X_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) N_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_2) M_2))))))) (forall ((G tptp.fun_a_bool) (C_6 tptp.com)) (=> (tptp.hBOOL (tptp.wt C_6)) (=> (forall ((X_2 tptp.pname)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) tptp.u)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.p G) (tptp.hAPP_f2050579477a_bool (tptp.hAPP_a1206381875a_bool tptp.insert_a (tptp.hAPP_pname_a tptp.mgt_call X_2)) tptp.bot_bot_fun_a_bool))))) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.p G) (tptp.hAPP_f2050579477a_bool (tptp.hAPP_a1206381875a_bool tptp.insert_a (tptp.mgt C_6)) tptp.bot_bot_fun_a_bool)))))) (forall ((A_2 tptp.int) (B_3 tptp.int) (C_6 tptp.int) (D_1 tptp.int)) (=> (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int A_2) B_3) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int C_6) D_1)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_2) B_3)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int C_6) D_1))))) (forall ((M tptp.nat) (Na tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat tptp.suc M)) Na)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.nat_case_bool tptp.fFalse (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M)) Na)))) (forall ((A_2 tptp.int)) (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int A_2) tptp.bot_bot_fun_int_bool)))) (forall ((A_2 tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_2) tptp.bot_bot_fun_nat_bool)))) (forall ((A_2 tptp.x_a)) (not (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a A_2) tptp.bot_bot_fun_a_bool)))) (forall ((A_2 tptp.pname)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A_2) tptp.bot_bo844097828e_bool)))) (forall ((B tptp.fun_int_bool) (A tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) B))))) (forall ((B tptp.fun_nat_bool) (A tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) B))))) (forall ((B tptp.fun_pname_bool) (A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A) B))))) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int tptp.bot_bot_fun_int_bool)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat tptp.bot_bot_fun_nat_bool)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname tptp.bot_bo844097828e_bool)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a tptp.bot_bot_fun_a_bool)) (forall ((A tptp.fun_nat_bool)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool tptp.bot_bot_fun_nat_bool) A))) (forall ((A tptp.fun_int_bool)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool tptp.bot_bot_fun_int_bool) A))) (forall ((A tptp.fun_a_bool)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool tptp.bot_bot_fun_a_bool) A))) (forall ((A_2 tptp.int) (A tptp.fun_int_bool)) (=> (= A tptp.bot_bot_fun_int_bool) (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int A_2) A))))) (forall ((A_2 tptp.nat) (A tptp.fun_nat_bool)) (=> (= A tptp.bot_bot_fun_nat_bool) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_2) A))))) (forall ((A_2 tptp.x_a) (A tptp.fun_a_bool)) (=> (= A tptp.bot_bot_fun_a_bool) (not (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a A_2) A))))) (forall ((A_2 tptp.pname) (A tptp.fun_pname_bool)) (=> (= A tptp.bot_bo844097828e_bool) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A_2) A))))) (forall ((Pa tptp.fun_int_bool)) (= (= (tptp.collect_int Pa) tptp.bot_bot_fun_int_bool) (forall ((X_2 tptp.int)) (not (tptp.hBOOL (tptp.hAPP_int_bool Pa X_2)))))) (forall ((Pa tptp.fun_nat_bool)) (= (= (tptp.collect_nat Pa) tptp.bot_bot_fun_nat_bool) (forall ((X_2 tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_nat_bool Pa X_2)))))) (forall ((Pa tptp.fun_a_bool)) (= (= (tptp.collect_a Pa) tptp.bot_bot_fun_a_bool) (forall ((X_2 tptp.x_a)) (not (tptp.hBOOL (tptp.hAPP_a_bool Pa X_2)))))) (forall ((A tptp.fun_nat_bool)) (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) A) tptp.bot_bot_fun_nat_bool)) (forall ((A tptp.fun_int_bool)) (= (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) A) tptp.bot_bot_fun_int_bool)) (forall ((A tptp.fun_a_bool)) (= (tptp.hAPP_f2050579477a_bool (tptp.hAPP_f1791771145a_bool tptp.minus_1762468890a_bool A) A) tptp.bot_bot_fun_a_bool)) (forall ((A tptp.fun_nat_bool)) (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) tptp.bot_bot_fun_nat_bool) A)) (forall ((A tptp.fun_int_bool)) (= (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) tptp.bot_bot_fun_int_bool) A)) (forall ((A tptp.fun_a_bool)) (= (tptp.hAPP_f2050579477a_bool (tptp.hAPP_f1791771145a_bool tptp.minus_1762468890a_bool A) tptp.bot_bot_fun_a_bool) A)) (forall ((C_6 tptp.int)) (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int C_6) tptp.bot_bot_fun_int_bool)))) (forall ((C_6 tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat C_6) tptp.bot_bot_fun_nat_bool)))) (forall ((C_6 tptp.x_a)) (not (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a C_6) tptp.bot_bot_fun_a_bool)))) (forall ((C_6 tptp.pname)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname C_6) tptp.bot_bo844097828e_bool)))) (forall ((Pa tptp.fun_int_bool)) (= (= tptp.bot_bot_fun_int_bool (tptp.collect_int Pa)) (forall ((X_2 tptp.int)) (not (tptp.hBOOL (tptp.hAPP_int_bool Pa X_2)))))) (forall ((Pa tptp.fun_nat_bool)) (= (= tptp.bot_bot_fun_nat_bool (tptp.collect_nat Pa)) (forall ((X_2 tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_nat_bool Pa X_2)))))) (forall ((Pa tptp.fun_a_bool)) (= (= tptp.bot_bot_fun_a_bool (tptp.collect_a Pa)) (forall ((X_2 tptp.x_a)) (not (tptp.hBOOL (tptp.hAPP_a_bool Pa X_2)))))) (forall ((A tptp.fun_nat_bool)) (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool tptp.bot_bot_fun_nat_bool) A) tptp.bot_bot_fun_nat_bool)) (forall ((A tptp.fun_int_bool)) (= (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool tptp.bot_bot_fun_int_bool) A) tptp.bot_bot_fun_int_bool)) (forall ((A tptp.fun_a_bool)) (= (tptp.hAPP_f2050579477a_bool (tptp.hAPP_f1791771145a_bool tptp.minus_1762468890a_bool tptp.bot_bot_fun_a_bool) A) tptp.bot_bot_fun_a_bool)) (forall ((A tptp.fun_int_bool)) (= (exists ((X_2 tptp.int)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_2) A))) (not (= A tptp.bot_bot_fun_int_bool)))) (forall ((A tptp.fun_nat_bool)) (= (exists ((X_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) A))) (not (= A tptp.bot_bot_fun_nat_bool)))) (forall ((A tptp.fun_a_bool)) (= (exists ((X_2 tptp.x_a)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a X_2) A))) (not (= A tptp.bot_bot_fun_a_bool)))) (forall ((A tptp.fun_pname_bool)) (= (exists ((X_2 tptp.pname)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A))) (not (= A tptp.bot_bo844097828e_bool)))) (forall ((A tptp.fun_int_bool)) (= (forall ((X_2 tptp.int)) (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_2) A)))) (= A tptp.bot_bot_fun_int_bool))) (forall ((A tptp.fun_nat_bool)) (= (forall ((X_2 tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) A)))) (= A tptp.bot_bot_fun_nat_bool))) (forall ((A tptp.fun_a_bool)) (= (forall ((X_2 tptp.x_a)) (not (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a X_2) A)))) (= A tptp.bot_bot_fun_a_bool))) (forall ((A tptp.fun_pname_bool)) (= (forall ((X_2 tptp.pname)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A)))) (= A tptp.bot_bo844097828e_bool))) (forall ((X_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool tptp.bot_bot_fun_nat_bool X_1)) (tptp.hBOOL tptp.bot_bot_bool))) (forall ((X_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool tptp.bot_bot_fun_int_bool X_1)) (tptp.hBOOL tptp.bot_bot_bool))) (forall ((X_1 tptp.x_a)) (= (tptp.hBOOL (tptp.hAPP_a_bool tptp.bot_bot_fun_a_bool X_1)) (tptp.hBOOL tptp.bot_bot_bool))) (= tptp.bot_bot_fun_int_bool (tptp.collect_int (tptp.cOMBK_bool_int tptp.fFalse))) (= tptp.bot_bot_fun_nat_bool (tptp.collect_nat (tptp.cOMBK_bool_nat tptp.fFalse))) (= tptp.bot_bot_fun_a_bool (tptp.collect_a (tptp.cOMBK_bool_a tptp.fFalse))) (forall ((X_2 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool tptp.bot_bot_fun_nat_bool X_2)) (tptp.hBOOL tptp.bot_bot_bool))) (forall ((X_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool tptp.bot_bot_fun_int_bool X_2)) (tptp.hBOOL tptp.bot_bot_bool))) (forall ((X_2 tptp.x_a)) (= (tptp.hBOOL (tptp.hAPP_a_bool tptp.bot_bot_fun_a_bool X_2)) (tptp.hBOOL tptp.bot_bot_bool))) (forall ((A_2 tptp.x_a) (A tptp.fun_a_bool)) (let ((_let_1 (tptp.hAPP_a1206381875a_bool tptp.insert_a A_2))) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a A_2) A)) (= (tptp.hAPP_f2050579477a_bool _let_1 (tptp.hAPP_f2050579477a_bool (tptp.hAPP_f1791771145a_bool tptp.minus_1762468890a_bool A) (tptp.hAPP_f2050579477a_bool _let_1 tptp.bot_bot_fun_a_bool))) A)))) (forall ((A_2 tptp.int) (A tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_i1529485324t_bool tptp.insert_int A_2))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int A_2) A)) (= (tptp.hAPP_f1805168059t_bool _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) (tptp.hAPP_f1805168059t_bool _let_1 tptp.bot_bot_fun_int_bool))) A)))) (forall ((A_2 tptp.nat) (A tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_2))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_2) A)) (= (tptp.hAPP_f800510211t_bool _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) (tptp.hAPP_f800510211t_bool _let_1 tptp.bot_bot_fun_nat_bool))) A)))) (forall ((A_2 tptp.pname) (A tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p905327722e_bool tptp.insert_pname A_2))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A_2) 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 ((X_1 tptp.x_a) (A tptp.fun_a_bool)) (let ((_let_1 (tptp.hAPP_a1206381875a_bool tptp.insert_a X_1))) (=> (not (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a X_1) A))) (= (tptp.hAPP_f2050579477a_bool (tptp.hAPP_f1791771145a_bool tptp.minus_1762468890a_bool (tptp.hAPP_f2050579477a_bool _let_1 A)) (tptp.hAPP_f2050579477a_bool _let_1 tptp.bot_bot_fun_a_bool)) A)))) (forall ((X_1 tptp.int) (A tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1))) (=> (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A))) (= (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool (tptp.hAPP_f1805168059t_bool _let_1 A)) (tptp.hAPP_f1805168059t_bool _let_1 tptp.bot_bot_fun_int_bool)) A)))) (forall ((X_1 tptp.nat) (A tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1))) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A))) (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool (tptp.hAPP_f800510211t_bool _let_1 A)) (tptp.hAPP_f800510211t_bool _let_1 tptp.bot_bot_fun_nat_bool)) A)))) (forall ((X_1 tptp.pname) (A tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1))) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A))) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool (tptp.hAPP_f759274231e_bool _let_1 A)) (tptp.hAPP_f759274231e_bool _let_1 tptp.bot_bo844097828e_bool)) A)))) (forall ((A_2 tptp.x_a) (A tptp.fun_a_bool)) (let ((_let_1 (tptp.hAPP_a1206381875a_bool tptp.insert_a A_2))) (= (tptp.hAPP_f2050579477a_bool _let_1 (tptp.hAPP_f2050579477a_bool (tptp.hAPP_f1791771145a_bool tptp.minus_1762468890a_bool A) (tptp.hAPP_f2050579477a_bool _let_1 tptp.bot_bot_fun_a_bool))) (tptp.hAPP_f2050579477a_bool _let_1 A)))) (forall ((A_2 tptp.nat) (A tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_2))) (= (tptp.hAPP_f800510211t_bool _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) (tptp.hAPP_f800510211t_bool _let_1 tptp.bot_bot_fun_nat_bool))) (tptp.hAPP_f800510211t_bool _let_1 A)))) (forall ((A_2 tptp.int) (A tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_i1529485324t_bool tptp.insert_int A_2))) (= (tptp.hAPP_f1805168059t_bool _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) (tptp.hAPP_f1805168059t_bool _let_1 tptp.bot_bot_fun_int_bool))) (tptp.hAPP_f1805168059t_bool _let_1 A)))) (forall ((A tptp.fun_a_bool) (A_2 tptp.x_a) (B tptp.fun_a_bool)) (let ((_let_1 (tptp.hAPP_a1206381875a_bool tptp.insert_a A_2))) (let ((_let_2 (tptp.hAPP_f1791771145a_bool tptp.minus_1762468890a_bool A))) (= (tptp.hAPP_f2050579477a_bool _let_2 (tptp.hAPP_f2050579477a_bool _let_1 B)) (tptp.hAPP_f2050579477a_bool (tptp.hAPP_f1791771145a_bool tptp.minus_1762468890a_bool (tptp.hAPP_f2050579477a_bool _let_2 (tptp.hAPP_f2050579477a_bool _let_1 tptp.bot_bot_fun_a_bool))) B))))) (forall ((A tptp.fun_nat_bool) (A_2 tptp.nat) (B tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_2))) (let ((_let_2 (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A))) (= (tptp.hAPP_f800510211t_bool _let_2 (tptp.hAPP_f800510211t_bool _let_1 B)) (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool (tptp.hAPP_f800510211t_bool _let_2 (tptp.hAPP_f800510211t_bool _let_1 tptp.bot_bot_fun_nat_bool))) B))))) (forall ((A tptp.fun_int_bool) (A_2 tptp.int) (B tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_i1529485324t_bool tptp.insert_int A_2))) (let ((_let_2 (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A))) (= (tptp.hAPP_f1805168059t_bool _let_2 (tptp.hAPP_f1805168059t_bool _let_1 B)) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool (tptp.hAPP_f1805168059t_bool _let_2 (tptp.hAPP_f1805168059t_bool _let_1 tptp.bot_bot_fun_int_bool))) B))))) (forall ((A tptp.fun_a_bool) (A_2 tptp.x_a) (B tptp.fun_a_bool)) (let ((_let_1 (tptp.hAPP_a1206381875a_bool tptp.insert_a A_2))) (let ((_let_2 (tptp.hAPP_f1791771145a_bool tptp.minus_1762468890a_bool A))) (= (tptp.hAPP_f2050579477a_bool _let_2 (tptp.hAPP_f2050579477a_bool _let_1 B)) (tptp.hAPP_f2050579477a_bool (tptp.hAPP_f1791771145a_bool tptp.minus_1762468890a_bool (tptp.hAPP_f2050579477a_bool _let_2 B)) (tptp.hAPP_f2050579477a_bool _let_1 tptp.bot_bot_fun_a_bool)))))) (forall ((A tptp.fun_nat_bool) (A_2 tptp.nat) (B tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_2))) (let ((_let_2 (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A))) (= (tptp.hAPP_f800510211t_bool _let_2 (tptp.hAPP_f800510211t_bool _let_1 B)) (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool (tptp.hAPP_f800510211t_bool _let_2 B)) (tptp.hAPP_f800510211t_bool _let_1 tptp.bot_bot_fun_nat_bool)))))) (forall ((A tptp.fun_int_bool) (A_2 tptp.int) (B tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_i1529485324t_bool tptp.insert_int A_2))) (let ((_let_2 (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A))) (= (tptp.hAPP_f1805168059t_bool _let_2 (tptp.hAPP_f1805168059t_bool _let_1 B)) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool (tptp.hAPP_f1805168059t_bool _let_2 B)) (tptp.hAPP_f1805168059t_bool _let_1 tptp.bot_bot_fun_int_bool)))))) (forall ((A tptp.fun_a_bool) (X_1 tptp.x_a) (B tptp.fun_a_bool)) (let ((_let_1 (tptp.hAPP_a1206381875a_bool tptp.insert_a X_1))) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool (tptp.hAPP_f2050579477a_bool (tptp.hAPP_f1791771145a_bool tptp.minus_1762468890a_bool A) (tptp.hAPP_f2050579477a_bool _let_1 tptp.bot_bot_fun_a_bool))) B)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a X_1) A)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool A) (tptp.hAPP_f2050579477a_bool _let_1 B))))))) (forall ((A tptp.fun_int_bool) (X_1 tptp.int) (B tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) (tptp.hAPP_f1805168059t_bool _let_1 tptp.bot_bot_fun_int_bool))) B)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A) (tptp.hAPP_f1805168059t_bool _let_1 B))))))) (forall ((A tptp.fun_nat_bool) (X_1 tptp.nat) (B tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) (tptp.hAPP_f800510211t_bool _let_1 tptp.bot_bot_fun_nat_bool))) B)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) (tptp.hAPP_f800510211t_bool _let_1 B))))))) (forall ((A tptp.fun_pname_bool) (X_1 tptp.pname) (B tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A) (tptp.hAPP_f759274231e_bool _let_1 tptp.bot_bo844097828e_bool))) B)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) (tptp.hAPP_f759274231e_bool _let_1 B))))))) (forall ((A tptp.fun_a_bool) (X_1 tptp.x_a) (B tptp.fun_a_bool)) (let ((_let_1 (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool A))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a X_1) A)))) (let ((_let_3 (tptp.hAPP_a1206381875a_bool tptp.insert_a X_1))) (= (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 (tptp.hAPP_f2050579477a_bool _let_3 B))) (and (=> _let_2 (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool (tptp.hAPP_f2050579477a_bool (tptp.hAPP_f1791771145a_bool tptp.minus_1762468890a_bool A) (tptp.hAPP_f2050579477a_bool _let_3 tptp.bot_bot_fun_a_bool))) B))) (=> (not _let_2) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 B))))))))) (forall ((A tptp.fun_int_bool) (X_1 tptp.int) (B tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A)))) (let ((_let_3 (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1))) (= (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 (tptp.hAPP_f1805168059t_bool _let_3 B))) (and (=> _let_2 (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) (tptp.hAPP_f1805168059t_bool _let_3 tptp.bot_bot_fun_int_bool))) B))) (=> (not _let_2) (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 B))))))))) (forall ((A tptp.fun_nat_bool) (X_1 tptp.nat) (B tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)))) (let ((_let_3 (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1))) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f800510211t_bool _let_3 B))) (and (=> _let_2 (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) (tptp.hAPP_f800510211t_bool _let_3 tptp.bot_bot_fun_nat_bool))) B))) (=> (not _let_2) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B))))))))) (forall ((A tptp.fun_pname_bool) (X_1 tptp.pname) (B tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A)))) (let ((_let_3 (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1))) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool _let_3 B))) (and (=> _let_2 (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A) (tptp.hAPP_f759274231e_bool _let_3 tptp.bot_bo844097828e_bool))) B))) (=> (not _let_2) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B))))))))) (forall ((A tptp.fun_int_bool) (B tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int B)) (= (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) B))) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A))))) (forall ((A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat B)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) B))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A))))) (forall ((A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B)) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A) B))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A))))) (forall ((A tptp.fun_a_bool) (X_1 tptp.x_a) (B tptp.fun_a_bool)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a X_1) B)) (= (tptp.hAPP_f2050579477a_bool (tptp.hAPP_f1791771145a_bool tptp.minus_1762468890a_bool (tptp.hAPP_f2050579477a_bool (tptp.hAPP_a1206381875a_bool tptp.insert_a X_1) A)) B) (tptp.hAPP_f2050579477a_bool (tptp.hAPP_f1791771145a_bool tptp.minus_1762468890a_bool A) B)))) (forall ((A tptp.fun_int_bool) (X_1 tptp.int) (B tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) B)) (= (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1) A)) B) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) B)))) (forall ((A tptp.fun_nat_bool) (X_1 tptp.nat) (B tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) B)) (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) A)) B) (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) B)))) (forall ((A tptp.fun_pname_bool) (X_1 tptp.pname) (B tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) B)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1) A)) B) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A) B)))) (forall ((A tptp.fun_a_bool) (X_1 tptp.x_a) (B tptp.fun_a_bool)) (let ((_let_1 (tptp.hAPP_f2050579477a_bool (tptp.hAPP_f1791771145a_bool tptp.minus_1762468890a_bool A) B))) (let ((_let_2 (tptp.hAPP_a1206381875a_bool tptp.insert_a X_1))) (let ((_let_3 (tptp.hAPP_f2050579477a_bool (tptp.hAPP_f1791771145a_bool tptp.minus_1762468890a_bool (tptp.hAPP_f2050579477a_bool _let_2 A)) B))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a X_1) B)))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (tptp.hAPP_f2050579477a_bool _let_2 _let_1))))))))) (forall ((A tptp.fun_int_bool) (X_1 tptp.int) (B tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) B))) (let ((_let_2 (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1))) (let ((_let_3 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool (tptp.hAPP_f1805168059t_bool _let_2 A)) B))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) B)))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (tptp.hAPP_f1805168059t_bool _let_2 _let_1))))))))) (forall ((A tptp.fun_nat_bool) (X_1 tptp.nat) (B tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) B))) (let ((_let_2 (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1))) (let ((_let_3 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool (tptp.hAPP_f800510211t_bool _let_2 A)) B))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) B)))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (tptp.hAPP_f800510211t_bool _let_2 _let_1))))))))) (forall ((A tptp.fun_pname_bool) (X_1 tptp.pname) (B tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A) B))) (let ((_let_2 (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1))) (let ((_let_3 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool (tptp.hAPP_f759274231e_bool _let_2 A)) B))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) B)))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (tptp.hAPP_f759274231e_bool _let_2 _let_1))))))))) (forall ((C_11 tptp.fun_int_bool) (A tptp.fun_int_bool) (B tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool B) C_11)) (= (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool B) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool C_11) A)) A)))) (forall ((C_11 tptp.fun_nat_bool) (A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool B) C_11)) (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool B) (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool C_11) A)) A)))) (forall ((C_11 tptp.fun_a_bool) (A tptp.fun_a_bool) (B tptp.fun_a_bool)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool B) C_11)) (= (tptp.hAPP_f2050579477a_bool (tptp.hAPP_f1791771145a_bool tptp.minus_1762468890a_bool B) (tptp.hAPP_f2050579477a_bool (tptp.hAPP_f1791771145a_bool tptp.minus_1762468890a_bool C_11) A)) A)))) (forall ((D_4 tptp.fun_int_bool) (B tptp.fun_int_bool) (A tptp.fun_int_bool) (C_11 tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A) C_11)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool D_4) B)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) B)) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool C_11) D_4)))))) (forall ((D_4 tptp.fun_nat_bool) (B tptp.fun_nat_bool) (A tptp.fun_nat_bool) (C_11 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) C_11)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool D_4) B)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) B)) (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool C_11) D_4)))))) (forall ((D_4 tptp.fun_a_bool) (B tptp.fun_a_bool) (A tptp.fun_a_bool) (C_11 tptp.fun_a_bool)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool A) C_11)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool D_4) B)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool (tptp.hAPP_f2050579477a_bool (tptp.hAPP_f1791771145a_bool tptp.minus_1762468890a_bool A) B)) (tptp.hAPP_f2050579477a_bool (tptp.hAPP_f1791771145a_bool tptp.minus_1762468890a_bool C_11) D_4)))))) (forall ((A tptp.fun_int_bool) (B tptp.fun_int_bool)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) B)) A))) (forall ((A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) B)) A))) (forall ((A tptp.fun_a_bool) (B tptp.fun_a_bool)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool (tptp.hAPP_f2050579477a_bool (tptp.hAPP_f1791771145a_bool tptp.minus_1762468890a_bool A) B)) A))) (forall ((A_2 tptp.x_a) (B_3 tptp.x_a)) (=> (= (tptp.hAPP_f2050579477a_bool (tptp.hAPP_a1206381875a_bool tptp.insert_a A_2) tptp.bot_bot_fun_a_bool) (tptp.hAPP_f2050579477a_bool (tptp.hAPP_a1206381875a_bool tptp.insert_a B_3) tptp.bot_bot_fun_a_bool)) (= A_2 B_3))) (forall ((A_2 tptp.nat) (B_3 tptp.nat)) (=> (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_2) tptp.bot_bot_fun_nat_bool) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat B_3) tptp.bot_bot_fun_nat_bool)) (= A_2 B_3))) (forall ((A_2 tptp.int) (B_3 tptp.int)) (=> (= (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_2) tptp.bot_bot_fun_int_bool) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int B_3) tptp.bot_bot_fun_int_bool)) (= A_2 B_3))) (forall ((B_3 tptp.x_a) (A_2 tptp.x_a)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a B_3) (tptp.hAPP_f2050579477a_bool (tptp.hAPP_a1206381875a_bool tptp.insert_a A_2) tptp.bot_bot_fun_a_bool))) (= B_3 A_2))) (forall ((B_3 tptp.int) (A_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int