TSTP Solution File: SCT171_3 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SCT171_3 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n017.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 : Thu Aug 31 14:12:24 EDT 2023
% Result : Theorem 1.44s 1.69s
% Output : Proof 1.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.38 % Problem : SCT171_3 : TPTP v8.1.2. Released v5.3.0.
% 0.39/0.39 % Command : do_cvc5 %s %d
% 0.40/0.60 % Computer : n017.cluster.edu
% 0.40/0.60 % Model : x86_64 x86_64
% 0.40/0.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.40/0.60 % Memory : 8042.1875MB
% 0.40/0.60 % OS : Linux 3.10.0-693.el7.x86_64
% 0.40/0.60 % CPULimit : 300
% 0.40/0.61 % WCLimit : 300
% 0.40/0.61 % DateTime : Thu Aug 24 14:54:54 EDT 2023
% 0.40/0.61 % CPUTime :
% 0.84/1.04 %----Proving TF0_NAR, FOF, or CNF
% 1.44/1.69 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.8cGYXoacDB/cvc5---1.0.5_22480.p...
% 1.44/1.69 ------- get file name : TPTP file name is SCT171_3
% 1.44/1.69 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_22480.smt2...
% 1.44/1.69 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 1.44/1.69 % SZS status Theorem for SCT171_3
% 1.44/1.69 % SZS output start Proof for SCT171_3
% 1.44/1.69 (
% 1.44/1.69 (let ((_let_1 (tptp.hAPP_A1146194953le_alt tptp.produc1590937303le_alt tptp.c))) (let ((_let_2 (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_A1299015393le_alt _let_1 tptp.d)))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_2 (tptp.hAPP_f2008608496t_bool tptp.f tptp.p))))) (let ((_let_4 (not _let_3))) (let ((_let_5 (tptp.hAPP_f846027769ol_nat tptp.finite1672073426e_indi tptp.top_to788185952i_bool))) (let ((_let_6 (tptp.hAPP_f721434149i_bool tptp.cOMBC_722552198t_bool (tptp.hAPP_f966656047t_bool (tptp.cOMBB_1869811296e_indi tptp.ord_less_nat) tptp.h)))) (let ((_let_7 (tptp.cOMBB_1061985500e_indi tptp.if_fun523439385t_bool))) (let ((_let_8 (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_A1299015393le_alt (tptp.hAPP_A1146194953le_alt tptp.produc1590937303le_alt tptp.a) tptp.b)))) (let ((_let_9 (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_8 (tptp.hAPP_f2008608496t_bool tptp.f (tptp.hAPP_f480276746t_bool (tptp.hAPP_f601594885t_bool tptp.cOMBC_750853729t_bool (tptp.hAPP_f1344464862t_bool (tptp.hAPP_f1908974253t_bool tptp.cOMBC_156709173t_bool (tptp.hAPP_f668886383t_bool _let_7 (tptp.hAPP_n34002993i_bool _let_6 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat tptp.n) tptp.one_one_nat)))) tptp.lab)) tptp.lba)))))) (let ((_let_10 (tptp.hAPP_f668886383t_bool _let_7 (tptp.hAPP_n34002993i_bool _let_6 tptp.n)))) (let ((_let_11 (tptp.hAPP_f1302887663t_bool (tptp.cOMBS_1181656689t_bool (tptp.hAPP_f1001205955t_bool (tptp.cOMBS_1925466437t_bool _let_10) (tptp.hAPP_A425126512t_bool (tptp.hAPP_f1631649925t_bool tptp.cOMBC_1417338747t_bool (tptp.hAPP_f831214557t_bool (tptp.cOMBB_80760910e_indi tptp.arrow_1630265669_mktop) tptp.p)) tptp.e))) (tptp.hAPP_f1302887663t_bool (tptp.cOMBS_1181656689t_bool (tptp.hAPP_f1001205955t_bool (tptp.cOMBS_1925466437t_bool (tptp.hAPP_f668886383t_bool _let_7 (tptp.hAPP_n34002993i_bool (tptp.hAPP_f721434149i_bool tptp.cOMBC_722552198t_bool (tptp.hAPP_f966656047t_bool (tptp.cOMBB_1869811296e_indi tptp.fequal_nat) tptp.h)) tptp.n))) (tptp.hAPP_A425126512t_bool (tptp.hAPP_f1631649925t_bool tptp.cOMBC_1417338747t_bool (tptp.hAPP_A1889513822t_bool (tptp.hAPP_f2102110817t_bool tptp.cOMBC_1486904681t_bool (tptp.hAPP_f1751344075t_bool (tptp.cOMBB_1876517692e_indi tptp.arrow_216713899_above) tptp.p)) tptp.c)) tptp.e))) (tptp.hAPP_A425126512t_bool (tptp.hAPP_f1631649925t_bool tptp.cOMBC_1417338747t_bool (tptp.hAPP_f831214557t_bool (tptp.cOMBB_80760910e_indi tptp.arrow_1481558583_mkbot) tptp.p)) tptp.e))))) (let ((_let_12 (tptp.hAPP_f2008608496t_bool tptp.f _let_11))) (let ((_let_13 (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_A1299015393le_alt _let_1 tptp.e)) _let_12)))) (let ((_let_14 (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_A1299015393le_alt (tptp.hAPP_A1146194953le_alt tptp.produc1590937303le_alt tptp.b) tptp.a)))) (let ((_let_15 (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_A1299015393le_alt (tptp.hAPP_A1146194953le_alt tptp.produc1590937303le_alt tptp.e) tptp.d)) _let_12)))) (let ((_let_16 (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_2 _let_12)))) (let ((_let_17 (= _let_3 _let_16))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (ASSUME :args (_let_4)) (MACRO_RESOLUTION_TRUST (REORDERING (EQUIV_ELIM1 (SYMM (ASSUME :args (_let_17)))) :args ((or _let_3 (not _let_16)))) (ASSUME :args (_let_16)) :args (_let_3 false _let_16)) :args (false false _let_3)) :args ((tptp.hBOOL (tptp.hAPP_f1572141188l_bool tptp.arrow_1335103695le_IIA tptp.f)) (tptp.hBOOL (tptp.hAPP_f1572141188l_bool tptp.arrow_320876018nimity tptp.f)) (not (= tptp.c tptp.d)) (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f1225332775l_bool tptp.member933336803t_bool tptp.p) tptp.arrow_5070731e_Prof)) (forall ((X_2 tptp.arrow_1893660431le_alt) (Y_2 tptp.arrow_1893660431le_alt) (L_3 tptp.fun_Pr2067565481t_bool) (Z_2 tptp.arrow_1893660431le_alt)) (let ((_let_1 (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_A1299015393le_alt (tptp.hAPP_A1146194953le_alt tptp.produc1590937303le_alt X_2) Y_2)))) (let ((_let_2 (= X_2 Z_2))) (= (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_1 (tptp.hAPP_A1601437999t_bool (tptp.hAPP_f1761571331t_bool tptp.arrow_1481558583_mkbot L_3) Z_2))) (and (not (= Y_2 Z_2)) (=> _let_2 (not (= X_2 Y_2))) (=> (not _let_2) (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_1 L_3)))))))) (forall ((X_2 tptp.arrow_1893660431le_alt) (Y_2 tptp.arrow_1893660431le_alt) (L_3 tptp.fun_Pr2067565481t_bool) (Z_2 tptp.arrow_1893660431le_alt)) (let ((_let_1 (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_A1299015393le_alt (tptp.hAPP_A1146194953le_alt tptp.produc1590937303le_alt X_2) Y_2)))) (let ((_let_2 (= Y_2 Z_2))) (= (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_1 (tptp.hAPP_A1601437999t_bool (tptp.hAPP_f1761571331t_bool tptp.arrow_1630265669_mktop L_3) Z_2))) (and (not (= X_2 Z_2)) (=> _let_2 (not (= X_2 Y_2))) (=> (not _let_2) (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_1 L_3)))))))) (forall ((P_1 tptp.fun_Ar274636406t_bool) (Pa tptp.fun_Ar274636406t_bool) (A_34 tptp.arrow_1893660431le_alt) (B_32 tptp.arrow_1893660431le_alt) (Aa tptp.arrow_1893660431le_alt) (Ba tptp.arrow_1893660431le_alt)) (=> (not (= Aa Ba)) (=> (not (= A_34 B_32)) (=> (not (= Aa B_32)) (=> (not (= Ba A_34)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f1225332775l_bool tptp.member933336803t_bool Pa) tptp.arrow_5070731e_Prof)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f1225332775l_bool tptp.member933336803t_bool P_1) tptp.arrow_5070731e_Prof)) (=> (forall ((I_1 tptp.arrow_856714788e_indi)) (= (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_A1299015393le_alt (tptp.hAPP_A1146194953le_alt tptp.produc1590937303le_alt Aa) Ba)) (tptp.hAPP_A1646126530t_bool Pa I_1))) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_A1299015393le_alt (tptp.hAPP_A1146194953le_alt tptp.produc1590937303le_alt A_34) B_32)) (tptp.hAPP_A1646126530t_bool P_1 I_1))))) (= (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_A1299015393le_alt (tptp.hAPP_A1146194953le_alt tptp.produc1590937303le_alt Aa) Ba)) (tptp.hAPP_f2008608496t_bool tptp.f Pa))) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_A1299015393le_alt (tptp.hAPP_A1146194953le_alt tptp.produc1590937303le_alt A_34) B_32)) (tptp.hAPP_f2008608496t_bool tptp.f P_1)))))))))))) (forall ((P_1 tptp.fun_Ar274636406t_bool) (Pa tptp.fun_Ar274636406t_bool) (A_34 tptp.arrow_1893660431le_alt) (B_32 tptp.arrow_1893660431le_alt) (Aa tptp.arrow_1893660431le_alt) (Ba tptp.arrow_1893660431le_alt)) (=> (not (= Aa Ba)) (=> (not (= A_34 B_32)) (=> (not (= Aa B_32)) (=> (not (= Ba A_34)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f1225332775l_bool tptp.member933336803t_bool Pa) tptp.arrow_5070731e_Prof)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f1225332775l_bool tptp.member933336803t_bool P_1) tptp.arrow_5070731e_Prof)) (=> (forall ((I_1 tptp.arrow_856714788e_indi)) (= (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_A1299015393le_alt (tptp.hAPP_A1146194953le_alt tptp.produc1590937303le_alt Aa) Ba)) (tptp.hAPP_A1646126530t_bool Pa I_1))) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_A1299015393le_alt (tptp.hAPP_A1146194953le_alt tptp.produc1590937303le_alt A_34) B_32)) (tptp.hAPP_A1646126530t_bool P_1 I_1))))) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_A1299015393le_alt (tptp.hAPP_A1146194953le_alt tptp.produc1590937303le_alt Aa) Ba)) (tptp.hAPP_f2008608496t_bool tptp.f Pa))) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_A1299015393le_alt (tptp.hAPP_A1146194953le_alt tptp.produc1590937303le_alt A_34) B_32)) (tptp.hAPP_f2008608496t_bool tptp.f P_1)))))))))))) (forall ((P_1 tptp.fun_Ar274636406t_bool) (Pa tptp.fun_Ar274636406t_bool) (Ca tptp.arrow_1893660431le_alt) (Aa tptp.arrow_1893660431le_alt) (Ba tptp.arrow_1893660431le_alt)) (=> (not (= Aa Ba)) (=> (not (= Ba Ca)) (=> (not (= Aa Ca)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f1225332775l_bool tptp.member933336803t_bool Pa) tptp.arrow_5070731e_Prof)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f1225332775l_bool tptp.member933336803t_bool P_1) tptp.arrow_5070731e_Prof)) (=> (forall ((I_1 tptp.arrow_856714788e_indi)) (= (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_A1299015393le_alt (tptp.hAPP_A1146194953le_alt tptp.produc1590937303le_alt Aa) Ba)) (tptp.hAPP_A1646126530t_bool Pa I_1))) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_A1299015393le_alt (tptp.hAPP_A1146194953le_alt tptp.produc1590937303le_alt Ba) Ca)) (tptp.hAPP_A1646126530t_bool P_1 I_1))))) (= (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_A1299015393le_alt (tptp.hAPP_A1146194953le_alt tptp.produc1590937303le_alt Aa) Ba)) (tptp.hAPP_f2008608496t_bool tptp.f Pa))) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_A1299015393le_alt (tptp.hAPP_A1146194953le_alt tptp.produc1590937303le_alt Ba) Ca)) (tptp.hAPP_f2008608496t_bool tptp.f P_1))))))))))) (forall ((P_1 tptp.fun_Ar274636406t_bool) (Pa tptp.fun_Ar274636406t_bool) (A_34 tptp.arrow_1893660431le_alt) (B_32 tptp.arrow_1893660431le_alt) (Aa tptp.arrow_1893660431le_alt) (Ba tptp.arrow_1893660431le_alt)) (=> (not (= Aa Ba)) (=> (not (= A_34 B_32)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f1225332775l_bool tptp.member933336803t_bool Pa) tptp.arrow_5070731e_Prof)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f1225332775l_bool tptp.member933336803t_bool P_1) tptp.arrow_5070731e_Prof)) (=> (forall ((I_1 tptp.arrow_856714788e_indi)) (= (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_A1299015393le_alt (tptp.hAPP_A1146194953le_alt tptp.produc1590937303le_alt Aa) Ba)) (tptp.hAPP_A1646126530t_bool Pa I_1))) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_A1299015393le_alt (tptp.hAPP_A1146194953le_alt tptp.produc1590937303le_alt A_34) B_32)) (tptp.hAPP_A1646126530t_bool P_1 I_1))))) (= (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_A1299015393le_alt (tptp.hAPP_A1146194953le_alt tptp.produc1590937303le_alt Aa) Ba)) (tptp.hAPP_f2008608496t_bool tptp.f Pa))) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_A1299015393le_alt (tptp.hAPP_A1146194953le_alt tptp.produc1590937303le_alt A_34) B_32)) (tptp.hAPP_f2008608496t_bool tptp.f P_1)))))))))) (forall ((P_1 tptp.fun_Ar274636406t_bool) (Pa tptp.fun_Ar274636406t_bool) (Aa tptp.arrow_1893660431le_alt) (Ba tptp.arrow_1893660431le_alt)) (=> (not (= Aa Ba)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f1225332775l_bool tptp.member933336803t_bool Pa) tptp.arrow_5070731e_Prof)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f1225332775l_bool tptp.member933336803t_bool P_1) tptp.arrow_5070731e_Prof)) (=> (forall ((I_1 tptp.arrow_856714788e_indi)) (= (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_A1299015393le_alt (tptp.hAPP_A1146194953le_alt tptp.produc1590937303le_alt Aa) Ba)) (tptp.hAPP_A1646126530t_bool Pa I_1))) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_A1299015393le_alt (tptp.hAPP_A1146194953le_alt tptp.produc1590937303le_alt Ba) Aa)) (tptp.hAPP_A1646126530t_bool P_1 I_1))))) (= (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_A1299015393le_alt (tptp.hAPP_A1146194953le_alt tptp.produc1590937303le_alt Aa) Ba)) (tptp.hAPP_f2008608496t_bool tptp.f Pa))) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_A1299015393le_alt (tptp.hAPP_A1146194953le_alt tptp.produc1590937303le_alt Ba) Aa)) (tptp.hAPP_f2008608496t_bool tptp.f P_1))))))))) (forall ((I_1 tptp.arrow_856714788e_indi)) (let ((_let_1 (tptp.hAPP_A1646126530t_bool tptp.p I_1))) (let ((_let_2 (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_A1299015393le_alt (tptp.hAPP_A1146194953le_alt tptp.produc1590937303le_alt tptp.c) tptp.d)))) (let ((_let_3 (tptp.hAPP_A376526755di_nat tptp.h I_1))) (let ((_let_4 (= _let_3 tptp.n))) (let ((_let_5 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat _let_3) tptp.n)))) (= (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_2 _let_1)) (and (=> _let_5 (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_2 (tptp.hAPP_A1601437999t_bool (tptp.hAPP_f1761571331t_bool tptp.arrow_1630265669_mktop _let_1) tptp.e)))) (=> (not _let_5) (and (=> _let_4 (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_2 (tptp.hAPP_A1601437999t_bool (tptp.hAPP_A1058422557t_bool (tptp.hAPP_f1550387441t_bool tptp.arrow_216713899_above _let_1) tptp.c) tptp.e)))) (=> (not _let_4) (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_2 (tptp.hAPP_A1601437999t_bool (tptp.hAPP_f1761571331t_bool tptp.arrow_1481558583_mkbot _let_1) tptp.e)))))))))))))) (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_2 (tptp.hAPP_A1646126530t_bool tptp.p (tptp.hAPP_n1937165849e_indi (tptp.hilber1580028780di_nat tptp.top_to788185952i_bool tptp.h) tptp.n)))) _let_16 _let_17 (forall ((Pa tptp.fun_Pr2067565481t_bool)) (= (forall ((X1 tptp.produc472769767le_alt)) (tptp.hBOOL (tptp.hAPP_P1178790471t_bool Pa X1))) (forall ((A_27 tptp.arrow_1893660431le_alt) (B_25 tptp.arrow_1893660431le_alt)) (tptp.hBOOL (tptp.hAPP_P1178790471t_bool Pa (tptp.hAPP_A1299015393le_alt (tptp.hAPP_A1146194953le_alt tptp.produc1590937303le_alt A_27) B_25)))))) (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f1225332775l_bool tptp.member933336803t_bool _let_11) tptp.arrow_5070731e_Prof)) _let_13 _let_15 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.n) _let_5)) (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.inj_on1960344199di_nat tptp.h) tptp.top_to788185952i_bool)) (forall ((A_36 tptp.arrow_1893660431le_alt) (B_34 tptp.arrow_1893660431le_alt) (A_35 tptp.arrow_1893660431le_alt) (B_33 tptp.arrow_1893660431le_alt)) (=> (= (tptp.hAPP_A1299015393le_alt (tptp.hAPP_A1146194953le_alt tptp.produc1590937303le_alt A_36) B_34) (tptp.hAPP_A1299015393le_alt (tptp.hAPP_A1146194953le_alt tptp.produc1590937303le_alt A_35) B_33)) (not (=> (= A_36 A_35) (not (= B_34 B_33)))))) (forall ((Aa tptp.arrow_1893660431le_alt) (Ba tptp.arrow_1893660431le_alt) (A_34 tptp.arrow_1893660431le_alt) (B_32 tptp.arrow_1893660431le_alt)) (= (= (tptp.hAPP_A1299015393le_alt (tptp.hAPP_A1146194953le_alt tptp.produc1590937303le_alt Aa) Ba) (tptp.hAPP_A1299015393le_alt (tptp.hAPP_A1146194953le_alt tptp.produc1590937303le_alt A_34) B_32)) (and (= Aa A_34) (= Ba B_32)))) (forall ((Fa tptp.fun_fu2114379172t_bool)) (= (tptp.hBOOL (tptp.hAPP_f1572141188l_bool tptp.arrow_1335103695le_IIA Fa)) (forall ((X_1 tptp.fun_Ar274636406t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f1225332775l_bool tptp.member933336803t_bool X_1) tptp.arrow_5070731e_Prof)) (forall ((Xa tptp.fun_Ar274636406t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f1225332775l_bool tptp.member933336803t_bool Xa) tptp.arrow_5070731e_Prof)) (forall ((A_27 tptp.arrow_1893660431le_alt) (B_25 tptp.arrow_1893660431le_alt)) (let ((_let_1 (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_A1299015393le_alt (tptp.hAPP_A1146194953le_alt tptp.produc1590937303le_alt A_27) B_25)))) (=> (forall ((I_1 tptp.arrow_856714788e_indi)) (let ((_let_1 (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_A1299015393le_alt (tptp.hAPP_A1146194953le_alt tptp.produc1590937303le_alt A_27) B_25)))) (= (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_1 (tptp.hAPP_A1646126530t_bool X_1 I_1))) (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_1 (tptp.hAPP_A1646126530t_bool Xa I_1)))))) (= (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_1 (tptp.hAPP_f2008608496t_bool Fa X_1))) (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_1 (tptp.hAPP_f2008608496t_bool Fa Xa))))))))))))) (forall ((Fa tptp.fun_fu2114379172t_bool)) (= (tptp.hBOOL (tptp.hAPP_f1572141188l_bool tptp.arrow_320876018nimity Fa)) (forall ((X_1 tptp.fun_Ar274636406t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f1225332775l_bool tptp.member933336803t_bool X_1) tptp.arrow_5070731e_Prof)) (forall ((A_27 tptp.arrow_1893660431le_alt) (B_25 tptp.arrow_1893660431le_alt)) (=> (forall ((I_1 tptp.arrow_856714788e_indi)) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_A1299015393le_alt (tptp.hAPP_A1146194953le_alt tptp.produc1590937303le_alt A_27) B_25)) (tptp.hAPP_A1646126530t_bool X_1 I_1)))) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_A1299015393le_alt (tptp.hAPP_A1146194953le_alt tptp.produc1590937303le_alt A_27) B_25)) (tptp.hAPP_f2008608496t_bool Fa X_1))))))))) (forall ((X_2 tptp.fun_Pr2067565481t_bool)) (tptp.hBOOL (tptp.hAPP_f52567537l_bool tptp.top_to1312956197l_bool X_2))) (forall ((X_2 tptp.fun_Ar274636406t_bool)) (tptp.hBOOL (tptp.hAPP_f995490902l_bool tptp.top_to553140914l_bool X_2))) (forall ((X_2 tptp.fun_fu2114379172t_bool)) (tptp.hBOOL (tptp.hAPP_f1572141188l_bool tptp.top_to827110112l_bool X_2))) (forall ((X_2 tptp.produc472769767le_alt)) (tptp.hBOOL (tptp.hAPP_P1178790471t_bool tptp.top_to1138392227t_bool X_2))) (forall ((X_2 tptp.arrow_856714788e_indi)) (tptp.hBOOL (tptp.hAPP_A997847300i_bool tptp.top_to788185952i_bool X_2))) (forall ((X_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool tptp.top_top_fun_nat_bool X_2))) (forall ((X_2 tptp.product_unit)) (tptp.hBOOL (tptp.hAPP_P1676879539t_bool tptp.top_to1257323279t_bool X_2))) (forall ((X_2 tptp.bool)) (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.hAPP_b1787118453l_bool tptp.member_bool X_2) tptp.top_to1647826457l_bool))) (forall ((X_2 tptp.arrow_856714788e_indi)) (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_A1597696899l_bool tptp.member1479139729e_indi X_2) tptp.top_to788185952i_bool))) (forall ((X_2 tptp.product_unit)) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_P607165281l_bool tptp.member_Product_unit X_2) tptp.top_to1257323279t_bool))) (forall ((X_2 tptp.produc472769767le_alt)) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt X_2) tptp.top_to1138392227t_bool))) (forall ((X_2 tptp.fun_Ar274636406t_bool)) (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f1225332775l_bool tptp.member933336803t_bool X_2) tptp.top_to553140914l_bool))) (forall ((X_2 tptp.fun_fu2114379172t_bool)) (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f1714503811l_bool tptp.member173038353t_bool X_2) tptp.top_to827110112l_bool))) (forall ((X_2 tptp.fun_Pr2067565481t_bool)) (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1482930381l_bool tptp.member1069471740t_bool X_2) tptp.top_to1312956197l_bool))) (forall ((X_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) tptp.top_top_fun_nat_bool))) (forall ((X_2 tptp.bool)) (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.hAPP_b1787118453l_bool tptp.member_bool X_2) tptp.top_to1647826457l_bool))) (forall ((X_2 tptp.arrow_856714788e_indi)) (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_A1597696899l_bool tptp.member1479139729e_indi X_2) tptp.top_to788185952i_bool))) (forall ((X_2 tptp.product_unit)) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_P607165281l_bool tptp.member_Product_unit X_2) tptp.top_to1257323279t_bool))) (forall ((X_2 tptp.produc472769767le_alt)) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt X_2) tptp.top_to1138392227t_bool))) (forall ((X_2 tptp.fun_Ar274636406t_bool)) (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f1225332775l_bool tptp.member933336803t_bool X_2) tptp.top_to553140914l_bool))) (forall ((X_2 tptp.fun_fu2114379172t_bool)) (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f1714503811l_bool tptp.member173038353t_bool X_2) tptp.top_to827110112l_bool))) (forall ((X_2 tptp.fun_Pr2067565481t_bool)) (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1482930381l_bool tptp.member1069471740t_bool X_2) tptp.top_to1312956197l_bool))) (forall ((X_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) tptp.top_top_fun_nat_bool))) (forall ((X_2 tptp.fun_Pr2067565481t_bool)) (= (tptp.hBOOL (tptp.hAPP_f52567537l_bool tptp.top_to1312956197l_bool X_2)) (tptp.hBOOL tptp.top_top_bool))) (forall ((X_2 tptp.fun_Ar274636406t_bool)) (= (tptp.hBOOL (tptp.hAPP_f995490902l_bool tptp.top_to553140914l_bool X_2)) (tptp.hBOOL tptp.top_top_bool))) (forall ((X_2 tptp.fun_fu2114379172t_bool)) (= (tptp.hBOOL (tptp.hAPP_f1572141188l_bool tptp.top_to827110112l_bool X_2)) (tptp.hBOOL tptp.top_top_bool))) (forall ((X_2 tptp.produc472769767le_alt)) (= (tptp.hBOOL (tptp.hAPP_P1178790471t_bool tptp.top_to1138392227t_bool X_2)) (tptp.hBOOL tptp.top_top_bool))) (forall ((X_2 tptp.arrow_856714788e_indi)) (= (tptp.hBOOL (tptp.hAPP_A997847300i_bool tptp.top_to788185952i_bool X_2)) (tptp.hBOOL tptp.top_top_bool))) (forall ((X_2 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool tptp.top_top_fun_nat_bool X_2)) (tptp.hBOOL tptp.top_top_bool))) (forall ((X_2 tptp.product_unit)) (= (tptp.hBOOL (tptp.hAPP_P1676879539t_bool tptp.top_to1257323279t_bool X_2)) (tptp.hBOOL tptp.top_top_bool))) (forall ((Aa tptp.fun_fu638310559l_bool)) (not (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1727358153l_bool tptp.top_to1312956197l_bool) Aa)))) (forall ((Aa tptp.fun_fu3835832l_bool)) (not (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1959568910l_bool tptp.top_to553140914l_bool) Aa)))) (forall ((Aa tptp.fun_fu2098777574l_bool)) (not (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le119247420l_bool tptp.top_to827110112l_bool) Aa)))) (forall ((Aa tptp.bool)) (not (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_bool tptp.top_top_bool) Aa)))) (forall ((Aa tptp.fun_Pr2067565481t_bool)) (not (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1478665215t_bool tptp.top_to1138392227t_bool) Aa)))) (forall ((Aa tptp.fun_Ar1809396326i_bool)) (not (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool tptp.top_to788185952i_bool) Aa)))) (forall ((Aa tptp.fun_nat_bool)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool