%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWW473_1 : TPTP v8.1.2. Released v5.3.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n007.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 00:21:03 EDT 2023

% Result   : Theorem 0.56s 0.95s
% Output   : Proof 0.56s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.19  % Problem    : SWW473_1 : TPTP v8.1.2. Released v5.3.0.
% 0.12/0.20  % Command    : do_cvc5 %s %d
% 0.22/0.42  % Computer : n007.cluster.edu
% 0.22/0.42  % Model    : x86_64 x86_64
% 0.22/0.42  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.42  % Memory   : 8042.1875MB
% 0.22/0.42  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.22/0.42  % CPULimit   : 300
% 0.22/0.42  % WCLimit    : 300
% 0.22/0.42  % DateTime   : Sun Aug 27 20:09:57 EDT 2023
% 0.22/0.42  % CPUTime    : 
% 0.28/0.63  %----Proving TF0_NAR, FOF, or CNF
% 0.56/0.95  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.I4DLecPS9n/cvc5---1.0.5_12056.p...
% 0.56/0.95  ------- get file name : TPTP file name is SWW473_1
% 0.56/0.95  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_12056.smt2...
% 0.56/0.95  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.56/0.95  % SZS status Theorem for SWW473_1
% 0.56/0.95  % SZS output start Proof for SWW473_1
% 0.56/0.95  (
% 0.56/0.95  (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.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 (forall ((X_2 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.insert_a X_2 A)) B)) (and (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a X_2) B)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool A) B))))))) (let ((_let_11 (forall ((A tptp.fun_pname_bool) (B_1 tptp.x_a) (F tptp.fun_pname_a) (X_2 tptp.pname)) (=> (= B_1 (tptp.hAPP_pname_a F X_2)) (=> (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 B_1) (tptp.image_pname_a F A)))))))) (let ((_let_12 (forall ((A tptp.fun_pname_bool) (F tptp.fun_pname_a) (X_2 tptp.pname)) (or (not (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)) (tptp.image_pname_a F A))))))) (let ((_let_13 (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_5 _let_1)))) (let ((_let_14 (not _let_6))) (let ((_let_15 (or _let_14 _let_13))) (let ((_let_16 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_17 (not _let_15))) (let ((_let_18 (and _let_13 _let_9))) (let ((_let_19 (not _let_13))) (let ((_let_20 (= _let_3 _let_18))) (let ((_let_21 (not _let_18))) (let ((_let_22 (_let_10))) (let ((_let_23 (ASSUME :args _let_22))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_16 :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_2)) (tptp.image_pname_a F A))))) :args (_let_12))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_15)) :args ((or _let_14 _let_13 _let_17))) (ASSUME :args (_let_6)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_18)) :args ((or (not _let_9) _let_18 _let_19))) (ASSUME :args (_let_9)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_20)) :args ((or _let_3 _let_21 (not _let_20)))) (ASSUME :args (_let_4)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_23 :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.insert_a X_2 A)) B)))) :args _let_22)) _let_23 :args (_let_20 false _let_10)) :args (_let_21 true _let_3 false _let_20)) :args (_let_19 false _let_9 true _let_18)) :args (_let_17 false _let_6 true _let_13)) _let_16 :args (false true _let_15 false _let_12)) :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_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_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_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_fu814369080l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f937997336l_bool tptp.finite1701474069l_bool A)) (tptp.hBOOL (tptp.hAPP_f1295398978l_bool tptp.finite719726885l_bool (tptp.collec1874991203l_bool (tptp.hAPP_f760187903l_bool (tptp.cOMBC_1269652216l_bool tptp.ord_le65145710l_bool) A)))))) (forall ((A tptp.fun_fu399576434l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f389811538l_bool tptp.finite786885583l_bool A)) (tptp.hBOOL (tptp.hAPP_f595608956l_bool tptp.finite1491191519l_bool (tptp.collec792590109l_bool (tptp.hAPP_f1759205631l_bool (tptp.cOMBC_336095980l_bool tptp.ord_le1375671464l_bool) A)))))) (forall ((A tptp.fun_fu885608257l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f292226953l_bool tptp.finite1381704300l_bool A)) (tptp.hBOOL (tptp.hAPP_f1363661463l_bool tptp.finite1343359508l_bool (tptp.collec1635217238l_bool (tptp.hAPP_f1050622307l_bool (tptp.cOMBC_636888218l_bool tptp.ord_le967226251l_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_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_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 ((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_fu411113733ol_nat) (F_1 tptp.fun_fu814369080l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f937997336l_bool tptp.finite1701474069l_bool F_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.image_2089570637ol_nat H F_1))))) (forall ((H tptp.fun_fu1730389579ol_nat) (F_1 tptp.fun_fu399576434l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f389811538l_bool tptp.finite786885583l_bool F_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.image_1079571347ol_nat H F_1))))) (forall ((H tptp.fun_fu2020802748ol_nat) (F_1 tptp.fun_fu885608257l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f292226953l_bool tptp.finite1381704300l_bool F_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.image_1802975832ol_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_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_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_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_fu881587263_pname) (F_1 tptp.fun_fu814369080l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f937997336l_bool tptp.finite1701474069l_bool F_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.image_1604018183_pname H F_1))))) (forall ((H tptp.fun_fu1664106117_pname) (F_1 tptp.fun_fu399576434l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f389811538l_bool tptp.finite786885583l_bool F_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.image_1705983821_pname H F_1))))) (forall ((H tptp.fun_fu1175941238_pname) (F_1 tptp.fun_fu885608257l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f292226953l_bool tptp.finite1381704300l_bool F_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.image_990671762_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_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_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_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_na1436237685l_bool) (F_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat F_1)) (tptp.hBOOL (tptp.hAPP_f937997336l_bool tptp.finite1701474069l_bool (tptp.image_1607900221l_bool H F_1))))) (forall ((H tptp.fun_na2122364079l_bool) (F_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat F_1)) (tptp.hBOOL (tptp.hAPP_f389811538l_bool tptp.finite786885583l_bool (tptp.image_1874789623l_bool H F_1))))) (forall ((H tptp.fun_na1632405922l_bool) (F_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat F_1)) (tptp.hBOOL (tptp.hAPP_f292226953l_bool tptp.finite1381704300l_bool (tptp.image_1208015684l_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_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_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_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_pn1165013435l_bool) (F_1 tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname F_1)) (tptp.hBOOL (tptp.hAPP_f937997336l_bool tptp.finite1701474069l_bool (tptp.image_1154884483l_bool H F_1))))) (forall ((H tptp.fun_pn422929397l_bool) (F_1 tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname F_1)) (tptp.hBOOL (tptp.hAPP_f389811538l_bool tptp.finite786885583l_bool (tptp.image_1642285373l_bool H F_1))))) (forall ((H tptp.fun_pn1038293468l_bool) (F_1 tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname F_1)) (tptp.hBOOL (tptp.hAPP_f292226953l_bool tptp.finite1381704300l_bool (tptp.image_1420695166l_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_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_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_pname_pname) (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.finite_finite_pname (tptp.image_pname_pname H F_1))))) (forall ((H tptp.fun_a_a) (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.finite_finite_a (tptp.image_a_a H F_1))))) (forall ((H tptp.fun_fun_nat_bool_a) (F_1 tptp.fun_fu425979586l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool F_1)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a (tptp.image_fun_nat_bool_a H F_1))))) (forall ((H tptp.fun_fun_pname_bool_a) (F_1 tptp.fun_fu1430349052l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool F_1)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a (tptp.image_876012084bool_a H F_1))))) (forall ((H tptp.fun_fun_a_bool_a) (F_1 tptp.fun_fun_a_bool_bool)) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool F_1)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a (tptp.image_fun_a_bool_a H F_1))))) (forall ((H tptp.fun_pname_nat) (F_1 tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname F_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.image_pname_nat H F_1))))) (forall ((H tptp.fun_nat_pname) (F_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat F_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.image_nat_pname H F_1))))) (forall ((A_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.finite_finite_a (tptp.insert_a A_1 A))))) (forall ((A_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.finite_finite_nat (tptp.insert_nat A_1 A))))) (forall ((A_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.finite_finite_pname (tptp.insert_pname A_1 A))))) (forall ((A_1 tptp.fun_fu425979586l_bool) (A tptp.fun_fu814369080l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f937997336l_bool tptp.finite1701474069l_bool A)) (tptp.hBOOL (tptp.hAPP_f937997336l_bool tptp.finite1701474069l_bool (tptp.insert2003652156l_bool A_1 A))))) (forall ((A_1 tptp.fun_fu1430349052l_bool) (A tptp.fun_fu399576434l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f389811538l_bool tptp.finite786885583l_bool A)) (tptp.hBOOL (tptp.hAPP_f389811538l_bool tptp.finite786885583l_bool (tptp.insert1117693814l_bool A_1 A))))) (forall ((A_1 tptp.fun_fun_a_bool_bool) (A tptp.fun_fu885608257l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f292226953l_bool tptp.finite1381704300l_bool A)) (tptp.hBOOL (tptp.hAPP_f292226953l_bool tptp.finite1381704300l_bool (tptp.insert1457093509l_bool A_1 A))))) (forall ((A_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_f621171935l_bool tptp.finite347923420a_bool (tptp.insert_fun_a_bool A_1 A))))) (forall ((A_1 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.insert1325755072e_bool A_1 A))))) (forall ((A_1 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.insert_fun_nat_bool A_1 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_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_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_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_fu897950882bool_a) (A tptp.fun_fu814369080l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f937997336l_bool tptp.finite1701474069l_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_526090948bool_a F A))) (tptp.hAPP_f1690079119ol_nat tptp.finite1352710292l_bool A))))) (forall ((F tptp.fun_fu2061654492bool_a) (A tptp.fun_fu399576434l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f389811538l_bool tptp.finite786885583l_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_349102846bool_a F A))) (tptp.hAPP_f98387925ol_nat tptp.finite269641166l_bool A))))) (forall ((F tptp.fun_fu1373417771bool_a) (A tptp.fun_fu885608257l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f292226953l_bool tptp.finite1381704300l_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_573985017bool_a F A))) (tptp.hAPP_f1253658590ol_nat tptp.finite1659325229l_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_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_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_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_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_pn406123357t_bool) (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_f696928925ol_nat tptp.finite346522414t_bool (tptp.image_2129980159t_bool F A))) (tptp.hAPP_f921600141ol_nat tptp.finite_card_pname A))))) (forall ((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_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f55526627ol_nat tptp.finite1340463720e_bool (tptp.image_47868345e_bool F A))) (tptp.hAPP_f921600141ol_nat tptp.finite_card_pname A))))) (forall ((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_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f2009550088ol_nat tptp.finite1306199131a_bool (tptp.image_112932426a_bool F A))) (tptp.hAPP_f921600141ol_nat tptp.finite_card_pname A))))) (forall ((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_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_fun_a_bool_nat tptp.finite_card_a (tptp.image_nat_a F A))) (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat A))))) (forall ((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_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f696928925ol_nat