B_3) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_2) tptp.bot_bot_fun_int_bool))) (= B_3 A_2))) (forall ((B_3 tptp.nat) (A_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat B_3) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_2) tptp.bot_bot_fun_nat_bool))) (= B_3 A_2))) (forall ((B_3 tptp.pname) (A_2 tptp.pname)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname B_3) (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A_2) tptp.bot_bo844097828e_bool))) (= B_3 A_2))) (forall ((A_2 tptp.x_a) (B_3 tptp.x_a) (C_6 tptp.x_a) (D_1 tptp.x_a)) (= (= (tptp.hAPP_f2050579477a_bool (tptp.hAPP_a1206381875a_bool tptp.insert_a A_2) (tptp.hAPP_f2050579477a_bool (tptp.hAPP_a1206381875a_bool tptp.insert_a B_3) tptp.bot_bot_fun_a_bool)) (tptp.hAPP_f2050579477a_bool (tptp.hAPP_a1206381875a_bool tptp.insert_a C_6) (tptp.hAPP_f2050579477a_bool (tptp.hAPP_a1206381875a_bool tptp.insert_a D_1) tptp.bot_bot_fun_a_bool))) (or (and (= A_2 C_6) (= B_3 D_1)) (and (= A_2 D_1) (= B_3 C_6))))) (forall ((A_2 tptp.nat) (B_3 tptp.nat) (C_6 tptp.nat) (D_1 tptp.nat)) (= (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_2) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat B_3) tptp.bot_bot_fun_nat_bool)) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat C_6) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat D_1) tptp.bot_bot_fun_nat_bool))) (or (and (= A_2 C_6) (= B_3 D_1)) (and (= A_2 D_1) (= B_3 C_6))))) (forall ((A_2 tptp.int) (B_3 tptp.int) (C_6 tptp.int) (D_1 tptp.int)) (= (= (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_2) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int B_3) tptp.bot_bot_fun_int_bool)) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int C_6) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int D_1) tptp.bot_bot_fun_int_bool))) (or (and (= A_2 C_6) (= B_3 D_1)) (and (= A_2 D_1) (= B_3 C_6))))) (forall ((B_3 tptp.x_a) (A_2 tptp.x_a)) (= (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a B_3) (tptp.hAPP_f2050579477a_bool (tptp.hAPP_a1206381875a_bool tptp.insert_a A_2) tptp.bot_bot_fun_a_bool))) (= B_3 A_2))) (forall ((B_3 tptp.int) (A_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int B_3) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_2) tptp.bot_bot_fun_int_bool))) (= B_3 A_2))) (forall ((B_3 tptp.nat) (A_2 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat B_3) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_2) tptp.bot_bot_fun_nat_bool))) (= B_3 A_2))) (forall ((B_3 tptp.pname) (A_2 tptp.pname)) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname B_3) (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A_2) tptp.bot_bo844097828e_bool))) (= B_3 A_2))) (forall ((A_2 tptp.x_a) (A tptp.fun_a_bool)) (not (= (tptp.hAPP_f2050579477a_bool (tptp.hAPP_a1206381875a_bool tptp.insert_a A_2) A) tptp.bot_bot_fun_a_bool))) (forall ((A_2 tptp.nat) (A tptp.fun_nat_bool)) (not (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_2) A) tptp.bot_bot_fun_nat_bool))) (forall ((A_2 tptp.int) (A tptp.fun_int_bool)) (not (= (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_2) A) tptp.bot_bot_fun_int_bool))) (forall ((A_2 tptp.x_a) (A tptp.fun_a_bool)) (not (= tptp.bot_bot_fun_a_bool (tptp.hAPP_f2050579477a_bool (tptp.hAPP_a1206381875a_bool tptp.insert_a A_2) A)))) (forall ((A_2 tptp.nat) (A tptp.fun_nat_bool)) (not (= tptp.bot_bot_fun_nat_bool (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_2) A)))) (forall ((A_2 tptp.int) (A tptp.fun_int_bool)) (not (= tptp.bot_bot_fun_int_bool (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_2) A)))) (forall ((A tptp.fun_nat_bool)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) tptp.bot_bot_fun_nat_bool)) (= A tptp.bot_bot_fun_nat_bool))) (forall ((A tptp.fun_int_bool)) (= (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A) tptp.bot_bot_fun_int_bool)) (= A tptp.bot_bot_fun_int_bool))) (forall ((A tptp.fun_a_bool)) (= (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool A) tptp.bot_bot_fun_a_bool)) (= A tptp.bot_bot_fun_a_bool))) (forall ((F tptp.fun_nat_int) (A tptp.fun_nat_bool)) (= (= (tptp.image_nat_int F A) tptp.bot_bot_fun_int_bool) (= A tptp.bot_bot_fun_nat_bool))) (forall ((F tptp.fun_pname_a) (A tptp.fun_pname_bool)) (= (= (tptp.image_pname_a F A) tptp.bot_bot_fun_a_bool) (= A tptp.bot_bo844097828e_bool))) (forall ((F tptp.fun_nat_int)) (= (tptp.image_nat_int F tptp.bot_bot_fun_nat_bool) tptp.bot_bot_fun_int_bool)) (forall ((F tptp.fun_pname_a)) (= (tptp.image_pname_a F tptp.bot_bo844097828e_bool) tptp.bot_bot_fun_a_bool)) (forall ((F tptp.fun_nat_int) (A tptp.fun_nat_bool)) (= (= tptp.bot_bot_fun_int_bool (tptp.image_nat_int F A)) (= A tptp.bot_bot_fun_nat_bool))) (forall ((F tptp.fun_pname_a) (A tptp.fun_pname_bool)) (= (= tptp.bot_bot_fun_a_bool (tptp.image_pname_a F A)) (= A tptp.bot_bo844097828e_bool))) (forall ((A_2 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A_2) tptp.bot_bot_fun_nat_bool)) (= A_2 tptp.bot_bot_fun_nat_bool))) (forall ((A_2 tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A_2) tptp.bot_bot_fun_int_bool)) (= A_2 tptp.bot_bot_fun_int_bool))) (forall ((A_17 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_17) tptp.bot_bot_nat)) (= A_17 tptp.bot_bot_nat))) (forall ((A_2 tptp.fun_a_bool)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool A_2) tptp.bot_bot_fun_a_bool)) (= A_2 tptp.bot_bot_fun_a_bool))) (forall ((A_2 tptp.fun_nat_bool)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A_2) tptp.bot_bot_fun_nat_bool)) (= A_2 tptp.bot_bot_fun_nat_bool))) (forall ((A_2 tptp.fun_int_bool)) (= (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A_2) tptp.bot_bot_fun_int_bool)) (= A_2 tptp.bot_bot_fun_int_bool))) (forall ((A_2 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_2) tptp.bot_bot_nat)) (= A_2 tptp.bot_bot_nat))) (forall ((A_2 tptp.fun_a_bool)) (= (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool A_2) tptp.bot_bot_fun_a_bool)) (= A_2 tptp.bot_bot_fun_a_bool))) (forall ((A_2 tptp.fun_nat_bool)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool tptp.bot_bot_fun_nat_bool) A_2))) (forall ((A_2 tptp.fun_int_bool)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool tptp.bot_bot_fun_int_bool) A_2))) (forall ((A_16 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.bot_bot_nat) A_16))) (forall ((A_2 tptp.fun_a_bool)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool tptp.bot_bot_fun_a_bool) A_2))) (forall ((Pa tptp.fun_a_bool) (A_2 tptp.x_a)) (let ((_let_1 (tptp.collect_a (tptp.cOMBS_a_bool_bool (tptp.cOMBB_1972296269bool_a tptp.fconj (tptp.hAPP_a_fun_a_bool (tptp.cOMBC_a_a_bool tptp.fequal_a) A_2)) Pa)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_a_bool Pa A_2)))) (and (=> _let_2 (= _let_1 (tptp.hAPP_f2050579477a_bool (tptp.hAPP_a1206381875a_bool tptp.insert_a A_2) tptp.bot_bot_fun_a_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bot_fun_a_bool)))))) (forall ((Pa tptp.fun_int_bool) (A_2 tptp.int)) (let ((_let_1 (tptp.collect_int (tptp.cOMBS_int_bool_bool (tptp.cOMBB_1652995168ol_int tptp.fconj (tptp.hAPP_i1948725293t_bool (tptp.cOMBC_int_int_bool tptp.fequal_int) A_2)) Pa)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_int_bool Pa A_2)))) (and (=> _let_2 (= _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_2) tptp.bot_bot_fun_int_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bot_fun_int_bool)))))) (forall ((Pa tptp.fun_nat_bool) (A_2 tptp.nat)) (let ((_let_1 (tptp.collect_nat (tptp.cOMBS_nat_bool_bool (tptp.cOMBB_1015721476ol_nat tptp.fconj (tptp.hAPP_n1699378549t_bool (tptp.cOMBC_nat_nat_bool tptp.fequal_nat) A_2)) Pa)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_nat_bool Pa A_2)))) (and (=> _let_2 (= _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_2) tptp.bot_bot_fun_nat_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bot_fun_nat_bool)))))) (forall ((Pa tptp.fun_a_bool) (A_2 tptp.x_a)) (let ((_let_1 (tptp.collect_a (tptp.cOMBS_a_bool_bool (tptp.cOMBB_1972296269bool_a tptp.fconj (tptp.hAPP_a_fun_a_bool tptp.fequal_a A_2)) Pa)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_a_bool Pa A_2)))) (and (=> _let_2 (= _let_1 (tptp.hAPP_f2050579477a_bool (tptp.hAPP_a1206381875a_bool tptp.insert_a A_2) tptp.bot_bot_fun_a_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bot_fun_a_bool)))))) (forall ((Pa tptp.fun_int_bool) (A_2 tptp.int)) (let ((_let_1 (tptp.collect_int (tptp.cOMBS_int_bool_bool (tptp.cOMBB_1652995168ol_int tptp.fconj (tptp.hAPP_i1948725293t_bool tptp.fequal_int A_2)) Pa)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_int_bool Pa A_2)))) (and (=> _let_2 (= _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_2) tptp.bot_bot_fun_int_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bot_fun_int_bool)))))) (forall ((Pa tptp.fun_nat_bool) (A_2 tptp.nat)) (let ((_let_1 (tptp.collect_nat (tptp.cOMBS_nat_bool_bool (tptp.cOMBB_1015721476ol_nat tptp.fconj (tptp.hAPP_n1699378549t_bool tptp.fequal_nat A_2)) Pa)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_nat_bool Pa A_2)))) (and (=> _let_2 (= _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_2) tptp.bot_bot_fun_nat_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bot_fun_nat_bool)))))) (forall ((A_2 tptp.x_a)) (= (tptp.collect_a (tptp.hAPP_a_fun_a_bool (tptp.cOMBC_a_a_bool tptp.fequal_a) A_2)) (tptp.hAPP_f2050579477a_bool (tptp.hAPP_a1206381875a_bool tptp.insert_a A_2) tptp.bot_bot_fun_a_bool))) (forall ((A_2 tptp.int)) (= (tptp.collect_int (tptp.hAPP_i1948725293t_bool (tptp.cOMBC_int_int_bool tptp.fequal_int) A_2)) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_2) tptp.bot_bot_fun_int_bool))) (forall ((A_2 tptp.nat)) (= (tptp.collect_nat (tptp.hAPP_n1699378549t_bool (tptp.cOMBC_nat_nat_bool tptp.fequal_nat) A_2)) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_2) tptp.bot_bot_fun_nat_bool))) (forall ((A_2 tptp.x_a)) (= (tptp.collect_a (tptp.hAPP_a_fun_a_bool tptp.fequal_a A_2)) (tptp.hAPP_f2050579477a_bool (tptp.hAPP_a1206381875a_bool tptp.insert_a A_2) tptp.bot_bot_fun_a_bool))) (forall ((A_2 tptp.int)) (= (tptp.collect_int (tptp.hAPP_i1948725293t_bool tptp.fequal_int A_2)) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_2) tptp.bot_bot_fun_int_bool))) (forall ((A_2 tptp.nat)) (= (tptp.collect_nat (tptp.hAPP_n1699378549t_bool tptp.fequal_nat A_2)) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_2) tptp.bot_bot_fun_nat_bool))) (forall ((X_1 tptp.x_a) (A tptp.fun_a_bool)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a A)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a X_1) A)) (= (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_fun_a_bool_nat tptp.finite_card_a (tptp.hAPP_f2050579477a_bool (tptp.hAPP_f1791771145a_bool tptp.minus_1762468890a_bool A) (tptp.hAPP_f2050579477a_bool (tptp.hAPP_a1206381875a_bool tptp.insert_a X_1) tptp.bot_bot_fun_a_bool)))) (tptp.hAPP_fun_a_bool_nat tptp.finite_card_a A))))) (forall ((X_1 tptp.int) (A tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A)) (= (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_f957591787ol_nat tptp.finite_card_int (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1) tptp.bot_bot_fun_int_bool)))) (tptp.hAPP_f957591787ol_nat tptp.finite_card_int A))))) (forall ((X_1 tptp.nat) (A tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)) (= (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) tptp.bot_bot_fun_nat_bool)))) (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat A))))) (forall ((X_1 tptp.pname) (A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A)) (= (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_f921600141ol_nat tptp.finite_card_pname (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)))) (tptp.hAPP_f921600141ol_nat tptp.finite_card_pname A))))) (forall ((X_1 tptp.x_a) (A tptp.fun_a_bool)) (let ((_let_1 (tptp.hAPP_a1206381875a_bool tptp.insert_a X_1))) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a A)) (= (tptp.hAPP_fun_a_bool_nat tptp.finite_card_a (tptp.hAPP_f2050579477a_bool _let_1 A)) (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_fun_a_bool_nat tptp.finite_card_a (tptp.hAPP_f2050579477a_bool (tptp.hAPP_f1791771145a_bool tptp.minus_1762468890a_bool A) (tptp.hAPP_f2050579477a_bool _let_1 tptp.bot_bot_fun_a_bool)))))))) (forall ((X_1 tptp.int) (A tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (= (tptp.hAPP_f957591787ol_nat tptp.finite_card_int (tptp.hAPP_f1805168059t_bool _let_1 A)) (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_f957591787ol_nat tptp.finite_card_int (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) (tptp.hAPP_f1805168059t_bool _let_1 tptp.bot_bot_fun_int_bool)))))))) (forall ((X_1 tptp.nat) (A tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (= (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat (tptp.hAPP_f800510211t_bool _let_1 A)) (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) (tptp.hAPP_f800510211t_bool _let_1 tptp.bot_bot_fun_nat_bool)))))))) (forall ((X_1 tptp.pname) (A tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (= (tptp.hAPP_f921600141ol_nat tptp.finite_card_pname (tptp.hAPP_f759274231e_bool _let_1 A)) (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_f921600141ol_nat tptp.finite_card_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A) (tptp.hAPP_f759274231e_bool _let_1 tptp.bot_bo844097828e_bool)))))))) (forall ((X_1 tptp.x_a) (A tptp.fun_a_bool)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a A)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_fun_a_bool_nat tptp.finite_card_a (tptp.hAPP_f2050579477a_bool (tptp.hAPP_f1791771145a_bool tptp.minus_1762468890a_bool A) (tptp.hAPP_f2050579477a_bool (tptp.hAPP_a1206381875a_bool tptp.insert_a X_1) tptp.bot_bot_fun_a_bool)))) (tptp.hAPP_fun_a_bool_nat tptp.finite_card_a A))))) (forall ((X_1 tptp.int) (A tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f957591787ol_nat tptp.finite_card_int (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1) tptp.bot_bot_fun_int_bool)))) (tptp.hAPP_f957591787ol_nat tptp.finite_card_int A))))) (forall ((X_1 tptp.nat) (A tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) tptp.bot_bot_fun_nat_bool)))) (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat A))))) (forall ((X_1 tptp.pname) (A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f921600141ol_nat tptp.finite_card_pname (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)))) (tptp.hAPP_f921600141ol_nat tptp.finite_card_pname A))))) (forall ((A tptp.fun_a_bool) (A_2 tptp.x_a) (B tptp.fun_a_bool)) (let ((_let_1 (tptp.hAPP_f1791771145a_bool tptp.minus_1762468890a_bool A))) (= (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a (tptp.hAPP_f2050579477a_bool _let_1 (tptp.hAPP_f2050579477a_bool (tptp.hAPP_a1206381875a_bool tptp.insert_a A_2) B)))) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a (tptp.hAPP_f2050579477a_bool _let_1 B)))))) (forall ((A tptp.fun_int_bool) (A_2 tptp.int) (B tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A))) (= (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.hAPP_f1805168059t_bool _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_2) B)))) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.hAPP_f1805168059t_bool _let_1 B)))))) (forall ((A tptp.fun_nat_bool) (A_2 tptp.nat) (B tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A))) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.hAPP_f800510211t_bool _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_2) B)))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.hAPP_f800510211t_bool _let_1 B)))))) (forall ((A tptp.fun_pname_bool) (A_2 tptp.pname) (B tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A))) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A_2) B)))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f759274231e_bool _let_1 B)))))) (forall ((F tptp.fun_nat_int) (A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool (tptp.image_nat_int F A)) (tptp.image_nat_int F B))) (tptp.image_nat_int F (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) B))))) (forall ((F tptp.fun_pname_a) (A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool (tptp.hAPP_f2050579477a_bool (tptp.hAPP_f1791771145a_bool tptp.minus_1762468890a_bool (tptp.image_pname_a F A)) (tptp.image_pname_a F B))) (tptp.image_pname_a F (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A) B))))) (forall ((A tptp.fun_a_bool) (X_1 tptp.x_a)) (let ((_let_1 (tptp.hAPP_f2050579477a_bool (tptp.hAPP_a1206381875a_bool tptp.insert_a X_1) tptp.bot_bot_fun_a_bool))) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool A) _let_1)) (or (= A tptp.bot_bot_fun_a_bool) (= A _let_1))))) (forall ((A tptp.fun_nat_bool) (X_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) tptp.bot_bot_fun_nat_bool))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) _let_1)) (or (= A tptp.bot_bot_fun_nat_bool) (= A _let_1))))) (forall ((A tptp.fun_int_bool) (X_1 tptp.int)) (let ((_let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1) tptp.bot_bot_fun_int_bool))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A) _let_1)) (or (= A tptp.bot_bot_fun_int_bool) (= A _let_1))))) (forall ((F1 tptp.nat) (F2 tptp.fun_nat_nat) (Nat_3 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.nat_case_nat F1 F2) (tptp.hAPP_nat_nat tptp.suc Nat_3)) (tptp.hAPP_nat_nat F2 Nat_3))) (forall ((F1 tptp.bool) (F2 tptp.fun_nat_bool) (Nat_3 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.nat_case_bool F1 F2) (tptp.hAPP_nat_nat tptp.suc Nat_3))) (tptp.hBOOL (tptp.hAPP_nat_bool F2 Nat_3)))) (forall ((C_6 tptp.int) (X_1 tptp.nat) (A tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)) (= (tptp.image_nat_int (tptp.cOMBK_int_nat C_6) A) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int C_6) tptp.bot_bot_fun_int_bool)))) (forall ((C_6 tptp.x_a) (X_1 tptp.pname) (A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A)) (= (tptp.image_pname_a (tptp.cOMBK_a_pname C_6) A) (tptp.hAPP_f2050579477a_bool (tptp.hAPP_a1206381875a_bool tptp.insert_a C_6) tptp.bot_bot_fun_a_bool)))) (forall ((C_6 tptp.int) (A tptp.fun_nat_bool)) (let ((_let_1 (tptp.image_nat_int (tptp.cOMBK_int_nat C_6) A))) (let ((_let_2 (= A tptp.bot_bot_fun_nat_bool))) (and (=> _let_2 (= _let_1 tptp.bot_bot_fun_int_bool)) (=> (not _let_2) (= _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int C_6) tptp.bot_bot_fun_int_bool))))))) (forall ((C_6 tptp.x_a) (A tptp.fun_pname_bool)) (let ((_let_1 (tptp.image_pname_a (tptp.cOMBK_a_pname C_6) A))) (let ((_let_2 (= A tptp.bot_bo844097828e_bool))) (and (=> _let_2 (= _let_1 tptp.bot_bot_fun_a_bool)) (=> (not _let_2) (= _let_1 (tptp.hAPP_f2050579477a_bool (tptp.hAPP_a1206381875a_bool tptp.insert_a C_6) tptp.bot_bot_fun_a_bool))))))) (forall ((A_2 tptp.int) (B_3 tptp.int) (C_6 tptp.int) (D_1 tptp.int)) (=> (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int A_2) B_3) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int C_6) D_1)) (= (= A_2 B_3) (= C_6 D_1)))) (forall ((A tptp.fun_int_bool) (B tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int B)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool B) A)) (= (tptp.hAPP_f957591787ol_nat tptp.finite_card_int (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) B)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_f957591787ol_nat tptp.finite_card_int A)) (tptp.hAPP_f957591787ol_nat tptp.finite_card_int B)))))) (forall ((A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat B)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool B) A)) (= (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) B)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat A)) (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat B)))))) (forall ((A tptp.fun_a_bool) (B tptp.fun_a_bool)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a B)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool B) A)) (= (tptp.hAPP_fun_a_bool_nat tptp.finite_card_a (tptp.hAPP_f2050579477a_bool (tptp.hAPP_f1791771145a_bool tptp.minus_1762468890a_bool A) B)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_fun_a_bool_nat tptp.finite_card_a A)) (tptp.hAPP_fun_a_bool_nat tptp.finite_card_a B)))))) (forall ((A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) A)) (= (tptp.hAPP_f921600141ol_nat tptp.finite_card_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A) B)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_f921600141ol_nat tptp.finite_card_pname A)) (tptp.hAPP_f921600141ol_nat tptp.finite_card_pname B)))))) (forall ((A tptp.fun_int_bool) (B tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int B)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_f957591787ol_nat tptp.finite_card_int A)) (tptp.hAPP_f957591787ol_nat tptp.finite_card_int B))) (tptp.hAPP_f957591787ol_nat tptp.finite_card_int (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) B)))))) (forall ((A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat B)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat A)) (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat B))) (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) B)))))) (forall ((A tptp.fun_a_bool) (B tptp.fun_a_bool)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a B)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_fun_a_bool_nat tptp.finite_card_a A)) (tptp.hAPP_fun_a_bool_nat tptp.finite_card_a B))) (tptp.hAPP_fun_a_bool_nat tptp.finite_card_a (tptp.hAPP_f2050579477a_bool (tptp.hAPP_f1791771145a_bool tptp.minus_1762468890a_bool A) B)))))) (forall ((A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_f921600141ol_nat tptp.finite_card_pname A)) (tptp.hAPP_f921600141ol_nat tptp.finite_card_pname B))) (tptp.hAPP_f921600141ol_nat tptp.finite_card_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A) B)))))) (forall ((Pa tptp.fun_fun_a_bool_bool) (A tptp.fun_a_bool) (F_1 tptp.fun_a_bool)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a F_1)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool F_1) A)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool Pa tptp.bot_bot_fun_a_bool)) (=> (forall ((A_14 tptp.x_a) (F_2 tptp.fun_a_bool)) (let ((_let_1 (tptp.hAPP_a85458249l_bool tptp.member_a A_14))) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a F_2)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 A)) (=> (not (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 F_2))) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool Pa F_2)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool Pa (tptp.hAPP_f2050579477a_bool (tptp.hAPP_a1206381875a_bool tptp.insert_a A_14) F_2))))))))) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool Pa F_1))))))) (forall ((Pa tptp.fun_fu819804446l_bool) (A tptp.fun_int_bool) (F_1 tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int F_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool F_1) A)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool Pa tptp.bot_bot_fun_int_bool)) (=> (forall ((A_14 tptp.int) (F_2 tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_i2112223885l_bool tptp.member_int A_14))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int F_2)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 A)) (=> (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 F_2))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool Pa F_2)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool Pa (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_14) F_2))))))))) (tptp.hBOOL (tptp.hAPP_f448129468l_bool Pa F_1))))))) (forall ((Pa tptp.fun_fu425979586l_bool) (A tptp.fun_nat_bool) (F_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat F_1)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool F_1) A)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool Pa tptp.bot_bot_fun_nat_bool)) (=> (forall ((A_14 tptp.nat) (F_2 tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat A_14))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat F_2)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 A)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 F_2))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool Pa F_2)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool Pa (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_14) F_2))))))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool Pa F_1))))))) (forall ((Pa tptp.fun_fu1430349052l_bool) (A tptp.fun_pname_bool) (F_1 tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname F_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool F_1) A)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool Pa tptp.bot_bo844097828e_bool)) (=> (forall ((A_14 tptp.pname) (F_2 tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname A_14))) (=> (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 Pa F_2)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool Pa (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A_14) F_2))))))))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool Pa F_1))))))) (forall ((Pn tptp.pname) (G tptp.fun_a_bool)) (let ((_let_1 (tptp.hAPP_a1206381875a_bool tptp.insert_a (tptp.hAPP_pname_a tptp.mgt_call