tptp.top_top_fun_nat_bool) Aa)))) (forall ((Aa tptp.fun_Pr1643180309t_bool)) (not (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool tptp.top_to1257323279t_bool) Aa)))) (forall ((Aa tptp.fun_fu638310559l_bool)) (= (not (= Aa tptp.top_to1312956197l_bool)) (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1727358153l_bool Aa) tptp.top_to1312956197l_bool)))) (forall ((Aa tptp.fun_fu3835832l_bool)) (= (not (= Aa tptp.top_to553140914l_bool)) (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1959568910l_bool Aa) tptp.top_to553140914l_bool)))) (forall ((Aa tptp.fun_fu2098777574l_bool)) (= (not (= Aa tptp.top_to827110112l_bool)) (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le119247420l_bool Aa) tptp.top_to827110112l_bool)))) (forall ((Aa tptp.bool)) (= (not (= (tptp.hBOOL Aa) (tptp.hBOOL tptp.top_top_bool))) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_bool Aa) tptp.top_top_bool)))) (forall ((Aa tptp.fun_Pr2067565481t_bool)) (= (not (= Aa tptp.top_to1138392227t_bool)) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1478665215t_bool Aa) tptp.top_to1138392227t_bool)))) (forall ((Aa tptp.fun_Ar1809396326i_bool)) (= (not (= Aa tptp.top_to788185952i_bool)) (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool Aa) tptp.top_to788185952i_bool)))) (forall ((Aa tptp.fun_nat_bool)) (= (not (= Aa tptp.top_top_fun_nat_bool)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool Aa) tptp.top_top_fun_nat_bool)))) (forall ((Aa tptp.fun_Pr1643180309t_bool)) (= (not (= Aa tptp.top_to1257323279t_bool)) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool Aa) tptp.top_to1257323279t_bool)))) (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f1714503811l_bool tptp.member173038353t_bool tptp.f) (tptp.pi_fun1746584570t_bool tptp.arrow_5070731e_Prof (tptp.hAPP_f1104294872l_bool tptp.cOMBK_1701906001t_bool tptp.arrow_1361987423le_Lin)))) (= _let_15 (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_14 (tptp.hAPP_f2008608496t_bool tptp.f (tptp.hAPP_f480276746t_bool (tptp.hAPP_f601594885t_bool tptp.cOMBC_750853729t_bool (tptp.hAPP_f1344464862t_bool (tptp.hAPP_f1908974253t_bool tptp.cOMBC_156709173t_bool _let_10) tptp.lab)) tptp.lba))))) (forall ((Fa tptp.fun_fu2114379172t_bool) (I tptp.arrow_856714788e_indi)) (= (tptp.hBOOL (tptp.hAPP_A997847300i_bool (tptp.hAPP_f399308031i_bool tptp.arrow_1765888670ctator Fa) I)) (forall ((X_1 tptp.fun_Ar274636406t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f1225332775l_bool tptp.member933336803t_bool X_1) tptp.arrow_5070731e_Prof)) (= (tptp.hAPP_f2008608496t_bool Fa X_1) (tptp.hAPP_A1646126530t_bool X_1 I)))))) (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1482930381l_bool tptp.member1069471740t_bool tptp.lab) tptp.arrow_1361987423le_Lin)) (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1482930381l_bool tptp.member1069471740t_bool tptp.lba) tptp.arrow_1361987423le_Lin)) (not (= tptp.a tptp.b)) (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_8 tptp.lab)) (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_14 tptp.lba)) (not (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_8 tptp.lba))) (not (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_14 tptp.lab))) (forall ((Na tptp.nat)) (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f1225332775l_bool tptp.member933336803t_bool (tptp.hAPP_f480276746t_bool (tptp.hAPP_f601594885t_bool tptp.cOMBC_750853729t_bool (tptp.hAPP_f1344464862t_bool (tptp.hAPP_f1908974253t_bool tptp.cOMBC_156709173t_bool (tptp.hAPP_f668886383t_bool (tptp.cOMBB_1061985500e_indi tptp.if_fun523439385t_bool) (tptp.hAPP_n34002993i_bool (tptp.hAPP_f721434149i_bool tptp.cOMBC_722552198t_bool (tptp.hAPP_f966656047t_bool (tptp.cOMBB_1869811296e_indi tptp.ord_less_nat) tptp.h)) Na))) tptp.lab)) tptp.lba)) tptp.arrow_5070731e_Prof))) (not (forall ((Lab tptp.fun_Pr2067565481t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_A1299015393le_alt (tptp.hAPP_A1146194953le_alt tptp.produc1590937303le_alt tptp.a) tptp.b)) Lab)) (not (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1482930381l_bool tptp.member1069471740t_bool Lab) tptp.arrow_1361987423le_Lin)))))) (not (forall ((Lba tptp.fun_Pr2067565481t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_A1299015393le_alt (tptp.hAPP_A1146194953le_alt tptp.produc1590937303le_alt tptp.b) tptp.a)) Lba)) (not (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1482930381l_bool tptp.member1069471740t_bool Lba) tptp.arrow_1361987423le_Lin)))))) (forall ((I_1 tptp.arrow_856714788e_indi)) (let ((_let_1 (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_A1299015393le_alt (tptp.hAPP_A1146194953le_alt tptp.produc1590937303le_alt tptp.b) tptp.a)))) (let ((_let_2 (tptp.hAPP_A376526755di_nat tptp.h I_1))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat _let_2) tptp.n)))) (let ((_let_4 (not _let_3))) (let ((_let_5 (tptp.hAPP_A1646126530t_bool tptp.p I_1))) (let ((_let_6 (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_A1299015393le_alt (tptp.hAPP_A1146194953le_alt tptp.produc1590937303le_alt tptp.e) tptp.d)))) (let ((_let_7 (= _let_2 tptp.n))) (= (and (=> _let_3 (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_6 (tptp.hAPP_A1601437999t_bool (tptp.hAPP_f1761571331t_bool tptp.arrow_1630265669_mktop _let_5) tptp.e)))) (=> _let_4 (and (=> _let_7 (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_6 (tptp.hAPP_A1601437999t_bool (tptp.hAPP_A1058422557t_bool (tptp.hAPP_f1550387441t_bool tptp.arrow_216713899_above _let_5) tptp.c) tptp.e)))) (=> (not _let_7) (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_6 (tptp.hAPP_A1601437999t_bool (tptp.hAPP_f1761571331t_bool tptp.arrow_1481558583_mkbot _let_5) tptp.e))))))) (and (=> _let_3 (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_1 tptp.lab))) (=> _let_4 (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_1 tptp.lba))))))))))))) (forall ((M tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) tptp.n)) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_A1299015393le_alt (tptp.hAPP_A1146194953le_alt tptp.produc1590937303le_alt tptp.b) tptp.a)) (tptp.hAPP_f2008608496t_bool tptp.f (tptp.hAPP_f480276746t_bool (tptp.hAPP_f601594885t_bool tptp.cOMBC_750853729t_bool (tptp.hAPP_f1344464862t_bool (tptp.hAPP_f1908974253t_bool tptp.cOMBC_156709173t_bool (tptp.hAPP_f668886383t_bool (tptp.cOMBB_1061985500e_indi tptp.if_fun523439385t_bool) (tptp.hAPP_n34002993i_bool (tptp.hAPP_f721434149i_bool tptp.cOMBC_722552198t_bool (tptp.hAPP_f966656047t_bool (tptp.cOMBB_1869811296e_indi tptp.ord_less_nat) tptp.h)) M))) tptp.lab)) tptp.lba)))))) (forall ((X_2 tptp.arrow_1893660431le_alt) (Y_2 tptp.arrow_1893660431le_alt) (L_3 tptp.fun_Pr2067565481t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1482930381l_bool tptp.member1069471740t_bool L_3) tptp.arrow_1361987423le_Lin)) (=> (not (= X_2 Y_2)) (= (not (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_A1299015393le_alt (tptp.hAPP_A1146194953le_alt tptp.produc1590937303le_alt X_2) Y_2)) L_3))) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_A1299015393le_alt (tptp.hAPP_A1146194953le_alt tptp.produc1590937303le_alt Y_2) X_2)) L_3)))))) (forall ((Aa tptp.arrow_1893660431le_alt) (Ba tptp.arrow_1893660431le_alt) (L_3 tptp.fun_Pr2067565481t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1482930381l_bool tptp.member1069471740t_bool L_3) tptp.arrow_1361987423le_Lin)) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_A1299015393le_alt (tptp.hAPP_A1146194953le_alt tptp.produc1590937303le_alt Aa) Ba)) L_3)) (not (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_A1299015393le_alt (tptp.hAPP_A1146194953le_alt tptp.produc1590937303le_alt Ba) Aa)) L_3)))))) (forall ((X_2 tptp.arrow_1893660431le_alt) (L_3 tptp.fun_Pr2067565481t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1482930381l_bool tptp.member1069471740t_bool L_3) tptp.arrow_1361987423le_Lin)) (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1482930381l_bool tptp.member1069471740t_bool (tptp.hAPP_A1601437999t_bool (tptp.hAPP_f1761571331t_bool tptp.arrow_1630265669_mktop L_3) X_2)) tptp.arrow_1361987423le_Lin)))) (forall ((X_2 tptp.arrow_1893660431le_alt) (L_3 tptp.fun_Pr2067565481t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1482930381l_bool tptp.member1069471740t_bool L_3) tptp.arrow_1361987423le_Lin)) (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1482930381l_bool tptp.member1069471740t_bool (tptp.hAPP_A1601437999t_bool (tptp.hAPP_f1761571331t_bool tptp.arrow_1481558583_mkbot L_3) X_2)) tptp.arrow_1361987423le_Lin)))) (forall ((L_3 tptp.fun_Pr2067565481t_bool) (X_2 tptp.arrow_1893660431le_alt) (Y_2 tptp.arrow_1893660431le_alt)) (=> (not (= X_2 Y_2)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1482930381l_bool tptp.member1069471740t_bool L_3) tptp.arrow_1361987423le_Lin)) (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1482930381l_bool tptp.member1069471740t_bool (tptp.hAPP_A1601437999t_bool (tptp.hAPP_A1058422557t_bool (tptp.hAPP_f1550387441t_bool tptp.arrow_216713899_above L_3) X_2) Y_2)) tptp.arrow_1361987423le_Lin))))) (forall ((L_3 tptp.fun_Pr2067565481t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1482930381l_bool tptp.member1069471740t_bool L_3) tptp.arrow_1361987423le_Lin)) (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f1225332775l_bool tptp.member933336803t_bool (tptp.hAPP_f480276746t_bool tptp.cOMBK_1650320063e_indi L_3)) tptp.arrow_5070731e_Prof)))) (forall ((X_32 tptp.nat) (Y_30 tptp.nat)) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_32) Y_30))) (=> (not (= X_32 Y_30)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Y_30) X_32))))) (forall ((X_2 tptp.fun_nat_bool) (Y_2 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool X_2) Y_2)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool Y_2) X_2))))) (forall ((X_2 tptp.fun_Pr1643180309t_bool) (Y_2 tptp.fun_Pr1643180309t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool X_2) Y_2)) (not (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool Y_2) X_2))))) (forall ((X_2 tptp.fun_Ar1809396326i_bool) (Y_2 tptp.fun_Ar1809396326i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool X_2) Y_2)) (not (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool Y_2) X_2))))) (forall ((X_31 tptp.nat) (Y_29 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_31) Y_29)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Y_29) X_31))))) (forall ((Z_2 tptp.fun_nat_bool) (Y_2 tptp.fun_nat_bool) (X_2 tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool Z_2))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool Y_2) X_2)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 Y_2)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 X_2)))))) (forall ((Z_2 tptp.fun_Pr1643180309t_bool) (Y_2 tptp.fun_Pr1643180309t_bool) (X_2 tptp.fun_Pr1643180309t_bool)) (let ((_let_1 (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool Z_2))) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool Y_2) X_2)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool _let_1 Y_2)) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool _let_1 X_2)))))) (forall ((Z_2 tptp.fun_Ar1809396326i_bool) (Y_2 tptp.fun_Ar1809396326i_bool) (X_2 tptp.fun_Ar1809396326i_bool)) (let ((_let_1 (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool Z_2))) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool Y_2) X_2)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool _let_1 Y_2)) (tptp.hBOOL (tptp.hAPP_f584385070l_bool _let_1 X_2)))))) (forall ((Z_9 tptp.nat) (Y_28 tptp.nat) (X_30 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Z_9))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Y_28) X_30)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Y_28)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 X_30)))))) (forall ((Z_2 tptp.fun_nat_bool) (X_2 tptp.fun_nat_bool) (Y_2 tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool X_2))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 Y_2)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool Y_2) Z_2)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 Z_2)))))) (forall ((Z_2 tptp.fun_Pr1643180309t_bool) (X_2 tptp.fun_Pr1643180309t_bool) (Y_2 tptp.fun_Pr1643180309t_bool)) (let ((_let_1 (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool X_2))) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool _let_1 Y_2)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool Y_2) Z_2)) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool _let_1 Z_2)))))) (forall ((Z_2 tptp.fun_Ar1809396326i_bool) (X_2 tptp.fun_Ar1809396326i_bool) (Y_2 tptp.fun_Ar1809396326i_bool)) (let ((_let_1 (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool X_2))) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool _let_1 Y_2)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool Y_2) Z_2)) (tptp.hBOOL (tptp.hAPP_f584385070l_bool _let_1 Z_2)))))) (forall ((Z_8 tptp.nat) (X_29 tptp.nat) (Y_27 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_29))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Y_27)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Y_27) Z_8)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Z_8)))))) (forall ((Ca tptp.fun_nat_bool) (Ba tptp.fun_nat_bool) (Aa tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool Ba) Aa)) (=> (= Ba Ca) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool Ca) Aa))))) (forall ((Ca tptp.fun_Pr1643180309t_bool) (Ba tptp.fun_Pr1643180309t_bool) (Aa tptp.fun_Pr1643180309t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool Ba) Aa)) (=> (= Ba Ca) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool Ca) Aa))))) (forall ((Ca tptp.fun_Ar1809396326i_bool) (Ba tptp.fun_Ar1809396326i_bool) (Aa tptp.fun_Ar1809396326i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool Ba) Aa)) (=> (= Ba Ca) (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool Ca) Aa))))) (forall ((C_24 tptp.nat) (B_31 tptp.nat) (A_33 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat B_31) A_33)) (=> (= B_31 C_24) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat C_24) A_33))))) (forall ((Ca tptp.fun_nat_bool) (Aa tptp.fun_nat_bool) (Ba tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool Aa))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 Ba)) (=> (= Ba Ca) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 Ca)))))) (forall ((Ca tptp.fun_Pr1643180309t_bool) (Aa tptp.fun_Pr1643180309t_bool) (Ba tptp.fun_Pr1643180309t_bool)) (let ((_let_1 (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool Aa))) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool _let_1 Ba)) (=> (= Ba Ca) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool _let_1 Ca)))))) (forall ((Ca tptp.fun_Ar1809396326i_bool) (Aa tptp.fun_Ar1809396326i_bool) (Ba tptp.fun_Ar1809396326i_bool)) (let ((_let_1 (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool Aa))) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool _let_1 Ba)) (=> (= Ba Ca) (tptp.hBOOL (tptp.hAPP_f584385070l_bool _let_1 Ca)))))) (forall ((C_23 tptp.nat) (A_32 tptp.nat) (B_30 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_32))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_30)) (=> (= B_30 C_23) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 C_23)))))) (forall ((Ca tptp.fun_nat_bool) (Aa tptp.fun_nat_bool) (Ba tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool Ca))) (=> (= Aa Ba) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 Ba)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 Aa)))))) (forall ((Ca tptp.fun_Pr1643180309t_bool) (Aa tptp.fun_Pr1643180309t_bool) (Ba tptp.fun_Pr1643180309t_bool)) (let ((_let_1 (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool Ca))) (=> (= Aa Ba) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool _let_1 Ba)) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool _let_1 Aa)))))) (forall ((Ca tptp.fun_Ar1809396326i_bool) (Aa tptp.fun_Ar1809396326i_bool) (Ba tptp.fun_Ar1809396326i_bool)) (let ((_let_1 (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool Ca))) (=> (= Aa Ba) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool _let_1 Ba)) (tptp.hBOOL (tptp.hAPP_f584385070l_bool _let_1 Aa)))))) (forall ((C_22 tptp.nat) (A_31 tptp.nat) (B_29 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat C_22))) (=> (= A_31 B_29) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_29)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A_31)))))) (forall ((Ca tptp.fun_nat_bool) (Aa tptp.fun_nat_bool) (Ba tptp.fun_nat_bool)) (=> (= Aa Ba) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool Ba) Ca)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool Aa) Ca))))) (forall ((Ca tptp.fun_Pr1643180309t_bool) (Aa tptp.fun_Pr1643180309t_bool) (Ba tptp.fun_Pr1643180309t_bool)) (=> (= Aa Ba) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool Ba) Ca)) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool Aa) Ca))))) (forall ((Ca tptp.fun_Ar1809396326i_bool) (Aa tptp.fun_Ar1809396326i_bool) (Ba tptp.fun_Ar1809396326i_bool)) (=> (= Aa Ba) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool Ba) Ca)) (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool Aa) Ca))))) (forall ((C_21 tptp.nat) (A_30 tptp.nat) (B_28 tptp.nat)) (=> (= A_30 B_28) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat B_28) C_21)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_30) C_21))))) (forall ((Ba tptp.fun_nat_bool) (Aa tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool Ba) Aa)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool Aa) Ba))))) (forall ((Ba tptp.fun_Pr1643180309t_bool) (Aa tptp.fun_Pr1643180309t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool Ba) Aa)) (not (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool Aa) Ba))))) (forall ((Ba tptp.fun_Ar1809396326i_bool) (Aa tptp.fun_Ar1809396326i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool Ba) Aa)) (not (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool Aa) Ba))))) (forall ((B_27 tptp.nat) (A_29 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat B_27) A_29)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_29) B_27))))) (forall ((Aa tptp.fun_nat_bool) (Ba tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool Aa) Ba)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool Ba) Aa))))) (forall ((Aa tptp.fun_Pr1643180309t_bool) (Ba tptp.fun_Pr1643180309t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool Aa) Ba)) (not (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool Ba) Aa))))) (forall ((Aa tptp.fun_Ar1809396326i_bool) (Ba tptp.fun_Ar1809396326i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool Aa) Ba)) (not (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool Ba) Aa))))) (forall ((A_28 tptp.nat) (B_26 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_28) B_26)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat B_26) A_28))))) (forall ((Pa tptp.bool) (X_2 tptp.fun_nat_bool) (Y_2 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool X_2) Y_2)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool Y_2) X_2)) (tptp.hBOOL Pa)))) (forall ((Pa tptp.bool) (X_2 tptp.fun_Pr1643180309t_bool) (Y_2 tptp.fun_Pr1643180309t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool X_2) Y_2)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool Y_2) X_2)) (tptp.hBOOL Pa)))) (forall ((Pa tptp.bool) (X_2 tptp.fun_Ar1809396326i_bool) (Y_2 tptp.fun_Ar1809396326i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool X_2) Y_2)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool Y_2) X_2)) (tptp.hBOOL Pa)))) (forall ((Pa tptp.bool) (X_2 tptp.nat) (Y_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_2) Y_2)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Y_2) X_2)) (tptp.hBOOL Pa)))) (forall ((X_2 tptp.fun_nat_bool) (Y_2 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool X_2) Y_2)) (not (= Y_2 X_2)))) (forall ((X_2 tptp.fun_Pr1643180309t_bool) (Y_2 tptp.fun_Pr1643180309t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool X_2) Y_2)) (not (= Y_2 X_2)))) (forall ((X_2 tptp.fun_Ar1809396326i_bool) (Y_2 tptp.fun_Ar1809396326i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool X_2) Y_2)) (not (= Y_2 X_2)))) (forall ((X_28 tptp.nat) (Y_26 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_28) Y_26)) (not (= Y_26 X_28)))) (forall ((X_2 tptp.fun_nat_bool) (Y_2 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool X_2) Y_2)) (not (= X_2 Y_2)))) (forall ((X_2 tptp.fun_Pr1643180309t_bool) (Y_2 tptp.fun_Pr1643180309t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool X_2) Y_2)) (not (= X_2 Y_2)))) (forall ((X_2 tptp.fun_Ar1809396326i_bool) (Y_2 tptp.fun_Ar1809396326i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool X_2) Y_2)) (not (= X_2 Y_2)))) (forall ((X_27 tptp.nat) (Y_25 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_27) Y_25)) (not (= X_27 Y_25)))) (forall ((X_2 tptp.fun_nat_bool) (Y_2 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool X_2) Y_2)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool Y_2) X_2))))) (forall ((X_2 tptp.fun_Pr1643180309t_bool) (Y_2 tptp.fun_Pr1643180309t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool X_2) Y_2)) (not (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool Y_2) X_2))))) (forall ((X_2 tptp.fun_Ar1809396326i_bool) (Y_2 tptp.fun_Ar1809396326i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool X_2) Y_2)) (not (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool Y_2) X_2))))) (forall ((X_26 tptp.nat) (Y_24 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_26) Y_24)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Y_24) X_26))))) (forall ((X_2 tptp.fun_nat_bool) (Y_2 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool X_2) Y_2)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool Y_2) X_2))))) (forall ((X_2 tptp.fun_Pr1643180309t_bool) (Y_2 tptp.fun_Pr1643180309t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool X_2) Y_2)) (not (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool Y_2) X_2))))) (forall ((X_2 tptp.fun_Ar1809396326i_bool) (Y_2 tptp.fun_Ar1809396326i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool X_2) Y_2)) (not (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool Y_2) X_2))))) (forall ((X_25 tptp.nat) (Y_23 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_25) Y_23)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Y_23) X_25))))) (forall ((X_2 tptp.fun_nat_bool) (Y_2 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool X_2) Y_2)) (not (= X_2 Y_2)))) (forall ((X_2 tptp.fun_Pr1643180309t_bool) (Y_2 tptp.fun_Pr1643180309t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool X_2) Y_2)) (not (= X_2 Y_2)))) (forall ((X_2 tptp.fun_Ar1809396326i_bool) (Y_2 tptp.fun_Ar1809396326i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool X_2) Y_2)) (not (= X_2 Y_2)))) (forall ((X_24 