tptp.finite346522414t_bool (tptp.image_26036933t_bool F A))) (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat A))))) (forall ((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_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f55526627ol_nat tptp.finite1340463720e_bool (tptp.image_1655916159e_bool F A))) (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat A))))) (forall ((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_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f2009550088ol_nat tptp.finite1306199131a_bool (tptp.image_nat_fun_a_bool F A))) (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat A))))) (forall ((F tptp.fun_fu665170229_pname) (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_f921600141ol_nat tptp.finite_card_pname (tptp.image_1921560913_pname F A))) (tptp.hAPP_f696928925ol_nat tptp.finite346522414t_bool A))))) (forall ((F tptp.fun_fu1499449723_pname) (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_f921600141ol_nat tptp.finite_card_pname (tptp.image_1283814551_pname F A))) (tptp.hAPP_f55526627ol_nat tptp.finite1340463720e_bool A))))) (forall ((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_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f921600141ol_nat tptp.finite_card_pname (tptp.image_1854862208_pname F A))) (tptp.hAPP_f2009550088ol_nat tptp.finite1306199131a_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_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_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 ((X_2 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.insert_fun_nat_bool X_2 A)))))) (forall ((X_2 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.insert1325755072e_bool X_2 A)))))) (forall ((X_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_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.insert_fun_a_bool X_2 A)))))) (forall ((X_2 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.insert_pname X_2 A)))))) (forall ((X_2 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.insert_nat X_2 A)))))) (forall ((X_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_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.insert_a X_2 A)))))) (forall ((X_2 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.insert_fun_nat_bool X_2 A)))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP_f1637334154l_bool (tptp.hAPP_f1951378235l_bool tptp.member_fun_nat_bool X_2) 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_2 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.insert1325755072e_bool X_2 A)))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool X_2) 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_2 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.insert_fun_a_bool X_2 A)))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP_f621171935l_bool (tptp.hAPP_f285962445l_bool tptp.member_fun_a_bool X_2) 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_2 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.insert_nat X_2 A)))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) 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_2 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.insert_pname X_2 A)))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) 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_2 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.insert_a X_2 A)))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a X_2) 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_2 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_2) A))) (= (tptp.hAPP_f696928925ol_nat tptp.finite346522414t_bool (tptp.insert_fun_nat_bool X_2 A)) (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_f696928925ol_nat tptp.finite346522414t_bool A)))))) (forall ((X_2 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_2) A))) (= (tptp.hAPP_f55526627ol_nat tptp.finite1340463720e_bool (tptp.insert1325755072e_bool X_2 A)) (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_f55526627ol_nat tptp.finite1340463720e_bool A)))))) (forall ((X_2 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_2) A))) (= (tptp.hAPP_f2009550088ol_nat tptp.finite1306199131a_bool (tptp.insert_fun_a_bool X_2 A)) (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_f2009550088ol_nat tptp.finite1306199131a_bool A)))))) (forall ((X_2 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_2) A))) (= (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat (tptp.insert_nat X_2 A)) (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat A)))))) (forall ((X_2 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_2) A))) (= (tptp.hAPP_f921600141ol_nat tptp.finite_card_pname (tptp.insert_pname X_2 A)) (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_f921600141ol_nat tptp.finite_card_pname A)))))) (forall ((X_2 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_2) A))) (= (tptp.hAPP_fun_a_bool_nat tptp.finite_card_a (tptp.insert_a X_2 A)) (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_fun_a_bool_nat tptp.finite_card_a A)))))) (forall ((Q_1 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_1)))) (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_1)))))) (forall ((Q_1 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_1)))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.collec1974731493e_bool (tptp.cOMBS_350070575l_bool (tptp.cOMBB_2095475776e_bool tptp.fconj Pa) Q_1)))))) (forall ((Q_1 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_1)))) (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_1)))))) (forall ((Q_1 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_1)))) (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_1)))))) (forall ((Q_1 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_1)))) (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_1)))))) (forall ((Q_1 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_1)))) (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_1)))))) (forall ((N_1 tptp.nat) (M_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_1) M_2)) (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat tptp.suc M_2)) N_1) (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.minus_minus_nat M_2) N_1))))) (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_1 tptp.nat) (Nat tptp.nat)) (= (= (tptp.hAPP_nat_nat tptp.suc Nat_1) (tptp.hAPP_nat_nat tptp.suc Nat)) (= Nat_1 Nat))) (forall ((N_1 tptp.nat)) (not (= (tptp.hAPP_nat_nat tptp.suc N_1) N_1))) (forall ((N_1 tptp.nat)) (not (= N_1 (tptp.hAPP_nat_nat tptp.suc N_1)))) (forall ((M_2 tptp.nat) (N_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_2) N_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_1) M_2)) (= M_2 