Pn)))) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.p (tptp.hAPP_f2050579477a_bool _let_1 G)) (tptp.hAPP_f2050579477a_bool (tptp.hAPP_a1206381875a_bool tptp.insert_a (tptp.mgt (tptp.the_com (tptp.body Pn)))) tptp.bot_bot_fun_a_bool))) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.p G) (tptp.hAPP_f2050579477a_bool _let_1 tptp.bot_bot_fun_a_bool)))))) (forall ((Pa tptp.fun_fun_a_bool_bool) (A tptp.fun_a_bool)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a A)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool Pa A)) (=> (forall ((A_14 tptp.x_a) (A_15 tptp.fun_a_bool)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a A_15)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a A_14) A_15)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool Pa A_15)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool Pa (tptp.hAPP_f2050579477a_bool (tptp.hAPP_f1791771145a_bool tptp.minus_1762468890a_bool A_15) (tptp.hAPP_f2050579477a_bool (tptp.hAPP_a1206381875a_bool tptp.insert_a A_14) tptp.bot_bot_fun_a_bool)))))))) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool Pa tptp.bot_bot_fun_a_bool)))))) (forall ((Pa tptp.fun_fu819804446l_bool) (A tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool Pa A)) (=> (forall ((A_14 tptp.int) (A_15 tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A_15)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int A_14) A_15)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool Pa A_15)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool Pa (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A_15) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_14) tptp.bot_bot_fun_int_bool)))))))) (tptp.hBOOL (tptp.hAPP_f448129468l_bool Pa tptp.bot_bot_fun_int_bool)))))) (forall ((Pa tptp.fun_fu425979586l_bool) (A tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool Pa A)) (=> (forall ((A_14 tptp.nat) (A_15 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A_15)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_14) A_15)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool Pa A_15)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool Pa (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A_15) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_14) tptp.bot_bot_fun_nat_bool)))))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool Pa tptp.bot_bot_fun_nat_bool)))))) (forall ((Pa tptp.fun_fu1430349052l_bool) (A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool Pa A)) (=> (forall ((A_14 tptp.pname) (A_15 tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A_15)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A_14) A_15)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool Pa A_15)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool Pa (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A_15) (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A_14) tptp.bot_bo844097828e_bool)))))))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool Pa tptp.bot_bo844097828e_bool)))))) (forall ((Pa tptp.fun_fun_a_bool_bool) (F_1 tptp.fun_a_bool)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a F_1)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool Pa tptp.bot_bot_fun_a_bool)) (=> (forall ((X_2 tptp.x_a) (F_2 tptp.fun_a_bool)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a F_2)) (=> (not (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a X_2) F_2))) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool Pa F_2)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool Pa (tptp.hAPP_f2050579477a_bool (tptp.hAPP_a1206381875a_bool tptp.insert_a X_2) F_2))))))) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool Pa F_1)))))) (forall ((Pa tptp.fun_fu819804446l_bool) (F_1 tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int F_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool Pa tptp.bot_bot_fun_int_bool)) (=> (forall ((X_2 tptp.int) (F_2 tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int F_2)) (=> (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_2) F_2))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool Pa F_2)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool Pa (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_2) F_2))))))) (tptp.hBOOL (tptp.hAPP_f448129468l_bool Pa F_1)))))) (forall ((Pa tptp.fun_fu425979586l_bool) (F_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat F_1)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool Pa tptp.bot_bot_fun_nat_bool)) (=> (forall ((X_2 tptp.nat) (F_2 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat F_2)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) F_2))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool Pa F_2)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool Pa (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_2) F_2))))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool Pa F_1)))))) (forall ((Pa tptp.fun_fu1430349052l_bool) (F_1 tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname F_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool Pa tptp.bot_bo844097828e_bool)) (=> (forall ((X_2 tptp.pname) (F_2 tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname F_2)) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) F_2))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool Pa F_2)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool Pa (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname X_2) F_2))))))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool Pa F_1)))))) (forall ((A_2 tptp.fun_a_bool)) (= (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a A_2)) (or (= A_2 tptp.bot_bot_fun_a_bool) (exists ((A_15 tptp.fun_a_bool) (A_14 tptp.x_a)) (and (= A_2 (tptp.hAPP_f2050579477a_bool (tptp.hAPP_a1206381875a_bool tptp.insert_a A_14) A_15)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a A_15))))))) (forall ((A_2 tptp.fun_int_bool)) (= (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A_2)) (or (= A_2 tptp.bot_bot_fun_int_bool) (exists ((A_15 tptp.fun_int_bool) (A_14 tptp.int)) (and (= A_2 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_14) A_15)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A_15))))))) (forall ((A_2 tptp.fun_nat_bool)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A_2)) (or (= A_2 tptp.bot_bot_fun_nat_bool) (exists ((A_15 tptp.fun_nat_bool) (A_14 tptp.nat)) (and (= A_2 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_14) A_15)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A_15))))))) (forall ((A_2 tptp.fun_pname_bool)) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A_2)) (or (= A_2 tptp.bot_bo844097828e_bool) (exists ((A_15 tptp.fun_pname_bool) (A_14 tptp.pname)) (and (= A_2 (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A_14) A_15)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A_15))))))) (forall ((U tptp.nat) (F tptp.fun_nat_nat)) (=> (forall ((N_1 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_1) (tptp.hAPP_nat_nat F N_1)))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.hAPP_n1699378549t_bool (tptp.cOMBC_nat_nat_bool (tptp.cOMBB_800536526ol_nat tptp.ord_less_eq_nat F)) U)))))) (forall ((X_1 tptp.x_a)) (= (tptp.hAPP_fun_a_bool_a tptp.the_elem_a (tptp.hAPP_f2050579477a_bool (tptp.hAPP_a1206381875a_bool tptp.insert_a X_1) tptp.bot_bot_fun_a_bool)) X_1)) (forall ((X_1 tptp.nat)) (= (tptp.hAPP_f22106695ol_nat tptp.the_elem_nat (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) tptp.bot_bot_fun_nat_bool)) X_1)) (forall ((X_1 tptp.int)) (= (tptp.hAPP_f1594865479ol_int tptp.the_elem_int (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1) tptp.bot_bot_fun_int_bool)) X_1)) (forall ((A tptp.fun_a_bool)) (= (not (= A tptp.bot_bot_fun_a_bool)) (exists ((X_2 tptp.x_a) (B_15 tptp.fun_a_bool)) (and (= A (tptp.hAPP_f2050579477a_bool (tptp.hAPP_a1206381875a_bool tptp.insert_a X_2) B_15)) (not (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a X_2) B_15))))))) (forall ((A tptp.fun_int_bool)) (= (not (= A tptp.bot_bot_fun_int_bool)) (exists ((X_2 tptp.int) (B_15 tptp.fun_int_bool)) (and (= A (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_2) B_15)) (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_2) B_15))))))) (forall ((A tptp.fun_nat_bool)) (= (not (= A tptp.bot_bot_fun_nat_bool)) (exists ((X_2 tptp.nat) (B_15 tptp.fun_nat_bool)) (and (= A (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_2) B_15)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) B_15))))))) (forall ((A tptp.fun_pname_bool)) (= (not (= A tptp.bot_bo844097828e_bool)) (exists ((X_2 tptp.pname) (B_15 tptp.fun_pname_bool)) (and (= A (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname X_2) B_15)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) B_15))))))) (forall ((Pn tptp.pname)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname Pn) tptp.u)) (tptp.hBOOL (tptp.wt (tptp.the_com (tptp.body Pn)))))) (forall ((C_6 tptp.int) (A tptp.fun_int_bool) (B tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_i2112223885l_bool tptp.member_int C_6))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) B))) (not (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 B))))))) (forall ((C_6 tptp.nat) (A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat C_6))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) B))) (not (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B))))))) (forall ((C_6 tptp.x_a) (A tptp.fun_a_bool) (B tptp.fun_a_bool)) (let ((_let_1 (tptp.hAPP_a85458249l_bool tptp.member_a C_6))) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 (tptp.hAPP_f2050579477a_bool (tptp.hAPP_f1791771145a_bool tptp.minus_1762468890a_bool A) B))) (not (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 B))))))) (forall ((C_6 tptp.pname) (A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname C_6))) (=> (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 ((B tptp.fun_int_bool) (C_6 tptp.int) (A tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_i2112223885l_bool tptp.member_int C_6))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 A)) (=> (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 B))) (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) B))))))) (forall ((B tptp.fun_nat_bool) (C_6 tptp.nat) (A tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat C_6))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 A)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) B))))))) (forall ((B tptp.fun_a_bool) (C_6 tptp.x_a) (A tptp.fun_a_bool)) (let ((_let_1 (tptp.hAPP_a85458249l_bool tptp.member_a C_6))) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 A)) (=> (not (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 B))) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 (tptp.hAPP_f2050579477a_bool (tptp.hAPP_f1791771145a_bool tptp.minus_1762468890a_bool A) B))))))) (forall ((B tptp.fun_pname_bool) (C_6 tptp.pname) (A tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname C_6))) (=> (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 ((C_6 tptp.int) (A tptp.fun_int_bool) (B tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_i2112223885l_bool tptp.member_int C_6))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) B))) (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 B)))))) (forall ((C_6 tptp.nat) (A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat C_6))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) B))) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B)))))) (forall ((C_6 tptp.x_a) (A tptp.fun_a_bool) (B tptp.fun_a_bool)) (let ((_let_1 (tptp.hAPP_a85458249l_bool tptp.member_a C_6))) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 (tptp.hAPP_f2050579477a_bool (tptp.hAPP_f1791771145a_bool tptp.minus_1762468890a_bool A) B))) (not (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 B)))))) (forall ((C_6 tptp.pname) (A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname C_6))) (=> (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_6 tptp.int) (A tptp.fun_int_bool) (B tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_i2112223885l_bool tptp.member_int C_6))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) B))) (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 A))))) (forall ((C_6 tptp.nat) (A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat C_6))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) B))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 A))))) (forall ((C_6 tptp.x_a) (A tptp.fun_a_bool) (B tptp.fun_a_bool)) (let ((_let_1 (tptp.hAPP_a85458249l_bool tptp.member_a C_6))) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 (tptp.hAPP_f2050579477a_bool (tptp.hAPP_f1791771145a_bool tptp.minus_1762468890a_bool A) B))) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 A))))) (forall ((C_6 tptp.pname) (A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname C_6))) (=> (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_6 tptp.int) (A tptp.fun_int_bool) (B tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_i2112223885l_bool tptp.member_int C_6))) (= (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) B))) (and (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 A)) (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 B))))))) (forall ((C_6 tptp.nat) (A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat C_6))) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) B))) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 A)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B))))))) (forall ((C_6 tptp.x_a) (A tptp.fun_a_bool) (B tptp.fun_a_bool)) (let ((_let_1 (tptp.hAPP_a85458249l_bool tptp.member_a C_6))) (= (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 (tptp.hAPP_f2050579477a_bool (tptp.hAPP_f1791771145a_bool tptp.minus_1762468890a_bool A) B))) (and (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 A)) (not (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 B))))))) (forall ((C_6 tptp.pname) (A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname C_6))) (= (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 ((A tptp.fun_int_bool) (B tptp.fun_int_bool)) (let ((_let_1 (tptp.cOMBC_94739984l_bool tptp.member_int))) (= (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) B) (tptp.collect_int (tptp.cOMBS_int_bool_bool (tptp.cOMBB_1652995168ol_int tptp.fconj (tptp.hAPP_f1805168059t_bool _let_1 A)) (tptp.cOMBB_bool_bool_int tptp.fNot (tptp.hAPP_f1805168059t_bool _let_1 B))))))) (forall ((A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (let ((_let_1 (tptp.cOMBC_226598744l_bool tptp.member_nat))) (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) B) (tptp.collect_nat (tptp.cOMBS_nat_bool_bool (tptp.cOMBB_1015721476ol_nat tptp.fconj (tptp.hAPP_f800510211t_bool _let_1 A)) (tptp.cOMBB_bool_bool_nat tptp.fNot (tptp.hAPP_f800510211t_bool _let_1 B))))))) (forall ((A tptp.fun_a_bool) (B tptp.fun_a_bool)) (let ((_let_1 (tptp.cOMBC_1355376034l_bool tptp.member_a))) (= (tptp.hAPP_f2050579477a_bool (tptp.hAPP_f1791771145a_bool tptp.minus_1762468890a_bool A) B) (tptp.collect_a (tptp.cOMBS_a_bool_bool (tptp.cOMBB_1972296269bool_a tptp.fconj (tptp.hAPP_f2050579477a_bool _let_1 A)) (tptp.cOMBB_bool_bool_a tptp.fNot (tptp.hAPP_f2050579477a_bool _let_1 B))))))) (forall ((A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (let ((_let_1 (tptp.cOMBC_1058051404l_bool tptp.member_pname))) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A) B) (tptp.collect_pname (tptp.cOMBS_568398431l_bool (tptp.cOMBB_675860798_pname tptp.fconj (tptp.hAPP_f759274231e_bool _let_1 A)) (tptp.cOMBB_647938656_pname tptp.fNot (tptp.hAPP_f759274231e_bool _let_1 B))))))) (forall ((X_1 tptp.x_a) (A tptp.fun_a_bool) (F tptp.fun_a_fun_a_a) (F_1 tptp.fun_fun_a_bool_a)) (let ((_let_1 (tptp.hAPP_a1206381875a_bool tptp.insert_a X_1))) (let ((_let_2 (tptp.hAPP_f2050579477a_bool (tptp.hAPP_f1791771145a_bool tptp.minus_1762468890a_bool A) (tptp.hAPP_f2050579477a_bool _let_1 tptp.bot_bot_fun_a_bool)))) (let ((_let_3 (tptp.hAPP_fun_a_bool_a F_1 (tptp.hAPP_f2050579477a_bool _let_1 A)))) (let ((_let_4 (= _let_2 tptp.bot_bot_fun_a_bool))) (=> (tptp.hBOOL (tptp.finite_folding_one_a F F_1)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a A)) (and (=> _let_4 (= _let_3 X_1)) (=> (not _let_4) (= _let_3 (tptp.hAPP_a_a (tptp.hAPP_a_fun_a_a F X_1) (tptp.hAPP_fun_a_bool_a F_1 _let_2)))))))))))) (forall ((X_1 tptp.int) (A tptp.fun_int_bool) (F tptp.fun_int_fun_int_int) (F_1 tptp.fun_fun_int_bool_int)) (let ((_let_1 (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1))) (let ((_let_2 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) (tptp.hAPP_f1805168059t_bool _let_1 tptp.bot_bot_fun_int_bool)))) (let ((_let_3 (tptp.hAPP_f1594865479ol_int F_1 (tptp.hAPP_f1805168059t_bool _let_1 A)))) (let ((_let_4 (= _let_2 tptp.bot_bot_fun_int_bool))) (=> (tptp.hBOOL (tptp.finite1626084323ne_int F F_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (and (=> _let_4 (= _let_3 X_1)) (=> (not _let_4) (= _let_3 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int F X_1) (tptp.hAPP_f1594865479ol_int F_1 _let_2)))))))))))) (forall ((X_1 tptp.nat) (A tptp.fun_nat_bool) (F tptp.fun_nat_fun_nat_nat) (F_1 tptp.fun_fun_nat_bool_nat)) (let ((_let_1 (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1))) (let ((_let_2 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) (tptp.hAPP_f800510211t_bool _let_1 tptp.bot_bot_fun_nat_bool)))) (let ((_let_3 (tptp.hAPP_f22106695ol_nat F_1 (tptp.hAPP_f800510211t_bool _let_1 A)))) (let ((_let_4 (= _let_2 tptp.bot_bot_fun_nat_bool))) (=> (tptp.hBOOL (tptp.finite988810631ne_nat F F_1)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (and (=> _let_4 (= _let_3 X_1)) (=> (not _let_4) (= _let_3 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat F X_1) (tptp.hAPP_f22106695ol_nat F_1 _let_2)))))))))))) (forall ((X_1 tptp.pname) (A tptp.fun_pname_bool) (F tptp.fun_pn1208287926_pname) (F_1 tptp.fun_fu1499449723_pname)) (let ((_let_1 (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1))) (let ((_let_2 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A) (tptp.hAPP_f759274231e_bool _let_1 tptp.bot_bo844097828e_bool)))) (let ((_let_3 (tptp.hAPP_f1297739591_pname F_1 (tptp.hAPP_f759274231e_bool _let_1 A)))) (let ((_let_4 (= _let_2 tptp.bot_bo844097828e_bool))) (=> (tptp.hBOOL (tptp.finite1282449217_pname F F_1)) (=> (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 F_1 _let_2)))))))))))) (forall ((X_1 tptp.x_a) (A tptp.fun_a_bool) (F tptp.fun_a_fun_a_a) (F_1 tptp.fun_fun_a_bool_a)) (let ((_let_1 (tptp.hAPP_f2050579477a_bool (tptp.hAPP_f1791771145a_bool tptp.minus_1762468890a_bool A) (tptp.hAPP_f2050579477a_bool (tptp.hAPP_a1206381875a_bool tptp.insert_a X_1) tptp.bot_bot_fun_a_bool)))) (let ((_let_2 (tptp.hAPP_fun_a_bool_a F_1 A))) (let ((_let_3 (= _let_1 tptp.bot_bot_fun_a_bool))) (=> (tptp.hBOOL (tptp.finite_folding_one_a F F_1)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a A)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a X_1) A)) (and (=> _let_3 (= _let_2 X_1)) (=> (not _let_3) (= _let_2 (tptp.hAPP_a_a (tptp.hAPP_a_fun_a_a F X_1) (tptp.hAPP_fun_a_bool_a F_1 _let_1)))))))))))) (forall ((X_1 tptp.int) (A tptp.fun_int_bool) (F tptp.fun_int_fun_int_int) (F_1 tptp.fun_fun_int_bool_int)) (let ((_let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1) tptp.bot_bot_fun_int_bool)))) (let ((_let_2 (tptp.hAPP_f1594865479ol_int F_1 A))) (let ((_let_3 (= _let_1 tptp.bot_bot_fun_int_bool))) (=> (tptp.hBOOL (tptp.finite1626084323ne_int F F_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A)) (and (=> _let_3 (= _let_2 X_1)) (=> (not _let_3) (= _let_2 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int F X_1) (tptp.hAPP_f1594865479ol_int F_1 _let_1)))))))))))) (forall ((X_1 tptp.nat) (A tptp.fun_nat_bool) (F tptp.fun_nat_fun_nat_nat) (F_1 tptp.fun_fun_nat_bool_nat)) (let ((_let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) tptp.bot_bot_fun_nat_bool)))) (let ((_let_2 (tptp.hAPP_f22106695ol_nat F_1 A))) (let ((_let_3 (= _let_1 tptp.bot_bot_fun_nat_bool))) (=> (tptp.hBOOL (tptp.finite988810631ne_nat F F_1)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)) (and (=> _let_3 (= _let_2 X_1)) (=> (not _let_3) (= _let_2 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat F X_1) (tptp.hAPP_f22106695ol_nat F_1 _let_1)))))))))))) (forall ((X_1 tptp.pname) (A tptp.fun_pname_bool) (F tptp.fun_pn1208287926_pname) (F_1 tptp.fun_fu1499449723_pname)) (let ((_let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A) (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1) tptp.bot_bo844097828e_bool)))) (let ((_let_2 (tptp.hAPP_f1297739591_pname F_1 A))) (let ((_let_3 (= _let_1 tptp.bot_bo844097828e_bool))) (=> (tptp.hBOOL (tptp.finite1282449217_pname F F_1)) (=> (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 F_1 _let_1)))))))))))) (forall ((X_1 tptp.x_a) (A tptp.fun_a_bool)) (let ((_let_1 (tptp.hAPP_fun_a_bool_nat tptp.finite_card_a A))) (let ((_let_2 (tptp.hAPP_fun_a_bool_nat tptp.finite_card_a (tptp.hAPP_f2050579477a_bool (tptp.hAPP_f1791771145a_bool tptp.minus_1762468890a_bool A) (tptp.hAPP_f2050579477a_bool (tptp.hAPP_a1206381875a_bool tptp.insert_a X_1) tptp.bot_bot_fun_a_bool))))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a X_1) A)))) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a A)) (and (=> _let_3 (= _let_2 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat _let_1) tptp.one_one_nat))) (=> (not _let_3) (= _let_2 _let_1)))))))) (forall ((X_1 tptp.int) (A tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_f957591787ol_nat tptp.finite_card_int A))) (let ((_let_2 (tptp.hAPP_f957591787ol_nat tptp.finite_card_int (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1) tptp.bot_bot_fun_int_bool))))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A)))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (and (=> _let_3 (= _let_2 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat _let_1) tptp.one_one_nat))) (=> (not _let_3) (= _let_2 _let_1)))))))) (forall ((X_1 tptp.nat) (A tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat A))) (let ((_let_2 (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) tptp.bot_bot_fun_nat_bool))))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (and (=> _let_3 (= _let_2 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat _let_1) tptp.one_one_nat))) (=> (not _let_3) (= _let_2 _let_1)))))))) (forall ((X_1 tptp.pname) (A tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f921600141ol_nat tptp.finite_card_pname A))) (let ((_let_2 (tptp.hAPP_f921600141ol_nat tptp.finite_card_pname (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_3 (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A)))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (and (=> _let_3 (= _let_2 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat _let_1) tptp.one_one_nat))) (=> (not _let_3) (= _let_2 _let_1)))))))) (forall ((X_1 tptp.x_a) (A tptp.fun_a_bool)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a A)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a X_1) A)) (= (tptp.hAPP_fun_a_bool_nat tptp.finite_card_a (tptp.hAPP_f2050579477a_bool (tptp.hAPP_f1791771145a_bool tptp.minus_1762468890a_bool A) (tptp.hAPP_f2050579477a_bool (tptp.hAPP_a1206381875a_bool tptp.insert_a X_1) tptp.bot_bot_fun_a_bool))) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_fun_a_bool_nat tptp.finite_card_a A)) tptp.one_one_nat))))) (forall ((X_1 tptp.int) (A tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A)) (= (tptp.hAPP_f957591787ol_nat tptp.finite_card_int (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1) tptp.bot_bot_fun_int_bool))) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_f957591787ol_nat tptp.finite_card_int A)) tptp.one_one_nat))))) (forall ((X_1 tptp.nat) (A tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)) (= (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) tptp.bot_bot_fun_nat_bool))) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat A)) tptp.one_one_nat))))) (forall ((X_1 tptp.pname) (A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A)) (= (tptp.hAPP_f921600141ol_nat tptp.finite_card_pname (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))) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_f921600141ol_nat tptp.finite_card_pname A)) tptp.one_one_nat))))) (forall ((X_1 tptp.int)) (= (= tptp.one_one_int X_1) (= X_1 tptp.one_one_int))) (forall ((X_1 tptp.nat)) (= (= tptp.one_one_nat X_1) (= X_1 tptp.one_one_nat))) (forall ((N tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat tptp.suc N)) tptp.one_one_nat) N)) (forall ((M_1 tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M_1))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat tptp.suc N)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat _let_1 tptp.one_one_nat)) N)))) (forall ((X_1 tptp.x_a) (F tptp.fun_a_fun_a_a) (F_1 tptp.fun_fun_a_bool_a)) (=> (tptp.hBOOL (tptp.finite_folding_one_a F F_1)) (= (tptp.hAPP_fun_a_bool_a F_1 (tptp.hAPP_f2050579477a_bool (tptp.hAPP_a1206381875a_bool tptp.insert_a