tptp.nat) (Y_22 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_24) Y_22)) (not (= X_24 Y_22)))) (forall ((X_23 tptp.nat) (Y_21 tptp.nat)) (=> (not (= X_23 Y_21)) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_23) Y_21))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Y_21) X_23))))) (forall ((Y_2 tptp.nat) (X_2 tptp.nat)) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Y_2) X_2))) (= (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_2) Y_2))) (= X_2 Y_2)))) (forall ((X_22 tptp.nat) (Y_20 tptp.nat)) (or (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_22) Y_20)) (= X_22 Y_20) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Y_20) X_22)))) (forall ((X_2 tptp.nat) (Y_2 tptp.nat)) (= (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_2) Y_2))) (or (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Y_2) X_2)) (= X_2 Y_2)))) (forall ((X_2 tptp.nat) (Y_2 tptp.nat)) (= (not (= X_2 Y_2)) (or (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_2) Y_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Y_2) X_2))))) (forall ((X_2 tptp.fun_nat_bool)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool X_2) X_2)))) (forall ((X_2 tptp.fun_Pr1643180309t_bool)) (not (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool X_2) X_2)))) (forall ((X_2 tptp.fun_Ar1809396326i_bool)) (not (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool X_2) X_2)))) (forall ((X_21 tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_21) X_21)))) (forall ((X_2 tptp.arrow_856714788e_indi) (A tptp.fun_Ar1809396326i_bool)) (= (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_A1597696899l_bool tptp.member1479139729e_indi X_2) A)) (tptp.hBOOL (tptp.hAPP_A997847300i_bool A X_2)))) (forall ((X_2 tptp.bool) (A tptp.fun_bool_bool)) (= (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.hAPP_b1787118453l_bool tptp.member_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_bool_bool A X_2)))) (forall ((X_2 tptp.product_unit) (A tptp.fun_Pr1643180309t_bool)) (= (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_P607165281l_bool tptp.member_Product_unit X_2) A)) (tptp.hBOOL (tptp.hAPP_P1676879539t_bool A X_2)))) (forall ((X_2 tptp.produc472769767le_alt) (A tptp.fun_Pr2067565481t_bool)) (= (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt X_2) A)) (tptp.hBOOL (tptp.hAPP_P1178790471t_bool A X_2)))) (forall ((X_2 tptp.fun_Ar274636406t_bool) (A tptp.fun_fu3835832l_bool)) (= (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f1225332775l_bool tptp.member933336803t_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f995490902l_bool A X_2)))) (forall ((X_2 tptp.fun_fu2114379172t_bool) (A tptp.fun_fu2098777574l_bool)) (= (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f1714503811l_bool tptp.member173038353t_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f1572141188l_bool A X_2)))) (forall ((X_2 tptp.fun_Pr2067565481t_bool) (A tptp.fun_fu638310559l_bool)) (= (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1482930381l_bool tptp.member1069471740t_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f52567537l_bool A X_2)))) (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 ((Pa tptp.fun_Pr1643180309t_bool)) (= (tptp.hAPP_f427533077t_bool tptp.collect_Product_unit Pa) Pa)) (forall ((Pa tptp.fun_Ar1809396326i_bool)) (= (tptp.hAPP_f1612707285i_bool tptp.collec1597001935e_indi Pa) Pa)) (forall ((Pa tptp.fun_nat_bool)) (= (tptp.hAPP_f800510211t_bool tptp.collect_nat Pa) Pa)) (= tptp.top_to1312956197l_bool (tptp.hAPP_f1060563265l_bool tptp.collec2125531966t_bool (tptp.hAPP_b1272691967l_bool tptp.cOMBK_81143760t_bool tptp.fTrue))) (= tptp.top_to553140914l_bool (tptp.hAPP_f819682389l_bool tptp.collec1236161569t_bool (tptp.hAPP_b1078573912l_bool tptp.cOMBK_445086735t_bool tptp.fTrue))) (= tptp.top_to827110112l_bool (tptp.hAPP_f1181604821l_bool tptp.collec71394895t_bool (tptp.hAPP_b1777246598l_bool tptp.cOMBK_1279003709t_bool tptp.fTrue))) (= tptp.top_to1138392227t_bool (tptp.hAPP_f1356305429t_bool tptp.collec1988958098le_alt (tptp.hAPP_b128655177t_bool tptp.cOMBK_198697344le_alt tptp.fTrue))) (= tptp.top_to788185952i_bool (tptp.hAPP_f1612707285i_bool tptp.collec1597001935e_indi (tptp.hAPP_b549570054i_bool tptp.cOMBK_561380029e_indi tptp.fTrue))) (= tptp.top_to1257323279t_bool (tptp.hAPP_f427533077t_bool tptp.collect_Product_unit (tptp.hAPP_b1096750261t_bool tptp.cOMBK_790042732t_unit tptp.fTrue))) (= tptp.top_top_fun_nat_bool (tptp.hAPP_f800510211t_bool tptp.collect_nat (tptp.hAPP_b1013836512t_bool tptp.cOMBK_bool_nat tptp.fTrue))) (forall ((X_2 tptp.arrow_1893660431le_alt) (Y_2 tptp.arrow_1893660431le_alt) (L_3 tptp.fun_Pr2067565481t_bool) (Aa tptp.arrow_1893660431le_alt) (Ba tptp.arrow_1893660431le_alt)) (let ((_let_1 (tptp.hAPP_A1146194953le_alt tptp.produc1590937303le_alt X_2))) (let ((_let_2 (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_A1299015393le_alt _let_1 Y_2)))) (let ((_let_3 (= Y_2 Ba))) (let ((_let_4 (= X_2 Ba))) (=> (not (= Aa Ba)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1482930381l_bool tptp.member1069471740t_bool L_3) tptp.arrow_1361987423le_Lin)) (= (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_2 (tptp.hAPP_A1601437999t_bool (tptp.hAPP_A1058422557t_bool (tptp.hAPP_f1550387441t_bool tptp.arrow_216713899_above L_3) Aa) Ba))) (and (not (= X_2 Y_2)) (=> _let_4 (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_A1299015393le_alt (tptp.hAPP_A1146194953le_alt tptp.produc1590937303le_alt Aa) Y_2)) L_3))) (=> (not _let_4) (and (=> _let_3 (or (= X_2 Aa) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_A1299015393le_alt _let_1 Aa)) L_3)))) (=> (not _let_3) (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_2 L_3)))))))))))))) (forall ((S_1 tptp.fun_Pr2067565481t_bool) (R_1 tptp.fun_Pr2067565481t_bool)) (= (forall ((X_1 tptp.arrow_1893660431le_alt) (Xa tptp.arrow_1893660431le_alt)) (let ((_let_1 (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_A1299015393le_alt (tptp.hAPP_A1146194953le_alt tptp.produc1590937303le_alt X_1) Xa)))) (= (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_1 R_1)) (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_1 S_1))))) (= R_1 S_1))) (forall ((I tptp.arrow_856714788e_indi) (Fa tptp.fun_fu2114379172t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f1714503811l_bool tptp.member173038353t_bool Fa) (tptp.pi_fun1746584570t_bool tptp.arrow_5070731e_Prof (tptp.hAPP_f1104294872l_bool tptp.cOMBK_1701906001t_bool tptp.arrow_1361987423le_Lin)))) (=> (forall ((X_1 tptp.fun_Ar274636406t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f1225332775l_bool tptp.member933336803t_bool X_1) tptp.arrow_5070731e_Prof)) (forall ((A_27 tptp.arrow_1893660431le_alt) (B_25 tptp.arrow_1893660431le_alt)) (let ((_let_1 (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_A1299015393le_alt (tptp.hAPP_A1146194953le_alt tptp.produc1590937303le_alt A_27) B_25)))) (=> (not (= A_27 B_25)) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_1 (tptp.hAPP_A1646126530t_bool X_1 I))) (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_1 (tptp.hAPP_f2008608496t_bool Fa X_1))))))))) (tptp.hBOOL (tptp.hAPP_A997847300i_bool (tptp.hAPP_f399308031i_bool tptp.arrow_1765888670ctator Fa) I))))) _let_9 (= _let_13 _let_9) (forall ((I_1 tptp.arrow_856714788e_indi)) (let ((_let_1 (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_A1299015393le_alt (tptp.hAPP_A1146194953le_alt tptp.produc1590937303le_alt tptp.a) tptp.b)))) (let ((_let_2 (tptp.hAPP_A376526755di_nat tptp.h I_1))) (let ((_let_3 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat _let_2))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP_nat_bool _let_3 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat tptp.n) tptp.one_one_nat))))) (let ((_let_5 (tptp.hAPP_A1646126530t_bool tptp.p I_1))) (let ((_let_6 (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_A1299015393le_alt (tptp.hAPP_A1146194953le_alt tptp.produc1590937303le_alt tptp.c) tptp.e)))) (let ((_let_7 (= _let_2 tptp.n))) (let ((_let_8 (tptp.hBOOL (tptp.hAPP_nat_bool _let_3 tptp.n)))) (= (and (=> _let_8 (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_6 (tptp.hAPP_A1601437999t_bool (tptp.hAPP_f1761571331t_bool tptp.arrow_1630265669_mktop _let_5) tptp.e)))) (=> (not _let_8) (and (=> _let_7 (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_6 (tptp.hAPP_A1601437999t_bool (tptp.hAPP_A1058422557t_bool (tptp.hAPP_f1550387441t_bool tptp.arrow_216713899_above _let_5) tptp.c) tptp.e)))) (=> (not _let_7) (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_6 (tptp.hAPP_A1601437999t_bool (tptp.hAPP_f1761571331t_bool tptp.arrow_1481558583_mkbot _let_5) tptp.e))))))) (and (=> _let_4 (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_1 tptp.lab))) (=> (not _let_4) (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_1 tptp.lba)))))))))))))) (forall ((X_2 tptp.arrow_856714788e_indi) (Y_2 tptp.nat) (F tptp.fun_Ar671024215di_nat)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.inj_on1960344199di_nat F) tptp.top_to788185952i_bool)) (=> (= (tptp.hAPP_A376526755di_nat F X_2) Y_2) (= (tptp.hAPP_n1937165849e_indi (tptp.hilber1580028780di_nat tptp.top_to788185952i_bool F) Y_2) X_2)))) (forall ((X_2 tptp.nat) (Y_2 tptp.nat) (F tptp.fun_nat_nat)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.inj_on_nat_nat F) tptp.top_top_fun_nat_bool)) (=> (= (tptp.hAPP_nat_nat F X_2) Y_2) (= (tptp.hAPP_nat_nat (tptp.hilber195283148at_nat tptp.top_top_fun_nat_bool F) Y_2) X_2)))) (forall ((X_2 tptp.arrow_856714788e_indi) (F tptp.fun_Ar671024215di_nat)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.inj_on1960344199di_nat F) tptp.top_to788185952i_bool)) (= (tptp.hAPP_n1937165849e_indi (tptp.hilber1580028780di_nat tptp.top_to788185952i_bool F) (tptp.hAPP_A376526755di_nat F X_2)) X_2))) (forall ((X_2 tptp.nat) (F tptp.fun_nat_nat)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.inj_on_nat_nat F) tptp.top_top_fun_nat_bool)) (= (tptp.hAPP_nat_nat (tptp.hilber195283148at_nat tptp.top_top_fun_nat_bool F) (tptp.hAPP_nat_nat F X_2)) X_2))) (forall ((X_2 tptp.produc472769767le_alt) (F tptp.fun_Pr2067565481t_bool) (A tptp.fun_Pr2067565481t_bool) (B tptp.fun_Pr1780397033l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1482930381l_bool tptp.member1069471740t_bool F) (tptp.pi_Pro1238944957t_bool A B))) (=> (not (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.hAPP_b1787118453l_bool tptp.member_bool (tptp.hAPP_P1178790471t_bool F X_2)) (tptp.hAPP_P1103642805l_bool B X_2)))) (not (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt X_2) A)))))) (forall ((X_2 tptp.arrow_856714788e_indi) (F tptp.fun_Ar338949104le_alt) (A tptp.fun_Ar1809396326i_bool) (B tptp.fun_Ar274636406t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1754488902l_bool (tptp.hAPP_f766019597l_bool tptp.member387840963le_alt F) (tptp.pi_Arr1460528004le_alt A B))) (=> (not (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_A899858958le_alt F X_2)) (tptp.hAPP_A1646126530t_bool B X_2)))) (not (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_A1597696899l_bool tptp.member1479139729e_indi X_2) A)))))) (forall ((X_2 tptp.bool) (F tptp.fun_bo1682907689le_alt) (A tptp.fun_bool_bool) (B tptp.fun_bo1431306493t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1620711039l_bool (tptp.hAPP_f334747853l_bool tptp.member684813948le_alt F) (tptp.pi_boo7125949le_alt A B))) (=> (not (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_b2094455111le_alt F X_2)) (tptp.hAPP_b128655177t_bool B X_2)))) (not (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.hAPP_b1787118453l_bool tptp.member_bool X_2) A)))))) (forall ((X_2 tptp.product_unit) (F tptp.fun_Pr2090226719le_alt) (A tptp.fun_Pr1643180309t_bool) (B tptp.fun_Pr1887398791t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f684683381l_bool (tptp.hAPP_f41367117l_bool tptp.member869664626le_alt F) (tptp.pi_Pro1820940723le_alt A B))) (=> (not (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_P396106045le_alt F X_2)) (tptp.hAPP_P1914371027t_bool B X_2)))) (not (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_P607165281l_bool tptp.member_Product_unit X_2) A)))))) (forall ((X_2 tptp.arrow_856714788e_indi) (F tptp.fun_Ar624010239t_bool) (A tptp.fun_Ar1809396326i_bool) (B tptp.fun_Ar1998664965l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f826064725l_bool (tptp.hAPP_f1364091725l_bool tptp.member1124505298t_bool F) (tptp.pi_Arr2025169427t_bool A B))) (=> (not (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f1225332775l_bool tptp.member933336803t_bool (tptp.hAPP_A2107398813t_bool F X_2)) (tptp.hAPP_A1411662545l_bool B X_2)))) (not (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_A1597696899l_bool tptp.member1479139729e_indi X_2) A)))))) (forall ((X_2 tptp.bool) (F tptp.fun_bo1476023096t_bool) (A tptp.fun_bool_bool) (B tptp.fun_bo2107365004l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1605957262l_bool (tptp.hAPP_f1525863565l_bool tptp.member344984203t_bool F) (tptp.pi_boo347863884t_bool A B))) (=> (not (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f1225332775l_bool tptp.member933336803t_bool (tptp.hAPP_b489616086t_bool F X_2)) (tptp.hAPP_b1078573912l_bool B X_2)))) (not (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.hAPP_b1787118453l_bool tptp.member_bool X_2) A)))))) (forall ((X_2 tptp.product_unit) (F tptp.fun_Pr1531194158t_bool) (A tptp.fun_Pr1643180309t_bool) (B tptp.fun_Pr537467670l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1851324036l_bool (tptp.hAPP_f1974966541l_bool tptp.member364267905t_bool F) (tptp.pi_Pro782712642t_bool A B))) (=> (not (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f1225332775l_bool tptp.member933336803t_bool (tptp.hAPP_P913627340t_bool F X_2)) (tptp.hAPP_P284783074l_bool B X_2)))) (not (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_P607165281l_bool tptp.member_Product_unit X_2) A)))))) (forall ((X_2 tptp.arrow_856714788e_indi) (F tptp.fun_Ar286530093t_bool) (A tptp.fun_Ar1809396326i_bool) (B tptp.fun_Ar1321653811l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f686820739l_bool (tptp.hAPP_f692361165l_bool tptp.member785631232t_bool F) (tptp.pi_Arr687740481t_bool A B))) (=> (not (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f1714503811l_bool tptp.member173038353t_bool (tptp.hAPP_A1378093259t_bool F X_2)) (tptp.hAPP_A2084592127l_bool B X_2)))) (not (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_A1597696899l_bool tptp.member1479139729e_indi X_2) A)))))) (forall ((X_2 tptp.bool) (F tptp.fun_bo559790694t_bool) (A tptp.fun_bool_bool) (B tptp.fun_bo1445676730l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1211446716l_bool (tptp.hAPP_f1134773005l_bool tptp.member1782492345t_bool F) (tptp.pi_boo769613946t_bool A B))) (=> (not (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f1714503811l_bool tptp.member173038353t_bool (tptp.hAPP_b1029214724t_bool F X_2)) (tptp.hAPP_b1777246598l_bool B X_2)))) (not (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.hAPP_b1787118453l_bool tptp.member_bool X_2) A)))))) (forall ((X_2 tptp.product_unit) (F tptp.fun_Pr2016729180t_bool) (A tptp.fun_Pr1643180309t_bool) (B tptp.fun_Pr151242052l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f2068478898l_bool (tptp.hAPP_f1883507597l_bool tptp.member480326063t_bool F) (tptp.pi_Pro1533274736t_bool A B))) (=> (not (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f1714503811l_bool tptp.member173038353t_bool (tptp.hAPP_P1858715130t_bool F X_2)) (tptp.hAPP_P283873808l_bool B X_2)))) (not (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_P607165281l_bool tptp.member_Product_unit X_2) A)))))) (forall ((X_2 tptp.bool) (F tptp.fun_bo1431306493t_bool) (A tptp.fun_bool_bool) (B tptp.fun_bo377688929l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f398210311l_bool (tptp.hAPP_f416878261l_bool tptp.member1133581546t_bool F) (tptp.pi_boo1111177555t_bool A B))) (=> (not (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1482930381l_bool tptp.member1069471740t_bool (tptp.hAPP_b128655177t_bool F X_2)) (tptp.hAPP_b1272691967l_bool B X_2)))) (not (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.hAPP_b1787118453l_bool tptp.member_bool X_2) A)))))) (forall ((X_2 tptp.product_unit) (F tptp.fun_Pr1887398791t_bool) (A tptp.fun_Pr1643180309t_bool) (B tptp.fun_Pr1791323223l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1426814865l_bool (tptp.hAPP_f1942212041l_bool tptp.member803887220t_bool F) (tptp.pi_Pro1290680285t_bool A B))) (=> (not (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1482930381l_bool tptp.member1069471740t_bool (tptp.hAPP_P1914371027t_bool F X_2)) (tptp.hAPP_P754918389l_bool B X_2)))) (not (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_P607165281l_bool tptp.member_Product_unit X_2) A)))))) (forall ((X_2 tptp.arrow_856714788e_indi) (F tptp.fun_Ar671024215di_nat) (A tptp.fun_Ar1809396326i_bool) (B tptp.fun_Ar603939593t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f225240161l_bool (tptp.hAPP_f677301097l_bool tptp.member1502495556di_nat F) (tptp.pi_Arr1233262509di_nat A B))) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat (tptp.hAPP_A376526755di_nat F X_2)) (tptp.hAPP_A1686943911t_bool B X_2)))) (not (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_A1597696899l_bool tptp.member1479139729e_indi X_2) A)))))) (forall ((X_2 tptp.bool) (F tptp.fun_bool_nat) (A tptp.fun_bool_bool) (B tptp.fun_bo1570548802t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f67777128l_bool (tptp.hAPP_f144393719l_bool tptp.member_fun_bool_nat F) (tptp.pi_bool_nat A B))) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat (tptp.hAPP_bool_nat F X_2)) (tptp.hAPP_b1013836512t_bool B X_2)))) (not (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.hAPP_b1787118453l_bool tptp.member_bool X_2) A)))))) (forall ((X_2 tptp.product_unit) (F tptp.fun_Product_unit_nat) (A tptp.fun_Pr1643180309t_bool) (B tptp.fun_Pr1029464120t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f339859954l_bool (tptp.hAPP_f1950626059l_bool tptp.member87760213it_nat F) (tptp.pi_Product_unit_nat A B))) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat (tptp.hAPP_P426034740it_nat F X_2)) (tptp.hAPP_P32877782t_bool B X_2)))) (not (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_P607165281l_bool tptp.member_Product_unit X_2) A)))))) (forall ((X_2 tptp.produc472769767le_alt) (F tptp.fun_Pr1509342064e_indi) (A tptp.fun_Pr2067565481t_bool) (B tptp.fun_Pr895221296i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f2124588998l_bool (tptp.hAPP_f1187850253l_bool tptp.member1558233923e_indi F) (tptp.pi_Pro837265796e_indi A B))) (=> (not (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_A1597696899l_bool tptp.member1479139729e_indi (tptp.hAPP_P276596750e_indi F X_2)) (tptp.hAPP_P1859429372i_bool B X_2)))) (not (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt X_2) A)))))) (forall ((X_2 tptp.produc472769767le_alt) (F tptp.fun_Pr376858015t_unit) (A tptp.fun_Pr2067565481t_bool) (B tptp.fun_Pr1069395679t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1159856629l_bool (tptp.hAPP_f1700632141l_bool tptp.member1303779570t_unit F) (tptp.pi_Pro346842291t_unit A B))) (=> (not (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_P607165281l_bool tptp.member_Product_unit (tptp.hAPP_P1069491261t_unit F X_2)) (tptp.hAPP_P2037731755t_bool B X_2)))) (not (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt X_2) A)))))) (forall ((X_2 tptp.fun_Ar274636406t_bool) (F tptp.fun_fu1929591039e_indi) (A tptp.fun_fu3835832l_bool) (B tptp.fun_fu223278561i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f665932885l_bool (tptp.hAPP_f430646093l_bool tptp.member282602450e_indi F) (tptp.pi_fun520512275e_indi A B))) (=> (not (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_A1597696899l_bool tptp.member1479139729e_indi (tptp.hAPP_f602741661e_indi F X_2)) (tptp.hAPP_f391644589i_bool B X_2)))) (not (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f1225332775l_bool tptp.member933336803t_bool X_2) A)))))) (forall ((X_2 tptp.fun_Ar274636406t_bool) (F tptp.fun_fu3835832l_bool) (A tptp.fun_fu3835832l_bool) (B tptp.fun_fu916327706l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1867557646l_bool (tptp.hAPP_f1048573069l_bool tptp.member1020280587l_bool F) (tptp.pi_fun853738700l_bool A B))) (=> (not (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.hAPP_b1787118453l_bool tptp.member_bool (tptp.hAPP_f995490902l_bool F X_2)) (tptp.hAPP_f1676084198l_bool B X_2)))) (not (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f1225332775l_bool tptp.member933336803t_bool X_2) A)))))) (forall ((X_2 tptp.fun_Ar274636406t_bool) (F tptp.fun_fu1023022254t_unit) (A tptp.fun_fu3835832l_bool) (B tptp.fun_fu1734317328t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f115957764l_bool (tptp.hAPP_f1184790797l_bool tptp.member2003579649t_unit F) (tptp.pi_fun1644711874t_unit A B))) (=> (not (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_P607165281l_bool tptp.member_Product_unit (tptp.hAPP_f1775626572t_unit F X_2)) (tptp.hAPP_f1438163420t_bool B X_2)))) (not (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f1225332775l_bool tptp.member933336803t_bool X_2) A)))))) (forall ((X_2 tptp.fun_fu2114379172t_bool) (F tptp.fun_fu748153389e_indi) (A tptp.fun_fu2098777574l_bool) (B tptp.fun_fu2109152051i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f2350467l_bool (tptp.hAPP_f1411422157l_bool tptp.member1247254528e_indi F) (tptp.pi_fun1807454273e_indi A B))) (=> (not (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_A1597696899l_bool tptp.member1479139729e_indi (tptp.hAPP_f350323403e_indi F X_2)) (tptp.hAPP_f399308031i_bool B X_2)))) (not (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f1714503811l_bool tptp.member173038353t_bool X_2) A)))))) (forall ((X_2 tptp.fun_fu2114379172t_bool) (F tptp.fun_fu2098777574l_bool) (A tptp.fun_fu2098777574l_bool) (B tptp.fun_fu1522163052l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f2047920444l_bool (tptp.hAPP_f59810573l_bool tptp.member1173995577l_bool F) (tptp.pi_fun1312540410l_bool A B))) (=> (not (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.hAPP_b1787118453l_bool tptp.member_bool (tptp.hAPP_f1572141188l_bool F X_2)) (tptp.hAPP_f414129720l_bool B X_2)))) (not (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f1714503811l_bool tptp.member173038353t_bool X_2) A)))))) (forall ((X_2 tptp.fun_fu2114379172t_bool) (F tptp.fun_fu1480298716t_unit) (A tptp.fun_fu2098777574l_bool) (B tptp.fun_fu1143287650t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f92582962l_bool (tptp.hAPP_f1494690701l_bool tptp.member2091379247t_unit F) (tptp.pi_fun1540376560t_unit A B))) (=> (not (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_P607165281l_bool tptp.member_Product_unit (tptp.hAPP_f1865816954t_unit F X_2)) (tptp.hAPP_f151782958t_bool