N_1)))) (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_2 tptp.nat) (N_1 tptp.nat)) (=> (= M_2 N_1) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_2) N_1)))) (forall ((M_2 tptp.nat) (N_1 tptp.nat)) (or (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_2) N_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_1) M_2)))) (forall ((N_1 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_1) N_1))) (forall ((I_1 tptp.nat) (J tptp.nat) (K_1 tptp.nat)) (let ((_let_1 (tptp.minus_minus_nat I_1))) (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat _let_1 J)) K_1) (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat _let_1 K_1)) J)))) (forall ((Pa tptp.fun_pname_bool) (Q_1 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_1)))) (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_1)))))) (forall ((Pa tptp.fun_fu425979586l_bool) (Q_1 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_1)))) (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_1)))))) (forall ((Pa tptp.fun_fu1430349052l_bool) (Q_1 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_1)))) (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_1)))))) (forall ((Pa tptp.fun_fun_a_bool_bool) (Q_1 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_1)))) (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_1)))))) (forall ((Pa tptp.fun_nat_bool) (Q_1 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_1)))) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.collect_nat Pa))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.collect_nat Q_1)))))) (forall ((Pa tptp.fun_a_bool) (Q_1 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_1)))) (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_1)))))) (forall ((A_1 tptp.nat) (A tptp.fun_nat_bool)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.insert_nat A_1 A))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)))) (forall ((A_1 tptp.pname) (A tptp.fun_pname_bool)) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.insert_pname A_1 A))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)))) (forall ((A_1 tptp.x_a) (A tptp.fun_a_bool)) (= (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a (tptp.insert_a A_1 A))) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a A)))) (forall ((A_1 tptp.fun_nat_bool) (A tptp.fun_fu425979586l_bool)) (= (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool (tptp.insert_fun_nat_bool A_1 A))) (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool A)))) (forall ((A_1 tptp.fun_pname_bool) (A tptp.fun_fu1430349052l_bool)) (= (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.insert1325755072e_bool A_1 A))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)))) (forall ((A_1 tptp.fun_a_bool) (A tptp.fun_fun_a_bool_bool)) (= (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool (tptp.insert_fun_a_bool A_1 A))) (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_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_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_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_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_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_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_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_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_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_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 ((M_2 tptp.nat) (N_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat tptp.suc M_2)) N_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_2) N_1)))) (forall ((M_2 tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat tptp.suc N_1))) (let ((_let_2 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_2))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 _let_1)) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 N_1))) (= M_2 _let_1)))))) (forall ((M_2 tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_2))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N_1)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat tptp.suc N_1)))))) (forall ((Na tptp.nat) (M_3 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_3))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Na) M_3)))) (forall ((M_3 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_3))) (= (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 _let_1)) (or (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 Na)) (= M_3 _let_1)))))) (forall ((M_3 tptp.nat) (Na tptp.nat)) (= (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_3) Na))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat tptp.suc Na)) M_3)))) (forall ((N_1 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_1)) N_1)))) (forall ((M_2 tptp.nat) (N_1 tptp.nat) (K_1 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat tptp.suc M_2)) N_1)) (tptp.hAPP_nat_nat tptp.suc K_1)) (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.minus_minus_nat M_2) N_1)) K_1))) (forall ((M_2 tptp.nat) (N_1 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat tptp.suc M_2)) (tptp.hAPP_nat_nat tptp.suc N_1)) (tptp.hAPP_nat_nat (tptp.minus_minus_nat M_2) N_1))) (forall ((Na tptp.nat) (K tptp.nat) (M_3 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M_3)) (=> (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.minus_minus_nat M_3) K)) (tptp.hAPP_nat_nat (tptp.minus_minus_nat Na) K))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_3) Na))))))) (forall ((N_1 tptp.nat) (K_1 tptp.nat) (M_2 tptp.nat)) (let ((_let_1 (tptp.minus_minus_nat M_2))) (let ((_let_2 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 M_2)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 N_1)) (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat _let_1 K_1)) (tptp.hAPP_nat_nat (tptp.minus_minus_nat N_1) K_1)) (tptp.hAPP_nat_nat _let_1 N_1))))))) (forall ((Na tptp.nat) (K tptp.nat) (M_3 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M_3)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Na)) (= (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat M_3) K) (tptp.hAPP_nat_nat (tptp.minus_minus_nat Na) K)) (= M_3 Na)))))) (forall ((I_1 tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.minus_minus_nat N_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_1) N_1)) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat _let_1 I_1)) I_1)))) (forall ((L tptp.nat) (M_2 tptp.nat) (N_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_2) N_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.minus_minus_nat M_2) L)) (tptp.hAPP_nat_nat (tptp.minus_minus_nat N_1) L))))) (forall ((L tptp.nat) (M_2 tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.minus_minus_nat