X_1) tptp.bot_bot_fun_a_bool)) X_1))) (forall ((X_1 tptp.nat) (F tptp.fun_nat_fun_nat_nat) (F_1 tptp.fun_fun_nat_bool_nat)) (=> (tptp.hBOOL (tptp.finite988810631ne_nat F F_1)) (= (tptp.hAPP_f22106695ol_nat F_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) tptp.bot_bot_fun_nat_bool)) X_1))) (forall ((X_1 tptp.int) (F tptp.fun_int_fun_int_int) (F_1 tptp.fun_fun_int_bool_int)) (=> (tptp.hBOOL (tptp.finite1626084323ne_int F F_1)) (= (tptp.hAPP_f1594865479ol_int F_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1) tptp.bot_bot_fun_int_bool)) X_1))) (forall ((B tptp.fun_a_bool) (A_2 tptp.x_a) (A tptp.fun_a_bool)) (let ((_let_1 (tptp.hAPP_f1791771145a_bool tptp.minus_1762468890a_bool A))) (let ((_let_2 (tptp.hAPP_a85458249l_bool tptp.member_a A_2))) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a A)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_2 A)) (=> (not (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_2 B))) (= (tptp.hAPP_fun_a_bool_nat tptp.finite_card_a (tptp.hAPP_f2050579477a_bool _let_1 (tptp.hAPP_f2050579477a_bool (tptp.hAPP_a1206381875a_bool tptp.insert_a A_2) B))) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_fun_a_bool_nat tptp.finite_card_a (tptp.hAPP_f2050579477a_bool _let_1 B))) tptp.one_one_nat)))))))) (forall ((B tptp.fun_int_bool) (A_2 tptp.int) (A tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A))) (let ((_let_2 (tptp.hAPP_i2112223885l_bool tptp.member_int A_2))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_2 A)) (=> (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_2 B))) (= (tptp.hAPP_f957591787ol_nat tptp.finite_card_int (tptp.hAPP_f1805168059t_bool _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_2) B))) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_f957591787ol_nat tptp.finite_card_int (tptp.hAPP_f1805168059t_bool _let_1 B))) tptp.one_one_nat)))))))) (forall ((B tptp.fun_nat_bool) (A_2 tptp.nat) (A tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A))) (let ((_let_2 (tptp.hAPP_n215258509l_bool tptp.member_nat A_2))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_2 A)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_2 B))) (= (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat (tptp.hAPP_f800510211t_bool _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_2) B))) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat (tptp.hAPP_f800510211t_bool _let_1 B))) tptp.one_one_nat)))))))) (forall ((B tptp.fun_pname_bool) (A_2 tptp.pname) (A tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A))) (let ((_let_2 (tptp.hAPP_p338031245l_bool tptp.member_pname A_2))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_2 A)) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_2 B))) (= (tptp.hAPP_f921600141ol_nat tptp.finite_card_pname (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A_2) B))) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_f921600141ol_nat tptp.finite_card_pname (tptp.hAPP_f759274231e_bool _let_1 B))) tptp.one_one_nat)))))))) (forall ((X_1 tptp.x_a) (A tptp.fun_a_bool) (F tptp.fun_a_fun_a_a) (F_1 tptp.fun_fun_a_bool_a)) (=> (tptp.hBOOL (tptp.finite_folding_one_a F F_1)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a A)) (=> (not (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a X_1) A))) (=> (not (= A tptp.bot_bot_fun_a_bool)) (= (tptp.hAPP_fun_a_bool_a F_1 (tptp.hAPP_f2050579477a_bool (tptp.hAPP_a1206381875a_bool tptp.insert_a X_1) A)) (tptp.hAPP_a_a (tptp.hAPP_a_fun_a_a F X_1) (tptp.hAPP_fun_a_bool_a F_1 A)))))))) (forall ((X_1 tptp.int) (A tptp.fun_int_bool) (F tptp.fun_int_fun_int_int) (F_1 tptp.fun_fun_int_bool_int)) (=> (tptp.hBOOL (tptp.finite1626084323ne_int F F_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (=> (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A))) (=> (not (= A tptp.bot_bot_fun_int_bool)) (= (tptp.hAPP_f1594865479ol_int F_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1) A)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int F X_1) (tptp.hAPP_f1594865479ol_int F_1 A)))))))) (forall ((X_1 tptp.nat) (A tptp.fun_nat_bool) (F tptp.fun_nat_fun_nat_nat) (F_1 tptp.fun_fun_nat_bool_nat)) (=> (tptp.hBOOL (tptp.finite988810631ne_nat F F_1)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A))) (=> (not (= A tptp.bot_bot_fun_nat_bool)) (= (tptp.hAPP_f22106695ol_nat F_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) A)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat F X_1) (tptp.hAPP_f22106695ol_nat F_1 A)))))))) (forall ((X_1 tptp.pname) (A tptp.fun_pname_bool) (F tptp.fun_pn1208287926_pname) (F_1 tptp.fun_fu1499449723_pname)) (=> (tptp.hBOOL (tptp.finite1282449217_pname F F_1)) (=> (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 F_1 (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 F_1 A)))))))) (forall ((A tptp.fun_a_bool) (F tptp.fun_a_fun_a_a) (F_1 tptp.fun_fun_a_bool_a)) (=> (tptp.hBOOL (tptp.finite_folding_one_a F F_1)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a A)) (=> (not (= A tptp.bot_bot_fun_a_bool)) (=> (forall ((X_2 tptp.x_a) (Y_2 tptp.x_a)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a (tptp.hAPP_a_a (tptp.hAPP_a_fun_a_a F X_2) Y_2)) (tptp.hAPP_f2050579477a_bool (tptp.hAPP_a1206381875a_bool tptp.insert_a X_2) (tptp.hAPP_f2050579477a_bool (tptp.hAPP_a1206381875a_bool tptp.insert_a Y_2) tptp.bot_bot_fun_a_bool))))) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a (tptp.hAPP_fun_a_bool_a F_1 A)) A))))))) (forall ((A tptp.fun_int_bool) (F tptp.fun_int_fun_int_int) (F_1 tptp.fun_fun_int_bool_int)) (=> (tptp.hBOOL (tptp.finite1626084323ne_int F F_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (=> (not (= A tptp.bot_bot_fun_int_bool)) (=> (forall ((X_2 tptp.int) (Y_2 tptp.int)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int F X_2) Y_2)) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_2) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int Y_2) tptp.bot_bot_fun_int_bool))))) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int (tptp.hAPP_f1594865479ol_int F_1 A)) A))))))) (forall ((A tptp.fun_nat_bool) (F tptp.fun_nat_fun_nat_nat) (F_1 tptp.fun_fun_nat_bool_nat)) (=> (tptp.hBOOL (tptp.finite988810631ne_nat F F_1)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (not (= A tptp.bot_bot_fun_nat_bool)) (=> (forall ((X_2 tptp.nat) (Y_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat F X_2) Y_2)) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_2) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat Y_2) tptp.bot_bot_fun_nat_bool))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat (tptp.hAPP_f22106695ol_nat F_1 A)) A))))))) (forall ((A tptp.fun_pname_bool) (F tptp.fun_pn1208287926_pname) (F_1 tptp.fun_fu1499449723_pname)) (=> (tptp.hBOOL (tptp.finite1282449217_pname F F_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (=> (not (= A tptp.bot_bo844097828e_bool)) (=> (forall ((X_2 tptp.pname) (Y_2 tptp.pname)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname (tptp.hAPP_pname_pname (tptp.hAPP_p1170154830_pname F X_2) Y_2)) (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_2) tptp.bot_bo844097828e_bool))))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname (tptp.hAPP_f1297739591_pname F_1 A)) A))))))) (forall ((X_1 tptp.x_a) (A tptp.fun_a_bool)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a A)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a X_1) A)) (= (tptp.hAPP_fun_a_bool_nat tptp.finite_card_a A) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat tptp.one_one_nat) (tptp.hAPP_fun_a_bool_nat tptp.finite_card_a (tptp.hAPP_f2050579477a_bool (tptp.hAPP_f1791771145a_bool tptp.minus_1762468890a_bool A) (tptp.hAPP_f2050579477a_bool (tptp.hAPP_a1206381875a_bool tptp.insert_a X_1) tptp.bot_bot_fun_a_bool)))))))) (forall ((X_1 tptp.int) (A tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A)) (= (tptp.hAPP_f957591787ol_nat tptp.finite_card_int A) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat tptp.one_one_nat) (tptp.hAPP_f957591787ol_nat tptp.finite_card_int (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1) tptp.bot_bot_fun_int_bool)))))))) (forall ((X_1 tptp.nat) (A tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)) (= (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat A) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat tptp.one_one_nat) (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) tptp.bot_bot_fun_nat_bool)))))))) (forall ((X_1 tptp.pname) (A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A)) (= (tptp.hAPP_f921600141ol_nat tptp.finite_card_pname A) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat tptp.one_one_nat) (tptp.hAPP_f921600141ol_nat tptp.finite_card_pname (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)))))))) (forall ((X_1 tptp.x_a) (A tptp.fun_a_bool)) (let ((_let_1 (tptp.hAPP_a1206381875a_bool tptp.insert_a X_1))) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a A)) (= (tptp.hAPP_fun_a_bool_nat tptp.finite_card_a (tptp.hAPP_f2050579477a_bool _let_1 A)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat tptp.one_one_nat) (tptp.hAPP_fun_a_bool_nat tptp.finite_card_a (tptp.hAPP_f2050579477a_bool (tptp.hAPP_f1791771145a_bool tptp.minus_1762468890a_bool A) (tptp.hAPP_f2050579477a_bool _let_1 tptp.bot_bot_fun_a_bool)))))))) (forall ((X_1 tptp.int) (A tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (= (tptp.hAPP_f957591787ol_nat tptp.finite_card_int (tptp.hAPP_f1805168059t_bool _let_1 A)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat tptp.one_one_nat) (tptp.hAPP_f957591787ol_nat tptp.finite_card_int (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) (tptp.hAPP_f1805168059t_bool _let_1 tptp.bot_bot_fun_int_bool)))))))) (forall ((X_1 tptp.nat) (A tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (= (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat (tptp.hAPP_f800510211t_bool _let_1 A)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat tptp.one_one_nat) (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) (tptp.hAPP_f800510211t_bool _let_1 tptp.bot_bot_fun_nat_bool)))))))) (forall ((X_1 tptp.pname) (A tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (= (tptp.hAPP_f921600141ol_nat tptp.finite_card_pname (tptp.hAPP_f759274231e_bool _let_1 A)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat tptp.one_one_nat) (tptp.hAPP_f921600141ol_nat tptp.finite_card_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A) (tptp.hAPP_f759274231e_bool _let_1 tptp.bot_bo844097828e_bool)))))))) (forall ((B tptp.fun_int_bool) (A tptp.fun_int_bool) (F tptp.fun_int_fun_int_int) (F_1 tptp.fun_fun_int_bool_int)) (let ((_let_1 (tptp.hAPP_f1594865479ol_int F_1 A))) (=> (tptp.hBOOL (tptp.finite1432773856em_int F F_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (=> (not (= B tptp.bot_bot_fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool B) A)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int F (tptp.hAPP_f1594865479ol_int F_1 B)) _let_1) _let_1))))))) (forall ((B tptp.fun_nat_bool) (A tptp.fun_nat_bool) (F tptp.fun_nat_fun_nat_nat) (F_1 tptp.fun_fun_nat_bool_nat)) (let ((_let_1 (tptp.hAPP_f22106695ol_nat F_1 A))) (=> (tptp.hBOOL (tptp.finite795500164em_nat F F_1)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (not (= B tptp.bot_bot_fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool B) A)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat F (tptp.hAPP_f22106695ol_nat F_1 B)) _let_1) _let_1))))))) (forall ((B tptp.fun_pname_bool) (A tptp.fun_pname_bool) (F tptp.fun_pn1208287926_pname) (F_1 tptp.fun_fu1499449723_pname)) (let ((_let_1 (tptp.hAPP_f1297739591_pname F_1 A))) (=> (tptp.hBOOL (tptp.finite89670078_pname F F_1)) (=> (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 F_1 B)) _let_1) _let_1))))))) (forall ((B tptp.fun_a_bool) (A tptp.fun_a_bool) (F tptp.fun_a_fun_a_a) (F_1 tptp.fun_fun_a_bool_a)) (let ((_let_1 (tptp.hAPP_fun_a_bool_a F_1 A))) (=> (tptp.hBOOL (tptp.finite1819937229idem_a F F_1)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a A)) (=> (not (= B tptp.bot_bot_fun_a_bool)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool B) A)) (= (tptp.hAPP_a_a (tptp.hAPP_a_fun_a_a F (tptp.hAPP_fun_a_bool_a F_1 B)) _let_1) _let_1))))))) (forall ((X_1 tptp.x_a) (A tptp.fun_a_bool) (F tptp.fun_a_fun_a_a) (F_1 tptp.fun_fun_a_bool_a)) (=> (tptp.hBOOL (tptp.finite1819937229idem_a F F_1)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a A)) (=> (not (= A tptp.bot_bot_fun_a_bool)) (= (tptp.hAPP_fun_a_bool_a F_1 (tptp.hAPP_f2050579477a_bool (tptp.hAPP_a1206381875a_bool tptp.insert_a X_1) A)) (tptp.hAPP_a_a (tptp.hAPP_a_fun_a_a F X_1) (tptp.hAPP_fun_a_bool_a F_1 A))))))) (forall ((X_1 tptp.int) (A tptp.fun_int_bool) (F tptp.fun_int_fun_int_int) (F_1 tptp.fun_fun_int_bool_int)) (=> (tptp.hBOOL (tptp.finite1432773856em_int F F_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (=> (not (= A tptp.bot_bot_fun_int_bool)) (= (tptp.hAPP_f1594865479ol_int F_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1) A)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int F X_1) (tptp.hAPP_f1594865479ol_int F_1 A))))))) (forall ((X_1 tptp.nat) (A tptp.fun_nat_bool) (F tptp.fun_nat_fun_nat_nat) (F_1 tptp.fun_fun_nat_bool_nat)) (=> (tptp.hBOOL (tptp.finite795500164em_nat F F_1)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (not (= A tptp.bot_bot_fun_nat_bool)) (= (tptp.hAPP_f22106695ol_nat F_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) A)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat F X_1) (tptp.hAPP_f22106695ol_nat F_1 A))))))) (forall ((X_1 tptp.pname) (A tptp.fun_pname_bool) (F tptp.fun_pn1208287926_pname) (F_1 tptp.fun_fu1499449723_pname)) (=> (tptp.hBOOL (tptp.finite89670078_pname F F_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (=> (not (= A tptp.bot_bo844097828e_bool)) (= (tptp.hAPP_f1297739591_pname F_1 (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 F_1 A))))))) (forall ((Pa tptp.fun_fun_a_bool_bool) (F_1 tptp.fun_a_bool)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a F_1)) (=> (not (= F_1 tptp.bot_bot_fun_a_bool)) (=> (forall ((X_2 tptp.x_a)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool Pa (tptp.hAPP_f2050579477a_bool (tptp.hAPP_a1206381875a_bool tptp.insert_a X_2) tptp.bot_bot_fun_a_bool)))) (=> (forall ((X_2 tptp.x_a) (F_2 tptp.fun_a_bool)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a F_2)) (=> (not (= F_2 tptp.bot_bot_fun_a_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a X_2) F_2))) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool Pa F_2)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool Pa (tptp.hAPP_f2050579477a_bool (tptp.hAPP_a1206381875a_bool tptp.insert_a X_2) F_2)))))))) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool Pa F_1))))))) (forall ((Pa tptp.fun_fu819804446l_bool) (F_1 tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int F_1)) (=> (not (= F_1 tptp.bot_bot_fun_int_bool)) (=> (forall ((X_2 tptp.int)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool Pa (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_2) tptp.bot_bot_fun_int_bool)))) (=> (forall ((X_2 tptp.int) (F_2 tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int F_2)) (=> (not (= F_2 tptp.bot_bot_fun_int_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_2) F_2))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool Pa F_2)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool Pa (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_2) F_2)))))))) (tptp.hBOOL (tptp.hAPP_f448129468l_bool Pa F_1))))))) (forall ((Pa tptp.fun_fu425979586l_bool) (F_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat F_1)) (=> (not (= F_1 tptp.bot_bot_fun_nat_bool)) (=> (forall ((X_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool Pa (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_2) tptp.bot_bot_fun_nat_bool)))) (=> (forall ((X_2 tptp.nat) (F_2 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat F_2)) (=> (not (= F_2 tptp.bot_bot_fun_nat_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) F_2))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool Pa F_2)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool Pa (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_2) F_2)))))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool Pa F_1))))))) (forall ((Pa tptp.fun_fu1430349052l_bool) (F_1 tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname F_1)) (=> (not (= F_1 tptp.bot_bo844097828e_bool)) (=> (forall ((X_2 tptp.pname)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool Pa (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname X_2) tptp.bot_bo844097828e_bool)))) (=> (forall ((X_2 tptp.pname) (F_2 tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname F_2)) (=> (not (= F_2 tptp.bot_bo844097828e_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) F_2))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool Pa F_2)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool Pa (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname X_2) F_2)))))))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool Pa F_1))))))) (forall ((X_3 tptp.fun_a_bool)) (= (tptp.hAPP_fun_a_bool_a tptp.the_elem_a X_3) (tptp.hAPP_fun_a_bool_a tptp.the_a (tptp.cOMBB_1273333599bool_a (tptp.hAPP_f1631501043l_bool tptp.fequal_fun_a_bool X_3) (tptp.hAPP_f1038053735a_bool (tptp.cOMBC_394484100a_bool tptp.insert_a) tptp.bot_bot_fun_a_bool))))) (forall ((X_3 tptp.fun_nat_bool)) (= (tptp.hAPP_f22106695ol_nat tptp.the_elem_nat X_3) (tptp.hAPP_f22106695ol_nat tptp.the_nat (tptp.cOMBB_955900739ol_nat (tptp.hAPP_f103356543l_bool tptp.fequal_fun_nat_bool X_3) (tptp.hAPP_f1570313510t_bool (tptp.cOMBC_178881787t_bool tptp.insert_nat) tptp.bot_bot_fun_nat_bool))))) (forall ((X_3 tptp.fun_int_bool)) (= (tptp.hAPP_f1594865479ol_int tptp.the_elem_int X_3) (tptp.hAPP_f1594865479ol_int tptp.the_int (tptp.cOMBB_1418110531ol_int (tptp.hAPP_f284875647l_bool tptp.fequal_fun_int_bool X_3) (tptp.hAPP_f1048215610t_bool (tptp.cOMBC_1683390479t_bool tptp.insert_int) tptp.bot_bot_fun_int_bool))))) (forall ((A_13 tptp.int) (B_14 tptp.int) (C_10 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_13))) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int _let_1 B_14)) C_10) (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int B_14) C_10))))) (forall ((A_13 tptp.nat) (B_14 tptp.nat) (C_10 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_13))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 B_14)) C_10) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat B_14) C_10))))) (forall ((A_2 tptp.int) (B_3 tptp.int) (C_6 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_2))) (= (= (tptp.hAPP_int_int _let_1 B_3) (tptp.hAPP_int_int _let_1 C_6)) (= B_3 C_6)))) (forall ((A_2 tptp.nat) (B_3 tptp.nat) (C_6 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_2))) (= (= (tptp.hAPP_nat_nat _let_1 B_3) (tptp.hAPP_nat_nat _let_1 C_6)) (= B_3 C_6)))) (forall ((B_3 tptp.int) (A_2 tptp.int) (C_6 tptp.int)) (= (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int B_3) A_2) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int C_6) A_2)) (= B_3 C_6))) (forall ((B_3 tptp.nat) (A_2 tptp.nat) (C_6 tptp.nat)) (= (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat B_3) A_2) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat C_6) A_2)) (= B_3 C_6))) (forall ((A_12 tptp.int) (B_13 tptp.int) (C_9 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_12))) (=> (= (tptp.hAPP_int_int _let_1 B_13) (tptp.hAPP_int_int _let_1 C_9)) (= B_13 C_9)))) (forall ((A_12 tptp.nat) (B_13 tptp.nat) (C_9 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_12))) (=> (= (tptp.hAPP_nat_nat _let_1 B_13) (tptp.hAPP_nat_nat _let_1 C_9)) (= B_13 C_9)))) (forall ((A_11 tptp.int) (B_12 tptp.int) (C_8 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_11))) (=> (= (tptp.hAPP_int_int _let_1 B_12) (tptp.hAPP_int_int _let_1 C_8)) (= B_12 C_8)))) (forall ((A_11 tptp.nat) (B_12 tptp.nat) (C_8 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_11))) (=> (= (tptp.hAPP_nat_nat _let_1 B_12) (tptp.hAPP_nat_nat _let_1 C_8)) (= B_12 C_8)))) (forall ((B_11 tptp.int) (A_10 tptp.int) (C_7 tptp.int)) (=> (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int B_11) A_10) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int C_7) A_10)) (= B_11 C_7))) (forall ((B_11 tptp.nat) (A_10 tptp.nat) (C_7 tptp.nat)) (=> (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat B_11) A_10) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat C_7) A_10)) (= B_11 C_7))) (forall ((M_1 tptp.nat) (N tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_1) N) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat N) M_1))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat X))) (let ((_let_2 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Y))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat _let_2 Z)) (tptp.hAPP_nat_nat _let_2 (tptp.hAPP_nat_nat _let_1 Z)))))) (forall ((M_1 tptp.nat) (N tptp.nat) (K_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_1))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 N)) K_1) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat N) K_1))))) (forall ((K tptp.nat) (M tptp.nat) (Na tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat K))) (= (= (tptp.hAPP_nat_nat _let_1 M) (tptp.hAPP_nat_nat _let_1 Na)) (= M Na)))) (forall ((M tptp.nat) (K tptp.nat) (Na tptp.nat)) (= (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M) K) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Na) K)) (= M Na))) (forall ((A_2 tptp.int) (C_6 tptp.int) (B_3 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_2) C_6)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int B_3) C_6))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_2) B_3)))) (forall ((A_2 tptp.nat) (C_6 tptp.nat) (B_3 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_2) C_6)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat B_3) C_6))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_2) B_3)))) (forall ((C_6 tptp.int) (A_2 tptp.int) (B_3 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.plus_plus_int C_6))) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int _let_1 A_2)) (tptp.hAPP_int_int _let_1 B_3))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_2) B_3))))) (forall ((C_6 tptp.nat) (A_2 tptp.nat) (B_3 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat C_6))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 A_2)) (tptp.hAPP_nat_nat _let_1 B_3))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_2) B_3))))) (forall ((C_5 tptp.int) (A_9 tptp.int) (B_10 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_9) B_10)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_9) C_5)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int B_10) C_5))))) (forall ((C_5 tptp.nat) (A_9 tptp.nat) (B_10 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_9) B_10)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_9) C_5)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat B_10) C_5))))) (forall ((C_4 tptp.int) (A_8 tptp.int) (B_9 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.plus_plus_int C_4))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_8) B_9)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int _let_1 A_8)) (tptp.hAPP_int_int _let_1 B_9)))))) (forall ((C_4 tptp.nat) (A_8 tptp.nat) (B_9 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat C_4))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_8) B_9)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 A_8)) (tptp.hAPP_nat_nat _let_1 B_9)))))) (forall ((C_3 tptp.int) (D_3 tptp.int) (A_7 tptp.int) (B_8 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_7) B_8)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int C_3) D_3)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_7) C_3)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int B_8) D_3)))))) (forall ((C_3 tptp.nat) (D_3 tptp.nat) (A_7 tptp.nat) (B_8 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_7) B_8)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat C_3) D_3)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_7) C_3)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat B_8) D_3)))))) (forall ((A_6 tptp.int) (C_2 tptp.int) (B_7 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_6) C_2)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int B_7) C_2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_6) B_7)))) (forall ((A_6 tptp.nat) (C_2 tptp.nat) (B_7 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_6) C_2)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat B_7) C_2))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_6) B_7)))) (forall ((C_1 tptp.int) (A_5 tptp.int) (B_6 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.plus_plus_int C_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int _let_1 A_5)) (tptp.hAPP_int_int _let_1 B_6))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_5) B_6))))) (forall ((C_1 tptp.nat) (A_5 tptp.nat) (B_6 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat C_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 A_5)) (tptp.hAPP_nat_nat _let_1 B_6))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_5) B_6))))) (forall ((A_4 tptp.int) (B_5 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int A_4) B_5)) B_5) A_4)) (forall ((A_3 tptp.int) (B_4 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_3) B_4)) B_4) A_3)) (forall ((M_1 tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_1))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat tptp.suc N)) (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat _let_1 N))))) (forall ((M_1 tptp.nat) (N tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat tptp.suc M_1)) N) (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_1) N)))) (forall ((M_1 tptp.nat) (N tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat tptp.suc M_1)) N) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_1) (tptp.hAPP_nat_nat tptp.suc N)))) (forall ((N tptp.nat) (M_1 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_1) N)))) (forall ((N tptp.nat) (M_1 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat N) M_1)))) (forall ((M tptp.nat) (Na tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) Na)) (exists ((K_2 tptp.nat)) (= Na (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M) K_2))))) (forall ((K tptp.nat) (M tptp.nat) (Na tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat K))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 M)) (tptp.hAPP_nat_nat _let_1 Na))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) Na))))) (forall ((M_1 tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 J)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat J) M_1)))))) (forall ((M_1 tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 J)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_1) J)))))) (forall ((K_1 tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_1) J)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I_1) K_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat J) K_1))))) (forall ((K_1 tptp.nat) (L_1 tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_1) J)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_1) L_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I_1) K_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat J) L_1)))))) (forall ((M_1 tptp.nat) (K_1 tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_1) K_1)) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_1) N)))) (forall ((M_1 tptp.nat) (K_1 tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_1) K_1)) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_1) N)))) (forall ((M_1 tptp.nat) (K_1 tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_1) K_1)) N)) (not (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_1) N)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_1) N))))))) (forall ((M_1 tptp.nat) (N tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_1) N)) N) M_1)) (forall ((N tptp.nat) (M_1 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat N) M_1)) N) M_1)) (forall ((I_1 tptp.nat) (J tptp.nat) (K_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat I_1))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat _let_1 J)) K_1) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat J) K_1))))) (forall ((K_1 tptp.nat) (M_1 tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat K_1))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat _let_1 M_1)) (tptp.hAPP_nat_nat _let_1 N)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M_1) N)))) (forall ((M_1 tptp.nat) (K_1 tptp.nat) (N tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_1) K_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat N) K_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M_1) N))) (forall ((I_1 tptp.nat) (K_1 tptp.nat) (J tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_1) J)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat I_1) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat J) K_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I_1) K_1)) J)))) (forall ((J_1 tptp.nat) (K tptp.nat) (I_2 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat J_1) K)) I_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat J_1) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I_2) K))))) (forall ((M_1 tptp.nat) (K_1 tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_1) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_1) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat N) M_1)) K_1))))) (forall ((N tptp.nat) (M_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N) M_1)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat N) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M_1) N)) M_1))) (forall ((I_1 tptp.nat) (K_1 tptp.nat) (J tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_1) J)) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat J) K_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat _let_1 J)) K_1))))) (forall ((I_2 tptp.nat) (K tptp.nat) (J_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K) J_1)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_2) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat J_1) K))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I_2) K)) J_1))))) (forall ((N tptp.nat) (M_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N) M_1)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M_1) N)) N) M_1))) (forall ((K tptp.nat) (I_2 tptp.nat) (J_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_2) J_1)) (= (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat J_1) I_2) K) (= J_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat K) I_2))))) (forall ((I_1 tptp.nat) (K_1 tptp.nat) (J tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_1) J)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat _let_1 J)) K_1) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat J) K_1)))))) (forall ((I_1 tptp.nat) (K_1 tptp.nat) (J tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_1) J)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat J) K_1)) I_1) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat J) I_1)) K_1)))) (forall ((I_1 tptp.nat) (K_1 tptp.nat) (J tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_1) J)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat J) I_1)) K_1) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat J) K_1)) I_1)))) (forall ((N tptp.nat)) (= (tptp.hAPP_nat_nat tptp.suc N) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat tptp.one_one_nat) N))) (forall ((N tptp.nat)) (= (tptp.hAPP_nat_nat tptp.suc N) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat N) tptp.one_one_nat))) (forall ((M_1 tptp.nat) (K_1 tptp.nat) (J tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_1) J)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M_1) (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat J) K_1))) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_1) K_1)) (tptp.hAPP_nat_nat tptp.suc J))))) (forall ((M_1 tptp.nat) (K_1 tptp.nat) (J tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_1) J)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat J) K_1))) M_1) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat tptp.suc J)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat K_1) M_1))))) (forall ((Y tptp.nat) (X tptp.nat) (Z tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Z)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Y) Z)))))) (forall ((Z tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Y) Z)))))) (forall ((N tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N) (tptp.hAPP_nat_nat tptp.suc N)))) (forall ((M_1 tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_1) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat tptp.suc M_1)) (tptp.hAPP_nat_nat tptp.suc N))))) (forall ((K tptp.nat)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.hAPP_n1699378549t_bool (tptp.cOMBC_nat_nat_bool tptp.ord_less_nat) K))))) (forall ((N tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N) N)))) (forall ((M tptp.nat) (Na tptp.nat)) (= (not (= M Na)) (or (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) Na)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Na) M))))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (= X Y)) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X) Y))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Y) X))))) (forall ((N tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N) N)))) (forall ((N tptp.nat) (M_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N) M_1)) (not (= M_1 N)))) (forall ((S tptp.nat) (T tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat S) T)) (not (= S T)))) (forall ((Pa tptp.fun_nat_fun_nat_bool) (M tptp.nat) (Na tptp.nat)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool Pa Na) M)))) (=> (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) Na)) _let_1) (=> (=> (= M Na) _let_1) (=> (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Na) M)) _let_1) _let_1))))) (forall ((M tptp.nat) (Na tptp.nat)) (= (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) Na))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Na) (tptp.hAPP_nat_nat tptp.suc M))))) (forall ((M tptp.nat) (Na tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M))) (= (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat tptp.suc Na))) (or (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Na)) (= M Na))))) (forall ((M tptp.nat) (Na tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat tptp.suc M)) (tptp.hAPP_nat_nat tptp.suc Na))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) Na)))) (forall ((Na tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Na))) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M))) (= (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat tptp.suc M))) (= Na M))))) (forall ((N tptp.nat) (M_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N))) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat tptp.suc M_1))) (= M_1 N))))) (forall ((M_1 tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat tptp.suc N)))))) (forall ((M_1 tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat tptp.suc M_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_1) N)) (=> (not (= _let_1 N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat _let_1) N)))))) (forall ((K_1 tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_1) J)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat J) K_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat tptp.suc I_1)) K_1))))) (forall ((M_1 tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat tptp.suc N))) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N))) (= M_1 N))))) (forall ((M_1 tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat tptp.suc M_1)) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_1) N)))) (forall ((M_1 tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat tptp.suc M_1)) (tptp.hAPP_nat_nat tptp.suc N))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_1) N)))) (forall ((I_1 tptp.nat) (J tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I_1) J)) I_1)))) (forall ((J tptp.nat) (I_1 tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat J) I_1)) I_1)))) (forall ((K tptp.nat) (M tptp.nat) (Na tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat K))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 M)) (tptp.hAPP_nat_nat _let_1 Na))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) Na))))) (forall ((M_1 tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 J)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat J) M_1)))))) (forall ((M_1 tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 J)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_1) J)))))) (forall ((K_1 tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_1) J)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I_1) K_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat J) K_1))))) (forall ((K_1 tptp.nat) (L_1 tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_1) J)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat K_1) L_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I_1) K_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat J) L_1)))))) (forall ((M_1 tptp.nat) (N tptp.nat) (K_1 tptp.nat) (L_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat K_1) L_1)) (=> (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_1) L_1) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat K_1) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_1) N))))) (forall ((I_1 tptp.nat) (J tptp.nat) (K_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I_1) J)) K_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_1) K_1)))) (forall ((Z tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Y) Z)))))) (forall ((Y tptp.nat) (X tptp.nat) (Z tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Z)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Y) Z)))))) (forall ((M tptp.nat) (Na tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) Na)) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) Na)) (not (= M Na))))) (forall ((M tptp.nat) (Na tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) Na)) (or (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) Na)) (= M Na)))) (forall ((M_1 tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_1) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_1) N)))) (forall ((M_1 tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_1) N)) (=> (not (= M_1 N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_1) N))))) (forall ((M_1 tptp.nat) (N tptp.nat)) (=> (or (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_1) N)) (= M_1 N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_1) N)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X) Y)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X) Y)))) (forall ((N tptp.nat) (J tptp.nat) (K_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat J) K_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat J) N)) K_1)))) (forall ((L_1 tptp.nat) (M_1 tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat L_1))) (let ((_let_2 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 N)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 L_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 N)) (tptp.hAPP_nat_nat _let_1 M_1)))))))) (forall ((N_2 tptp.fun_nat_bool)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat N_2)) (exists ((M_2 tptp.nat)) (forall ((X_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) N_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_2) M_2))))))) (forall ((Na tptp.nat)) (= (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat (tptp.collect_nat (tptp.hAPP_n1699378549t_bool (tptp.cOMBC_nat_nat_bool tptp.ord_less_nat) Na))) Na)) (forall ((Pa tptp.fun_nat_bool) (I_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.cOMBS_nat_bool_bool (tptp.cOMBB_1015721476ol_nat tptp.fconj Pa) (tptp.hAPP_n1699378549t_bool (tptp.cOMBC_nat_nat_bool tptp.ord_less_nat) I_2)))))) (forall ((I_1 tptp.nat) (M_1 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_1) (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I_1) M_1))))) (forall ((I_1 tptp.nat) (M_1 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_1) (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_1) I_1))))) (forall ((M tptp.nat) (Na tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) Na)) (exists ((K_2 tptp.nat)) (= Na (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M) K_2)))))) (forall ((Na tptp.nat) (M tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Na) M)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat tptp.suc Na)) M)))) (forall ((M tptp.nat) (Na tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) (tptp.hAPP_nat_nat tptp.suc Na))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) Na)))) (forall ((M tptp.nat) (Na tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat tptp.suc M)) Na)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) Na)))) (forall ((M_1 tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_1) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_1) (tptp.hAPP_nat_nat tptp.suc N))))) (forall ((M_1 tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_1) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat tptp.suc M_1)) N)))) (forall ((M tptp.nat) (Na tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) Na)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Na) (tptp.hAPP_nat_nat tptp.suc M))) (= Na M)))) (forall ((M_1 tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat tptp.suc M_1)) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_1) N)))) (forall ((M_1 tptp.nat) (N tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M_1) N)) (tptp.hAPP_nat_nat tptp.suc M_1)))) (forall ((I_2 tptp.nat) (J_1 tptp.nat) (K tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_2) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat J_1) K))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I_2) K)) J_1)))) (forall ((M_1 tptp.nat) (N tptp.nat)) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_1) N))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat N) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M_1) N)) M_1))) (forall ((C tptp.nat) (A_1 tptp.nat) (B_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_1) B_2)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat C) A_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat A_1) C)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat B_2) C)))))) (forall ((Na tptp.nat) (K tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Na)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M) K)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat Na) K))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) Na))))))) (forall ((X_2 tptp.nat)) (= (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_2) (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat tptp.suc X_2)))) (forall ((M tptp.nat) (K tptp.nat) (F tptp.fun_nat_nat)) (=> (forall ((M_2 tptp.nat) (N_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_2) N_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat F M_2)) (tptp.hAPP_nat_nat F N_1))))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat F M)) K)) (tptp.hAPP_nat_nat F (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M) K)))))) (forall ((Pa tptp.fun_nat_bool) (I_2 tptp.nat) (J_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_2) J_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool Pa J_1)) (=> (forall ((I tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I) J_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool Pa (tptp.hAPP_nat_nat tptp.suc I))) (tptp.hBOOL (tptp.hAPP_nat_bool Pa I))))) (tptp.hBOOL (tptp.hAPP_nat_bool Pa I_2)))))) (forall ((M_1 tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_1) N)) (exists ((K_2 tptp.nat)) (= N (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_1) K_2)))))) (forall ((Na tptp.nat) (N_2 tptp.fun_nat_bool)) (=> (forall ((X_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) N_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_2) Na)))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat N_2)))) (forall ((I_2 tptp.nat) (J_1 tptp.nat) (F tptp.fun_nat_nat)) (=> (forall ((I tptp.nat) (J_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I) J_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat F I)) (tptp.hAPP_nat_nat F J_2))))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_2) J_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat F I_2)) (tptp.hAPP_nat_nat F J_1)))))) (forall ((I_1 tptp.nat) (K_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_1) K_1)) (=> (not (= K_1 (tptp.hAPP_nat_nat tptp.suc I_1))) (not (forall ((J_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_1) J_2)) (not (= K_1 (tptp.hAPP_nat_nat tptp.suc J_2))))))))) (forall ((I_1 tptp.nat) (K_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat tptp.suc I_1)) K_1)) (not (forall ((J_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_1) J_2)) (not (= K_1 (tptp.hAPP_nat_nat tptp.suc J_2)))))))) (forall ((N tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N) tptp.zero_zero_nat)))) (forall ((N tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) N))) (forall ((N tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.hAPP_nat_nat tptp.suc N)))) (forall ((Na tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Na) tptp.zero_zero_nat)) (= Na tptp.zero_zero_nat))) (forall ((N tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) N))) (forall ((M_1 tptp.nat) (N tptp.nat)) (=> (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M_1) N) tptp.zero_zero_nat) (=> (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N) M_1) tptp.zero_zero_nat) (= M_1 N)))) (forall ((M_1 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M_1) M_1) tptp.zero_zero_nat)) (forall ((M_1 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M_1) tptp.zero_zero_nat) M_1)) (forall ((N tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)) (= tptp.bot_bot_nat tptp.zero_zero_nat) (forall ((M_1 tptp.nat) (N tptp.nat)) (=> (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_1) N) M_1) (= N tptp.zero_zero_nat))) (forall ((M tptp.nat) (Na tptp.nat)) (= (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M) Na) tptp.zero_zero_nat) (and (= M tptp.zero_zero_nat) (= Na tptp.zero_zero_nat)))) (forall ((M_1 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_1) tptp.zero_zero_nat) M_1)) (forall ((N tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat tptp.zero_zero_nat) N) N)) (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N)))) (forall ((M_1 tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_1) N)) (not (= N tptp.zero_zero_nat)))) (forall ((N tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N) tptp.zero_zero_nat)))) (forall ((Na tptp.nat)) (= (not (= Na tptp.zero_zero_nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) Na)))) (forall ((N tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N) tptp.zero_zero_nat)))) (forall ((M_1 tptp.nat)) (not (= (tptp.hAPP_nat_nat tptp.suc M_1) tptp.zero_zero_nat))) (forall ((M_1 tptp.nat)) (not (= tptp.zero_zero_nat (tptp.hAPP_nat_nat tptp.suc M_1)))) (forall ((Nat_2 tptp.nat)) (not (= (tptp.hAPP_nat_nat tptp.suc Nat_2) tptp.zero_zero_nat))) (forall ((M_1 tptp.nat)) (not (= (tptp.hAPP_nat_nat tptp.suc M_1) tptp.zero_zero_nat))) (forall ((Nat_1 tptp.nat)) (not (= tptp.zero_zero_nat (tptp.hAPP_nat_nat tptp.suc Nat_1)))) (forall ((M_1 tptp.nat)) (not (= tptp.zero_zero_nat (tptp.hAPP_nat_nat tptp.suc M_1)))) (forall ((Na tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) Na)) (exists ((M_2 tptp.nat)) (= Na (tptp.hAPP_nat_nat tptp.suc M_2))))) (forall ((Na tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Na) (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat))) (= Na tptp.zero_zero_nat))) (forall ((M tptp.nat) (Na tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) (tptp.hAPP_nat_nat tptp.suc Na))) (or (= M tptp.zero_zero_nat) (exists ((J_2 tptp.nat)) (and (= M (tptp.hAPP_nat_nat tptp.suc J_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat J_2) Na))))))) (forall ((M tptp.nat) (Na tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat))) (= (= _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M) Na)) (or (and (= M _let_1) (= Na tptp.zero_zero_nat)) (and (= M tptp.zero_zero_nat) (= Na _let_1)))))) (forall ((M tptp.nat) (Na tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat))) (= (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M) Na) _let_1) (or (and (= M _let_1) (= Na tptp.zero_zero_nat)) (and (= M tptp.zero_zero_nat) (= Na _let_1)))))) (forall ((M tptp.nat) (Na tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat))) (= (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M) Na))) (or (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Na)))))) (forall ((Na tptp.nat) (M tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat Na) M))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) Na)))) (forall ((M_1 tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M_1) N)) M_1)))))) (forall ((N tptp.nat) (M_1 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat N) M_1)) tptp.zero_zero_nat)) (forall ((M tptp.nat) (Na tptp.nat)) (= (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M) Na) tptp.zero_zero_nat) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) Na)))) (forall ((M_1 tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_1) N)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M_1) N) tptp.zero_zero_nat))) (= tptp.one_one_nat _let_17) (forall ((M tptp.nat) (Na tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat tptp.suc Na)) (tptp.hAPP_nat_nat (tptp.nat_case_nat tptp.zero_zero_nat tptp.cOMBI_nat) (tptp.hAPP_nat_nat _let_1 Na))))) (forall ((N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N) (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat))) N))) (forall ((I_1 tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N) (tptp.hAPP_nat_nat