B X_2)))) (not (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f1714503811l_bool tptp.member173038353t_bool X_2) A)))))) (forall ((X_2 tptp.fun_Pr2067565481t_bool) (F tptp.fun_fu562005862e_indi) (A tptp.fun_fu638310559l_bool) (B tptp.fun_fu2142850746i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f679138160l_bool (tptp.hAPP_f1006969351l_bool tptp.member1220706259e_indi F) (tptp.pi_fun1470523330e_indi A B))) (=> (not (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_A1597696899l_bool tptp.member1479139729e_indi (tptp.hAPP_f9587896e_indi F X_2)) (tptp.hAPP_f2010315474i_bool B X_2)))) (not (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1482930381l_bool tptp.member1069471740t_bool X_2) A)))))) (forall ((X_2 tptp.fun_Pr2067565481t_bool) (F tptp.fun_fu638310559l_bool) (A tptp.fun_fu638310559l_bool) (B tptp.fun_fu237781875l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1686510249l_bool (tptp.hAPP_f1930590713l_bool tptp.member340585612l_bool F) (tptp.pi_fun1035089915l_bool A B))) (=> (not (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.hAPP_b1787118453l_bool tptp.member_bool (tptp.hAPP_f52567537l_bool F X_2)) (tptp.hAPP_f463104139l_bool B X_2)))) (not (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1482930381l_bool tptp.member1069471740t_bool X_2) A)))))) (forall ((X_2 tptp.fun_Pr2067565481t_bool) (F tptp.fun_fu665686165t_unit) (A tptp.fun_fu638310559l_bool) (B tptp.fun_fu643686505t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1478188703l_bool (tptp.hAPP_f1329172965l_bool tptp.member1729658242t_unit F) (tptp.pi_fun177985009t_unit A B))) (=> (not (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_P607165281l_bool tptp.member_Product_unit (tptp.hAPP_f801675751t_unit F X_2)) (tptp.hAPP_f1400551297t_bool B X_2)))) (not (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1482930381l_bool tptp.member1069471740t_bool X_2) A)))))) (forall ((X_2 tptp.nat) (F tptp.fun_na699243463e_indi) (A tptp.fun_nat_bool) (B tptp.fun_na2037635353i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f736267217l_bool (tptp.hAPP_f707406409l_bool tptp.member1530714804e_indi F) (tptp.pi_nat646417955e_indi A B))) (=> (not (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_A1597696899l_bool tptp.member1479139729e_indi (tptp.hAPP_n1937165849e_indi F X_2)) (tptp.hAPP_n34002993i_bool B X_2)))) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) A)))))) (forall ((X_2 tptp.nat) (F tptp.fun_nat_bool) (A tptp.fun_nat_bool) (B tptp.fun_na1469252690l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool (tptp.hAPP_f1951378235l_bool tptp.member_fun_nat_bool F) (tptp.pi_nat_bool A B))) (=> (not (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.hAPP_b1787118453l_bool tptp.member_bool (tptp.hAPP_nat_bool F X_2)) (tptp.hAPP_n1006566506l_bool B X_2)))) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) A)))))) (forall ((X_2 tptp.nat) (F tptp.fun_nat_Product_unit) (A tptp.fun_nat_bool) (B tptp.fun_na1041622088t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f537623936l_bool (tptp.hAPP_f1598887207l_bool tptp.member1024687843t_unit F) (tptp.pi_nat_Product_unit A B))) (=> (not (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_P607165281l_bool tptp.member_Product_unit (tptp.hAPP_n633340360t_unit F X_2)) (tptp.hAPP_n454528608t_bool B X_2)))) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) A)))))) (forall ((X_2 tptp.fun_Ar274636406t_bool) (F tptp.fun_fu2114379172t_bool) (A tptp.fun_fu3835832l_bool) (B tptp.fun_fu1863781882l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f1714503811l_bool tptp.member173038353t_bool F) (tptp.pi_fun1746584570t_bool A B))) (=> (not (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1482930381l_bool tptp.member1069471740t_bool (tptp.hAPP_f2008608496t_bool F X_2)) (tptp.hAPP_f1915815064l_bool B X_2)))) (not (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f1225332775l_bool tptp.member933336803t_bool X_2) A)))))) (forall ((X_2 tptp.arrow_856714788e_indi) (F tptp.fun_Ar274636406t_bool) (A tptp.fun_Ar1809396326i_bool) (B tptp.fun_Ar1474557608l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f1225332775l_bool tptp.member933336803t_bool F) (tptp.pi_Arr959578316t_bool A B))) (=> (not (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1482930381l_bool tptp.member1069471740t_bool (tptp.hAPP_A1646126530t_bool F X_2)) (tptp.hAPP_A897398598l_bool B X_2)))) (not (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_A1597696899l_bool tptp.member1479139729e_indi X_2) A)))))) (forall ((Aa tptp.arrow_1893660431le_alt) (Ba tptp.arrow_1893660431le_alt)) (=> (not (= Aa Ba)) (exists ((X_1 tptp.fun_Pr2067565481t_bool)) (and (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1482930381l_bool tptp.member1069471740t_bool X_1) tptp.arrow_1361987423le_Lin)) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_A1299015393le_alt (tptp.hAPP_A1146194953le_alt tptp.produc1590937303le_alt Aa) Ba)) X_1)))))) (forall ((A tptp.fun_Pr2067565481t_bool)) (= (tptp.pi_Pro1238944957t_bool A (tptp.hAPP_f699791347l_bool tptp.cOMBK_138598520le_alt tptp.top_to1647826457l_bool)) tptp.top_to1312956197l_bool)) (forall ((A tptp.fun_fu3835832l_bool)) (= (tptp.pi_fun1746584570t_bool A (tptp.hAPP_f1104294872l_bool tptp.cOMBK_1701906001t_bool tptp.top_to1312956197l_bool)) tptp.top_to827110112l_bool)) (forall ((A tptp.fun_Ar1809396326i_bool)) (= (tptp.pi_Arr959578316t_bool A (tptp.hAPP_f1717907078l_bool tptp.cOMBK_1520063231e_indi tptp.top_to1312956197l_bool)) tptp.top_to553140914l_bool)) (forall ((X_2 tptp.arrow_1893660431le_alt) (Y_2 tptp.arrow_1893660431le_alt) (L_3 tptp.fun_Pr2067565481t_bool) (Aa tptp.arrow_1893660431le_alt) (Ba tptp.arrow_1893660431le_alt)) (let ((_let_1 (tptp.hAPP_A1146194953le_alt tptp.produc1590937303le_alt X_2))) (let ((_let_2 (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_A1299015393le_alt _let_1 Y_2)))) (let ((_let_3 (= X_2 Aa))) (let ((_let_4 (= Y_2 Aa))) (=> (not (= Aa Ba)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1482930381l_bool tptp.member1069471740t_bool L_3) tptp.arrow_1361987423le_Lin)) (= (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_2 (tptp.arrow_1525312447_below L_3 Aa Ba))) (and (not (= X_2 Y_2)) (=> _let_4 (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_A1299015393le_alt _let_1 Ba)) L_3))) (=> (not _let_4) (and (=> _let_3 (or (= Y_2 Ba) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_A1299015393le_alt (tptp.hAPP_A1146194953le_alt tptp.produc1590937303le_alt Ba) Y_2)) L_3)))) (=> (not _let_3) (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_2 L_3)))))))))))))) (forall ((X_2 tptp.fun_fu638310559l_bool)) (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool X_2) X_2))) (forall ((X_2 tptp.fun_fu2098777574l_bool)) (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool X_2) X_2))) (forall ((X_2 tptp.fun_fu3835832l_bool)) (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool X_2) X_2))) (forall ((X_2 tptp.fun_Pr2067565481t_bool)) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool X_2) X_2))) (forall ((X_2 tptp.bool)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool X_2) X_2))) (forall ((X_2 tptp.fun_Ar1809396326i_bool)) (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool X_2) X_2))) (forall ((X_2 tptp.fun_Pr1643180309t_bool)) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool X_2) X_2))) (forall ((X_2 tptp.fun_Ar331856045t_bool)) (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool X_2) X_2))) (forall ((X_20 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_20) X_20))) (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))) (exists ((N_1 tptp.nat)) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N_1) (tptp.hAPP_f846027769ol_nat tptp.finite1672073426e_indi tptp.top_to788185952i_bool))) (forall ((M tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N_1)) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_A1299015393le_alt (tptp.hAPP_A1146194953le_alt tptp.produc1590937303le_alt tptp.b) tptp.a)) (tptp.hAPP_f2008608496t_bool tptp.f (tptp.hAPP_f480276746t_bool (tptp.hAPP_f601594885t_bool tptp.cOMBC_750853729t_bool (tptp.hAPP_f1344464862t_bool (tptp.hAPP_f1908974253t_bool tptp.cOMBC_156709173t_bool (tptp.hAPP_f668886383t_bool (tptp.cOMBB_1061985500e_indi tptp.if_fun523439385t_bool) (tptp.hAPP_n34002993i_bool (tptp.hAPP_f721434149i_bool tptp.cOMBC_722552198t_bool (tptp.hAPP_f966656047t_bool (tptp.cOMBB_1869811296e_indi tptp.ord_less_nat) tptp.h)) M))) tptp.lab)) tptp.lba)))))) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_A1299015393le_alt (tptp.hAPP_A1146194953le_alt tptp.produc1590937303le_alt tptp.a) tptp.b)) (tptp.hAPP_f2008608496t_bool tptp.f (tptp.hAPP_f480276746t_bool (tptp.hAPP_f601594885t_bool tptp.cOMBC_750853729t_bool (tptp.hAPP_f1344464862t_bool (tptp.hAPP_f1908974253t_bool tptp.cOMBC_156709173t_bool (tptp.hAPP_f668886383t_bool (tptp.cOMBB_1061985500e_indi tptp.if_fun523439385t_bool) (tptp.hAPP_n34002993i_bool (tptp.hAPP_f721434149i_bool tptp.cOMBC_722552198t_bool (tptp.hAPP_f966656047t_bool (tptp.cOMBB_1869811296e_indi tptp.ord_less_nat) tptp.h)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat N_1) tptp.one_one_nat)))) tptp.lab)) tptp.lba)))))) (not (forall ((N_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N_1) (tptp.hAPP_f846027769ol_nat tptp.finite1672073426e_indi tptp.top_to788185952i_bool))) (=> (forall ((M tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N_1)) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_A1299015393le_alt (tptp.hAPP_A1146194953le_alt tptp.produc1590937303le_alt tptp.b) tptp.a)) (tptp.hAPP_f2008608496t_bool tptp.f (tptp.hAPP_f480276746t_bool (tptp.hAPP_f601594885t_bool tptp.cOMBC_750853729t_bool (tptp.hAPP_f1344464862t_bool (tptp.hAPP_f1908974253t_bool tptp.cOMBC_156709173t_bool (tptp.hAPP_f668886383t_bool (tptp.cOMBB_1061985500e_indi tptp.if_fun523439385t_bool) (tptp.hAPP_n34002993i_bool (tptp.hAPP_f721434149i_bool tptp.cOMBC_722552198t_bool (tptp.hAPP_f966656047t_bool (tptp.cOMBB_1869811296e_indi tptp.ord_less_nat) tptp.h)) M))) tptp.lab)) tptp.lba)))))) (not (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_A1299015393le_alt (tptp.hAPP_A1146194953le_alt tptp.produc1590937303le_alt tptp.a) tptp.b)) (tptp.hAPP_f2008608496t_bool tptp.f (tptp.hAPP_f480276746t_bool (tptp.hAPP_f601594885t_bool tptp.cOMBC_750853729t_bool (tptp.hAPP_f1344464862t_bool (tptp.hAPP_f1908974253t_bool tptp.cOMBC_156709173t_bool (tptp.hAPP_f668886383t_bool (tptp.cOMBB_1061985500e_indi tptp.if_fun523439385t_bool) (tptp.hAPP_n34002993i_bool (tptp.hAPP_f721434149i_bool tptp.cOMBC_722552198t_bool (tptp.hAPP_f966656047t_bool (tptp.cOMBB_1869811296e_indi tptp.ord_less_nat) tptp.h)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat N_1) tptp.one_one_nat)))) tptp.lab)) tptp.lba))))))))) (forall ((X_19 tptp.nat) (Y_19 tptp.nat)) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_19) Y_19))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_19) X_19)))) (forall ((X_2 tptp.fun_Pr2067565481t_bool) (F tptp.fun_fu638310559l_bool) (G tptp.fun_fu638310559l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool F) G)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_f52567537l_bool F X_2)) (tptp.hAPP_f52567537l_bool G X_2))))) (forall ((X_2 tptp.fun_fu2114379172t_bool) (F tptp.fun_fu2098777574l_bool) (G tptp.fun_fu2098777574l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool F) G)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_f1572141188l_bool F X_2)) (tptp.hAPP_f1572141188l_bool G X_2))))) (forall ((X_2 tptp.fun_Ar274636406t_bool) (F tptp.fun_fu3835832l_bool) (G tptp.fun_fu3835832l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool F) G)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_f995490902l_bool F X_2)) (tptp.hAPP_f995490902l_bool G X_2))))) (forall ((X_2 tptp.produc472769767le_alt) (F tptp.fun_Pr2067565481t_bool) (G tptp.fun_Pr2067565481t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool F) G)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_P1178790471t_bool F X_2)) (tptp.hAPP_P1178790471t_bool G X_2))))) (forall ((X_2 tptp.arrow_856714788e_indi) (F tptp.fun_Ar1809396326i_bool) (G tptp.fun_Ar1809396326i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool F) G)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_A997847300i_bool F X_2)) (tptp.hAPP_A997847300i_bool G X_2))))) (forall ((X_2 tptp.product_unit) (F tptp.fun_Pr1643180309t_bool) (G tptp.fun_Pr1643180309t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool F) G)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_P1676879539t_bool F X_2)) (tptp.hAPP_P1676879539t_bool G X_2))))) (forall ((X_2 tptp.arrow_1893660431le_alt) (F tptp.fun_Ar331856045t_bool) (G tptp.fun_Ar331856045t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool F) G)) (tptp.hBOOL (tptp.hAPP_f739344229l_bool (tptp.hAPP_f1549168575l_bool tptp.ord_le1779845435t_bool (tptp.hAPP_A2063800319t_bool F X_2)) (tptp.hAPP_A2063800319t_bool G X_2))))) (forall ((X_2 tptp.nat) (F tptp.fun_nat_bool) (G tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool F) G)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_nat_bool F X_2)) (tptp.hAPP_nat_bool G X_2))))) (forall ((Z_2 tptp.fun_fu638310559l_bool) (Y_2 tptp.fun_fu638310559l_bool) (X_2 tptp.fun_fu638310559l_bool)) (let ((_let_1 (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool Z_2))) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool Y_2) X_2)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool _let_1 Y_2)) (tptp.hBOOL (tptp.hAPP_f182583295l_bool _let_1 X_2)))))) (forall ((Z_2 tptp.fun_fu2098777574l_bool) (Y_2 tptp.fun_fu2098777574l_bool) (X_2 tptp.fun_fu2098777574l_bool)) (let ((_let_1 (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool Z_2))) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool Y_2) X_2)) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool _let_1 Y_2)) (tptp.hBOOL (tptp.hAPP_f975209902l_bool _let_1 X_2)))))) (forall ((Z_2 tptp.fun_fu3835832l_bool) (Y_2 tptp.fun_fu3835832l_bool) (X_2 tptp.fun_fu3835832l_bool)) (let ((_let_1 (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool Z_2))) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool Y_2) X_2)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool _let_1 Y_2)) (tptp.hBOOL (tptp.hAPP_f73423488l_bool _let_1 X_2)))))) (forall ((Z_2 tptp.fun_Pr2067565481t_bool) (Y_2 tptp.fun_Pr2067565481t_bool) (X_2 tptp.fun_Pr2067565481t_bool)) (let ((_let_1 (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool Z_2))) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool Y_2) X_2)) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_1 Y_2)) (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_1 X_2)))))) (forall ((Z_2 tptp.bool) (Y_2 tptp.bool) (X_2 tptp.bool)) (let ((_let_1 (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Z_2))) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Y_2) X_2)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 Y_2)) (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 X_2)))))) (forall ((Z_2 tptp.fun_Ar1809396326i_bool) (Y_2 tptp.fun_Ar1809396326i_bool) (X_2 tptp.fun_Ar1809396326i_bool)) (let ((_let_1 (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool Z_2))) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool Y_2) X_2)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool _let_1 Y_2)) (tptp.hBOOL (tptp.hAPP_f584385070l_bool _let_1 X_2)))))) (forall ((Z_2 tptp.fun_Pr1643180309t_bool) (Y_2 tptp.fun_Pr1643180309t_bool) (X_2 tptp.fun_Pr1643180309t_bool)) (let ((_let_1 (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool Z_2))) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool Y_2) X_2)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool _let_1 Y_2)) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool _let_1 X_2)))))) (forall ((Z_2 tptp.fun_Ar331856045t_bool) (Y_2 tptp.fun_Ar331856045t_bool) (X_2 tptp.fun_Ar331856045t_bool)) (let ((_let_1 (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool Z_2))) (=> (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool Y_2) X_2)) (=> (tptp.hBOOL (tptp.hAPP_f1452856589l_bool _let_1 Y_2)) (tptp.hBOOL (tptp.hAPP_f1452856589l_bool _let_1 X_2)))))) (forall ((Z_7 tptp.nat) (Y_18 tptp.nat) (X_18 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Z_7))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_18) X_18)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Y_18)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 X_18)))))) (forall ((Z_2 tptp.fun_nat_bool) (Y_2 tptp.fun_nat_bool) (X_2 tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Z_2))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Y_2) X_2)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 Y_2)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 X_2)))))) (forall ((Y_2 tptp.fun_fu638310559l_bool) (X_2 tptp.fun_fu638310559l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool Y_2) X_2)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool X_2) Y_2)) (= X_2 Y_2)))) (forall ((Y_2 tptp.fun_fu2098777574l_bool) (X_2 tptp.fun_fu2098777574l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool Y_2) X_2)) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool X_2) Y_2)) (= X_2 Y_2)))) (forall ((Y_2 tptp.fun_fu3835832l_bool) (X_2 tptp.fun_fu3835832l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool Y_2) X_2)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool X_2) Y_2)) (= X_2 Y_2)))) (forall ((Y_2 tptp.fun_Pr2067565481t_bool) (X_2 tptp.fun_Pr2067565481t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool Y_2) X_2)) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool X_2) Y_2)) (= X_2 Y_2)))) (forall ((Y_2 tptp.bool) (X_2 tptp.bool)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Y_2) X_2)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool X_2) Y_2)) (= (tptp.hBOOL X_2) (tptp.hBOOL Y_2))))) (forall ((Y_2 tptp.fun_Ar1809396326i_bool) (X_2 tptp.fun_Ar1809396326i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool Y_2) X_2)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool X_2) Y_2)) (= X_2 Y_2)))) (forall ((Y_2 tptp.fun_Pr1643180309t_bool) (X_2 tptp.fun_Pr1643180309t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool Y_2) X_2)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool X_2) Y_2)) (= X_2 Y_2)))) (forall ((Y_2 tptp.fun_Ar331856045t_bool) (X_2 tptp.fun_Ar331856045t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool Y_2) X_2)) (=> (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool X_2) Y_2)) (= X_2 Y_2)))) (forall ((Y_17 tptp.nat) (X_17 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_17) X_17)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_17) Y_17)) (= X_17 Y_17)))) (forall ((Y_2 tptp.fun_nat_bool) (X_2 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Y_2) X_2)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool X_2) Y_2)) (= X_2 Y_2)))) (forall ((Z_2 tptp.fun_fu638310559l_bool) (X_2 tptp.fun_fu638310559l_bool) (Y_2 tptp.fun_fu638310559l_bool)) (let ((_let_1 (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool X_2))) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool _let_1 Y_2)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool Y_2) Z_2)) (tptp.hBOOL (tptp.hAPP_f182583295l_bool _let_1 Z_2)))))) (forall ((Z_2 tptp.fun_fu2098777574l_bool) (X_2 tptp.fun_fu2098777574l_bool) (Y_2 tptp.fun_fu2098777574l_bool)) (let ((_let_1 (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool X_2))) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool _let_1 Y_2)) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool Y_2) Z_2)) (tptp.hBOOL (tptp.hAPP_f975209902l_bool _let_1 Z_2)))))) (forall ((Z_2 tptp.fun_fu3835832l_bool) (X_2 tptp.fun_fu3835832l_bool) (Y_2 tptp.fun_fu3835832l_bool)) (let ((_let_1 (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool X_2))) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool _let_1 Y_2)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool Y_2) Z_2)) (tptp.hBOOL (tptp.hAPP_f73423488l_bool _let_1 Z_2)))))) (forall ((Z_2 tptp.fun_Pr2067565481t_bool) (X_2 tptp.fun_Pr2067565481t_bool) (Y_2 tptp.fun_Pr2067565481t_bool)) (let ((_let_1 (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool X_2))) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_1 Y_2)) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool Y_2) Z_2)) (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_1 Z_2)))))) (forall ((Z_2 tptp.bool) (X_2 tptp.bool) (Y_2 tptp.bool)) (let ((_let_1 (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool X_2))) (=> (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 Y_2)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Y_2) Z_2)) (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 Z_2)))))) (forall ((Z_2 tptp.fun_Ar1809396326i_bool) (X_2 tptp.fun_Ar1809396326i_bool) (Y_2 tptp.fun_Ar1809396326i_bool)) (let ((_let_1 (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool X_2))) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool _let_1 Y_2)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool Y_2) Z_2)) (tptp.hBOOL (tptp.hAPP_f584385070l_bool _let_1 Z_2)))))) (forall ((Z_2 tptp.fun_Pr1643180309t_bool) (X_2 tptp.fun_Pr1643180309t_bool) (Y_2 tptp.fun_Pr1643180309t_bool)) (let ((_let_1 (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool X_2))) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool _let_1 Y_2)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool Y_2) Z_2)) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool _let_1 Z_2)))))) (forall ((Z_2 tptp.fun_Ar331856045t_bool) (X_2 tptp.fun_Ar331856045t_bool) (Y_2 tptp.fun_Ar331856045t_bool)) (let ((_let_1 (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool X_2))) (=> (tptp.hBOOL (tptp.hAPP_f1452856589l_bool _let_1 Y_2)) (=> (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool Y_2) Z_2)) (tptp.hBOOL (tptp.hAPP_f1452856589l_bool _let_1 Z_2)))))) (forall ((Z_6 tptp.nat) (X_16 tptp.nat) (Y_16 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_16))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Y_16)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_16) Z_6)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Z_6)))))) (forall ((Z_2 tptp.fun_nat_bool) (X_2 tptp.fun_nat_bool) (Y_2 tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool X_2))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 Y_2)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Y_2) Z_2)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 Z_2)))))) (forall ((X_2 tptp.fun_fu638310559l_bool) (Y_2 tptp.fun_fu638310559l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool X_2) Y_2)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool Y_2) X_2)) (= X_2 Y_2)))) (forall ((X_2 tptp.fun_fu2098777574l_bool) (Y_2 tptp.fun_fu2098777574l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool X_2) Y_2)) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool Y_2) X_2)) (= X_2 Y_2)))) (forall ((X_2 tptp.fun_fu3835832l_bool) (Y_2 tptp.fun_fu3835832l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool X_2) Y_2)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool Y_2) X_2)) (= X_2 Y_2)))) (forall ((X_2 tptp.fun_Pr2067565481t_bool) (Y_2 tptp.fun_Pr2067565481t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool X_2) Y_2)) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool Y_2) X_2)) (= X_2 Y_2)))) (forall ((X_2 tptp.bool) (Y_2 tptp.bool)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool X_2) Y_2)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Y_2) X_2)) (= (tptp.hBOOL X_2) (tptp.hBOOL Y_2))))) (forall ((X_2 tptp.fun_Ar1809396326i_bool) (Y_2 tptp.fun_Ar1809396326i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool X_2) Y_2)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool Y_2) X_2)) (= X_2 Y_2)))) (forall ((X_2 tptp.fun_Pr1643180309t_bool) (Y_2 tptp.fun_Pr1643180309t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool X_2) Y_2)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool Y_2) X_2)) (= X_2 Y_2)))) (forall ((X_2 tptp.fun_Ar331856045t_bool) (Y_2 tptp.fun_Ar331856045t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool X_2) Y_2)) (=> (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool Y_2) X_2)) (= X_2 Y_2)))) (forall ((X_15 tptp.nat) (Y_15 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_15) Y_15)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_15) X_15)) (= X_15 Y_15)))) (forall ((X_2 tptp.fun_nat_bool) (Y_2 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool X_2) Y_2)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Y_2) X_2)) (= X_2 Y_2)))) (forall ((Ca tptp.fun_fu638310559l_bool) (Ba tptp.fun_fu638310559l_bool) (Aa tptp.fun_fu638310559l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool Ba) Aa)) (=> (= Ba Ca) (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool Ca) Aa))))) (forall ((Ca tptp.fun_fu2098777574l_bool) (Ba tptp.fun_fu2098777574l_bool) (Aa tptp.fun_fu2098777574l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool Ba) Aa)) (=> (= Ba Ca) (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool Ca) Aa))))) (forall ((Ca tptp.fun_fu3835832l_bool) (Ba tptp.fun_fu3835832l_bool) (Aa tptp.fun_fu3835832l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool Ba) Aa)) (=> (= Ba Ca) (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool Ca) Aa))))) (forall ((Ca tptp.fun_Pr2067565481t_bool) (Ba tptp.fun_Pr2067565481t_bool) (Aa tptp.fun_Pr2067565481t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool Ba) Aa)) (=> (= Ba Ca) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool Ca) Aa))))) (forall ((Ca tptp.bool) (Ba tptp.bool) (Aa tptp.bool)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Ba) Aa)) (=> (= (tptp.hBOOL Ba) (tptp.hBOOL Ca)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Ca) Aa))))) (forall ((Ca tptp.fun_Ar1809396326i_bool) (Ba tptp.fun_Ar1809396326i_bool) (Aa tptp.fun_Ar1809396326i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool Ba) Aa)) (=> (= Ba Ca) (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool Ca) Aa))))) (forall ((Ca tptp.fun_Pr1643180309t_bool) (Ba tptp.fun_Pr1643180309t_bool) (Aa tptp.fun_Pr1643180309t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool Ba) Aa)) (=> (= Ba Ca) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool Ca) Aa))))) (forall ((Ca tptp.fun_Ar331856045t_bool) (Ba tptp.fun_Ar331856045t_bool) (Aa tptp.fun_Ar331856045t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool Ba) Aa)) (=> (= Ba Ca) (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool Ca) Aa))))) (forall ((C_20 tptp.nat) (B_24 tptp.nat) (A_26 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat B_24) A_26)) (=> (= B_24 C_20) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat C_20) A_26))))) (forall ((Ca tptp.fun_nat_bool) (Ba tptp.fun_nat_bool) (Aa tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Ba) Aa)) (=> (= Ba Ca) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Ca) Aa))))) (forall ((Ca tptp.fun_fu638310559l_bool) (Aa tptp.fun_fu638310559l_bool) (Ba tptp.fun_fu638310559l_bool)) (let ((_let_1 (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool Aa))) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool _let_1 Ba)) (=> (= Ba Ca) (tptp.hBOOL (tptp.hAPP_f182583295l_bool _let_1 Ca)))))) (forall ((Ca tptp.fun_fu2098777574l_bool) (Aa tptp.fun_fu2098777574l_bool) (Ba tptp.fun_fu2098777574l_bool)) (let ((_let_1 (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool Aa))) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool _let_1 Ba)) (=> (= Ba Ca) (tptp.hBOOL (tptp.hAPP_f975209902l_bool _let_1 Ca)))))) (forall ((Ca tptp.fun_fu3835832l_bool) (Aa tptp.fun_fu3835832l_bool) (Ba tptp.fun_fu3835832l_bool)) (let ((_let_1 (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool Aa))) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool _let_1 Ba)) (=> (= Ba Ca) (tptp.hBOOL (tptp.hAPP_f73423488l_bool _let_1 Ca)))))) (forall ((Ca tptp.fun_Pr2067565481t_bool) (Aa tptp.fun_Pr2067565481t_bool) (Ba tptp.fun_Pr2067565481t_bool)) (let ((_let_1 (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool Aa))) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_1 Ba)) (=> (= Ba Ca) (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_1 Ca)))))) (forall ((Ca tptp.bool) (Aa tptp.bool) (Ba tptp.bool)) (let ((_let_1 (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Aa))) (=> (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 Ba)) (=> (= (tptp.hBOOL Ba) (tptp.hBOOL Ca)) (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 Ca)))))) (forall ((Ca tptp.fun_Ar1809396326i_bool) (Aa tptp.fun_Ar1809396326i_bool) (Ba tptp.fun_Ar1809396326i_bool)) (let ((_let_1 (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool Aa))) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool _let_1 Ba)) (=> (= Ba Ca) (tptp.hBOOL (tptp.hAPP_f584385070l_bool _let_1 Ca)))))) (forall ((Ca tptp.fun_Pr1643180309t_bool) (Aa tptp.fun_Pr1643180309t_bool) (Ba tptp.fun_Pr1643180309t_bool)) (let ((_let_1 (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool Aa))) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool _let_1 Ba)) (=> (= Ba Ca) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool _let_1 Ca)))))) (forall ((Ca tptp.fun_Ar331856045t_bool) (Aa tptp.fun_Ar331856045t_bool) (Ba tptp.fun_Ar331856045t_bool)) (let ((_let_1 (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool Aa))) (=> (tptp.hBOOL (tptp.hAPP_f1452856589l_bool _let_1 Ba)) (=> (= Ba Ca) (tptp.hBOOL (tptp.hAPP_f1452856589l_bool _let_1 Ca)))))) (forall ((C_19 tptp.nat) (A_25 tptp.nat) (B_23 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_25))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_23)) (=> (= B_23 C_19) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 C_19)))))) (forall ((Ca tptp.fun_nat_bool) (Aa tptp.fun_nat_bool) (Ba tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Aa))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 Ba)) (=> (= Ba Ca) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 Ca)))))) (forall ((Ca tptp.fun_fu638310559l_bool) (Aa tptp.fun_fu638310559l_bool) (Ba tptp.fun_fu638310559l_bool)) (let ((_let_1 (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool Ca))) (=> (= Aa Ba) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool _let_1 Ba)) (tptp.hBOOL (tptp.hAPP_f182583295l_bool _let_1 Aa)))))) (forall ((Ca tptp.fun_fu2098777574l_bool) (Aa tptp.fun_fu2098777574l_bool) (Ba tptp.fun_fu2098777574l_bool)) (let ((_let_1 (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool Ca))) (=> (= Aa Ba) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool _let_1 Ba)) (tptp.hBOOL (tptp.hAPP_f975209902l_bool _let_1 Aa)))))) (forall ((Ca tptp.fun_fu3835832l_bool) (Aa tptp.fun_fu3835832l_bool) (Ba tptp.fun_fu3835832l_bool)) (let ((_let_1 (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool Ca))) (=> (= Aa Ba) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool _let_1 Ba)) (tptp.hBOOL (tptp.hAPP_f73423488l_bool _let_1 Aa)))))) (forall ((Ca tptp.fun_Pr2067565481t_bool) (Aa tptp.fun_Pr2067565481t_bool) (Ba tptp.fun_Pr2067565481t_bool)) (let ((_let_1 (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool Ca))) (=> (= Aa Ba) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_1 Ba)) (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_1 Aa)))))) (forall ((Ca tptp.bool) (Ba tptp.bool) (Aa tptp.bool)) (let ((_let_1 (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Ca))) (=> (= (tptp.hBOOL Aa) (tptp.hBOOL Ba)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 Ba)) (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 Aa)))))) (forall ((Ca tptp.fun_Ar1809396326i_bool) (Aa tptp.fun_Ar1809396326i_bool) (Ba tptp.fun_Ar1809396326i_bool)) (let ((_let_1 (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool Ca))) (=> (= Aa Ba) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool _let_1 Ba)) (tptp.hBOOL (tptp.hAPP_f584385070l_bool _let_1 Aa)))))) (forall ((Ca tptp.fun_Pr1643180309t_bool) (Aa tptp.fun_Pr1643180309t_bool) (Ba tptp.fun_Pr1643180309t_bool)) (let ((_let_1 (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool Ca))) (=> (= Aa Ba) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool _let_1 Ba)) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool _let_1 Aa)))))) (forall ((Ca tptp.fun_Ar331856045t_bool) (Aa tptp.fun_Ar331856045t_bool) (Ba tptp.fun_Ar331856045t_bool)) (let ((_let_1 (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool Ca))) (=> (= Aa Ba) (=> (tptp.hBOOL (tptp.hAPP_f1452856589l_bool _let_1 Ba)) (tptp.hBOOL (tptp.hAPP_f1452856589l_bool _let_1 Aa)))))) (forall ((C_18 tptp.nat) (A_24 tptp.nat) (B_22 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat C_18))) (=> (= A_24 B_22) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_22)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A_24)))))) (forall ((Ca tptp.fun_nat_bool) (Aa tptp.fun_nat_bool) (Ba tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Ca))) (=> (= Aa Ba) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 Ba)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 Aa)))))) (forall ((Ca tptp.fun_fu638310559l_bool) (Aa tptp.fun_fu638310559l_bool) (Ba tptp.fun_fu638310559l_bool)) (=> (= Aa Ba) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool Ba) Ca)) (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool Aa) Ca))))) (forall ((Ca tptp.fun_fu2098777574l_bool) (Aa tptp.fun_fu2098777574l_bool) (Ba tptp.fun_fu2098777574l_bool)) (=> (= Aa Ba) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool Ba) Ca)) (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool Aa) Ca))))) (forall ((Ca tptp.fun_fu3835832l_bool) (Aa tptp.fun_fu3835832l_bool) (Ba tptp.fun_fu3835832l_bool)) (=> (= Aa Ba) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool Ba) Ca)) (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool Aa) Ca))))) (forall ((Ca tptp.fun_Pr2067565481t_bool) (Aa tptp.fun_Pr2067565481t_bool) (Ba tptp.fun_Pr2067565481t_bool)) (=> (= Aa Ba) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool Ba) Ca)) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool Aa) Ca))))) (forall ((Ca tptp.bool) (Ba tptp.bool) (Aa tptp.bool)) (=> (= (tptp.hBOOL Aa) (tptp.hBOOL Ba)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Ba) Ca)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Aa) Ca))))) (forall ((Ca tptp.fun_Ar1809396326i_bool) (Aa tptp.fun_Ar1809396326i_bool) (Ba tptp.fun_Ar1809396326i_bool)) (=> (= Aa Ba) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool Ba) Ca)) (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool Aa) Ca))))) (forall ((Ca tptp.fun_Pr1643180309t_bool) (Aa tptp.fun_Pr1643180309t_bool) (Ba tptp.fun_Pr1643180309t_bool)) (=> (= Aa Ba) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool Ba) Ca)) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool Aa) Ca))))) (forall ((Ca tptp.fun_Ar331856045t_bool) (Aa tptp.fun_Ar331856045t_bool) (Ba tptp.fun_Ar331856045t_bool)) (=> (= Aa Ba) (=> (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool Ba) Ca)) (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool Aa) Ca))))) (forall ((C_17 tptp.nat) (A_23 tptp.nat) (B_21 tptp.nat)) (=> (= A_23 B_21) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat B_21) C_17)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_23) C_17))))) (forall ((Ca tptp.fun_nat_bool) (Aa tptp.fun_nat_bool) (Ba tptp.fun_nat_bool)) (=> (= Aa Ba) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Ba) Ca)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Aa) Ca))))) (forall ((Y_2 tptp.fun_fu638310559l_bool) (X_2 tptp.fun_fu638310559l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool Y_2) X_2)) (= (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool X_2) Y_2)) (= X_2 Y_2)))) (forall ((Y_2 tptp.fun_fu2098777574l_bool) (X_2 tptp.fun_fu2098777574l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool Y_2) X_2)) (= (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool X_2) Y_2)) (= X_2 Y_2)))) (forall ((Y_2 tptp.fun_fu3835832l_bool) (X_2 tptp.fun_fu3835832l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool Y_2) X_2)) (= (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool X_2) Y_2)) (= X_2 Y_2)))) (forall ((Y_2 tptp.fun_Pr2067565481t_bool) (X_2 tptp.fun_Pr2067565481t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool Y_2) X_2)) (= (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool X_2) Y_2)) (= X_2 Y_2)))) (forall ((Y_2 tptp.bool) (X_2 tptp.bool)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Y_2) X_2)) (= (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool X_2) Y_2)) (= (tptp.hBOOL X_2) (tptp.hBOOL Y_2))))) (forall ((Y_2 tptp.fun_Ar1809396326i_bool) (X_2 tptp.fun_Ar1809396326i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool Y_2) X_2)) (= (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool X_2) Y_2)) (= X_2 Y_2)))) (forall ((Y_2 tptp.fun_Pr1643180309t_bool) (X_2 tptp.fun_Pr1643180309t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool Y_2) X_2)) (= (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool X_2) Y_2)) (= X_2 Y_2)))) (forall ((Y_2 tptp.fun_Ar331856045t_bool) (X_2 tptp.fun_Ar331856045t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool Y_2) X_2)) (= (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool X_2) Y_2)) (= X_2 Y_2)))) (forall ((Y_2 tptp.nat) (X_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_2) X_2)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_2) Y_2)) (= X_2 Y_2)))) (forall ((Y_2 tptp.fun_nat_bool) (X_2 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Y_2) X_2)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool X_2) Y_2)) (= X_2 Y_2)))) (forall ((X_2 tptp.fun_Pr2067565481t_bool) (F tptp.fun_fu638310559l_bool) (G tptp.fun_fu638310559l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool F) G)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_f52567537l_bool F X_2)) (tptp.hAPP_f52567537l_bool G X_2))))) (forall ((X_2 tptp.fun_fu2114379172t_bool) (F tptp.fun_fu2098777574l_bool) (G tptp.fun_fu2098777574l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool F) G)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_f1572141188l_bool F X_2)) (tptp.hAPP_f1572141188l_bool G X_2))))) (forall ((X_2 tptp.fun_Ar274636406t_bool) (F tptp.fun_fu3835832l_bool) (G tptp.fun_fu3835832l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool F) G)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_f995490902l_bool F X_2)) (tptp.hAPP_f995490902l_bool G X_2))))) (forall ((X_2 tptp.produc472769767le_alt) (F tptp.fun_Pr2067565481t_bool) (G tptp.fun_Pr2067565481t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool F) G)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_P1178790471t_bool F X_2)) (tptp.hAPP_P1178790471t_bool G X_2))))) (forall ((X_2 tptp.arrow_856714788e_indi) (F tptp.fun_Ar1809396326i_bool) (G tptp.fun_Ar1809396326i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool F) G)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_A997847300i_bool F X_2)) (tptp.hAPP_A997847300i_bool G X_2))))) (forall ((X_2 tptp.product_unit) (F tptp.fun_Pr1643180309t_bool) (G tptp.fun_Pr1643180309t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool F) G)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_P1676879539t_bool F X_2)) (tptp.hAPP_P1676879539t_bool G X_2))))) (forall ((X_2 tptp.arrow_1893660431le_alt) (F tptp.fun_Ar331856045t_bool) (G tptp.fun_Ar331856045t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool F) G)) (tptp.hBOOL (tptp.hAPP_f739344229l_bool (tptp.hAPP_f1549168575l_bool tptp.ord_le1779845435t_bool (tptp.hAPP_A2063800319t_bool F X_2)) (tptp.hAPP_A2063800319t_bool G X_2))))) (forall ((X_2 tptp.nat) (F tptp.fun_nat_bool) (G tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool F) G)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_nat_bool F X_2)) (tptp.hAPP_nat_bool G X_2))))) (forall ((X_2 tptp.fun_fu638310559l_bool) (Y_2 tptp.fun_fu638310559l_bool)) (=> (= X_2 Y_2) (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool X_2) Y_2)))) (forall ((X_2 tptp.fun_fu2098777574l_bool) (Y_2 tptp.fun_fu2098777574l_bool)) (=> (= X_2 Y_2) (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool X_2) Y_2)))) (forall ((X_2 tptp.fun_fu3835832l_bool) (Y_2 tptp.fun_fu3835832l_bool)) (=> (= X_2 Y_2) (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool X_2) Y_2)))) (forall ((X_2 tptp.fun_Pr2067565481t_bool) (Y_2 tptp.fun_Pr2067565481t_bool)) (=> (= X_2 Y_2) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool X_2) Y_2)))) (forall ((Y_2 tptp.bool) (X_2 tptp.bool)) (=> (= (tptp.hBOOL X_2) (tptp.hBOOL Y_2)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool X_2) Y_2)))) (forall ((X_2 tptp.fun_Ar1809396326i_bool) (Y_2 tptp.fun_Ar1809396326i_bool)) (=> (= X_2 Y_2) (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool X_2) Y_2)))) (forall ((X_2 tptp.fun_Pr1643180309t_bool) (Y_2 tptp.fun_Pr1643180309t_bool)) (=> (= X_2 Y_2) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool X_2) Y_2)))) (forall ((X_2 tptp.fun_Ar331856045t_bool) (Y_2 tptp.fun_Ar331856045t_bool)) (=> (= X_2 Y_2) (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool X_2) Y_2)))) (forall ((X_14 tptp.nat) (Y_14 tptp.nat)) (=> (= X_14 Y_14) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_14) Y_14)))) (forall ((X_2 tptp.fun_nat_bool) (Y_2 tptp.fun_nat_bool)) (=> (= X_2 Y_2) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool X_2) Y_2)))) (forall ((X_2 tptp.fun_fu638310559l_bool) (Y_2 tptp.fun_fu638310559l_bool)) (= (= X_2 Y_2) (and (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool X_2) Y_2)) (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool Y_2) X_2))))) (forall ((X_2 tptp.fun_fu2098777574l_bool) (Y_2 tptp.fun_fu2098777574l_bool)) (= (= X_2 Y_2) (and (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool X_2) Y_2)) (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool Y_2) X_2))))) (forall ((X_2 tptp.fun_fu3835832l_bool) (Y_2 tptp.fun_fu3835832l_bool)) (= (= X_2 Y_2) (and (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool X_2) Y_2)) (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool Y_2) X_2))))) (forall ((X_2 tptp.fun_Pr2067565481t_bool) (Y_2 tptp.fun_Pr2067565481t_bool)) (= (= X_2 Y_2) (and (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool X_2) Y_2)) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool Y_2) X_2))))) (forall ((Y_2 tptp.bool) (X_2 tptp.bool)) (= (= (tptp.hBOOL X_2) (tptp.hBOOL Y_2)) (and (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool X_2) Y_2)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Y_2) X_2))))) (forall ((X_2 tptp.fun_Ar1809396326i_bool) (Y_2 tptp.fun_Ar1809396326i_bool)) (= (= X_2 Y_2) (and (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool X_2) Y_2)) (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool Y_2) X_2))))) (forall ((X_2 tptp.fun_Pr1643180309t_bool) (Y_2 tptp.fun_Pr1643180309t_bool)) (= (= X_2 Y_2) (and (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool X_2) Y_2)) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool Y_2) X_2))))) (forall ((X_2 tptp.fun_Ar331856045t_bool) (Y_2 tptp.fun_Ar331856045t_bool)) (= (= X_2 Y_2) (and (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool X_2) Y_2)) (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool Y_2) X_2))))) (forall ((X_2 tptp.nat) (Y_2 tptp.nat)) (= (= X_2 Y_2) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_2) Y_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_2) X_2))))) (forall ((X_2 tptp.fun_nat_bool) (Y_2 tptp.fun_nat_bool)) (= (= X_2 Y_2) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool X_2) Y_2)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Y_2) X_2))))) (forall ((X_13 tptp.nat) (Y_13 tptp.nat)) (or (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_13) Y_13)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_13) X_13)))) (forall ((F tptp.fun_fu638310559l_bool) (G tptp.fun_fu638310559l_bool)) (= (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool F) G)) (forall ((X_1 tptp.fun_Pr2067565481t_bool)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_f52567537l_bool F X_1)) (tptp.hAPP_f52567537l_bool G X_1)))))) (forall ((F tptp.fun_fu2098777574l_bool) (G tptp.fun_fu2098777574l_bool)) (= (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool F) G)) (forall ((X_1 tptp.fun_fu2114379172t_bool)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_f1572141188l_bool F X_1)) (tptp.hAPP_f1572141188l_bool G X_1)))))) (forall ((F tptp.fun_fu3835832l_bool) (G tptp.fun_fu3835832l_bool)) (= (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool F) G)) (forall ((X_1 tptp.fun_Ar274636406t_bool)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_f995490902l_bool F X_1)) (tptp.hAPP_f995490902l_bool G X_1)))))) (forall ((F tptp.fun_Pr2067565481t_bool) (G tptp.fun_Pr2067565481t_bool)) (= (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool F) G)) (forall ((X_1 tptp.produc472769767le_alt)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_P1178790471t_bool F X_1)) (tptp.hAPP_P1178790471t_bool G X_1)))))) (forall ((F tptp.fun_Ar1809396326i_bool) (G tptp.fun_Ar1809396326i_bool)) (= (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool F) G)) (forall ((X_1 tptp.arrow_856714788e_indi)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_A997847300i_bool F X_1)) (tptp.hAPP_A997847300i_bool G X_1)))))) (forall ((F tptp.fun_Pr1643180309t_bool) (G tptp.fun_Pr1643180309t_bool)) (= (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool F) G)) (forall ((X_1 tptp.product_unit)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_P1676879539t_bool F X_1)) (tptp.hAPP_P1676879539t_bool G X_1)))))) (forall ((F tptp.fun_Ar331856045t_bool) (G