L))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_2) N_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 N_1)) (tptp.hAPP_nat_nat _let_1 M_2)))))) (forall ((M_2 tptp.nat) (N_1 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.minus_minus_nat M_2) N_1)) M_2))) (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 ((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_2 tptp.fun_pname_bool)) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool C_2) A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname C_2)) (= B (tptp.image_pname_a F C_2))))))) (forall ((Na tptp.nat) (N_3 tptp.nat) (F tptp.fun_nat_fun_nat_bool)) (=> (forall ((N_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_n1699378549t_bool F N_2)) (tptp.hAPP_n1699378549t_bool F (tptp.hAPP_nat_nat tptp.suc N_2))))) (=> (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_na936072029e_bool)) (=> (forall ((N_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_n1025906991e_bool F N_2)) (tptp.hAPP_n1025906991e_bool F (tptp.hAPP_nat_nat tptp.suc N_2))))) (=> (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_nat)) (=> (forall ((N_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat F N_2)) (tptp.hAPP_nat_nat F (tptp.hAPP_nat_nat tptp.suc N_2))))) (=> (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_fun_a_bool)) (=> (forall ((N_2 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_2)) (tptp.hAPP_nat_fun_a_bool F (tptp.hAPP_nat_nat tptp.suc N_2))))) (=> (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 ((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_1 tptp.pname)) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) 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_1)))))))))))) _let_11 (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_pname_bool) (B tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) A)) (= A B)))) (forall ((A tptp.fun_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_1 tptp.nat) (A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat C_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 ((C_1 tptp.x_a) (A tptp.fun_a_bool) (B tptp.fun_a_bool)) (let ((_let_1 (tptp.hAPP_a85458249l_bool tptp.member_a C_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 ((C_1 tptp.pname) (A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname C_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_1 tptp.nat) (A_1 tptp.nat) (B tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat A_1))) (=> (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B))) (= A_1 B_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.insert_nat B_1 B)))))) (forall ((B_1 tptp.pname) (A_1 tptp.pname) (B tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname A_1))) (=> (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B))) (= A_1 B_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.insert_pname B_1 B)))))) (forall ((B_1 tptp.x_a) (A_1 tptp.x_a) (B tptp.fun_a_bool)) (let ((_let_1 (tptp.hAPP_a85458249l_bool tptp.member_a A_1))) (=> (=> (not (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 B))) (= A_1 B_1)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 (tptp.insert_a B_1 B)))))) (forall ((A_1 tptp.nat) (B_1 tptp.nat) (A tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat A_1))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.insert_nat B_1 A))) (=> (not (= A_1 B_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 A)))))) (forall ((A_1 tptp.pname) (B_1 tptp.pname) (A tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname A_1))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.insert_pname B_1 A))) (=> (not (= A_1 B_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A)))))) (forall ((A_1 tptp.x_a) (B_1 tptp.x_a) (A tptp.fun_a_bool)) (let ((_let_1 (tptp.hAPP_a85458249l_bool tptp.member_a A_1))) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 (tptp.insert_a B_1 A))) (=> (not (= A_1 B_1)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 A)))))) (forall ((A_1 tptp.nat) (B tptp.fun_nat_bool)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_1) (tptp.insert_nat A_1 B)))) (forall ((A_1 tptp.pname) (B tptp.fun_pname_bool)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A_1) (tptp.insert_pname A_1 B)))) (forall ((A_1 tptp.x_a) (B tptp.fun_a_bool)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a A_1) (tptp.insert_a A_1 B)))) (forall ((A_1 tptp.nat) (B tptp.fun_nat_bool)) (= (tptp.insert_nat A_1 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_1)) (tptp.hAPP_f800510211t_bool (tptp.cOMBC_226598744l_bool tptp.member_nat) B))))) (forall ((A_1 tptp.pname) (B tptp.fun_pname_bool)) (= (tptp.insert_pname A_1 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_1)) (tptp.hAPP_f759274231e_bool (tptp.cOMBC_1058051404l_bool tptp.member_pname) B))))) (forall ((A_1 tptp.x_a) (B tptp.fun_a_bool)) (= (tptp.insert_a A_1 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_1)) (tptp.hAPP_f2050579477a_bool (tptp.cOMBC_1355376034l_bool tptp.member_a) B))))) (forall ((A_1 tptp.fun_nat_bool) (B tptp.fun_fu425979586l_bool)) (= (tptp.insert_fun_nat_bool A_1 B) (tptp.collect_fun_nat_bool (tptp.cOMBS_1187019125l_bool (tptp.cOMBB_444170502t_bool tptp.fdisj (tptp.hAPP_f103356543l_bool (tptp.cOMBC_1693257480l_bool tptp.fequal_fun_nat_bool) A_1)) (tptp.hAPP_f1246832597l_bool (tptp.cOMBC_1245412066l_bool tptp.member_fun_nat_bool) B))))) (forall ((A_1 tptp.fun_pname_bool) (B tptp.fun_fu1430349052l_bool)) (= (tptp.insert1325755072e_bool A_1 B) (tptp.collec1974731493e_bool (tptp.cOMBS_350070575l_bool (tptp.cOMBB_2095475776e_bool tptp.fdisj (tptp.hAPP_f434788991l_bool (tptp.cOMBC_1284144636l_bool tptp.fequal533582459e_bool) A_1)) (tptp.hAPP_f559147733l_bool (tptp.cOMBC_1988546018l_bool tptp.member799430823e_bool) B))))) (forall ((A_1 tptp.fun_a_bool) (B tptp.fun_fun_a_bool_bool)) (= (tptp.insert_fun_a_bool A_1 B) (tptp.collect_fun_a_bool (tptp.cOMBS_1035972772l_bool (tptp.cOMBB_338059395a_bool tptp.fdisj (tptp.hAPP_f1631501043l_bool (tptp.cOMBC_1732670874l_bool tptp.fequal_fun_a_bool) A_1)) (tptp.hAPP_f2117159681l_bool (tptp.cOMBC_1880041174l_bool tptp.member_fun_a_bool) B))))) (forall ((A_1 tptp.nat) (Pa tptp.fun_nat_bool)) (= (tptp.insert_nat A_1 (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_1))) Pa)))) (forall ((A_1 tptp.pname) (Pa tptp.fun_pname_bool)) (= (tptp.insert_pname A_1 (tptp.collect_pname Pa)) (tptp.collect_pname (tptp.cOMBS_568398431l_bool (tptp.cOMBB_675860798_pname tptp.fimplies (tptp.cOMBB_647938656_pname tptp.fNot (tptp.hAPP_p61793385e_bool (tptp.cOMBC_1149511130e_bool tptp.fequal_pname) A_1))) Pa)))) (forall ((A_1 tptp.x_a) (Pa tptp.fun_a_bool)) (= (tptp.insert_a A_1 (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_1))) Pa)))) (forall ((A_1 tptp.fun_nat_bool) (Pa tptp.fun_fu425979586l_bool)) (= (tptp.insert_fun_nat_bool A_1 (tptp.collect_fun_nat_bool Pa)) (tptp.collect_fun_nat_bool (tptp.cOMBS_1187019125l_bool (tptp.cOMBB_444170502t_bool tptp.fimplies (tptp.cOMBB_238756964t_bool tptp.fNot (tptp.hAPP_f103356543l_bool (tptp.cOMBC_1693257480l_bool tptp.fequal_fun_nat_bool) A_1))) Pa)))) (forall ((A_1 tptp.fun_pname_bool) (Pa tptp.fun_fu1430349052l_bool)) (= (tptp.insert1325755072e_bool A_1 (tptp.collec1974731493e_bool Pa)) (tptp.collec1974731493e_bool (tptp.cOMBS_350070575l_bool (tptp.cOMBB_2095475776e_bool tptp.fimplies (tptp.cOMBB_307249310e_bool tptp.fNot (tptp.hAPP_f434788991l_bool (tptp.cOMBC_1284144636l_bool tptp.fequal533582459e_bool) A_1))) Pa)))) (forall ((A_1 tptp.fun_a_bool) (Pa tptp.fun_fun_a_bool_bool)) (= (tptp.insert_fun_a_bool A_1 (tptp.collect_fun_a_bool Pa)) (tptp.collect_fun_a_bool (tptp.cOMBS_1035972772l_bool (tptp.cOMBB_338059395a_bool tptp.fimplies (tptp.cOMBB_2140588453a_bool tptp.fNot (tptp.hAPP_f1631501043l_bool (tptp.cOMBC_1732670874l_bool tptp.fequal_fun_a_bool) A_1))) Pa)))) (forall ((X_2 tptp.nat) (A tptp.fun_nat_bool)) (let ((_let_1 (tptp.insert_nat X_2 A))) (= (tptp.insert_nat X_2 _let_1) _let_1))) (forall ((X_2 tptp.pname) (A tptp.fun_pname_bool)) (let ((_let_1 (tptp.insert_pname X_2 A))) (= (tptp.insert_pname X_2 _let_1) _let_1))) (forall ((X_2 tptp.x_a) (A tptp.fun_a_bool)) (let ((_let_1 (tptp.insert_a X_2 A))) (= (tptp.insert_a X_2 _let_1) _let_1))) (forall ((X_2 tptp.nat) (Y_1 tptp.nat) (A tptp.fun_nat_bool)) (= (tptp.insert_nat X_2 (tptp.insert_nat Y_1 A)) (tptp.insert_nat Y_1 (tptp.insert_nat X_2 A)))) (forall ((X_2 tptp.pname) (Y_1 tptp.pname) (A tptp.fun_pname_bool)) (= (tptp.insert_pname X_2 (tptp.insert_pname Y_1 A)) (tptp.insert_pname Y_1 (tptp.insert_pname X_2 A)))) (forall ((X_2 tptp.x_a) (Y_1 tptp.x_a) (A tptp.fun_a_bool)) (= (tptp.insert_a X_2 (tptp.insert_a Y_1 A)) (tptp.insert_a Y_1 (tptp.insert_a X_2 A)))) (forall ((A_1 tptp.nat) (B_1 tptp.nat) (A tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat A_1))) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.insert_nat B_1 A))) (or (= A_1 B_1) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 A)))))) (forall ((A_1 tptp.pname) (B_1 tptp.pname) (A tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname A_1))) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.insert_pname B_1 A))) (or (= A_1 B_1) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A)))))) (forall ((A_1 tptp.x_a) (B_1 tptp.x_a) (A tptp.fun_a_bool)) (let ((_let_1 (tptp.hAPP_a85458249l_bool tptp.member_a A_1))) (= (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 (tptp.insert_a B_1 A))) (or (= A_1 B_1) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 A)))))) (forall ((Y_1 tptp.nat) (A tptp.fun_nat_bool) (X_2 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.insert_nat Y_1 A) X_2)) (or (= Y_1 X_2) (tptp.hBOOL (tptp.hAPP_nat_bool A X_2))))) (forall ((Y_1 tptp.pname) (A tptp.fun_pname_bool) (X_2 tptp.pname)) (= (tptp.hBOOL (tptp.hAPP_pname_bool (tptp.insert_pname Y_1 A) X_2)) (or (= Y_1 X_2) (tptp.hBOOL (tptp.hAPP_pname_bool A X_2))))) (forall ((Y_1 tptp.x_a) (A tptp.fun_a_bool) (X_2 tptp.x_a)) (= (tptp.hBOOL (tptp.hAPP_a_bool (tptp.insert_a Y_1 A) X_2)) (or (= Y_1 X_2) (tptp.hBOOL (tptp.hAPP_a_bool A X_2))))) (forall ((B tptp.fun_nat_bool) (X_2 tptp.nat) (A tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat X_2))) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 A))) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B))) (= (= (tptp.insert_nat X_2 A) (tptp.insert_nat X_2 B)) (= A B)))))) (forall ((B tptp.fun_pname_bool) (X_2 tptp.pname) (A tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname X_2))) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A))) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B))) (= (= (tptp.insert_pname X_2 A) (tptp.insert_pname X_2 B)) (= A B)))))) (forall ((B tptp.fun_a_bool) (X_2 tptp.x_a) (A tptp.fun_a_bool)) (let ((_let_1 (tptp.hAPP_a85458249l_bool tptp.member_a X_2))) (=> (not (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 A))) (=> (not (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 B))) (= (= (tptp.insert_a X_2 A) (tptp.insert_a X_2 B)) (= A B)))))) (forall ((B_1 tptp.nat) (A_1 tptp.nat) (B tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat A_1))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.insert_nat B_1 B)))))) (forall ((B_1 tptp.pname) (A_1 tptp.pname) (B tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname A_1))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.insert_pname B_1 B)))))) (forall ((B_1 tptp.x_a) (A_1 tptp.x_a) (B tptp.fun_a_bool)) (let ((_let_1 (tptp.hAPP_a85458249l_bool tptp.member_a A_1))) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 B)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 (tptp.insert_a B_1 B)))))) (forall ((A_1 tptp.nat) (A tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_1) A)) (= (tptp.insert_nat A_1 A) A))) (forall ((A_1 tptp.pname) (A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A_1) A)) (= (tptp.insert_pname A_1 A) A))) (forall ((A_1 tptp.x_a) (A tptp.fun_a_bool)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a A_1) A)) (= (tptp.insert_a A_1 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_pname_bool)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_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_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_pname_bool) (B tptp.fun_pname_bool)) (= (= A B) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) B)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) A))))) (forall ((A tptp.fun_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_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_pname_bool) (B tptp.fun_pname_bool)) (=> (= A B) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) B)))) (forall ((A tptp.fun_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_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_pname_bool) (B tptp.fun_pname_bool)) (=> (= A B) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) A)))) (forall ((A tptp.fun_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_2 tptp.nat) (A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat X_2))) (=> (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_2 tptp.x_a) (A tptp.fun_a_bool) (B tptp.fun_a_bool)) (let ((_let_1 (tptp.hAPP_a85458249l_bool tptp.member_a X_2))) (=> (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_2 tptp.pname) (A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname X_2))) (=> (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_nat_bool) (X_2 tptp.nat) (A