tptp.suc I_1))) N)))) (forall ((Pa tptp.fun_nat_bool) (A_2 tptp.nat) (B_3 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool Pa (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat A_2) B_3))) (and (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_2) B_3)) (tptp.hBOOL (tptp.hAPP_nat_bool Pa tptp.zero_zero_nat))) (forall ((D_2 tptp.nat)) (=> (= A_2 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat B_3) D_2)) (tptp.hBOOL (tptp.hAPP_nat_bool Pa D_2))))))) (forall ((Pa tptp.fun_nat_bool) (A_2 tptp.nat) (B_3 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool Pa (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat A_2) B_3))) (not (or (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_2) B_3)) (not (tptp.hBOOL (tptp.hAPP_nat_bool Pa tptp.zero_zero_nat)))) (exists ((D_2 tptp.nat)) (and (= A_2 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat B_3) D_2)) (not (tptp.hBOOL (tptp.hAPP_nat_bool Pa D_2))))))))) (forall ((I_2 tptp.nat) (M_3 tptp.fun_nat_bool)) (let ((_let_1 (tptp.cOMBC_nat_nat_bool tptp.ord_less_nat))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat tptp.zero_zero_nat) M_3)) (= (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat (tptp.collect_nat (tptp.cOMBS_nat_bool_bool (tptp.cOMBB_1015721476ol_nat tptp.fconj (tptp.hAPP_f800510211t_bool (tptp.cOMBC_226598744l_bool (tptp.cOMBB_1146692694ol_nat tptp.member_nat tptp.suc)) M_3)) (tptp.hAPP_n1699378549t_bool _let_1 I_2))))) (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat (tptp.collect_nat (tptp.cOMBS_nat_bool_bool (tptp.cOMBB_1015721476ol_nat tptp.fconj (tptp.hAPP_f800510211t_bool (tptp.cOMBC_226598744l_bool tptp.member_nat) M_3)) (tptp.hAPP_n1699378549t_bool _let_1 (tptp.hAPP_nat_nat tptp.suc I_2))))))))) (forall ((I_2 tptp.nat) (M_3 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat tptp.zero_zero_nat) M_3)) (not (= (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat (tptp.collect_nat (tptp.cOMBS_nat_bool_bool (tptp.cOMBB_1015721476ol_nat tptp.fconj (tptp.hAPP_f800510211t_bool (tptp.cOMBC_226598744l_bool tptp.member_nat) M_3)) (tptp.hAPP_n1699378549t_bool (tptp.cOMBC_nat_nat_bool tptp.ord_less_nat) (tptp.hAPP_nat_nat tptp.suc I_2))))) tptp.zero_zero_nat)))) (forall ((I_2 tptp.nat) (M_3 tptp.fun_nat_bool)) (let ((_let_1 (tptp.cOMBC_nat_nat_bool tptp.ord_less_nat))) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat tptp.zero_zero_nat) M_3))) (= (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat (tptp.collect_nat (tptp.cOMBS_nat_bool_bool (tptp.cOMBB_1015721476ol_nat tptp.fconj (tptp.hAPP_f800510211t_bool (tptp.cOMBC_226598744l_bool (tptp.cOMBB_1146692694ol_nat tptp.member_nat tptp.suc)) M_3)) (tptp.hAPP_n1699378549t_bool _let_1 I_2)))) (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat (tptp.collect_nat (tptp.cOMBS_nat_bool_bool (tptp.cOMBB_1015721476ol_nat tptp.fconj (tptp.hAPP_f800510211t_bool (tptp.cOMBC_226598744l_bool tptp.member_nat) M_3)) (tptp.hAPP_n1699378549t_bool _let_1 (tptp.hAPP_nat_nat tptp.suc I_2))))))))) (forall ((N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N) tptp.one_one_nat)) N))) (forall ((N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= N (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N) tptp.one_one_nat))))) (forall ((N tptp.nat) (M_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_1) N))) (let ((_let_2 (= M_1 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 N)) (=> (not _let_2) (= _let_1 (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M_1) tptp.one_one_nat)) N)))))))) (forall ((Na tptp.nat) (Pa tptp.fun_nat_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool Pa tptp.zero_zero_nat))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool Pa Na)) (exists ((K_2 tptp.nat)) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat K_2) Na)) (forall ((I tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I) K_2)) (not (tptp.hBOOL (tptp.hAPP_nat_bool Pa I))))) (tptp.hBOOL (tptp.hAPP_nat_bool Pa (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat K_2) tptp.one_one_nat)))))))) (forall ((Na tptp.nat) (Pa tptp.fun_nat_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool Pa tptp.zero_zero_nat))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool Pa Na)) (exists ((K_2 tptp.nat)) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_2) Na)) (forall ((I tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I) K_2)) (not (tptp.hBOOL (tptp.hAPP_nat_bool Pa I))))) (tptp.hBOOL (tptp.hAPP_nat_bool Pa K_2))))))) (forall ((I_1 tptp.nat) (J tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_1) J)) (exists ((K_2 tptp.nat)) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K_2)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I_1) K_2) J))))) (forall ((N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (exists ((M_2 tptp.nat)) (= N (tptp.hAPP_nat_nat tptp.suc M_2))))) (forall ((Y tptp.nat)) (=> (not (= Y tptp.zero_zero_nat)) (not (forall ((Nat tptp.nat)) (not (= Y (tptp.hAPP_nat_nat tptp.suc Nat))))))) (forall ((Pa tptp.fun_nat_bool) (K tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool Pa K)) (=> (forall ((N_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool Pa (tptp.hAPP_nat_nat tptp.suc N_1))) (tptp.hBOOL (tptp.hAPP_nat_bool Pa N_1)))) (tptp.hBOOL (tptp.hAPP_nat_bool Pa tptp.zero_zero_nat))))) (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (exists ((M_2 tptp.nat)) (= N (tptp.hAPP_nat_nat tptp.suc M_2))))) (forall ((Na tptp.nat) (Pa tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool Pa tptp.zero_zero_nat)) (=> (forall ((N_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool Pa N_1)) (tptp.hBOOL (tptp.hAPP_nat_bool Pa (tptp.hAPP_nat_nat tptp.suc N_1))))) (tptp.hBOOL (tptp.hAPP_nat_bool Pa Na))))) (forall ((V tptp.int)) (let ((_let_1 (tptp.number_number_of_nat V))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) _let_1)) (= _let_1 (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat _let_1) tptp.one_one_nat)))))) (forall ((N tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)) (forall ((M_1 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M_1) tptp.zero_zero_nat) tptp.zero_zero_nat)) (forall ((M tptp.nat) (Na tptp.nat)) (= (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M) Na) tptp.zero_zero_nat) (or (= M tptp.zero_zero_nat) (= Na tptp.zero_zero_nat)))) (forall ((K tptp.nat) (M tptp.nat) (Na tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat K))) (= (= (tptp.hAPP_nat_nat _let_1 M) (tptp.hAPP_nat_nat _let_1 Na)) (or (= M Na) (= K tptp.zero_zero_nat))))) (forall ((M tptp.nat) (K tptp.nat) (Na tptp.nat)) (= (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M) K) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat Na) K)) (or (= M Na) (= K tptp.zero_zero_nat)))) (forall ((K tptp.nat) (M tptp.nat) (Na tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat tptp.suc K)))) (= (= (tptp.hAPP_nat_nat _let_1 M) (tptp.hAPP_nat_nat _let_1 Na)) (= M Na)))) (forall ((M_1 tptp.nat) (N tptp.nat) (K_1 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_1) N)) K_1) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M_1) K_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat N) K_1)))) (forall ((K_1 tptp.nat) (M_1 tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat K_1))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_1) N)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 M_1)) (tptp.hAPP_nat_nat _let_1 N))))) (forall ((K_1 tptp.nat) (L_1 tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_1) J)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_1) L_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat I_1) K_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat J) L_1)))))) (forall ((K_1 tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat K_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_1) J)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 I_1)) (tptp.hAPP_nat_nat _let_1 J)))))) (forall ((K_1 tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_1) J)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat I_1) K_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat J) K_1))))) (forall ((M_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_1) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat _let_1 M_1)))))) (forall ((M_1 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_1) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M_1) M_1)))) (forall ((M_1 tptp.nat) (N tptp.nat) (K_1 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M_1) N)) K_1) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M_1) K_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat N) K_1)))) (forall ((K_1 tptp.nat) (M_1 tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat K_1))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M_1) N)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat _let_1 M_1)) (tptp.hAPP_nat_nat _let_1 N))))) (forall ((M tptp.nat) (Na tptp.nat)) (= (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M) Na) tptp.one_one_nat) (and (= M tptp.one_one_nat) (= Na tptp.one_one_nat)))) (forall ((N tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat N) tptp.one_one_nat) N)) (forall ((M tptp.nat) (Na tptp.nat)) (= (= tptp.one_one_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M) Na)) (and (= M tptp.one_one_nat) (= Na tptp.one_one_nat)))) (forall ((N tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat tptp.one_one_nat) N) N)) (forall ((M tptp.nat) (Na tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat))) (= (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M) Na) _let_1) (and (= M _let_1) (= Na _let_1))))) (forall ((K_1 tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat K_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_1) J)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 I_1)) (tptp.hAPP_nat_nat _let_1 J))))))) (forall ((K_1 tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_1) J)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat I_1) K_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat J) K_1)))))) (forall ((M tptp.nat) (K tptp.nat) (Na tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M) K)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat Na) K))) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) Na))))) (forall ((K tptp.nat) (M tptp.nat) (Na tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat K))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 M)) (tptp.hAPP_nat_nat _let_1 Na))) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) Na)))))) (forall ((M tptp.nat) (Na tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat))) (= (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M) Na))) (and (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Na)))))) (forall ((K tptp.nat) (M tptp.nat) (Na tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat tptp.suc K)))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 M)) (tptp.hAPP_nat_nat _let_1 Na))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) Na))))) (forall ((M_1 tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M_1))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat tptp.suc N)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_1) (tptp.hAPP_nat_nat _let_1 N))))) (forall ((M_1 tptp.nat) (N tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat tptp.suc M_1)) N) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat N) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M_1) N)))) (forall ((K tptp.nat) (M tptp.nat) (Na tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat tptp.suc K)))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 M)) (tptp.hAPP_nat_nat _let_1 Na))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) Na))))) (forall ((M_1 tptp.nat) (N tptp.nat)) (=> (= M_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M_1) N)) (or (= N tptp.one_one_nat) (= M_1 tptp.zero_zero_nat)))) (forall ((M_1 tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat)))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M_1) N))))))) (forall ((M_1 tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat)))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat N) M_1))))))) (forall ((M_1 tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat)))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M_1)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M_1) N))))))) (forall ((M tptp.nat) (Na tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat)))) (= (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M) Na))) (and (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Na)))))) (forall ((K tptp.nat) (M tptp.nat) (Na tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat K))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 M)) (tptp.hAPP_nat_nat _let_1 Na))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) Na)))))) (forall ((M tptp.nat) (K tptp.nat) (Na tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M) K)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat Na) K))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) Na))))) (forall ((N tptp.nat) (M_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M_1) N))) (let ((_let_2 (= M_1 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.zero_zero_nat)) (=> (not _let_2) (= _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat N) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M_1) tptp.one_one_nat)) N)))))))) (forall ((U tptp.nat) (M tptp.nat) (Na tptp.nat) (I_2 tptp.nat) (J_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_2) J_1)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat I_2) U)) M)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat J_1) U)) Na))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat J_1) I_2)) U)) Na)))))) (forall ((M_1 tptp.nat) (N tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M_1) N) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat N) M_1))) (forall ((M_1 tptp.nat) (N tptp.nat) (K_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M_1))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat _let_1 N)) K_1) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat N) K_1))))) (forall ((K tptp.int) (L tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.number_number_of_int K)) (tptp.number_number_of_int L))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K) L)))) (forall ((Z tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int tptp.one_one_int) Z) Z)) (forall ((Z tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Z) tptp.one_one_int) Z)) (forall ((Z tptp.int) (W tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Z) W) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int W) Z))) (forall ((V tptp.int) (W tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.number_number_of_int V)) (tptp.number_number_of_int W)) (tptp.number_number_of_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int V) W)))) (forall ((Z1 tptp.int) (Z2 tptp.int) (Z3 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int Z1))) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int _let_1 Z2)) Z3) (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Z2) Z3))))) (forall ((K tptp.int) (L tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.number_number_of_int K)) (tptp.number_number_of_int L))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K) L)))) (forall ((Z1 tptp.int) (Z2 tptp.int) (W tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int Z1) Z2)) W) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Z1) W)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Z2) W)))) (forall ((W tptp.int) (Z1 tptp.int) (Z2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int W))) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int Z1) Z2)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_int_int _let_1 Z1)) (tptp.hAPP_int_int _let_1 Z2))))) (forall ((W tptp.int) (Z1 tptp.int) (Z2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int W))) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int Z1) Z2)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int _let_1 Z1)) (tptp.hAPP_int_int _let_1 Z2))))) (forall ((V tptp.int) (W tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.number_number_of_int V)) (tptp.number_number_of_int W)) (tptp.number_number_of_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int V) W)))) (forall ((Z1 tptp.int) (Z2 tptp.int) (W tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int Z1) Z2)) W) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Z1) W)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Z2) W)))) (forall ((K_1 tptp.int) (I_1 tptp.int) (J tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int K_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int I_1) J)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) K_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int _let_1 I_1)) (tptp.hAPP_int_int _let_1 J))))))) (forall ((Na tptp.int) (M tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) M)) (= (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int M) Na) tptp.one_one_int) (and (= M tptp.one_one_int) (= Na tptp.one_one_int))))) (forall ((Z tptp.int)) (not (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) Z)) Z) tptp.zero_zero_int))) (forall ((Z tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int Z) tptp.zero_zero_int) Z)) (forall ((Z tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int tptp.zero_zero_int) Z) Z)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) tptp.one_one_int)) (forall ((Z_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.one_one_int) Z_2)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) Z_2)))) (forall ((K tptp.int) (L tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K) L)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int K) L)) tptp.zero_zero_int)))) (forall ((Z tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) Z)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) Z))))) (forall ((Z_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) Z_2)) Z_2)) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Z_2) tptp.zero_zero_int)))) (forall ((K_1 tptp.int) (I_1 tptp.int) (J tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.plus_plus_int K_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int I_1) J)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int _let_1 I_1)) (tptp.hAPP_int_int _let_1 J)))))) (forall ((Z1 tptp.int) (Z2 tptp.int) (Z3 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.plus_plus_int Z1))) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int _let_1 Z2)) Z3) (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int Z2) Z3))))) (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.plus_plus_int X))) (let ((_let_2 (tptp.hAPP_int_fun_int_int tptp.plus_plus_int Y))) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int _let_2 Z)) (tptp.hAPP_int_int _let_2 (tptp.hAPP_int_int _let_1 Z)))))) (forall ((Z tptp.int) (W tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int Z) W) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int W) Z))) (forall ((W tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int W) W))) (forall ((Z tptp.int) (W tptp.int)) (or (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Z) W)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int W) Z)))) (forall ((K_1 tptp.int) (I_1 tptp.int) (J tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int I_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 J)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int J) K_1)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 K_1)))))) (forall ((Z tptp.int) (W tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Z) W)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int W) Z)) (= Z W)))) (forall ((W_1 tptp.int) (Z_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int W_1) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int Z_2) tptp.one_one_int))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int W_1) Z_2)))) (forall ((X tptp.int) (Y tptp.int)) (or (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X) Y)) (= X Y) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Y) X)))) (forall ((Z_2 tptp.int) (W_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Z_2) W_1)) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Z_2) W_1)) (not (= Z_2 W_1))))) (forall ((K_1 tptp.int) (I_1 tptp.int) (J tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int I_1) J)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int I_1) K_1)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int J) K_1))))) (forall ((Z_4 tptp.int) (Z tptp.int) (W_2 tptp.int) (W tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int W_2) W)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Z_4) Z)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int W_2) Z_4)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int W) Z)))))) (forall ((W_1 tptp.int) (Z_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int W_1) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int Z_2) tptp.one_one_int))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int W_1) Z_2)))) (forall ((W_1 tptp.int) (Z_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int W_1) tptp.one_one_int)) Z_2)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int W_1) Z_2)))) (forall ((W tptp.int) (Z tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int W) Z)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int W) tptp.one_one_int)) Z)))) (forall ((W_1 tptp.int) (Z_2 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int W_1))) (= (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int Z_2) tptp.one_one_int))) (or (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Z_2)) (= W_1 Z_2))))) (forall ((K tptp.nat) (M tptp.nat) (Na tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat K))) (= (= (tptp.hAPP_nat_nat _let_1 M) (tptp.hAPP_nat_nat _let_1 Na)) (or (= K tptp.zero_zero_nat) (= M Na))))) (forall ((I_1 tptp.nat) (U_1 tptp.nat) (J tptp.nat) (K_1 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat I_1) U_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat J) U_1)) K_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I_1) J)) U_1)) K_1))) (forall ((M tptp.nat) (Na tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat K))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (= (= (tptp.hAPP_nat_nat _let_1 M) (tptp.hAPP_nat_nat _let_1 Na)) (= M Na))))) (forall ((M tptp.nat) (Na tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat K))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 M)) (tptp.hAPP_nat_nat _let_1 Na))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) Na)))))) (forall ((M tptp.nat) (Na tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat K))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 M)) (tptp.hAPP_nat_nat _let_1 Na))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) Na)))))) (forall ((U tptp.nat) (M tptp.nat) (Na tptp.nat) (J_1 tptp.nat) (I_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat J_1) I_2)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat I_2) U)) M)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat J_1) U)) Na))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat I_2) J_1)) U)) M)) Na))))) (forall ((U_1 tptp.nat) (M_1 tptp.nat) (N tptp.nat) (J tptp.nat) (I_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat J) I_1)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat I_1) U_1)) M_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat J) U_1)) N)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat I_1) J)) U_1)) M_1)) N)))) (forall ((U tptp.nat) (M tptp.nat) (Na tptp.nat) (J_1 tptp.nat) (I_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat J_1) I_2)) (= (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat I_2) U)) M) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat J_1) U)) Na)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat I_2) J_1)) U)) M) Na)))) (forall ((U tptp.nat) (M tptp.nat) (Na tptp.nat) (I_2 tptp.nat) (J_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_2) J_1)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat I_2) U)) M)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat J_1) U)) Na))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat J_1) I_2)) U)) Na)))))) (forall ((U_1 tptp.nat) (M_1 tptp.nat) (N tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_1) J)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat I_1) U_1)) M_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat J) U_1)) N)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M_1) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat J) I_1)) U_1)) N))))) (forall ((U tptp.nat) (M tptp.nat) (Na tptp.nat) (I_2 tptp.nat) (J_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_2) J_1)) (= (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat I_2) U)) M) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat J_1) U)) Na)) (= M (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat J_1) I_2)) U)) Na))))) (forall ((U tptp.nat) (M tptp.nat) (Na tptp.nat) (J_1 tptp.nat) (I_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat J_1) I_2)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat I_2) U)) M)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat J_1) U)) Na))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat I_2) J_1)) U)) M)) Na))))) (forall ((B_2 tptp.int) (Q_2 tptp.int) (R_2 tptp.int) (B_1 tptp.int) (Q_1 tptp.int) (R_1 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_1) Q_1)) R_1))) (=> (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_2) Q_2)) R_2) _let_1) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int _let_1) tptp.zero_zero_int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int R_2) B_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) R_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_1) B_2)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Q_1) Q_2)))))))))) (forall ((B_2 tptp.int) (Q_1 tptp.int) (R_1 tptp.int) (Q_2 tptp.int) (R_2 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B_2))) (let ((_let_2 (tptp.hAPP_int_fun_int_int tptp.times_times_int B_2))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int _let_2 Q_1)) R_1)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int _let_2 Q_2)) R_2))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int R_2) tptp.zero_zero_int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 R_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 R_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Q_2) Q_1))))))))) (forall ((K_1 tptp.int)) (= (tptp.number_number_of_int K_1) K_1)) (not (= tptp.zero_zero_int tptp.one_one_int)) (forall ((R_2 tptp.int) (Q_2 tptp.int) (A_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) A_1)) (=> (= A_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int R_2) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_1) Q_2))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int R_2) A_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.one_one_int) Q_2)))))) (forall ((R_2 tptp.int) (Q_2 tptp.int) (A_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) A_1)) (=> (= A_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int R_2) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_1) Q_2))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) R_2)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Q_2) tptp.one_one_int)))))) (forall ((B_1 tptp.int) (Q_1 tptp.int) (R_1 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_1) Q_1)) R_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int R_1) B_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B_1)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Q_1))))))) (forall ((B_1 tptp.int) (Q_1 tptp.int) (R_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_1) Q_1)) R_1)) tptp.zero_zero_int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) R_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Q_1) tptp.zero_zero_int)))))) (forall ((B_2 tptp.int) (Q_1 tptp.int) (R_1 tptp.int) (Q_2 tptp.int) (R_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int B_2))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int _let_1 Q_1)) R_1)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int _let_1 Q_2)) R_2))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) R_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int R_1) B_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int R_2) B_2)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Q_1) Q_2)))))))) (forall ((B_2 tptp.int) (Q_2 tptp.int) (R_2 tptp.int) (B_1 tptp.int) (Q_1 tptp.int) (R_1 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_1) Q_1)) R_1))) (=> (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_2) Q_2)) R_2) _let_2) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 _let_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int R_1) B_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 R_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_1) B_2)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Q_2) Q_1))))))))))) (forall ((Pa tptp.fun_int_bool) (I_2 tptp.int) (K tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int I_2) K)) (=> (tptp.hBOOL (tptp.hAPP_int_bool Pa (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int K) tptp.one_one_int))) (=> (forall ((I tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int I) K)) (=> (tptp.hBOOL (tptp.hAPP_int_bool Pa I)) (tptp.hBOOL (tptp.hAPP_int_bool Pa (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int I) tptp.one_one_int)))))) (tptp.hBOOL (tptp.hAPP_int_bool Pa I_2)))))) (forall ((Pa tptp.fun_int_bool) (I_2 tptp.int) (K tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int I_2) K)) (=> (tptp.hBOOL (tptp.hAPP_int_bool Pa K)) (=> (forall ((I tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int I) K)) (=> (tptp.hBOOL (tptp.hAPP_int_bool Pa I)) (tptp.hBOOL (tptp.hAPP_int_bool Pa (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int I) tptp.one_one_int)))))) (tptp.hBOOL (tptp.hAPP_int_bool Pa I_2)))))) (forall ((Pa tptp.fun_int_bool) (K tptp.int) (I_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K) I_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool Pa (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int K) tptp.one_one_int))) (=> (forall ((I tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K) I)) (=> (tptp.hBOOL (tptp.hAPP_int_bool Pa I)) (tptp.hBOOL (tptp.hAPP_int_bool Pa (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int I) tptp.one_one_int)))))) (tptp.hBOOL (tptp.hAPP_int_bool Pa I_2)))))) (forall ((Pa tptp.fun_int_bool) (K tptp.int) (I_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K) I_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool Pa K)) (=> (forall ((I tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K) I)) (=> (tptp.hBOOL (tptp.hAPP_int_bool Pa I)) (tptp.hBOOL (tptp.hAPP_int_bool Pa (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int I) tptp.one_one_int)))))) (tptp.hBOOL (tptp.hAPP_int_bool Pa I_2)))))) (forall ((Y tptp.int) (X tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 X)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int X) Y))))))) (tptp.hBOOL (tptp.hAPP_int_bool _let_13 tptp.zero_zero_int)) (forall ((Y tptp.int) (X tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 X)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int X) Y))))))) (tptp.hBOOL (tptp.hAPP_int_bool _let_13 tptp.one_one_int)) (forall ((P_1 tptp.fun_int_bool) (Pa tptp.fun_int_bool)) (let ((_let_1 (tptp.cOMBB_1652995168ol_int tptp.fconj (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int)))) (=> (forall ((X_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) X_2)) (= (tptp.hBOOL (tptp.hAPP_int_bool Pa X_2)) (tptp.hBOOL (tptp.hAPP_int_bool P_1 X_2))))) (= (tptp.collect_int (tptp.cOMBS_int_bool_bool _let_1 Pa)) (tptp.collect_int (tptp.cOMBS_int_bool_bool _let_1 P_1)))))) (forall ((K tptp.int) (Pa tptp.fun_int_bool) (D_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) D_1)) (=> (forall ((X_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool Pa X_2)) (tptp.hBOOL (tptp.hAPP_int_bool Pa (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int X_2) D_1))))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) K)) (forall ((X_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool Pa X_2)) (tptp.hBOOL (tptp.hAPP_int_bool Pa (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int X_2) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int K) D_1)))))))))) (forall ((P_1 tptp.bool) (Pa tptp.bool) (X_1 tptp.int)) (let ((_let_1 (tptp.hBOOL P_1))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) X_1)))) (let ((_let_3 (tptp.hBOOL Pa))) (=> (=> _let_2 (= _let_3 _let_1)) (= (and _let_2 _let_3) (and _let_2 _let_1))))))) (forall ((P_1 tptp.bool) (Pa tptp.bool) (X_1 tptp.int)) (let ((_let_1 (tptp.hBOOL P_1))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) X_1)))) (let ((_let_3 (tptp.hBOOL Pa))) (=> (=> _let_2 (= _let_3 _let_1)) (= (=> _let_2 _let_3) (=> _let_2 _let_1))))))) (forall ((K tptp.int) (Pa tptp.fun_int_bool) (D_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) D_1)) (=> (forall ((X_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool Pa X_2)) (tptp.hBOOL (tptp.hAPP_int_bool Pa (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int X_2) D_1))))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) K)) (forall ((X_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool Pa X_2)) (tptp.hBOOL (tptp.hAPP_int_bool Pa (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int X_2) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int K) D_1)))))))))) (forall ((I_2 tptp.int) (Pa tptp.fun_int_bool) (K tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool Pa K)) (=> (forall ((I tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K) I)) (=> (tptp.hBOOL (tptp.hAPP_int_bool Pa I)) (tptp.hBOOL (tptp.hAPP_int_bool Pa (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int I) tptp.one_one_int)))))) (=> (forall ((I tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int I) K)) (=> (tptp.hBOOL (tptp.hAPP_int_bool Pa I)) (tptp.hBOOL (tptp.hAPP_int_bool Pa (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int I) tptp.one_one_int)))))) (tptp.hBOOL (tptp.hAPP_int_bool Pa I_2)))))) (forall ((Pa tptp.fun_int_bool) (P1 tptp.fun_int_bool) (D_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) D_1)) (=> (forall ((X_2 tptp.int) (K_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool P1 X_2)) (tptp.hBOOL (tptp.hAPP_int_bool P1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int X_2) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int K_2) D_1)))))) (=> (exists ((Z_3 tptp.int)) (forall ((X_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X_2) Z_3)) (= (tptp.hBOOL (tptp.hAPP_int_bool Pa X_2)) (tptp.hBOOL (tptp.hAPP_int_bool P1 X_2)))))) (=> (exists ((X1 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool P1 X1))) (exists ((X1 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool Pa X1)))))))) (forall ((Pa tptp.fun_int_bool) (P_1 tptp.fun_int_bool) (D_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) D_1)) (=> (forall ((X_2 tptp.int) (K_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool P_1 X_2)) (tptp.hBOOL (tptp.hAPP_int_bool P_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int X_2) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int K_2) D_1)))))) (=> (exists ((Z_3 tptp.int)) (forall ((X_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Z_3) X_2)) (= (tptp.hBOOL (tptp.hAPP_int_bool Pa X_2)) (tptp.hBOOL (tptp.hAPP_int_bool P_1 X_2)))))) (=> (exists ((X1 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool P_1 X1))) (exists ((X1 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool Pa X1)))))))) (forall ((Y tptp.int) (X tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.nat_tsub X) Y))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Y) X)))) (and (=> _let_2 (= _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int X) Y))) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))) (forall ((N tptp.nat)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.hAPP_nat_int tptp.semiri1621563631at_int N)))) (forall ((K_1 tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int K_1)) tptp.zero_zero_int)))) (= _let_20 tptp.one_one_int) (= _let_19 tptp.zero_zero_int) (forall ((Na tptp.nat)) (= (= (tptp.hAPP_nat_int tptp.semiri1621563631at_int Na) tptp.zero_zero_int) (= Na tptp.zero_zero_nat))) (forall ((M tptp.nat) (Na tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int M)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int Na))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) Na)))) (forall ((M tptp.nat) (Na tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int M)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int Na))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) Na)))) (forall ((M_1 tptp.nat) (N tptp.nat)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int M_1)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int N)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_1) N)))) (forall ((M_1 tptp.nat) (N tptp.nat) (Z tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int M_1)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int N)) Z)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_1) N))) Z))) (forall ((W_1 tptp.int) (Z_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int W_1) Z_2)) (exists ((N_1 tptp.nat)) (= Z_2 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int W_1) (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_1)))))) (forall ((M_1 tptp.nat) (N tptp.nat)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int M_1)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int N)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M_1) N)))) (forall ((M_1 tptp.nat) (N tptp.nat)) (= (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M_1) N)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int M_1)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int N)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int X)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int Y)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat X) Y)))) (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int X_1)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int Y_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_1) Y_1)))) (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int X_1)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int Y_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_1) Y_1)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.nat_tsub (tptp.hAPP_nat_int tptp.semiri1621563631at_int X)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int Y)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat X) Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int X)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int Y)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat X) Y)))) (forall ((A tptp.fun_nat_bool)) (= (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat A) (tptp.hAPP_f957591787ol_nat tptp.finite_card_int (tptp.image_nat_int tptp.semiri1621563631at_int A)))) (forall ((A tptp.fun_nat_bool)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.image_nat_int tptp.semiri1621563631at_int A))))) (= tptp.one_one_int _let_20) (= tptp.zero_zero_int _let_19) (forall ((Pa tptp.fun_int_bool)) (= (tptp.collect_int (tptp.cOMBS_int_bool_bool (tptp.cOMBB_1652995168ol_int tptp.fconj (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int)) Pa)) (tptp.image_nat_int tptp.semiri1621563631at_int (tptp.collect_nat (tptp.cOMBB_int_bool_nat Pa tptp.semiri1621563631at_int))))) (forall ((Z tptp.nat)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.hAPP_nat_int tptp.semiri1621563631at_int Z)))) (forall ((Pa tptp.fun_int_bool)) (= (exists ((X_2 tptp.int)) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) X_2)) (tptp.hBOOL (tptp.hAPP_int_bool Pa X_2)))) (exists ((X_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_int_bool Pa (tptp.hAPP_nat_int tptp.semiri1621563631at_int X_2)))))) (forall ((Pa tptp.fun_int_bool)) (= (forall ((X_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) X_2)) (tptp.hBOOL (tptp.hAPP_int_bool Pa X_2)))) (forall ((X_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_int_bool Pa (tptp.hAPP_nat_int tptp.semiri1621563631at_int X_2)))))) (forall ((Na tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int Na)) tptp.zero_zero_int)) (= Na tptp.zero_zero_nat))) (= (tptp.hAPP_nat_int tptp.semiri1621563631at_int _let_17) tptp.one_one_int) (forall ((W_1 tptp.int) (Z_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int W_1) Z_2)) (exists ((N_1 tptp.nat)) (= Z_2 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int W_1) (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat tptp.suc N_1))))))) (forall ((M_1 tptp.nat)) (= (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat tptp.suc M_1)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) (tptp.hAPP_nat_int tptp.semiri1621563631at_int M_1)))) (forall ((N tptp.nat) (M_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N) M_1)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int M_1)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int N)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M_1) N))))) (forall ((Na tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.hAPP_nat_int tptp.semiri1621563631at_int Na))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) Na)))) (forall ((K_1 tptp.nat) (I_1 tptp.int) (J tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int K_1)))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int I_1) J)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int _let_1 I_1)) (tptp.hAPP_int_int _let_1 J))))))) (forall ((Y tptp.int) (X tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 X)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.nat_tsub X) Y))))))) (forall ((Pa tptp.fun_int_bool) (X_1 tptp.nat) (Y_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_int_bool Pa (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat X_1) Y_1)))) (and (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_int_bool Pa (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int X_1)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int Y_1))))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_int_bool Pa tptp.zero_zero_int)))))) (forall ((Y tptp.int) (X tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Y) X)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.nat_tsub X) Y) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int X) Y)))) (forall ((K_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) K_1)) (exists ((N_1 tptp.nat)) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_1)) (= K_1 (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_1)))))) (forall ((M tptp.nat) (Na tptp.nat)) (= (= (tptp.hAPP_nat_int tptp.semiri1621563631at_int M) (tptp.hAPP_nat_int tptp.semiri1621563631at_int Na)) (= M Na))) (forall ((A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool A) B)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le1912455174t_bool (tptp.image_nat_int tptp.semiri1621563631at_int A)) (tptp.image_nat_int tptp.semiri1621563631at_int B))))) (forall ((A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) B)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool (tptp.image_nat_int tptp.semiri1621563631at_int A)) (tptp.image_nat_int tptp.semiri1621563631at_int B))))) (= tptp.bot_bot_fun_int_bool (tptp.image_nat_int tptp.semiri1621563631at_int tptp.bot_bot_fun_nat_bool)) (forall ((A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (= (= A B) (= (tptp.image_nat_int tptp.semiri1621563631at_int A) (tptp.image_nat_int tptp.semiri1621563631at_int B)))) (forall ((X_1 tptp.nat) (A tptp.fun_nat_bool)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int X_1)) (tptp.image_nat_int tptp.semiri1621563631at_int A))))) (forall ((X_1 tptp.nat) (Y_1 tptp.nat) (Pa tptp.bool)) (let ((_let_1 (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat (tptp.if_nat Pa) X_1) Y_1)))) (let ((_let_2 (tptp.hBOOL Pa))) (and (=> _let_2 (= (tptp.hAPP_nat_int tptp.semiri1621563631at_int X_1) _let_1)) (=> (not _let_2) (= (tptp.hAPP_nat_int tptp.semiri1621563631at_int Y_1) _let_1)))))) (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (= (= (tptp.hAPP_nat_int tptp.semiri1621563631at_int X_1) (tptp.hAPP_nat_int tptp.semiri1621563631at_int Y_1)) (= X_1 Y_1))) (forall ((K_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) K_1)) (not (forall ((N_1 tptp.nat)) (not (= K_1 (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_1))))))) (forall ((Z tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) Z)) (not (forall ((M_2 tptp.nat)) (not (= Z (tptp.hAPP_nat_int tptp.semiri1621563631at_int M_2))))))) (forall ((K_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) K_1)) (exists ((N_1 tptp.nat)) (= K_1 (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_1))))) (forall ((Z tptp.int)) (not (forall ((M_2 tptp.nat) (N_1 tptp.nat)) (not (= Z (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int M_2)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_1))))))) (forall ((X tptp.int) (Z tptp.int) (D tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.minus_minus_int X))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) D)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.abs_abs_int (tptp.hAPP_int_int _let_1 Z))) tptp.one_one_int)) D))) Z))))) (forall ((Z_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.abs_abs_int Z_2)) tptp.one_one_int)) (= Z_2 tptp.zero_zero_int))) (forall ((Z_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_neg Z_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Z_1) tptp.zero_zero_int)))) (forall ((X_1 tptp.int)) (= (not (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_neg X_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) X_1)))) (not (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_neg tptp.one_one_int))) (not (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_neg tptp.zero_zero_int))) (forall ((M_1 tptp.int) (N tptp.int)) (=> (= (tptp.abs_abs_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int M_1) N)) tptp.one_one_int) (= (tptp.abs_abs_int M_1) tptp.one_one_int))) (forall ((N tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_neg (tptp.hAPP_nat_int tptp.semiri1621563631at_int N))))) (forall ((M_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_int tptp.semiri1621563631at_int M_1))) (= (tptp.abs_abs_int _let_1) _let_1))) (forall ((V tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_neg (tptp.number_number_of_int V))) (= (tptp.number_number_of_nat V) tptp.zero_zero_nat))) (forall ((V_3 tptp.int) (V_2 tptp.int)) (let ((_let_1 (tptp.number_number_of_int V_2))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_neg _let_1)))) (let ((_let_3 (tptp.number_number_of_int V_3))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_neg _let_3)))) (= (= (tptp.number_number_of_nat V_3) (tptp.number_number_of_nat V_2)) (and (=> _let_4 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int _let_1) tptp.zero_zero_int))) (=> (not _let_4) (and (=> _let_2 (= _let_3 tptp.zero_zero_int)) (=> (not _let_2) (= V_3 V_2))))))))))) (forall ((V_1 tptp.int) (K_1 tptp.nat) (V tptp.int)) (let ((_let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.number_number_of_nat V_1)) K_1))) (let ((_let_2 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.number_number_of_nat V)))) (let ((_let_3 (tptp.hAPP_nat_nat _let_2 _let_1))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_neg (tptp.number_number_of_int V_1))))) (let ((_let_5 (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_neg (tptp.number_number_of_int V))))) (and (=> _let_5 (= _let_3 _let_1)) (=> (not _let_5) (and (=> _let_4 (= _let_3 (tptp.hAPP_nat_nat _let_2 K_1))) (=> (not _let_4) (= _let_3 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.number_number_of_nat (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int V) V_1))) K_1)))))))))))) (forall ((V tptp.int)) (let ((_let_1 (tptp.number_number_of_int V))) (let ((_let_2 (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.number_number_of_nat V)))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_neg _let_1)))) (and (=> _let_3 (= _let_2 tptp.zero_zero_int)) (=> (not _let_3) (= _let_2 _let_1))))))) (forall ((Z tptp.int) (X tptp.int) (D tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) D)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Z) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int X) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.abs_abs_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int X) Z))) tptp.one_one_int)) D)))))) (forall ((K tptp.int) (F tptp.fun_nat_int) (Na tptp.nat)) (=> (forall ((I tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I) Na)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.abs_abs_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_nat_int F (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I) tptp.one_one_nat))) (tptp.hAPP_nat_int F I)))) tptp.one_one_int)))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_nat_int F tptp.zero_zero_nat)) K)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K) (tptp.hAPP_nat_int F Na))) (exists ((I tptp.nat)) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I) Na)) (= (tptp.hAPP_nat_int F I) K))))))) (forall ((K tptp.int) (F tptp.fun_nat_int) (Na tptp.nat)) (=> (forall ((I tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I) Na)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.abs_abs_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_nat_int F (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I) tptp.one_one_nat))) (tptp.hAPP_nat_int F I)))) tptp.one_one_int)))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_nat_int F tptp.zero_zero_nat)) K)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K) (tptp.hAPP_nat_int F Na))) (exists ((I