tptp.fun_Ar331856045t_bool)) (= (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool F) G)) (forall ((X_1 tptp.arrow_1893660431le_alt)) (tptp.hBOOL (tptp.hAPP_f739344229l_bool (tptp.hAPP_f1549168575l_bool tptp.ord_le1779845435t_bool (tptp.hAPP_A2063800319t_bool F X_1)) (tptp.hAPP_A2063800319t_bool G X_1)))))) (forall ((F tptp.fun_nat_bool) (G tptp.fun_nat_bool)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool F) G)) (forall ((X_1 tptp.nat)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_nat_bool F X_1)) (tptp.hAPP_nat_bool G X_1)))))) (forall ((X_2 tptp.nat) (Y_2 tptp.nat)) (= (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_2) Y_2))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_2) X_2)))) (forall ((X_2 tptp.nat) (Y_2 tptp.nat)) (= (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_2) Y_2))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Y_2) X_2)))) (forall ((X_12 tptp.nat) (Y_12 tptp.nat)) (or (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_12) Y_12)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Y_12) X_12)))) (forall ((X_2 tptp.fun_Pr1643180309t_bool) (Y_2 tptp.fun_Pr1643180309t_bool)) (= (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool X_2) Y_2)) (and (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool X_2) Y_2)) (not (= X_2 Y_2))))) (forall ((X_2 tptp.fun_Ar1809396326i_bool) (Y_2 tptp.fun_Ar1809396326i_bool)) (= (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool X_2) Y_2)) (and (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool X_2) Y_2)) (not (= X_2 Y_2))))) (forall ((X_2 tptp.fun_fu638310559l_bool) (Y_2 tptp.fun_fu638310559l_bool)) (= (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1727358153l_bool X_2) Y_2)) (and (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool X_2) Y_2)) (not (= X_2 Y_2))))) (forall ((X_2 tptp.fun_fu2098777574l_bool) (Y_2 tptp.fun_fu2098777574l_bool)) (= (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le119247420l_bool X_2) Y_2)) (and (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool X_2) Y_2)) (not (= X_2 Y_2))))) (forall ((X_2 tptp.fun_fu3835832l_bool) (Y_2 tptp.fun_fu3835832l_bool)) (= (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1959568910l_bool X_2) Y_2)) (and (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool X_2) Y_2)) (not (= X_2 Y_2))))) (forall ((X_2 tptp.fun_Pr2067565481t_bool) (Y_2 tptp.fun_Pr2067565481t_bool)) (= (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1478665215t_bool X_2) Y_2)) (and (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool X_2) Y_2)) (not (= X_2 Y_2))))) (forall ((X_2 tptp.bool) (Y_2 tptp.bool)) (= (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_bool X_2) Y_2)) (and (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool X_2) Y_2)) (not (= (tptp.hBOOL X_2) (tptp.hBOOL Y_2)))))) (forall ((X_2 tptp.fun_Ar331856045t_bool) (Y_2 tptp.fun_Ar331856045t_bool)) (= (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le19409623t_bool X_2) Y_2)) (and (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool X_2) Y_2)) (not (= X_2 Y_2))))) (forall ((X_2 tptp.fun_nat_bool) (Y_2 tptp.fun_nat_bool)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool X_2) Y_2)) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool X_2) Y_2)) (not (= X_2 Y_2))))) (forall ((X_2 tptp.nat) (Y_2 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_2) Y_2)) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_2) Y_2)) (not (= X_2 Y_2))))) (forall ((X_2 tptp.fun_Pr1643180309t_bool) (Y_2 tptp.fun_Pr1643180309t_bool)) (= (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool X_2) Y_2)) (and (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool X_2) Y_2)) (not (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool Y_2) X_2)))))) (forall ((X_2 tptp.fun_Ar1809396326i_bool) (Y_2 tptp.fun_Ar1809396326i_bool)) (= (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool X_2) Y_2)) (and (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool X_2) Y_2)) (not (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool Y_2) X_2)))))) (forall ((X_2 tptp.fun_fu638310559l_bool) (Y_2 tptp.fun_fu638310559l_bool)) (= (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1727358153l_bool X_2) Y_2)) (and (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool X_2) Y_2)) (not (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool Y_2) X_2)))))) (forall ((X_2 tptp.fun_fu2098777574l_bool) (Y_2 tptp.fun_fu2098777574l_bool)) (= (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le119247420l_bool X_2) Y_2)) (and (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool X_2) Y_2)) (not (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool Y_2) X_2)))))) (forall ((X_2 tptp.fun_fu3835832l_bool) (Y_2 tptp.fun_fu3835832l_bool)) (= (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1959568910l_bool X_2) Y_2)) (and (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool X_2) Y_2)) (not (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool Y_2) X_2)))))) (forall ((X_2 tptp.fun_Pr2067565481t_bool) (Y_2 tptp.fun_Pr2067565481t_bool)) (= (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1478665215t_bool X_2) Y_2)) (and (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool X_2) Y_2)) (not (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool Y_2) X_2)))))) (forall ((X_2 tptp.bool) (Y_2 tptp.bool)) (= (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_bool X_2) Y_2)) (and (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool X_2) Y_2)) (not (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Y_2) X_2)))))) (forall ((X_2 tptp.fun_Ar331856045t_bool) (Y_2 tptp.fun_Ar331856045t_bool)) (= (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le19409623t_bool X_2) Y_2)) (and (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool X_2) Y_2)) (not (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool Y_2) X_2)))))) (forall ((X_2 tptp.fun_nat_bool) (Y_2 tptp.fun_nat_bool)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool X_2) Y_2)) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool X_2) Y_2)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Y_2) X_2)))))) (forall ((X_2 tptp.nat) (Y_2 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_2) Y_2)) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_2) Y_2)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_2) X_2)))))) (forall ((X_2 tptp.fun_Pr1643180309t_bool) (Y_2 tptp.fun_Pr1643180309t_bool)) (= (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool X_2) Y_2)) (or (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool X_2) Y_2)) (= X_2 Y_2)))) (forall ((X_2 tptp.fun_Ar1809396326i_bool) (Y_2 tptp.fun_Ar1809396326i_bool)) (= (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool X_2) Y_2)) (or (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool X_2) Y_2)) (= X_2 Y_2)))) (forall ((X_2 tptp.fun_fu638310559l_bool) (Y_2 tptp.fun_fu638310559l_bool)) (= (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool X_2) Y_2)) (or (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1727358153l_bool X_2) Y_2)) (= X_2 Y_2)))) (forall ((X_2 tptp.fun_fu2098777574l_bool) (Y_2 tptp.fun_fu2098777574l_bool)) (= (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool X_2) Y_2)) (or (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le119247420l_bool X_2) Y_2)) (= X_2 Y_2)))) (forall ((X_2 tptp.fun_fu3835832l_bool) (Y_2 tptp.fun_fu3835832l_bool)) (= (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool X_2) Y_2)) (or (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1959568910l_bool X_2) Y_2)) (= X_2 Y_2)))) (forall ((X_2 tptp.fun_Pr2067565481t_bool) (Y_2 tptp.fun_Pr2067565481t_bool)) (= (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool X_2) Y_2)) (or (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1478665215t_bool X_2) Y_2)) (= X_2 Y_2)))) (forall ((X_2 tptp.bool) (Y_2 tptp.bool)) (= (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool X_2) Y_2)) (or (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_bool X_2) Y_2)) (= (tptp.hBOOL X_2) (tptp.hBOOL Y_2))))) (forall ((X_2 tptp.fun_Ar331856045t_bool) (Y_2 tptp.fun_Ar331856045t_bool)) (= (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool X_2) Y_2)) (or (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le19409623t_bool X_2) Y_2)) (= X_2 Y_2)))) (forall ((X_2 tptp.fun_nat_bool) (Y_2 tptp.fun_nat_bool)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool X_2) Y_2)) (or (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool X_2) Y_2)) (= X_2 Y_2)))) (forall ((X_2 tptp.nat) (Y_2 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_2) Y_2)) (or (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_2) Y_2)) (= X_2 Y_2)))) (forall ((X_11 tptp.nat) (Y_11 tptp.nat)) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_11) Y_11))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_11) X_11)))) (forall ((Y_10 tptp.nat) (X_10 tptp.nat)) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_10) X_10))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_10) Y_10)))) (forall ((X_2 tptp.nat) (Y_2 tptp.nat)) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_2) Y_2))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_2) Y_2)) (= X_2 Y_2)))) (forall ((Aa tptp.fun_Pr1643180309t_bool) (Ba tptp.fun_Pr1643180309t_bool)) (=> (not (= Aa Ba)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool Aa) Ba)) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool Aa) Ba))))) (forall ((Aa tptp.fun_Ar1809396326i_bool) (Ba tptp.fun_Ar1809396326i_bool)) (=> (not (= Aa Ba)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool Aa) Ba)) (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool Aa) Ba))))) (forall ((Aa tptp.fun_fu638310559l_bool) (Ba tptp.fun_fu638310559l_bool)) (=> (not (= Aa Ba)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool Aa) Ba)) (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1727358153l_bool Aa) Ba))))) (forall ((Aa tptp.fun_fu2098777574l_bool) (Ba tptp.fun_fu2098777574l_bool)) (=> (not (= Aa Ba)) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool Aa) Ba)) (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le119247420l_bool Aa) Ba))))) (forall ((Aa tptp.fun_fu3835832l_bool) (Ba tptp.fun_fu3835832l_bool)) (=> (not (= Aa Ba)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool Aa) Ba)) (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1959568910l_bool Aa) Ba))))) (forall ((Aa tptp.fun_Pr2067565481t_bool) (Ba tptp.fun_Pr2067565481t_bool)) (=> (not (= Aa Ba)) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool Aa) Ba)) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1478665215t_bool Aa) Ba))))) (forall ((Ba tptp.bool) (Aa tptp.bool)) (=> (not (= (tptp.hBOOL Aa) (tptp.hBOOL Ba))) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Aa) Ba)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_bool Aa) Ba))))) (forall ((Aa tptp.fun_Ar331856045t_bool) (Ba tptp.fun_Ar331856045t_bool)) (=> (not (= Aa Ba)) (=> (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool Aa) Ba)) (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le19409623t_bool Aa) Ba))))) (forall ((Aa tptp.fun_nat_bool) (Ba tptp.fun_nat_bool)) (=> (not (= Aa Ba)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Aa) Ba)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool Aa) Ba))))) (forall ((A_22 tptp.nat) (B_20 tptp.nat)) (=> (not (= A_22 B_20)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_22) B_20)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_22) B_20))))) (forall ((Aa tptp.fun_Pr1643180309t_bool) (Ba tptp.fun_Pr1643180309t_bool)) (=> (not (= Aa Ba)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool Ba) Aa)) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool Ba) Aa))))) (forall ((Aa tptp.fun_Ar1809396326i_bool) (Ba tptp.fun_Ar1809396326i_bool)) (=> (not (= Aa Ba)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool Ba) Aa)) (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool Ba) Aa))))) (forall ((Aa tptp.fun_fu638310559l_bool) (Ba tptp.fun_fu638310559l_bool)) (=> (not (= Aa Ba)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool Ba) Aa)) (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1727358153l_bool Ba) Aa))))) (forall ((Aa tptp.fun_fu2098777574l_bool) (Ba tptp.fun_fu2098777574l_bool)) (=> (not (= Aa Ba)) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool Ba) Aa)) (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le119247420l_bool Ba) Aa))))) (forall ((Aa tptp.fun_fu3835832l_bool) (Ba tptp.fun_fu3835832l_bool)) (=> (not (= Aa Ba)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool Ba) Aa)) (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1959568910l_bool Ba) Aa))))) (forall ((Aa tptp.fun_Pr2067565481t_bool) (Ba tptp.fun_Pr2067565481t_bool)) (=> (not (= Aa Ba)) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool Ba) Aa)) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1478665215t_bool Ba) Aa))))) (forall ((Ba tptp.bool) (Aa tptp.bool)) (=> (not (= (tptp.hBOOL Aa) (tptp.hBOOL Ba))) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Ba) Aa)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_bool Ba) Aa))))) (forall ((Aa tptp.fun_Ar331856045t_bool) (Ba tptp.fun_Ar331856045t_bool)) (=> (not (= Aa Ba)) (=> (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool Ba) Aa)) (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le19409623t_bool Ba) Aa))))) (forall ((Aa tptp.fun_nat_bool) (Ba tptp.fun_nat_bool)) (=> (not (= Aa Ba)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Ba) Aa)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool Ba) Aa))))) (forall ((A_21 tptp.nat) (B_19 tptp.nat)) (=> (not (= A_21 B_19)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat B_19) A_21)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat B_19) A_21))))) (forall ((Y_9 tptp.nat) (X_9 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_9) X_9)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_9) Y_9))))) (forall ((X_2 tptp.fun_Pr1643180309t_bool) (Y_2 tptp.fun_Pr1643180309t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool X_2) Y_2)) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool X_2) Y_2)))) (forall ((X_2 tptp.fun_Ar1809396326i_bool) (Y_2 tptp.fun_Ar1809396326i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool X_2) Y_2)) (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool X_2) Y_2)))) (forall ((X_2 tptp.fun_fu638310559l_bool) (Y_2 tptp.fun_fu638310559l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1727358153l_bool X_2) Y_2)) (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool X_2) Y_2)))) (forall ((X_2 tptp.fun_fu2098777574l_bool) (Y_2 tptp.fun_fu2098777574l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le119247420l_bool X_2) Y_2)) (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool X_2) Y_2)))) (forall ((X_2 tptp.fun_fu3835832l_bool) (Y_2 tptp.fun_fu3835832l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1959568910l_bool X_2) Y_2)) (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool X_2) Y_2)))) (forall ((X_2 tptp.fun_Pr2067565481t_bool) (Y_2 tptp.fun_Pr2067565481t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1478665215t_bool X_2) Y_2)) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool X_2) Y_2)))) (forall ((X_2 tptp.bool) (Y_2 tptp.bool)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_bool X_2) Y_2)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool X_2) Y_2)))) (forall ((X_2 tptp.fun_Ar331856045t_bool) (Y_2 tptp.fun_Ar331856045t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le19409623t_bool X_2) Y_2)) (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool X_2) Y_2)))) (forall ((X_2 tptp.fun_nat_bool) (Y_2 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool X_2) Y_2)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool X_2) Y_2)))) (forall ((X_8 tptp.nat) (Y_8 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_8) Y_8)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_8) Y_8)))) (forall ((X_2 tptp.nat) (Y_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_2) Y_2)) (= (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_2) Y_2))) (= X_2 Y_2)))) (forall ((X_2 tptp.fun_Pr1643180309t_bool) (Y_2 tptp.fun_Pr1643180309t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool X_2) Y_2)) (or (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool X_2) Y_2)) (= X_2 Y_2)))) (forall ((X_2 tptp.fun_Ar1809396326i_bool) (Y_2 tptp.fun_Ar1809396326i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool X_2) Y_2)) (or (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool X_2) Y_2)) (= X_2 Y_2)))) (forall ((X_2 tptp.fun_fu638310559l_bool) (Y_2 tptp.fun_fu638310559l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool X_2) Y_2)) (or (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1727358153l_bool X_2) Y_2)) (= X_2 Y_2)))) (forall ((X_2 tptp.fun_fu2098777574l_bool) (Y_2 tptp.fun_fu2098777574l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool X_2) Y_2)) (or (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le119247420l_bool X_2) Y_2)) (= X_2 Y_2)))) (forall ((X_2 tptp.fun_fu3835832l_bool) (Y_2 tptp.fun_fu3835832l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool X_2) Y_2)) (or (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1959568910l_bool X_2) Y_2)) (= X_2 Y_2)))) (forall ((X_2 tptp.fun_Pr2067565481t_bool) (Y_2 tptp.fun_Pr2067565481t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool X_2) Y_2)) (or (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1478665215t_bool X_2) Y_2)) (= X_2 Y_2)))) (forall ((X_2 tptp.bool) (Y_2 tptp.bool)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool X_2) Y_2)) (or (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_bool X_2) Y_2)) (= (tptp.hBOOL X_2) (tptp.hBOOL Y_2))))) (forall ((X_2 tptp.fun_Ar331856045t_bool) (Y_2 tptp.fun_Ar331856045t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool X_2) Y_2)) (or (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le19409623t_bool X_2) Y_2)) (= X_2 Y_2)))) (forall ((X_2 tptp.fun_nat_bool) (Y_2 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool X_2) Y_2)) (or (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool X_2) Y_2)) (= X_2 Y_2)))) (forall ((X_7 tptp.nat) (Y_7 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_7) Y_7)) (or (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_7) Y_7)) (= X_7 Y_7)))) (forall ((Aa tptp.fun_Pr1643180309t_bool) (Ba tptp.fun_Pr1643180309t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool Aa) Ba)) (=> (not (= Aa Ba)) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool Aa) Ba))))) (forall ((Aa tptp.fun_Ar1809396326i_bool) (Ba tptp.fun_Ar1809396326i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool Aa) Ba)) (=> (not (= Aa Ba)) (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool Aa) Ba))))) (forall ((Aa tptp.fun_fu638310559l_bool) (Ba tptp.fun_fu638310559l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool Aa) Ba)) (=> (not (= Aa Ba)) (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1727358153l_bool Aa) Ba))))) (forall ((Aa tptp.fun_fu2098777574l_bool) (Ba tptp.fun_fu2098777574l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool Aa) Ba)) (=> (not (= Aa Ba)) (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le119247420l_bool Aa) Ba))))) (forall ((Aa tptp.fun_fu3835832l_bool) (Ba tptp.fun_fu3835832l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool Aa) Ba)) (=> (not (= Aa Ba)) (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1959568910l_bool Aa) Ba))))) (forall ((Aa tptp.fun_Pr2067565481t_bool) (Ba tptp.fun_Pr2067565481t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool Aa) Ba)) (=> (not (= Aa Ba)) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1478665215t_bool Aa) Ba))))) (forall ((Aa tptp.bool) (Ba tptp.bool)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Aa) Ba)) (=> (not (= (tptp.hBOOL Aa) (tptp.hBOOL Ba))) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_bool Aa) Ba))))) (forall ((Aa tptp.fun_Ar331856045t_bool) (Ba tptp.fun_Ar331856045t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool Aa) Ba)) (=> (not (= Aa Ba)) (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le19409623t_bool Aa) Ba))))) (forall ((Aa tptp.fun_nat_bool) (Ba tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Aa) Ba)) (=> (not (= Aa Ba)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool Aa) Ba))))) (forall ((A_20 tptp.nat) (B_18 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_20) B_18)) (=> (not (= A_20 B_18)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_20) B_18))))) (forall ((Ba tptp.fun_Pr1643180309t_bool) (Aa tptp.fun_Pr1643180309t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool Ba) Aa)) (=> (not (= Aa Ba)) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool Ba) Aa))))) (forall ((Ba tptp.fun_Ar1809396326i_bool) (Aa tptp.fun_Ar1809396326i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool Ba) Aa)) (=> (not (= Aa Ba)) (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool Ba) Aa))))) (forall ((Ba tptp.fun_fu638310559l_bool) (Aa tptp.fun_fu638310559l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool Ba) Aa)) (=> (not (= Aa Ba)) (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1727358153l_bool Ba) Aa))))) (forall ((Ba tptp.fun_fu2098777574l_bool) (Aa tptp.fun_fu2098777574l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool Ba) Aa)) (=> (not (= Aa Ba)) (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le119247420l_bool Ba) Aa))))) (forall ((Ba tptp.fun_fu3835832l_bool) (Aa tptp.fun_fu3835832l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool Ba) Aa)) (=> (not (= Aa Ba)) (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1959568910l_bool Ba) Aa))))) (forall ((Ba tptp.fun_Pr2067565481t_bool) (Aa tptp.fun_Pr2067565481t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool Ba) Aa)) (=> (not (= Aa Ba)) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1478665215t_bool Ba) Aa))))) (forall ((Ba tptp.bool) (Aa tptp.bool)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Ba) Aa)) (=> (not (= (tptp.hBOOL Aa) (tptp.hBOOL Ba))) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_bool Ba) Aa))))) (forall ((Ba tptp.fun_Ar331856045t_bool) (Aa tptp.fun_Ar331856045t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool Ba) Aa)) (=> (not (= Aa Ba)) (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le19409623t_bool Ba) Aa))))) (forall ((Ba tptp.fun_nat_bool) (Aa tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Ba) Aa)) (=> (not (= Aa Ba)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool Ba) Aa))))) (forall ((B_17 tptp.nat) (A_19 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat B_17) A_19)) (=> (not (= A_19 B_17)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat B_17) A_19))))) (forall ((Z_2 tptp.fun_Pr1643180309t_bool) (X_2 