tptp.fun_nat_bool)) (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 (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_2 tptp.x_a) (A tptp.fun_a_bool)) (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 (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_2 tptp.pname) (A tptp.fun_pname_bool)) (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 (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) B)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B)))))) (forall ((X_2 tptp.nat) (A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat X_2))) (=> (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_2 tptp.x_a) (A tptp.fun_a_bool) (B tptp.fun_a_bool)) (let ((_let_1 (tptp.hAPP_a85458249l_bool tptp.member_a X_2))) (=> (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_2 tptp.pname) (A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname X_2))) (=> (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 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)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 C)))))) (forall ((C tptp.fun_pname_bool) (A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) C)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 C)))))) (forall ((C 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)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 C)))))) (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_pname_bool) (B tptp.fun_pname_bool)) (=> (= A B) (not (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) B)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) A))))))) (forall ((A tptp.fun_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 ((X_2 tptp.nat) (A tptp.fun_nat_bool)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) A)) (tptp.hBOOL (tptp.hAPP_nat_bool A X_2)))) (forall ((X_2 tptp.x_a) (A tptp.fun_a_bool)) (= (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a X_2) A)) (tptp.hBOOL (tptp.hAPP_a_bool A X_2)))) (forall ((X_2 tptp.pname) (A tptp.fun_pname_bool)) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A)) (tptp.hBOOL (tptp.hAPP_pname_bool A X_2)))) (forall ((Pa tptp.fun_pname_bool)) (= (tptp.collect_pname Pa) Pa)) (forall ((Pa tptp.fun_fu425979586l_bool)) (= (tptp.collect_fun_nat_bool Pa) Pa)) (forall ((Pa tptp.fun_fu1430349052l_bool)) (= (tptp.collec1974731493e_bool Pa) Pa)) (forall ((Pa tptp.fun_fun_a_bool_bool)) (= (tptp.collect_fun_a_bool Pa) Pa)) (forall ((Pa tptp.fun_nat_bool)) (= (tptp.collect_nat Pa) Pa)) (forall ((Z 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) (tptp.image_pname_a F A))) (exists ((X_1 tptp.pname)) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A)) (= Z (tptp.hAPP_pname_a F X_1)))))) (forall ((F tptp.fun_pname_a) (X_2 tptp.pname) (A tptp.fun_pname_bool)) (=> (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)) (tptp.image_pname_a F A))))) (forall ((B_1 tptp.x_a) (F tptp.fun_pname_a) (X_2 tptp.pname) (A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A)) (=> (= B_1 (tptp.hAPP_pname_a F X_2)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a B_1) (tptp.image_pname_a F A)))))) (forall ((X_1 tptp.nat) (Xa tptp.fun_nat_bool)) (= (tptp.insert_nat X_1 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_1)) (tptp.hAPP_f800510211t_bool (tptp.cOMBC_226598744l_bool tptp.member_nat) Xa))))) (forall ((X_1 tptp.pname) (Xa tptp.fun_pname_bool)) (= (tptp.insert_pname X_1 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_1)) (tptp.hAPP_f759274231e_bool (tptp.cOMBC_1058051404l_bool tptp.member_pname) Xa))))) (forall ((X_1 tptp.x_a) (Xa tptp.fun_a_bool)) (= (tptp.insert_a X_1 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_1)) (tptp.hAPP_f2050579477a_bool (tptp.cOMBC_1355376034l_bool tptp.member_a) Xa))))) (forall ((X_1 tptp.fun_nat_bool) (Xa tptp.fun_fu425979586l_bool)) (= (tptp.insert_fun_nat_bool X_1 Xa) (tptp.collect_fun_nat_bool (tptp.cOMBS_1187019125l_bool (tptp.cOMBB_444170502t_bool tptp.fdisj (tptp.hAPP_f103356543l_bool (tptp.cOMBC_1693257480l_bool tptp.fequal_fun_nat_bool) X_1)) (tptp.hAPP_f1246832597l_bool (tptp.cOMBC_1245412066l_bool tptp.member_fun_nat_bool) Xa))))) (forall ((X_1 tptp.fun_pname_bool) (Xa tptp.fun_fu1430349052l_bool)) (= (tptp.insert1325755072e_bool X_1 Xa) (tptp.collec1974731493e_bool (tptp.cOMBS_350070575l_bool (tptp.cOMBB_2095475776e_bool tptp.fdisj (tptp.hAPP_f434788991l_bool (tptp.cOMBC_1284144636l_bool tptp.fequal533582459e_bool) X_1)) (tptp.hAPP_f559147733l_bool (tptp.cOMBC_1988546018l_bool tptp.member799430823e_bool) Xa))))) (forall ((X_1 tptp.fun_a_bool) (Xa tptp.fun_fun_a_bool_bool)) (= (tptp.insert_fun_a_bool X_1 Xa) (tptp.collect_fun_a_bool (tptp.cOMBS_1035972772l_bool (tptp.cOMBB_338059395a_bool tptp.fdisj (tptp.hAPP_f1631501043l_bool (tptp.cOMBC_1732670874l_bool tptp.fequal_fun_a_bool) X_1)) (tptp.hAPP_f2117159681l_bool (tptp.cOMBC_1880041174l_bool tptp.member_fun_a_bool) Xa))))) (forall ((B tptp.fun_nat_bool) (A_1 tptp.nat)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool B) (tptp.insert_nat A_1 B)))) (forall ((B tptp.fun_pname_bool) (A_1 tptp.pname)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) (tptp.insert_pname A_1 B)))) (forall ((B tptp.fun_a_bool) (A_1 tptp.x_a)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool B) (tptp.insert_a A_1 B)))) (forall ((X_2 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.insert_nat X_2 A)) B)) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) B)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) B))))) (forall ((X_2 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.insert_pname X_2 A)) B)) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) B)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) B))))) _let_10 (forall ((B tptp.fun_nat_bool) (X_2 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_2) A))) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.insert_nat X_2 B))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B)))))) (forall ((B tptp.fun_pname_bool) (X_2 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_2) A))) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.insert_pname X_2 B))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B)))))) (forall ((B tptp.fun_a_bool) (X_2 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_2) A))) (= (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 (tptp.insert_a X_2 B))) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 B)))))) (forall ((B_1 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.insert_nat B_1 B)))))) (forall ((B_1 tptp.pname) (A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.insert_pname B_1 B)))))) (forall ((B_1 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.insert_a B_1 B)))))) (forall ((A_1 tptp.nat) (C tptp.fun_nat_bool) (D tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool C) D)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.insert_nat A_1 C)) (tptp.insert_nat A_1 D))))) (forall ((A_1 tptp.pname) (C tptp.fun_pname_bool) (D tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool C) D)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.insert_pname A_1 C)) (tptp.insert_pname A_1 D))))) (forall ((A_1 tptp.x_a) (C tptp.fun_a_bool) (D tptp.fun_a_bool)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool C) D)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool (tptp.insert_a A_1 C)) (tptp.insert_a A_1 D))))) (forall ((F tptp.fun_pname_a) (A_1 tptp.pname) (B tptp.fun_pname_bool)) (= (tptp.image_pname_a F (tptp.insert_pname A_1 B)) (tptp.insert_a (tptp.hAPP_pname_a F A_1) (tptp.image_pname_a F B)))) (forall ((F tptp.fun_pname_a) (X_2 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_2) A)) (= (tptp.insert_a (tptp.hAPP_pname_a F X_2) _let_1) _let_1)))) (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_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_1 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_1) (tptp.image_pname_a F A))) (not (forall ((X_1 tptp.pname)) (=> (= B_1 (tptp.hAPP_pname_a F X_1)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A)))))))) (forall ((B tptp.fun_nat_bool) (A tptp.fun_nat_bool)) (=> (forall ((X_1 tptp.nat)) (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 _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_1 tptp.x_a)) (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 _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_1 tptp.pname)) (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 _let_1 B))))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) B)))) (forall ((I tptp.nat) (Pa tptp.fun_nat_bool) (K tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool Pa K)) (=> (forall ((N_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool Pa (tptp.hAPP_nat_nat tptp.suc N_2))) (tptp.hBOOL (tptp.hAPP_nat_bool Pa N_2)))) (tptp.hBOOL (tptp.hAPP_nat_bool Pa (tptp.hAPP_nat_nat (tptp.minus_minus_nat K) I)))))) (forall ((N_1 tptp.nat) (M_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat tptp.suc N_1)) M_1)) (exists ((M tptp.nat)) (= M_1 (tptp.hAPP_nat_nat tptp.suc M))))) (forall ((F tptp.fun_pname_a) (B tptp.fun_a_bool) (A tptp.fun_pname_bool)) (=> (forall ((X_1 tptp.pname)) (=> (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)) 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 ((X_2 tptp.fun_nat_bool)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool X_2) X_2))) (forall ((X_2 tptp.fun_pname_bool)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool X_2) X_2))) (forall ((X_3 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_3) X_3))) (forall ((X_2 tptp.fun_a_bool)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool X_2) X_2))) (forall ((N tptp.fun_nat_bool)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat N)) (exists ((M tptp.nat)) (forall ((X_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_1) M))))))) (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))) (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)) (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.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 ((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_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_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_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_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_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_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_bool_bool) (Q tptp.fun_fun_a_bool_bool) (R tptp.fun_a_bool)) (= (tptp.hAPP_fun_a_bool_bool (tptp.cOMBB_2140588453a_bool P Q) R) (tptp.hAPP_bool_bool P (tptp.hAPP_fun_a_bool_bool Q R)))) (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_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_bool_bool) (Q tptp.fun_fu425979586l_bool) (R tptp.fun_nat_bool)) (= (tptp.hAPP_f54304608l_bool (tptp.cOMBB_238756964t_bool P Q) R) (tptp.hAPP_bool_bool P (tptp.hAPP_f54304608l_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_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_bool_bool) (Q tptp.fun_fu1430349052l_bool) (R tptp.fun_pname_bool)) (= (tptp.hAPP_f1664156314l_bool (tptp.cOMBB_307249310e_bool P Q) R) (tptp.hAPP_bool_bool P (tptp.hAPP_f1664156314l_bool Q R)))) (forall ((P tptp.fun_bo1549164019l_bool) (Q tptp.fun_pname_bool) (R tptp.pname)) (= (tptp.hAPP_p393069232l_bool (tptp.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_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_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_fu386216885l_bool) (Q tptp.fun_fun_a_bool_bool) (R tptp.fun_a_bool)) (= (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f2117159681l_bool (tptp.cOMBC_1880041174l_bool P) Q) R) (tptp.hAPP_f621171935l_bool (tptp.hAPP_f285962445l_bool P R) Q))) (forall ((P tptp.fun_fu1436348701l_bool) (Q tptp.fun_fu425979586l_bool) (R tptp.fun_nat_bool)) (= (tptp.hAPP_f54304608l_bool (tptp.hAPP_f1246832597l_bool (tptp.cOMBC_1245412066l_bool P) Q) R) (tptp.hAPP_f1637334154l_bool (tptp.hAPP_f1951378235l_bool P R) Q))) (forall ((P tptp.fun_fu931343505l_bool) (Q tptp.fun_fu1430349052l_bool) (R tptp.fun_pname_bool)) (= (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f559147733l_bool (tptp.cOMBC_1988546018l_bool P) Q) R) (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool P R) Q))) (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_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))) (forall ((P tptp.fun_fu821736593l_bool) (Q tptp.fun_fu885608257l_bool) (R tptp.fun_fu885608257l_bool)) (= (tptp.hAPP_f292226953l_bool (tptp.hAPP_f1050622307l_bool (tptp.cOMBC_636888218l_bool P) Q) R) (tptp.hAPP_f292226953l_bool (tptp.hAPP_f1050622307l_bool P R) Q))) (forall ((P tptp.fun_fu1137991347l_bool) (Q tptp.fun_fu814369080l_bool) (R tptp.fun_fu814369080l_bool)) (= (tptp.hAPP_f937997336l_bool (tptp.hAPP_f760187903l_bool (tptp.cOMBC_1269652216l_bool P) Q) R) (tptp.hAPP_f937997336l_bool (tptp.hAPP_f760187903l_bool P R) Q))) (forall ((P tptp.fun_fu1086940979l_bool) (Q tptp.fun_fu399576434l_bool) (R tptp.fun_fu399576434l_bool)) (= (tptp.hAPP_f389811538l_bool (tptp.hAPP_f1759205631l_bool (tptp.cOMBC_336095980l_bool P) Q) R) (tptp.hAPP_f389811538l_bool (tptp.hAPP_f1759205631l_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.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))))))))))))))))))))))))))
% 0.56/0.95  )
% 0.56/0.96  % SZS output end Proof for SWW473_1
% 0.56/0.96  % cvc5---1.0.5 exiting
% 0.56/0.96  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------