tptp.nat)) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I) Na)) (= (tptp.hAPP_nat_int F I) K))))))) (forall ((K tptp.int) (F tptp.fun_nat_int) (Na tptp.nat) (M tptp.nat)) (=> (forall ((I tptp.nat)) (=> (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) I)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I) Na))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.abs_abs_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_nat_int F (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I) tptp.one_one_nat))) (tptp.hAPP_nat_int F I)))) tptp.one_one_int)))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) Na)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_nat_int F M)) K)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K) (tptp.hAPP_nat_int F Na))) (exists ((I tptp.nat)) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) I)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I) Na)) (= (tptp.hAPP_nat_int F I) K)))))))) (forall ((N tptp.nat) (V tptp.int)) (let ((_let_1 (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.number_number_of_nat V)) N)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_neg (tptp.number_number_of_int V))))) (and (=> _let_2 (= _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat tptp.one_one_nat) N))) (=> (not _let_2) (= _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.number_number_of_nat (tptp.succ V))) N))))))) (forall ((K_1 tptp.int)) (= (tptp.succ K_1) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int K_1) tptp.one_one_int))) (forall ((V tptp.int)) (let ((_let_1 (tptp.hAPP_nat_nat tptp.suc (tptp.number_number_of_nat V)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_neg (tptp.number_number_of_int V))))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 (tptp.number_number_of_nat (tptp.succ V)))))))) (forall ((W tptp.int)) (let ((_let_1 (tptp.number_number_of_nat W))) (let ((_let_2 (tptp.number_number_of_nat (tptp.bit1 W)))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_neg (tptp.number_number_of_int W))))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat _let_1) _let_1))))))))) (forall ((V tptp.int)) (let ((_let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat tptp.one_one_nat) (tptp.number_number_of_nat V)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int V) tptp.pls)))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 (tptp.number_number_of_nat (tptp.succ V)))))))) (= (tptp.succ tptp.pls) _let_10) (forall ((W_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_neg (tptp.number_number_of_int (tptp.bit1 W_1)))) (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_neg (tptp.number_number_of_int W_1))))) (not (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_neg _let_15))) (= _let_12 (tptp.hAPP_nat_int tptp.semiri1621563631at_int _let_18)) (= _let_16 _let_17) (= _let_18 (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat tptp.suc _let_17))) (forall ((N tptp.nat)) (= (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat tptp.suc N))) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.number_number_of_nat (tptp.bit1 (tptp.bit1 tptp.pls)))) N))) (= tptp.one_one_nat _let_16) (= _let_16 tptp.one_one_nat) (= tptp.one_one_int (tptp.number_number_of_int _let_10)) (= tptp.zero_zero_int _let_15) (forall ((K_1 tptp.int)) (= (tptp.bit1 K_1) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) K_1)) K_1))) (= _let_14 tptp.zero_zero_nat) (= tptp.zero_zero_nat _let_14) (= tptp.pls tptp.zero_zero_int) (forall ((K tptp.int) (L tptp.int)) (= (= (tptp.bit1 K) (tptp.bit1 L)) (= K L))) (forall ((K_1 tptp.int)) (not (= (tptp.bit1 K_1) tptp.pls))) (forall ((L_1 tptp.int)) (not (= tptp.pls (tptp.bit1 L_1)))) (forall ((K_1 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int K_1) tptp.pls) K_1)) (forall ((K_1 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int tptp.pls) K_1) K_1)) (forall ((K_1 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int K_1) tptp.pls) K_1)) (forall ((W tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int tptp.pls) W) tptp.pls)) (tptp.hBOOL (tptp.hAPP_int_bool _let_13 _let_12)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.pls) tptp.pls)) (forall ((K tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.pls))) (= (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.bit1 K))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 K))))) (forall ((K tptp.int) (L tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.bit1 K)) (tptp.bit1 L))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K) L)))) (forall ((K1 tptp.int) (K2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.bit1 K1)) (tptp.bit1 K2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K1) K2)))) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.pls) tptp.pls))) (forall ((K tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.bit1 K)) tptp.pls)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K) tptp.pls)))) (forall ((K tptp.int) (L tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.bit1 K)) (tptp.bit1 L))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K) L)))) (forall ((K1 tptp.int) (K2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.bit1 K1)) (tptp.bit1 K2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K1) K2)))) (forall ((K tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.bit1 K)) tptp.pls)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K) tptp.pls)))) (forall ((K tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.pls) (tptp.bit1 K))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.pls) K)))) (forall ((P tptp.bool)) (or (not (tptp.hBOOL (tptp.hAPP_bool_bool tptp.fNot P))) (not (tptp.hBOOL P)))) (forall ((P tptp.bool)) (or (tptp.hBOOL P) (tptp.hBOOL (tptp.hAPP_bool_bool tptp.fNot P)))) (forall ((Q tptp.bool) (P tptp.bool)) (or (not (tptp.hBOOL P)) (not (tptp.hBOOL Q)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fconj P) Q)))) (forall ((P tptp.bool) (Q tptp.bool)) (or (not (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fconj P) Q))) (tptp.hBOOL P))) (forall ((P tptp.bool) (Q tptp.bool)) (or (not (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fconj P) Q))) (tptp.hBOOL Q))) (forall ((Q tptp.bool) (P tptp.bool)) (or (not (tptp.hBOOL P)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fdisj P) Q)))) (forall ((P tptp.bool) (Q tptp.bool)) (or (not (tptp.hBOOL Q)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fdisj P) Q)))) (forall ((P tptp.bool) (Q tptp.bool)) (or (not (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fdisj P) Q))) (tptp.hBOOL P) (tptp.hBOOL Q))) (not (tptp.hBOOL tptp.fFalse)) (forall ((P tptp.bool)) (or (= P tptp.fTrue) (= P tptp.fFalse))) (forall ((Q tptp.bool) (P tptp.bool)) (or (tptp.hBOOL P) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fimplies P) Q)))) (forall ((P tptp.bool) (Q tptp.bool)) (or (not (tptp.hBOOL Q)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fimplies P) Q)))) (forall ((P tptp.bool) (Q tptp.bool)) (or (not (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fimplies P) Q))) (not (tptp.hBOOL P)) (tptp.hBOOL Q))) (forall ((X tptp.x_a) (Y tptp.x_a)) (or (not (tptp.hBOOL (tptp.hAPP_a_bool (tptp.hAPP_a_fun_a_bool tptp.fequal_a X) Y))) (= X Y))) (forall ((X tptp.x_a) (Y tptp.x_a)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_a_bool (tptp.hAPP_a_fun_a_bool tptp.fequal_a X) Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat (tptp.if_nat tptp.fTrue) X) Y) X)) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat (tptp.if_nat tptp.fFalse) X) Y) Y)) (forall ((P tptp.bool)) (or (= P tptp.fTrue) (= P tptp.fFalse))) (forall ((P tptp.nat)) (= (tptp.hAPP_nat_nat tptp.cOMBI_nat P) P)) (forall ((X tptp.int) (Y tptp.int)) (or (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.fequal_int X) Y))) (= X Y))) (forall ((X tptp.int) (Y tptp.int)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.fequal_int X) Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (or (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.fequal_nat X) Y))) (= X Y))) (forall ((X tptp.nat) (Y tptp.nat)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.fequal_nat X) Y)))) (forall ((X tptp.pname) (Y tptp.pname)) (or (not (tptp.hBOOL (tptp.hAPP_pname_bool (tptp.hAPP_p61793385e_bool tptp.fequal_pname X) Y))) (= X Y))) (forall ((X tptp.pname) (Y tptp.pname)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_pname_bool (tptp.hAPP_p61793385e_bool tptp.fequal_pname X) Y)))) (forall ((P tptp.bool) (Q tptp.x_a)) (= (tptp.hAPP_a_bool (tptp.cOMBK_bool_a P) Q) P)) (forall ((P tptp.x_a) (Q tptp.pname)) (= (tptp.hAPP_pname_a (tptp.cOMBK_a_pname P) Q) P)) (forall ((P tptp.fun_a_fun_a_bool) (Q tptp.x_a) (R tptp.x_a)) (= (tptp.hAPP_a_bool (tptp.hAPP_a_fun_a_bool (tptp.cOMBC_a_a_bool P) Q) R) (tptp.hAPP_a_bool (tptp.hAPP_a_fun_a_bool P R) Q))) (forall ((P tptp.int) (Q tptp.nat)) (= (tptp.hAPP_nat_int (tptp.cOMBK_int_nat P) Q) P)) (forall ((P tptp.bool) (Q tptp.int)) (= (tptp.hAPP_int_bool (tptp.cOMBK_bool_int P) Q) P)) (forall ((P tptp.bool) (Q tptp.nat)) (= (tptp.hAPP_nat_bool (tptp.cOMBK_bool_nat P) Q) P)) (forall ((X tptp.fun_a_bool) (Y tptp.fun_a_bool)) (or (not (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.fequal_fun_a_bool X) Y))) (= X Y))) (forall ((X tptp.fun_a_bool) (Y tptp.fun_a_bool)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.fequal_fun_a_bool X) Y)))) (forall ((P tptp.fun_int_fun_a_bool) (Q tptp.x_a) (R tptp.int)) (= (tptp.hAPP_int_bool (tptp.hAPP_a_fun_int_bool (tptp.cOMBC_int_a_bool P) Q) R) (tptp.hAPP_a_bool (tptp.hAPP_int_fun_a_bool P R) Q))) (forall ((P tptp.fun_bool_bool) (Q tptp.fun_a_bool) (R tptp.x_a)) (= (tptp.hAPP_a_bool (tptp.cOMBB_bool_bool_a P Q) R) (tptp.hAPP_bool_bool P (tptp.hAPP_a_bool Q R)))) (forall ((P tptp.fun_a_fun_bool_bool) (Q tptp.fun_a_bool) (R tptp.x_a)) (= (tptp.hAPP_a_bool (tptp.cOMBS_a_bool_bool P Q) R) (tptp.hAPP_bool_bool (tptp.hAPP_a_fun_bool_bool P R) (tptp.hAPP_a_bool Q R)))) (forall ((P tptp.fun_pname_fun_a_bool) (Q tptp.x_a) (R tptp.pname)) (= (tptp.hAPP_pname_bool (tptp.hAPP_a93125764e_bool (tptp.cOMBC_pname_a_bool P) Q) R) (tptp.hAPP_a_bool (tptp.hAPP_p1534023578a_bool P R) Q))) (forall ((X tptp.fun_int_bool) (Y tptp.fun_int_bool)) (or (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.fequal_fun_int_bool X) Y))) (= X Y))) (forall ((X tptp.fun_int_bool) (Y tptp.fun_int_bool)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.fequal_fun_int_bool X) Y)))) (forall ((X tptp.fun_nat_bool) (Y tptp.fun_nat_bool)) (or (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.fequal_fun_nat_bool X) Y))) (= X Y))) (forall ((X tptp.fun_nat_bool) (Y tptp.fun_nat_bool)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.fequal_fun_nat_bool X) Y)))) (forall ((X tptp.fun_pname_bool) (Y tptp.fun_pname_bool)) (or (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.fequal533582459e_bool X) Y))) (= X Y))) (forall ((X tptp.fun_pname_bool) (Y tptp.fun_pname_bool)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.fequal533582459e_bool X) Y)))) (forall ((P tptp.fun_int_bool) (Q tptp.fun_nat_int) (R tptp.nat)) (= (tptp.hAPP_nat_bool (tptp.cOMBB_int_bool_nat P Q) R) (tptp.hAPP_int_bool P (tptp.hAPP_nat_int Q R)))) (forall ((P tptp.fun_int_fun_int_bool) (Q tptp.int) (R tptp.int)) (= (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.cOMBC_int_int_bool P) Q) R) (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool P R) Q))) (forall ((P tptp.fun_nat_fun_int_bool) (Q tptp.int) (R tptp.nat)) (= (tptp.hAPP_nat_bool (tptp.hAPP_i418383825t_bool (tptp.cOMBC_nat_int_bool P) Q) R) (tptp.hAPP_int_bool (tptp.hAPP_n1082236369t_bool P R) Q))) (forall ((P tptp.fun_nat_fun_nat_bool) (Q tptp.nat) (R tptp.nat)) (= (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool (tptp.cOMBC_nat_nat_bool P) Q) R) (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool P R) Q))) (forall ((P tptp.fun_bool_bool) (Q tptp.fun_int_bool) (R tptp.int)) (= (tptp.hAPP_int_bool (tptp.cOMBB_bool_bool_int P Q) R) (tptp.hAPP_bool_bool P (tptp.hAPP_int_bool Q R)))) (forall ((P tptp.fun_bool_bool) (Q tptp.fun_nat_bool) (R tptp.nat)) (= (tptp.hAPP_nat_bool (tptp.cOMBB_bool_bool_nat P Q) R) (tptp.hAPP_bool_bool P (tptp.hAPP_nat_bool Q R)))) (forall ((P tptp.fun_in531499254l_bool) (Q tptp.fun_int_bool) (R tptp.int)) (= (tptp.hAPP_int_bool (tptp.cOMBS_int_bool_bool P Q) R) (tptp.hAPP_bool_bool (tptp.hAPP_i68813070l_bool P R) (tptp.hAPP_int_bool Q R)))) (forall ((P tptp.fun_na1469252690l_bool) (Q tptp.fun_nat_bool) (R tptp.nat)) (= (tptp.hAPP_nat_bool (tptp.cOMBS_nat_bool_bool P Q) R) (tptp.hAPP_bool_bool (tptp.hAPP_n1006566506l_bool P R) (tptp.hAPP_nat_bool Q R)))) (forall ((P tptp.fun_bool_bool) (Q tptp.fun_pname_bool) (R tptp.pname)) (= (tptp.hAPP_pname_bool (tptp.cOMBB_647938656_pname P Q) R) (tptp.hAPP_bool_bool P (tptp.hAPP_pname_bool Q R)))) (forall ((P tptp.fun_pn250273176l_bool) (Q tptp.fun_pname_bool) (R tptp.pname)) (= (tptp.hAPP_pname_bool (tptp.cOMBS_568398431l_bool P Q) R) (tptp.hAPP_bool_bool (tptp.hAPP_p393069232l_bool P R) (tptp.hAPP_pname_bool Q R)))) (forall ((P tptp.fun_pn800050071e_bool) (Q tptp.pname) (R tptp.pname)) (= (tptp.hAPP_pname_bool (tptp.hAPP_p61793385e_bool (tptp.cOMBC_1149511130e_bool P) Q) R) (tptp.hAPP_pname_bool (tptp.hAPP_p61793385e_bool P R) Q))) (forall ((P tptp.fun_a_fun_a_bool) (Q tptp.fun_int_a) (R tptp.int)) (= (tptp.hAPP_int_fun_a_bool (tptp.cOMBB_375279840ol_int P Q) R) (tptp.hAPP_a_fun_a_bool P (tptp.hAPP_int_a Q R)))) (forall ((P tptp.fun_fun_a_bool_bool) (Q tptp.fun_a_fun_a_bool) (R tptp.x_a)) (= (tptp.hAPP_a_bool (tptp.cOMBB_1273333599bool_a P Q) R) (tptp.hAPP_fun_a_bool_bool P (tptp.hAPP_a_fun_a_bool Q R)))) (forall ((P tptp.fun_a_1255737515l_bool) (Q tptp.fun_a_bool) (R tptp.x_a)) (= (tptp.hAPP_a_bool (tptp.hAPP_f2050579477a_bool (tptp.cOMBC_1355376034l_bool P) Q) R) (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool P R) Q))) (forall ((P tptp.fun_a_fun_a_bool) (Q tptp.fun_pname_a) (R tptp.pname)) (= (tptp.hAPP_p1534023578a_bool (tptp.cOMBB_1897541054_pname P Q) R) (tptp.hAPP_a_fun_a_bool P (tptp.hAPP_pname_a Q R)))) (forall ((P tptp.fun_in1106722302l_bool) (Q tptp.fun_a_bool) (R tptp.int)) (= (tptp.hAPP_int_bool (tptp.hAPP_f1812805200t_bool (tptp.cOMBC_1753430397l_bool P) Q) R) (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_i888906320l_bool P R) Q))) (forall ((P tptp.fun_na1632405922l_bool) (Q tptp.fun_a_bool) (R tptp.nat)) (= (tptp.hAPP_nat_bool (tptp.hAPP_f282463732t_bool (tptp.cOMBC_1928494297l_bool P) Q) R) (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_n1414589940l_bool P R) Q))) (forall ((P tptp.fun_bo1549164019l_bool) (Q tptp.fun_a_bool) (R tptp.x_a)) (= (tptp.hAPP_a_fun_bool_bool (tptp.cOMBB_1972296269bool_a P Q) R) (tptp.hAPP_b589554111l_bool P (tptp.hAPP_a_bool Q R)))) (forall ((P tptp.fun_fu554186387l_bool) (Q tptp.fun_fun_a_bool_bool) (R tptp.fun_a_bool)) (= (tptp.hAPP_fun_a_bool_bool (tptp.cOMBS_1035972772l_bool P Q) R) (tptp.hAPP_bool_bool (tptp.hAPP_f198738859l_bool P R) (tptp.hAPP_fun_a_bool_bool Q R)))) (forall ((P tptp.fun_int_fun_int_bool) (Q tptp.fun_nat_int) (R tptp.nat)) (= (tptp.hAPP_n1082236369t_bool (tptp.cOMBB_1628441366ol_nat P Q) R) (tptp.hAPP_i1948725293t_bool P (tptp.hAPP_nat_int Q R)))) (forall ((P tptp.fun_nat_fun_nat_bool) (Q tptp.fun_nat_nat) (R tptp.nat)) (= (tptp.hAPP_n1699378549t_bool (tptp.cOMBB_800536526ol_nat P Q) R) (tptp.hAPP_n1699378549t_bool P (tptp.hAPP_nat_nat Q R)))) (forall ((P tptp.fun_a_1752562919a_bool) (Q tptp.fun_a_bool) (R tptp.x_a)) (= (tptp.hAPP_a_fun_a_bool (tptp.hAPP_f1038053735a_bool (tptp.cOMBC_394484100a_bool P) Q) R) (tptp.hAPP_f2050579477a_bool (tptp.hAPP_a1206381875a_bool P R) Q))) (forall ((P tptp.fun_fu819804446l_bool) (Q tptp.fun_int_fun_int_bool) (R tptp.int)) (= (tptp.hAPP_int_bool (tptp.cOMBB_1418110531ol_int P Q) R) (tptp.hAPP_f448129468l_bool P (tptp.hAPP_i1948725293t_bool Q R)))) (forall ((P tptp.fun_fu425979586l_bool) (Q tptp.fun_nat_fun_nat_bool) (R tptp.nat)) (= (tptp.hAPP_nat_bool (tptp.cOMBB_955900739ol_nat P Q) R) (tptp.hAPP_f54304608l_bool P (tptp.hAPP_n1699378549t_bool Q R)))) (forall ((P tptp.fun_in938817141l_bool) (Q tptp.fun_int_bool) (R tptp.int)) (= (tptp.hAPP_int_bool (tptp.hAPP_f1805168059t_bool (tptp.cOMBC_94739984l_bool P) Q) R) (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool P R) Q))) (forall ((P tptp.fun_in791894553l_bool) (Q tptp.fun_nat_bool) (R tptp.int)) (= (tptp.hAPP_int_bool (tptp.hAPP_f183368031t_bool (tptp.cOMBC_1848398772l_bool P) Q) R) (tptp.hAPP_f54304608l_bool (tptp.hAPP_i1718399025l_bool P R) Q))) (forall ((P tptp.fun_na1583160273l_bool) (Q tptp.fun_int_bool) (R tptp.nat)) (= (tptp.hAPP_nat_bool (tptp.hAPP_f274826591t_bool (tptp.cOMBC_620423604l_bool P) Q) R) (tptp.hAPP_f448129468l_bool (tptp.hAPP_n609083369l_bool P R) Q))) (forall ((P tptp.fun_na1436237685l_bool) (Q tptp.fun_nat_bool) (R tptp.nat)) (= (tptp.hAPP_nat_bool (tptp.hAPP_f800510211t_bool (tptp.cOMBC_226598744l_bool P) Q) R) (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool P R) Q))) (forall ((P tptp.fun_bo1549164019l_bool) (Q tptp.fun_int_bool) (R tptp.int)) (= (tptp.hAPP_i68813070l_bool (tptp.cOMBB_1652995168ol_int P Q) R) (tptp.hAPP_b589554111l_bool P (tptp.hAPP_int_bool Q R)))) (forall ((P tptp.fun_bo1549164019l_bool) (Q tptp.fun_nat_bool) (R tptp.nat)) (= (tptp.hAPP_n1006566506l_bool (tptp.cOMBB_1015721476ol_nat P Q) R) (tptp.hAPP_b589554111l_bool P (tptp.hAPP_nat_bool Q R)))) (forall ((P tptp.fun_fu989146164l_bool) (Q tptp.fun_fu819804446l_bool) (R tptp.fun_int_bool)) (= (tptp.hAPP_f448129468l_bool (tptp.cOMBS_1912792529l_bool P Q) R) (tptp.hAPP_bool_bool (tptp.hAPP_f1721100032l_bool P R) (tptp.hAPP_f448129468l_bool Q R)))) (forall ((P tptp.fun_fu1016514960l_bool) (Q tptp.fun_fu425979586l_bool) (R tptp.fun_nat_bool)) (= (tptp.hAPP_f54304608l_bool (tptp.cOMBS_1187019125l_bool P Q) R) (tptp.hAPP_bool_bool (tptp.hAPP_f1748468828l_bool P R) (tptp.hAPP_f54304608l_bool Q R)))) (forall ((P tptp.fun_in711834963l_bool) (Q tptp.fun_pname_bool) (R tptp.int)) (= (tptp.hAPP_int_bool (tptp.hAPP_f449020825t_bool (tptp.cOMBC_316919022l_bool P) Q) R) (tptp.hAPP_f1664156314l_bool (tptp.hAPP_i1587699435l_bool P R) Q))) (forall ((P tptp.fun_na2122364079l_bool) (Q tptp.fun_pname_bool) (R tptp.nat)) (= (tptp.hAPP_nat_bool (tptp.hAPP_f1066163005t_bool (tptp.cOMBC_386238098l_bool P) Q) R) (tptp.hAPP_f1664156314l_bool (tptp.hAPP_n850744903l_bool P R) Q))) (forall ((P tptp.fun_bo1549164019l_bool) (Q tptp.fun_pname_bool) (R tptp.pname)) (= (tptp.hAPP_p393069232l_bool (tptp.cOMBB_675860798_pname P Q) R) (tptp.hAPP_b589554111l_bool P (tptp.hAPP_pname_bool Q R)))) (forall ((P tptp.fun_fu31783638l_bool) (Q tptp.fun_fu1430349052l_bool) (R tptp.fun_pname_bool)) (= (tptp.hAPP_f1664156314l_bool (tptp.cOMBS_350070575l_bool P Q) R) (tptp.hAPP_bool_bool (tptp.hAPP_f1476298914l_bool P R) (tptp.hAPP_f1664156314l_bool Q R)))) (forall ((P tptp.fun_pn422929397l_bool) (Q tptp.fun_pname_bool) (R tptp.pname)) (= (tptp.hAPP_pname_bool (tptp.hAPP_f759274231e_bool (tptp.cOMBC_1058051404l_bool P) Q) R) (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool P R) Q))) (forall ((P tptp.fun_fu1471507361l_bool) (Q tptp.fun_a_bool) (R tptp.fun_a_bool)) (= (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool (tptp.cOMBC_1732670874l_bool P) Q) R) (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool P R) Q))) (forall ((P tptp.fun_bo1549164019l_bool) (Q tptp.fun_fun_a_bool_bool) (R tptp.fun_a_bool)) (= (tptp.hAPP_f198738859l_bool (tptp.cOMBB_338059395a_bool P Q) R) (tptp.hAPP_b589554111l_bool P (tptp.hAPP_fun_a_bool_bool Q R)))) (forall ((P tptp.fun_na1436237685l_bool) (Q tptp.fun_nat_nat) (R tptp.nat)) (= (tptp.hAPP_n215258509l_bool (tptp.cOMBB_1146692694ol_nat P Q) R) (tptp.hAPP_n215258509l_bool P (tptp.hAPP_nat_nat Q R)))) (forall ((P tptp.fun_in719570932t_bool) (Q tptp.fun_int_bool) (R tptp.int)) (= (tptp.hAPP_i1948725293t_bool (tptp.hAPP_f1048215610t_bool (tptp.cOMBC_1683390479t_bool P) Q) R) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool P R) Q))) (forall ((P tptp.fun_na35521688t_bool) (Q tptp.fun_nat_bool) (R tptp.nat)) (= (tptp.hAPP_n1699378549t_bool (tptp.hAPP_f1570313510t_bool (tptp.cOMBC_178881787t_bool P) Q) R) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool P R) Q))) (forall ((P tptp.fun_fu1151772339l_bool) (Q tptp.fun_int_bool) (R tptp.fun_int_bool)) (= (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool (tptp.cOMBC_605892544l_bool P) Q) R) (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool P R) Q))) (forall ((P tptp.fun_fu1217155507l_bool) (Q tptp.fun_nat_bool) (R tptp.fun_nat_bool)) (= (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool (tptp.cOMBC_1693257480l_bool P) Q) R) (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool P R) Q))) (forall ((P tptp.fun_bo1549164019l_bool) (Q tptp.fun_fu819804446l_bool) (R tptp.fun_int_bool)) (= (tptp.hAPP_f1721100032l_bool (tptp.cOMBB_1974511970t_bool P Q) R) (tptp.hAPP_b589554111l_bool P (tptp.hAPP_f448129468l_bool Q R)))) (forall ((P tptp.fun_bo1549164019l_bool) (Q tptp.fun_fu425979586l_bool) (R tptp.fun_nat_bool)) (= (tptp.hAPP_f1748468828l_bool (tptp.cOMBB_444170502t_bool P Q) R) (tptp.hAPP_b589554111l_bool P (tptp.hAPP_f54304608l_bool Q R)))) (forall ((P tptp.fun_bo1549164019l_bool) (Q tptp.fun_fu1430349052l_bool) (R tptp.fun_pname_bool)) (= (tptp.hAPP_f1476298914l_bool (tptp.cOMBB_2095475776e_bool P Q) R) (tptp.hAPP_b589554111l_bool P (tptp.hAPP_f1664156314l_bool Q R)))) (forall ((P tptp.fun_fu802393907l_bool) (Q tptp.fun_pname_bool) (R tptp.fun_pname_bool)) (= (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool (tptp.cOMBC_1284144636l_bool P) Q) R) (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool P R) Q))) (forall ((P tptp.fun_fu1471507361l_bool) (Q tptp.fun_int_fun_a_bool) (R tptp.int)) (= (tptp.hAPP_i888906320l_bool (tptp.cOMBB_313729068ol_int P Q) R) (tptp.hAPP_f1631501043l_bool P (tptp.hAPP_int_fun_a_bool Q R)))) (forall ((P tptp.fun_fu1471507361l_bool) (Q tptp.fun_nat_fun_a_bool) (R tptp.nat)) (= (tptp.hAPP_n1414589940l_bool (tptp.cOMBB_1823939024ol_nat P Q) R) (tptp.hAPP_f1631501043l_bool P (tptp.hAPP_nat_fun_a_bool Q R)))) (forall ((P tptp.fun_fu1151772339l_bool) (Q tptp.fun_int_fun_int_bool) (R tptp.int)) (= (tptp.hAPP_i2112223885l_bool (tptp.cOMBB_1761098400ol_int P Q) R) (tptp.hAPP_f284875647l_bool P (tptp.hAPP_i1948725293t_bool Q R)))) (forall ((P tptp.fun_fu1151772339l_bool) (Q tptp.fun_nat_fun_int_bool) (R tptp.nat)) (= (tptp.hAPP_n609083369l_bool (tptp.cOMBB_1123824708ol_nat P Q) R) (tptp.hAPP_f284875647l_bool P (tptp.hAPP_n1082236369t_bool Q R)))) (forall ((P tptp.fun_fu1217155507l_bool) (Q tptp.fun_int_fun_nat_bool) (R tptp.int)) (= (tptp.hAPP_i1718399025l_bool (tptp.cOMBB_516767136ol_int P Q) R) (tptp.hAPP_f103356543l_bool P (tptp.hAPP_i418383825t_bool Q R)))) (forall ((P tptp.fun_fu1217155507l_bool) (Q tptp.fun_nat_fun_nat_bool) (R tptp.nat)) (= (tptp.hAPP_n215258509l_bool (tptp.cOMBB_2026977092ol_nat P Q) R) (tptp.hAPP_f103356543l_bool P (tptp.hAPP_n1699378549t_bool Q R)))) (forall ((P tptp.fun_fu802393907l_bool) (Q tptp.fun_in2065004473e_bool) (R tptp.int)) (= (tptp.hAPP_i1587699435l_bool (tptp.cOMBB_607112096ol_int P Q) R) (tptp.hAPP_f434788991l_bool P (tptp.hAPP_i7355787e_bool Q R)))) (forall ((P tptp.fun_fu802393907l_bool) (Q tptp.fun_na936072029e_bool) (R tptp.nat)) (= (tptp.hAPP_n850744903l_bool (tptp.cOMBB_2117322052ol_nat P Q) R) (tptp.hAPP_f434788991l_bool P (tptp.hAPP_n1025906991e_bool Q R)))) (forall ((P tptp.fun_fu418465139l_bool) (Q tptp.fun_fun_a_bool_bool) (R tptp.fun_fun_a_bool_bool)) (= (tptp.hAPP_f621171935l_bool (tptp.hAPP_f1434722111l_bool (tptp.cOMBC_331553030l_bool P) Q) R) (tptp.hAPP_f621171935l_bool (tptp.hAPP_f1434722111l_bool P R) Q))) (forall ((P tptp.fun_fu209342027l_bool) (Q tptp.fun_fu819804446l_bool) (R tptp.fun_fu819804446l_bool)) (= (tptp.hAPP_f215623910l_bool (tptp.hAPP_f317860125l_bool (tptp.cOMBC_348868698l_bool P) Q) R) (tptp.hAPP_f215623910l_bool (tptp.hAPP_f317860125l_bool P R) Q))) (forall ((P tptp.fun_fu140186515l_bool) (Q tptp.fun_fu425979586l_bool) (R tptp.fun_fu425979586l_bool)) (= (tptp.hAPP_f1637334154l_bool (tptp.hAPP_f1772781669l_bool (tptp.cOMBC_595898202l_bool P) Q) R) (tptp.hAPP_f1637334154l_bool (tptp.hAPP_f1772781669l_bool P R) Q))) (forall ((P tptp.fun_fu1911931399l_bool) (Q tptp.fun_fu1430349052l_bool) (R tptp.fun_fu1430349052l_bool)) (= (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool (tptp.cOMBC_7971162l_bool P) Q) R) (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool P R) Q))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname tptp.u)) _let_9 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat _let_7) _let_8)) (= (tptp.hAPP_fun_a_bool_nat tptp.finite_card_a tptp.g) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat _let_8) _let_7)) _let_6 (not (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_5 tptp.g))) _let_4 true)))))))))))))))))))))))))))))))))))))
% 3.67/3.86 )
% 3.67/3.86 % SZS output end Proof for SWW473_3
% 3.67/3.86 % cvc5---1.0.5 exiting
% 3.67/3.86 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------