tptp.fun_Pr1643180309t_bool) (Y_2 tptp.fun_Pr1643180309t_bool)) (let ((_let_1 (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool X_2))) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool _let_1 Y_2)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool Y_2) Z_2)) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool _let_1 Z_2)))))) (forall ((Z_2 tptp.fun_Ar1809396326i_bool) (X_2 tptp.fun_Ar1809396326i_bool) (Y_2 tptp.fun_Ar1809396326i_bool)) (let ((_let_1 (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool X_2))) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool _let_1 Y_2)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool Y_2) Z_2)) (tptp.hBOOL (tptp.hAPP_f584385070l_bool _let_1 Z_2)))))) (forall ((Z_2 tptp.fun_fu638310559l_bool) (X_2 tptp.fun_fu638310559l_bool) (Y_2 tptp.fun_fu638310559l_bool)) (let ((_let_1 (tptp.hAPP_f1722316607l_bool tptp.ord_le1727358153l_bool X_2))) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool _let_1 Y_2)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool Y_2) Z_2)) (tptp.hBOOL (tptp.hAPP_f182583295l_bool _let_1 Z_2)))))) (forall ((Z_2 tptp.fun_fu2098777574l_bool) (X_2 tptp.fun_fu2098777574l_bool) (Y_2 tptp.fun_fu2098777574l_bool)) (let ((_let_1 (tptp.hAPP_f916323245l_bool tptp.ord_le119247420l_bool X_2))) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool _let_1 Y_2)) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool Y_2) Z_2)) (tptp.hBOOL (tptp.hAPP_f975209902l_bool _let_1 Z_2)))))) (forall ((Z_2 tptp.fun_fu3835832l_bool) (X_2 tptp.fun_fu3835832l_bool) (Y_2 tptp.fun_fu3835832l_bool)) (let ((_let_1 (tptp.hAPP_f585353809l_bool tptp.ord_le1959568910l_bool X_2))) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool _let_1 Y_2)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool Y_2) Z_2)) (tptp.hBOOL (tptp.hAPP_f73423488l_bool _let_1 Z_2)))))) (forall ((Z_2 tptp.fun_Pr2067565481t_bool) (X_2 tptp.fun_Pr2067565481t_bool) (Y_2 tptp.fun_Pr2067565481t_bool)) (let ((_let_1 (tptp.hAPP_f930900275l_bool tptp.ord_le1478665215t_bool X_2))) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_1 Y_2)) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool Y_2) Z_2)) (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_1 Z_2)))))) (forall ((Z_2 tptp.bool) (X_2 tptp.bool) (Y_2 tptp.bool)) (let ((_let_1 (tptp.hAPP_b589554111l_bool tptp.ord_less_bool X_2))) (=> (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 Y_2)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Y_2) Z_2)) (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 Z_2)))))) (forall ((Z_2 tptp.fun_Ar331856045t_bool) (X_2 tptp.fun_Ar331856045t_bool) (Y_2 tptp.fun_Ar331856045t_bool)) (let ((_let_1 (tptp.hAPP_f1055587775l_bool tptp.ord_le19409623t_bool X_2))) (=> (tptp.hBOOL (tptp.hAPP_f1452856589l_bool _let_1 Y_2)) (=> (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool Y_2) Z_2)) (tptp.hBOOL (tptp.hAPP_f1452856589l_bool _let_1 Z_2)))))) (forall ((Z_2 tptp.fun_nat_bool) (X_2 tptp.fun_nat_bool) (Y_2 tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool X_2))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 Y_2)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Y_2) Z_2)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 Z_2)))))) (forall ((Z_5 tptp.nat) (X_6 tptp.nat) (Y_6 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_6))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Y_6)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_6) Z_5)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Z_5)))))) (forall ((Z_2 tptp.fun_Pr1643180309t_bool) (Y_2 tptp.fun_Pr1643180309t_bool) (X_2 tptp.fun_Pr1643180309t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool Y_2) X_2)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool Z_2) Y_2)) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool Z_2) X_2))))) (forall ((Z_2 tptp.fun_Ar1809396326i_bool) (Y_2 tptp.fun_Ar1809396326i_bool) (X_2 tptp.fun_Ar1809396326i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool Y_2) X_2)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool Z_2) Y_2)) (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool Z_2) X_2))))) (forall ((Z_2 tptp.fun_fu638310559l_bool) (Y_2 tptp.fun_fu638310559l_bool) (X_2 tptp.fun_fu638310559l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1727358153l_bool Y_2) X_2)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool Z_2) Y_2)) (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1727358153l_bool Z_2) X_2))))) (forall ((Z_2 tptp.fun_fu2098777574l_bool) (Y_2 tptp.fun_fu2098777574l_bool) (X_2 tptp.fun_fu2098777574l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le119247420l_bool Y_2) X_2)) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool Z_2) Y_2)) (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le119247420l_bool Z_2) X_2))))) (forall ((Z_2 tptp.fun_fu3835832l_bool) (Y_2 tptp.fun_fu3835832l_bool) (X_2 tptp.fun_fu3835832l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1959568910l_bool Y_2) X_2)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool Z_2) Y_2)) (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1959568910l_bool Z_2) X_2))))) (forall ((Z_2 tptp.fun_Pr2067565481t_bool) (Y_2 tptp.fun_Pr2067565481t_bool) (X_2 tptp.fun_Pr2067565481t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1478665215t_bool Y_2) X_2)) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool Z_2) Y_2)) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1478665215t_bool Z_2) X_2))))) (forall ((Z_2 tptp.bool) (Y_2 tptp.bool) (X_2 tptp.bool)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_bool Y_2) X_2)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Z_2) Y_2)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_bool Z_2) X_2))))) (forall ((Z_2 tptp.fun_Ar331856045t_bool) (Y_2 tptp.fun_Ar331856045t_bool) (X_2 tptp.fun_Ar331856045t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le19409623t_bool Y_2) X_2)) (=> (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool Z_2) Y_2)) (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le19409623t_bool Z_2) X_2))))) (forall ((Z_2 tptp.fun_nat_bool) (Y_2 tptp.fun_nat_bool) (X_2 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool Y_2) X_2)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Z_2) Y_2)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool Z_2) X_2))))) (forall ((Z_4 tptp.nat) (Y_5 tptp.nat) (X_5 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Y_5) X_5)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Z_4) Y_5)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Z_4) X_5))))) (forall ((Z_2 tptp.fun_Pr1643180309t_bool) (X_2 tptp.fun_Pr1643180309t_bool) (Y_2 tptp.fun_Pr1643180309t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool X_2) Y_2)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool Y_2) Z_2)) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool X_2) Z_2))))) (forall ((Z_2 tptp.fun_Ar1809396326i_bool) (X_2 tptp.fun_Ar1809396326i_bool) (Y_2 tptp.fun_Ar1809396326i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool X_2) Y_2)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool Y_2) Z_2)) (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool X_2) Z_2))))) (forall ((Z_2 tptp.fun_fu638310559l_bool) (X_2 tptp.fun_fu638310559l_bool) (Y_2 tptp.fun_fu638310559l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool X_2) Y_2)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1727358153l_bool Y_2) Z_2)) (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1727358153l_bool X_2) Z_2))))) (forall ((Z_2 tptp.fun_fu2098777574l_bool) (X_2 tptp.fun_fu2098777574l_bool) (Y_2 tptp.fun_fu2098777574l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool X_2) Y_2)) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le119247420l_bool Y_2) Z_2)) (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le119247420l_bool X_2) Z_2))))) (forall ((Z_2 tptp.fun_fu3835832l_bool) (X_2 tptp.fun_fu3835832l_bool) (Y_2 tptp.fun_fu3835832l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool X_2) Y_2)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1959568910l_bool Y_2) Z_2)) (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1959568910l_bool X_2) Z_2))))) (forall ((Z_2 tptp.fun_Pr2067565481t_bool) (X_2 tptp.fun_Pr2067565481t_bool) (Y_2 tptp.fun_Pr2067565481t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool X_2) Y_2)) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1478665215t_bool Y_2) Z_2)) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1478665215t_bool X_2) Z_2))))) (forall ((Z_2 tptp.bool) (X_2 tptp.bool) (Y_2 tptp.bool)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool X_2) Y_2)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_bool Y_2) Z_2)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_bool X_2) Z_2))))) (forall ((Z_2 tptp.fun_Ar331856045t_bool) (X_2 tptp.fun_Ar331856045t_bool) (Y_2 tptp.fun_Ar331856045t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool X_2) Y_2)) (=> (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le19409623t_bool Y_2) Z_2)) (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le19409623t_bool X_2) Z_2))))) (forall ((Z_2 tptp.fun_nat_bool) (X_2 tptp.fun_nat_bool) (Y_2 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool X_2) Y_2)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool Y_2) Z_2)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool X_2) Z_2))))) (forall ((Z_3 tptp.nat) (X_4 tptp.nat) (Y_4 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_4) Y_4)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Y_4) Z_3)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_4) Z_3))))) (forall ((Z_2 tptp.fun_Pr1643180309t_bool) (Y_2 tptp.fun_Pr1643180309t_bool) (X_2 tptp.fun_Pr1643180309t_bool)) (let ((_let_1 (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool Z_2))) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool Y_2) X_2)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool _let_1 Y_2)) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool _let_1 X_2)))))) (forall ((Z_2 tptp.fun_Ar1809396326i_bool) (Y_2 tptp.fun_Ar1809396326i_bool) (X_2 tptp.fun_Ar1809396326i_bool)) (let ((_let_1 (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool Z_2))) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool Y_2) X_2)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool _let_1 Y_2)) (tptp.hBOOL (tptp.hAPP_f584385070l_bool _let_1 X_2)))))) (forall ((Z_2 tptp.fun_fu638310559l_bool) (Y_2 tptp.fun_fu638310559l_bool) (X_2 tptp.fun_fu638310559l_bool)) (let ((_let_1 (tptp.hAPP_f1722316607l_bool tptp.ord_le1727358153l_bool Z_2))) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool Y_2) X_2)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool _let_1 Y_2)) (tptp.hBOOL (tptp.hAPP_f182583295l_bool _let_1 X_2)))))) (forall ((Z_2 tptp.fun_fu2098777574l_bool) (Y_2 tptp.fun_fu2098777574l_bool) (X_2 tptp.fun_fu2098777574l_bool)) (let ((_let_1 (tptp.hAPP_f916323245l_bool tptp.ord_le119247420l_bool Z_2))) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool Y_2) X_2)) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool _let_1 Y_2)) (tptp.hBOOL (tptp.hAPP_f975209902l_bool _let_1 X_2)))))) (forall ((Z_2 tptp.fun_fu3835832l_bool) (Y_2 tptp.fun_fu3835832l_bool) (X_2 tptp.fun_fu3835832l_bool)) (let ((_let_1 (tptp.hAPP_f585353809l_bool tptp.ord_le1959568910l_bool Z_2))) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool Y_2) X_2)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool _let_1 Y_2)) (tptp.hBOOL (tptp.hAPP_f73423488l_bool _let_1 X_2)))))) (forall ((Z_2 tptp.fun_Pr2067565481t_bool) (Y_2 tptp.fun_Pr2067565481t_bool) (X_2 tptp.fun_Pr2067565481t_bool)) (let ((_let_1 (tptp.hAPP_f930900275l_bool tptp.ord_le1478665215t_bool Z_2))) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool Y_2) X_2)) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_1 Y_2)) (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_1 X_2)))))) (forall ((Z_2 tptp.bool) (Y_2 tptp.bool) (X_2 tptp.bool)) (let ((_let_1 (tptp.hAPP_b589554111l_bool tptp.ord_less_bool Z_2))) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Y_2) X_2)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 Y_2)) (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 X_2)))))) (forall ((Z_2 tptp.fun_Ar331856045t_bool) (Y_2 tptp.fun_Ar331856045t_bool) (X_2 tptp.fun_Ar331856045t_bool)) (let ((_let_1 (tptp.hAPP_f1055587775l_bool tptp.ord_le19409623t_bool Z_2))) (=> (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool Y_2) X_2)) (=> (tptp.hBOOL (tptp.hAPP_f1452856589l_bool _let_1 Y_2)) (tptp.hBOOL (tptp.hAPP_f1452856589l_bool _let_1 X_2)))))) (forall ((Z_2 tptp.fun_nat_bool) (Y_2 tptp.fun_nat_bool) (X_2 tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool Z_2))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Y_2) X_2)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 Y_2)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 X_2)))))) (forall ((Z_1 tptp.nat) (Y_3 tptp.nat) (X_3 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Z_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_3) X_3)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Y_3)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 X_3)))))) (forall ((Aa tptp.fun_fu638310559l_bool)) (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool Aa) tptp.top_to1312956197l_bool))) (forall ((Aa tptp.fun_fu3835832l_bool)) (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool Aa) tptp.top_to553140914l_bool))) (forall ((Aa tptp.fun_fu2098777574l_bool)) (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool Aa) tptp.top_to827110112l_bool))) (forall ((Aa tptp.bool)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Aa) tptp.top_top_bool))) (forall ((Aa tptp.fun_Pr2067565481t_bool)) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool Aa) tptp.top_to1138392227t_bool))) (forall ((Aa tptp.fun_Ar331856045t_bool)) (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool Aa) tptp.top_to951839027t_bool))) (forall ((Aa tptp.fun_Ar1809396326i_bool)) (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool Aa) tptp.top_to788185952i_bool))) (forall ((Aa tptp.fun_nat_bool)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Aa) tptp.top_top_fun_nat_bool))) (forall ((Aa tptp.fun_Pr1643180309t_bool)) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool Aa) tptp.top_to1257323279t_bool))) (forall ((Aa tptp.fun_fu638310559l_bool)) (= (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool tptp.top_to1312956197l_bool) Aa)) (= Aa tptp.top_to1312956197l_bool))) (forall ((Aa tptp.fun_fu3835832l_bool)) (= (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool tptp.top_to553140914l_bool) Aa)) (= Aa tptp.top_to553140914l_bool))) (forall ((Aa tptp.fun_fu2098777574l_bool)) (= (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool tptp.top_to827110112l_bool) Aa)) (= Aa tptp.top_to827110112l_bool))) (forall ((Aa tptp.bool)) (= (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool tptp.top_top_bool) Aa)) (= (tptp.hBOOL Aa) (tptp.hBOOL tptp.top_top_bool)))) (forall ((Aa tptp.fun_Pr2067565481t_bool)) (= (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool tptp.top_to1138392227t_bool) Aa)) (= Aa tptp.top_to1138392227t_bool))) (forall ((Aa tptp.fun_Ar331856045t_bool)) (= (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool tptp.top_to951839027t_bool) Aa)) (= Aa tptp.top_to951839027t_bool))) (forall ((Aa tptp.fun_Ar1809396326i_bool)) (= (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool tptp.top_to788185952i_bool) Aa)) (= Aa tptp.top_to788185952i_bool))) (forall ((Aa tptp.fun_nat_bool)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool tptp.top_top_fun_nat_bool) Aa)) (= Aa tptp.top_top_fun_nat_bool))) (forall ((Aa tptp.fun_Pr1643180309t_bool)) (= (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool tptp.top_to1257323279t_bool) Aa)) (= Aa tptp.top_to1257323279t_bool))) (forall ((Aa tptp.fun_fu638310559l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool tptp.top_to1312956197l_bool) Aa)) (= Aa tptp.top_to1312956197l_bool))) (forall ((Aa tptp.fun_fu3835832l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool tptp.top_to553140914l_bool) Aa)) (= Aa tptp.top_to553140914l_bool))) (forall ((Aa tptp.fun_fu2098777574l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool tptp.top_to827110112l_bool) Aa)) (= Aa tptp.top_to827110112l_bool))) (forall ((Aa tptp.bool)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool tptp.top_top_bool) Aa)) (= (tptp.hBOOL Aa) (tptp.hBOOL tptp.top_top_bool)))) (forall ((Aa tptp.fun_Pr2067565481t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool tptp.top_to1138392227t_bool) Aa)) (= Aa tptp.top_to1138392227t_bool))) (forall ((Aa tptp.fun_Ar331856045t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool tptp.top_to951839027t_bool) Aa)) (= Aa tptp.top_to951839027t_bool))) (forall ((Aa tptp.fun_Ar1809396326i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool tptp.top_to788185952i_bool) Aa)) (= Aa tptp.top_to788185952i_bool))) (forall ((Aa tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool tptp.top_top_fun_nat_bool) Aa)) (= Aa tptp.top_top_fun_nat_bool))) (forall ((Aa tptp.fun_Pr1643180309t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool tptp.top_to1257323279t_bool) Aa)) (= Aa tptp.top_to1257323279t_bool))) (forall ((F tptp.fun_Ar671024215di_nat) (A tptp.fun_Ar1809396326i_bool)) (= (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.inj_on1960344199di_nat F) A)) (forall ((X_1 tptp.arrow_856714788e_indi)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_A1597696899l_bool tptp.member1479139729e_indi X_1) A)) (forall ((Xa tptp.arrow_856714788e_indi)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_A1597696899l_bool tptp.member1479139729e_indi Xa) A)) (=> (= (tptp.hAPP_A376526755di_nat F X_1) (tptp.hAPP_A376526755di_nat F Xa)) (= X_1 Xa)))))))) (forall ((F tptp.fun_nat_nat) (A tptp.fun_nat_bool)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.inj_on_nat_nat F) A)) (forall ((X_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)) (forall ((Xa tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat Xa) A)) (=> (= (tptp.hAPP_nat_nat F X_1) (tptp.hAPP_nat_nat F Xa)) (= X_1 Xa)))))))) (forall ((X_2 tptp.arrow_856714788e_indi) (Y_2 tptp.arrow_856714788e_indi) (F tptp.fun_Ar671024215di_nat) (A tptp.fun_Ar1809396326i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.inj_on1960344199di_nat F) A)) (=> (not (= X_2 Y_2)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_A1597696899l_bool tptp.member1479139729e_indi X_2) A)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_A1597696899l_bool tptp.member1479139729e_indi Y_2) A)) (not (= (tptp.hAPP_A376526755di_nat F X_2) (tptp.hAPP_A376526755di_nat F Y_2)))))))) (forall ((X_2 tptp.nat) (Y_2 tptp.nat) (F tptp.fun_nat_nat) (A tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.inj_on_nat_nat F) A)) (=> (not (= X_2 Y_2)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) A)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat Y_2) A)) (not (= (tptp.hAPP_nat_nat F X_2) (tptp.hAPP_nat_nat F Y_2)))))))) (forall ((Y_2 tptp.arrow_856714788e_indi) (X_2 tptp.arrow_856714788e_indi) (F tptp.fun_Ar671024215di_nat) (A tptp.fun_Ar1809396326i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.inj_on1960344199di_nat F) A)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_A1597696899l_bool tptp.member1479139729e_indi X_2) A)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_A1597696899l_bool tptp.member1479139729e_indi Y_2) A)) (= (= (tptp.hAPP_A376526755di_nat F X_2) (tptp.hAPP_A376526755di_nat F Y_2)) (= X_2 Y_2)))))) (forall ((Y_2 tptp.nat) (X_2 tptp.nat) (F tptp.fun_nat_nat) (A tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.inj_on_nat_nat F) A)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) A)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat Y_2) A)) (= (= (tptp.hAPP_nat_nat F X_2) (tptp.hAPP_nat_nat F Y_2)) (= X_2 Y_2)))))) (forall ((X_2 tptp.arrow_856714788e_indi) (Y_2 tptp.arrow_856714788e_indi) (F tptp.fun_Ar671024215di_nat) (A tptp.fun_Ar1809396326i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.inj_on1960344199di_nat F) A)) (=> (= (tptp.hAPP_A376526755di_nat F X_2) (tptp.hAPP_A376526755di_nat F Y_2)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_A1597696899l_bool tptp.member1479139729e_indi X_2) A)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_A1597696899l_bool tptp.member1479139729e_indi Y_2) A)) (= X_2 Y_2)))))) (forall ((X_2 tptp.nat) (Y_2 tptp.nat) (F tptp.fun_nat_nat) (A tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.inj_on_nat_nat F) A)) (=> (= (tptp.hAPP_nat_nat F X_2) (tptp.hAPP_nat_nat F Y_2)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) A)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat Y_2) A)) (= X_2 Y_2)))))) (forall ((X_2 tptp.produc472769767le_alt) (F tptp.fun_Pr2067565481t_bool) (A tptp.fun_Pr2067565481t_bool) (B tptp.fun_Pr1780397033l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1482930381l_bool tptp.member1069471740t_bool F) (tptp.pi_Pro1238944957t_bool A B))) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt X_2) A)) (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.hAPP_b1787118453l_bool tptp.member_bool (tptp.hAPP_P1178790471t_bool F X_2)) (tptp.hAPP_P1103642805l_bool B X_2)))))) (forall ((X_2 tptp.produc472769767le_alt) (F tptp.fun_Pr1509342064e_indi) (A tptp.fun_Pr2067565481t_bool) (B tptp.fun_Pr895221296i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f2124588998l_bool (tptp.hAPP_f1187850253l_bool tptp.member1558233923e_indi F) (tptp.pi_Pro837265796e_indi A B))) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt X_2) A)) (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_A1597696899l_bool tptp.member1479139729e_indi (tptp.hAPP_P276596750e_indi F X_2)) (tptp.hAPP_P1859429372i_bool B X_2)))))) (forall ((X_2 tptp.produc472769767le_alt) (F tptp.fun_Pr376858015t_unit) (A tptp.fun_Pr2067565481t_bool) (B tptp.fun_Pr1069395679t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1159856629l_bool (tptp.hAPP_f1700632141l_bool tptp.member1303779570t_unit F) (tptp.pi_Pro346842291t_unit A B))) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt X_2) A)) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_P607165281l_bool tptp.member_Product_unit (tptp.hAPP_P1069491261t_unit F X_2)) (tptp.hAPP_P2037731755t_bool B X_2)))))) (forall ((X_2 tptp.fun_Ar274636406t_bool) (F tptp.fun_fu1929591039e_indi) (A tptp.fun_fu3835832l_bool) (B tptp.fun_fu223278561i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f665932885l_bool (tptp.hAPP_f430646093l_bool tptp.member282602450e_indi F) (tptp.pi_fun520512275e_indi A B))) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f1225332775l_bool tptp.member933336803t_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_A1597696899l_bool tptp.member1479139729e_indi (tptp.hAPP_f602741661e_indi F X_2)) (tptp.hAPP_f391644589i_bool B X_2)))))) (forall ((X_2 tptp.fun_Ar274636406t_bool) (F tptp.fun_fu3835832l_bool) (A tptp.fun_fu3835832l_bool) (B tptp.fun_fu916327706l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1867557646l_bool (tptp.hAPP_f1048573069l_bool tptp.member1020280587l_bool F) (tptp.pi_fun853738700l_bool A B))) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f1225332775l_bool tptp.member933336803t_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.hAPP_b1787118453l_bool tptp.member_bool (tptp.hAPP_f995490902l_bool F X_2)) (tptp.hAPP_f1676084198l_bool B X_2)))))) (forall ((X_2 tptp.fun_Ar274636406t_bool) (F tptp.fun_fu1023022254t_unit) (A tptp.fun_fu3835832l_bool) (B tptp.fun_fu1734317328t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f115957764l_bool (tptp.hAPP_f1184790797l_bool tptp.member2003579649t_unit F) (tptp.pi_fun1644711874t_unit A B))) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f1225332775l_bool tptp.member933336803t_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_P607165281l_bool tptp.member_Product_unit (tptp.hAPP_f1775626572t_unit F X_2)) (tptp.hAPP_f1438163420t_bool B X_2)))))) (forall ((X_2 tptp.fun_fu2114379172t_bool) (F tptp.fun_fu748153389e_indi) (A tptp.fun_fu2098777574l_bool) (B tptp.fun_fu2109152051i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f2350467l_bool (tptp.hAPP_f1411422157l_bool tptp.member1247254528e_indi F) (tptp.pi_fun1807454273e_indi A B))) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f1714503811l_bool tptp.member173038353t_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_A1597696899l_bool tptp.member1479139729e_indi (tptp.hAPP_f350323403e_indi F X_2)) (tptp.hAPP_f399308031i_bool B X_2)))))) (forall ((X_2 tptp.fun_fu2114379172t_bool) (F tptp.fun_fu2098777574l_bool) (A tptp.fun_fu2098777574l_bool) (B tptp.fun_fu1522163052l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f2047920444l_bool (tptp.hAPP_f59810573l_bool tptp.member1173995577l_bool F) (tptp.pi_fun1312540410l_bool A B))) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f1714503811l_bool tptp.member173038353t_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.hAPP_b1787118453l_bool tptp.member_bool (tptp.hAPP_f1572141188l_bool F X_2)) (tptp.hAPP_f414129720l_bool B X_2)))))) (forall ((X_2 tptp.fun_fu2114379172t_bool) (F tptp.fun_fu1480298716t_unit) (A tptp.fun_fu2098777574l_bool) (B tptp.fun_fu1143287650t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f92582962l_bool (tptp.hAPP_f1494690701l_bool tptp.member2091379247t_unit F) (tptp.pi_fun1540376560t_unit A B))) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f1714503811l_bool tptp.member173038353t_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_P607165281l_bool tptp.member_Product_unit (tptp.hAPP_f1865816954t_unit F X_2)) (tptp.hAPP_f151782958t_bool B X_2)))))) (forall ((X_2 tptp.fun_Pr2067565481t_bool) (F tptp.fun_fu562005862e_indi) (A tptp.fun_fu638310559l_bool) (B tptp.fun_fu2142850746i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f679138160l_bool (tptp.hAPP_f1006969351l_bool tptp.member1220706259e_indi F) (tptp.pi_fun1470523330e_indi A B))) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1482930381l_bool tptp.member1069471740t_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_A1597696899l_bool tptp.member1479139729e_indi (tptp.hAPP_f9587896e_indi F X_2)) (tptp.hAPP_f2010315474i_bool B X_2)))))) (forall ((X_2 tptp.fun_Pr2067565481t_bool) (F tptp.fun_fu638310559l_bool) (A tptp.fun_fu638310559l_bool) (B tptp.fun_fu237781875l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1686510249l_bool (tptp.hAPP_f1930590713l_bool tptp.member340585612l_bool F) (tptp.pi_fun1035089915l_bool A B))) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1482930381l_bool tptp.member1069471740t_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.hAPP_b1787118453l_bool tptp.member_bool (tptp.hAPP_f52567537l_bool F X_2)) (tptp.hAPP_f463104139l_bool B X_2)))))) (forall ((X_2 tptp.fun_Pr2067565481t_bool) (F tptp.fun_fu665686165t_unit) (A tptp.fun_fu638310559l_bool) (B tptp.fun_fu643686505t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1478188703l_bool (tptp.hAPP_f1329172965l_bool tptp.member1729658242t_unit F) (tptp.pi_fun177985009t_unit A B))) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1482930381l_bool tptp.member1069471740t_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_P607165281l_bool tptp.member_Product_unit (tptp.hAPP_f801675751t_unit F X_2)) (tptp.hAPP_f1400551297t_bool B X_2)))))) (forall ((X_2 tptp.nat) (F tptp.fun_na699243463e_indi) (A tptp.fun_nat_bool) (B tptp.fun_na2037635353i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f736267217l_bool (tptp.hAPP_f707406409l_bool tptp.member1530714804e_indi F) (tptp.pi_nat646417955e_indi A B))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) A)) (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_A1597696899l_bool tptp.member1479139729e_indi (tptp.hAPP_n1937165849e_indi F X_2)) (tptp.hAPP_n34002993i_bool B X_2)))))) (forall ((X_2 tptp.nat) (F tptp.fun_nat_bool) (A tptp.fun_nat_bool) (B tptp.fun_na1469252690l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool (tptp.hAPP_f1951378235l_bool tptp.member_fun_nat_bool F) (tptp.pi_nat_bool A B))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) A)) (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.hAPP_b1787118453l_bool tptp.member_bool (tptp.hAPP_nat_bool F X_2)) (tptp.hAPP_n1006566506l_bool B X_2)))))) (forall ((X_2 tptp.nat) (F tptp.fun_nat_Product_unit) (A tptp.fun_nat_bool) (B tptp.fun_na1041622088t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f537623936l_bool (tptp.hAPP_f1598887207l_bool tptp.member1024687843t_unit F) (tptp.pi_nat_Product_unit A B))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) A)) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_P607165281l_bool tptp.member_Product_unit (tptp.hAPP_n633340360t_unit F X_2)) (tptp.hAPP_n454528608t_bool B X_2)))))) (forall ((X_2 tptp.arrow_856714788e_indi) (F tptp.fun_Ar338949104le_alt) (A tptp.fun_Ar1809396326i_bool) (B tptp.fun_Ar274636406t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1754488902l_bool (tptp.hAPP_f766019597l_bool tptp.member387840963le_alt F) (tptp.pi_Arr1460528004le_alt A B))) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_A1597696899l_bool tptp.member1479139729e_indi X_2) A)) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_A899858958le_alt F X_2)) (tptp.hAPP_A1646126530t_bool B X_2)))))) (forall ((X_2 tptp.bool) (F tptp.fun_bo1682907689le_alt) (A tptp.fun_bool_bool) (B tptp.fun_bo1431306493t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1620711039l_bool (tptp.hAPP_f334747853l_bool tptp.member684813948le_alt F) (tptp.pi_boo7125949le_alt A B))) (=> (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.hAPP_b1787118453l_bool tptp.member_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_b2094455111le_alt F X_2)) (tptp.hAPP_b128655177t_bool B X_2)))))) (forall ((X_2 tptp.product_unit) (F tptp.fun_Pr2090226719le_alt) (A tptp.fun_Pr1643180309t_bool) (B tptp.fun_Pr1887398791t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f684683381l_bool (tptp.hAPP_f41367117l_bool tptp.member869664626le_alt F) (tptp.pi_Pro1820940723le_alt A B))) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_P607165281l_bool tptp.member_Product_unit X_2) A)) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_P396106045le_alt F X_2)) (tptp.hAPP_P1914371027t_bool B X_2)))))) (forall ((X_2 tptp.arrow_856714788e_indi) (F tptp.fun_Ar624010239t_bool) (A tptp.fun_Ar1809396326i_bool) (B tptp.fun_Ar1998664965l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f826064725l_bool (tptp.hAPP_f1364091725l_bool tptp.member1124505298t_bool F) (tptp.pi_Arr2025169427t_bool A B))) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_A1597696899l_bool tptp.member1479139729e_indi X_2) A)) (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f1225332775l_bool tptp.member933336803t_bool (tptp.hAPP_A2107398813t_bool F X_2)) (tptp.hAPP_A1411662545l_bool B X_2)))))) (forall ((X_2 tptp.bool) (F tptp.fun_bo1476023096t_bool) (A tptp.fun_bool_bool) (B tptp.fun_bo2107365004l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1605957262l_bool (tptp.hAPP_f1525863565l_bool tptp.member344984203t_bool F) (tptp.pi_boo347863884t_bool A B))) (=> (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.hAPP_b1787118453l_bool tptp.member_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f1225332775l_bool tptp.member933336803t_bool (tptp.hAPP_b489616086t_bool F X_2)) (tptp.hAPP_b1078573912l_bool B X_2)))))) (forall ((X_2 tptp.product_unit) (F tptp.fun_Pr1531194158t_bool) (A tptp.fun_Pr1643180309t_bool) (B tptp.fun_Pr537467670l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1851324036l_bool (tptp.hAPP_f1974966541l_bool tptp.member364267905t_bool F) (tptp.pi_Pro782712642t_bool A B))) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_P607165281l_bool tptp.member_Product_unit X_2) A)) (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f1225332775l_bool tptp.member933336803t_bool (tptp.hAPP_P913627340t_bool F X_2)) (tptp.hAPP_P284783074l_bool B X_2)))))) (forall ((X_2 tptp.arrow_856714788e_indi) (F tptp.fun_Ar286530093t_bool) (A tptp.fun_Ar1809396326i_bool) (B tptp.fun_Ar1321653811l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f686820739l_bool (tptp.hAPP_f692361165l_bool tptp.member785631232t_bool F) (tptp.pi_Arr687740481t_bool A B))) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_A1597696899l_bool tptp.member1479139729e_indi X_2) A)) (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f1714503811l_bool tptp.member173038353t_bool (tptp.hAPP_A1378093259t_bool F X_2)) (tptp.hAPP_A2084592127l_bool B X_2)))))) (forall ((X_2 tptp.bool) (F tptp.fun_bo559790694t_bool) (A tptp.fun_bool_bool) (B tptp.fun_bo1445676730l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1211446716l_bool (tptp.hAPP_f1134773005l_bool tptp.member1782492345t_bool F) (tptp.pi_boo769613946t_bool A B))) (=> (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.hAPP_b1787118453l_bool tptp.member_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f1714503811l_bool tptp.member173038353t_bool (tptp.hAPP_b1029214724t_bool F X_2)) (tptp.hAPP_b1777246598l_bool B X_2)))))) (forall ((X_2 tptp.product_unit) (F tptp.fun_Pr2016729180t_bool) (A tptp.fun_Pr1643180309t_bool) (B tptp.fun_Pr151242052l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f2068478898l_bool (tptp.hAPP_f1883507597l_bool tptp.member480326063t_bool F) (tptp.pi_Pro1533274736t_bool A B))) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_P607165281l_bool tptp.member_Product_unit X_2) A)) (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f1714503811l_bool tptp.member173038353t_bool (tptp.hAPP_P1858715130t_bool F X_2)) (tptp.hAPP_P283873808l_bool B X_2)))))) (forall ((X_2 tptp.bool) (F tptp.fun_bo1431306493t_bool) (A tptp.fun_bool_bool) (B tptp.fun_bo377688929l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f398210311l_bool (tptp.hAPP_f416878261l_bool tptp.member1133581546t_bool F) (tptp.pi_boo1111177555t_bool A B))) (=> (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.hAPP_b1787118453l_bool tptp.member_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1482930381l_bool tptp.member1069471740t_bool (tptp.hAPP_b128655177t_bool F X_2)) (tptp.hAPP_b1272691967l_bool B X_2)))))) (forall ((X_2 tptp.product_unit) (F tptp.fun_Pr1887398791t_bool) (A tptp.fun_Pr1643180309t_bool) (B tptp.fun_Pr1791323223l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1426814865l_bool (tptp.hAPP_f1942212041l_bool tptp.member803887220t_bool F) (tptp.pi_Pro1290680285t_bool A B))) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_P607165281l_bool tptp.member_Product_unit X_2) A)) (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1482930381l_bool tptp.member1069471740t_bool (tptp.hAPP_P1914371027t_bool F X_2)) (tptp.hAPP_P754918389l_bool B X_2)))))) (forall ((X_2 tptp.arrow_856714788e_indi) (F tptp.fun_Ar671024215di_nat) (A tptp.fun_Ar1809396326i_bool) (B tptp.fun_Ar603939593t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f225240161l_bool (tptp.hAPP_f677301097l_bool tptp.member1502495556di_nat F) (tptp.pi_Arr1233262509di_nat A B))) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_A1597696899l_bool tptp.member1479139729e_indi X_2) A)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat (tptp.hAPP_A376526755di_nat F X_2)) (tptp.hAPP_A1686943911t_bool B X_2)))))) (forall ((X_2 tptp.bool) (F tptp.fun_bool_nat) (A tptp.fun_bool_bool) (B tptp.fun_bo1570548802t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f67777128l_bool (tptp.hAPP_f144393719l_bool tptp.member_fun_bool_nat F) (tptp.pi_bool_nat A B))) (=> (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.hAPP_b1787118453l_bool tptp.member_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat (tptp.hAPP_bool_nat F X_2)) (tptp.hAPP_b1013836512t_bool B X_2)))))) (forall ((X_2 tptp.product_unit) (F tptp.fun_Product_unit_nat) (A tptp.fun_Pr1643180309t_bool) (B tptp.fun_Pr1029464120t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f339859954l_bool (tptp.hAPP_f1950626059l_bool tptp.member87760213it_nat F) (tptp.pi_Product_unit_nat A B))) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_P607165281l_bool tptp.member_Product_unit X_2) A)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat (tptp.hAPP_P426034740it_nat F X_2)) (tptp.hAPP_P32877782t_bool B X_2)))))) (forall ((X_2 tptp.fun_Ar274636406t_bool) (F tptp.fun_fu2114379172t_bool) (A tptp.fun_fu3835832l_bool) (B tptp.fun_fu1863781882l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f1714503811l_bool tptp.member173038353t_bool F) (tptp.pi_fun1746584570t_bool A B))) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f1225332775l_bool tptp.member933336803t_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1482930381l_bool tptp.member1069471740t_bool (tptp.hAPP_f2008608496t_bool F X_2)) (tptp.hAPP_f1915815064l_bool B X_2)))))) (forall ((X_2 tptp.arrow_856714788e_indi) (F tptp.fun_Ar274636406t_bool) (A tptp.fun_Ar1809396326i_bool) (B tptp.fun_Ar1474557608l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f1225332775l_bool tptp.member933336803t_bool F) (tptp.pi_Arr959578316t_bool A B))) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_A1597696899l_bool tptp.member1479139729e_indi X_2) A)) (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1482930381l_bool tptp.member1069471740t_bool (tptp.hAPP_A1646126530t_bool F X_2)) (tptp.hAPP_A897398598l_bool B X_2)))))) (forall ((L_3 tptp.fun_Pr2067565481t_bool) (X_2 tptp.arrow_1893660431le_alt) (Y_2 tptp.arrow_1893660431le_alt)) (=> (not (= X_2 Y_2)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1482930381l_bool tptp.member1069471740t_bool L_3) tptp.arrow_1361987423le_Lin)) (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1482930381l_bool tptp.member1069471740t_bool (tptp.arrow_1525312447_below L_3 X_2 Y_2)) tptp.arrow_1361987423le_Lin))))) (= tptp.arrow_5070731e_Prof (tptp.pi_Arr959578316t_bool tptp.top_to788185952i_bool (tptp.hAPP_f1717907078l_bool tptp.cOMBK_1520063231e_indi tptp.arrow_1361987423le_Lin))) (forall ((A tptp.fun_nat_bool)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.inj_on_nat_nat tptp.cOMBI_nat) A))) (forall ((X_2 tptp.produc472769767le_alt) (F tptp.fun_Pr2067565481t_bool) (A tptp.fun_Pr2067565481t_bool) (B tptp.fun_bool_bool)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1482930381l_bool tptp.member1069471740t_bool F) (tptp.pi_Pro1238944957t_bool A (tptp.hAPP_f699791347l_bool tptp.cOMBK_138598520le_alt B)))) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt X_2) A)) (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.hAPP_b1787118453l_bool tptp.member_bool (tptp.hAPP_P1178790471t_bool F X_2)) B))))) (forall ((X_2 tptp.produc472769767le_alt) (F tptp.fun_Pr1509342064e_indi) (A tptp.fun_Pr2067565481t_bool) (B tptp.fun_Ar1809396326i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f2124588998l_bool (tptp.hAPP_f1187850253l_bool tptp.member1558233923e_indi F) (tptp.pi_Pro837265796e_indi A (tptp.hAPP_f359069313i_bool tptp.cOMBK_1987648063le_alt B)))) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt X_2) A)) (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_A1597696899l_bool tptp.member1479139729e_indi (tptp.hAPP_P276596750e_indi F X_2)) B))))) (forall ((X_2 tptp.produc472769767le_alt) (F tptp.fun_Pr376858015t_unit) (A tptp.fun_Pr2067565481t_bool) (B tptp.fun_Pr1643180309t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1159856629l_bool (tptp.hAPP_f1700632141l_bool tptp.member1303779570t_unit F) (tptp.pi_Pro346842291t_unit A (tptp.hAPP_f723483871t_bool tptp.cOMBK_751896174le_alt B)))) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt X_2) A)) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_P607165281l_bool tptp.member_Product_unit (tptp.hAPP_P1069491261t_unit F X_2)) B))))) (forall ((X_2 tptp.fun_Ar274636406t_bool) (F tptp.fun_fu1929591039e_indi) (A tptp.fun_fu3835832l_bool) (B tptp.fun_Ar1809396326i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f665932885l_bool (tptp.hAPP_f430646093l_bool tptp.member282602450e_indi F) (tptp.pi_fun520512275e_indi A (tptp.hAPP_f2022065970i_bool tptp.cOMBK_818801614t_bool B)))) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f1225332775l_bool tptp.member933336803t_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_A1597696899l_bool tptp.member1479139729e_indi (tptp.hAPP_f602741661e_indi F X_2)) B))))) (forall ((X_2 tptp.fun_Ar274636406t_bool) (F tptp.fun_fu3835832l_bool) (A tptp.fun_fu3835832l_bool) (B tptp.fun_bool_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1867557646l_bool (tptp.hAPP_f1048573069l_bool tptp.member1020280587l_bool F) (tptp.pi_fun853738700l_bool A (tptp.hAPP_f1582869284l_bool tptp.cOMBK_542452487t_bool B)))) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f1225332775l_bool tptp.member933336803t_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.hAPP_b1787118453l_bool tptp.member_bool (tptp.hAPP_f995490902l_bool F X_2)) B))))) (forall ((X_2 tptp.fun_Ar274636406t_bool) (F tptp.fun_fu1023022254t_unit) (A tptp.fun_fu3835832l_bool) (B tptp.fun_Pr1643180309t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f115957764l_bool (tptp.hAPP_f1184790797l_bool tptp.member2003579649t_unit F) (tptp.pi_fun1644711874t_unit A (tptp.hAPP_f134177552t_bool tptp.cOMBK_1220673277t_bool B)))) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f1225332775l_bool tptp.member933336803t_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_P607165281l_bool tptp.member_Product_unit (tptp.hAPP_f1775626572t_unit F X_2)) B))))) (forall ((X_2 tptp.fun_fu2114379172t_bool) (F tptp.fun_fu748153389e_indi) (A tptp.fun_fu2098777574l_bool) (B tptp.fun_Ar1809396326i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f2350467l_bool (tptp.hAPP_f1411422157l_bool tptp.member1247254528e_indi F) (tptp.pi_fun1807454273e_indi A (tptp.hAPP_f448050564i_bool tptp.cOMBK_443335420t_bool B)))) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f1714503811l_bool tptp.member173038353t_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_A1597696899l_bool tptp.member1479139729e_indi (tptp.hAPP_f350323403e_indi F X_2)) B))))) (forall ((X_2 tptp.fun_fu2114379172t_bool) (F tptp.fun_fu2098777574l_bool) (A tptp.fun_fu2098777574l_bool) (B tptp.fun_bool_bool)) (=> (tptp.hBOOL (tptp.hAPP_f2047920444l_bool (tptp.hAPP_f59810573l_bool tptp.member1173995577l_bool F) (tptp.pi_fun1312540410l_bool A (tptp.hAPP_f1152234870l_bool tptp.cOMBK_1770320693t_bool B)))) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f1714503811l_bool tptp.member173038353t_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.hAPP_b1787118453l_bool tptp.member_bool (tptp.hAPP_f1572141188l_bool F X_2)) B))))) (forall ((X_2 tptp.fun_fu2114379172t_bool) (F tptp.fun_fu1480298716t_unit) (A tptp.fun_fu2098777574l_bool) (B tptp.fun_Pr1643180309t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f92582962l_bool (tptp.hAPP_f1494690701l_bool tptp.member2091379247t_unit F) (tptp.pi_fun1540376560t_unit A (tptp.hAPP_f1327693154t_bool tptp.cOMBK_1385893163t_bool B)))) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f1714503811l_bool tptp.member173038353t_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_P607165281l_bool tptp.member_Product_unit (tptp.hAPP_f1865816954t_unit F X_2)) B))))) (forall ((X_2 tptp.fun_Pr2067565481t_bool) (F tptp.fun_fu562005862e_indi) (A tptp.fun_fu638310559l_bool) (B tptp.fun_Ar1809396326i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f679138160l_bool (tptp.hAPP_f1006969351l_bool tptp.member1220706259e_indi F) (tptp.pi_fun1470523330e_indi A (tptp.hAPP_f1128827177i_bool tptp.cOMBK_814147665t_bool B)))) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1482930381l_bool tptp.member1069471740t_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_A1597696899l_bool tptp.member1479139729e_indi (tptp.hAPP_f9587896e_indi F X_2)) B))))) (forall ((X_2 tptp.fun_Pr2067565481t_bool) (F tptp.fun_fu638310559l_bool) (A tptp.fun_fu638310559l_bool) (B tptp.fun_bool_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1686510249l_bool (tptp.hAPP_f1930590713l_bool tptp.member340585612l_bool F) (tptp.pi_fun1035089915l_bool A (tptp.hAPP_f1713038057l_bool tptp.cOMBK_118864600t_bool B)))) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1482930381l_bool tptp.member1069471740t_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.hAPP_b1787118453l_bool tptp.member_bool (tptp.hAPP_f52567537l_bool F X_2)) B))))) (forall ((X_2 tptp.fun_Pr2067565481t_bool) (F tptp.fun_fu665686165t_unit) (A tptp.fun_fu638310559l_bool) (B tptp.fun_Pr1643180309t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1478188703l_bool (tptp.hAPP_f1329172965l_bool tptp.member1729658242t_unit F) (tptp.pi_fun177985009t_unit A (tptp.hAPP_f168465001t_bool tptp.cOMBK_14887266t_bool B)))) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1482930381l_bool tptp.member1069471740t_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_P607165281l_bool tptp.member_Product_unit (tptp.hAPP_f801675751t_unit F X_2)) B))))) (forall ((X_2 tptp.nat) (F tptp.fun_na699243463e_indi) (A tptp.fun_nat_bool) (B tptp.fun_Ar1809396326i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f736267217l_bool (tptp.hAPP_f707406409l_bool tptp.member1530714804e_indi F) (tptp.pi_nat646417955e_indi A (tptp.hAPP_f1549597448i_bool tptp.cOMBK_341987762ol_nat B)))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) A)) (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_A1597696899l_bool tptp.member1479139729e_indi (tptp.hAPP_n1937165849e_indi F X_2)) B))))) (forall ((X_2 tptp.nat) (F tptp.fun_nat_bool) (A tptp.fun_nat_bool) (B tptp.fun_bool_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool (tptp.hAPP_f1951378235l_bool tptp.member_fun_nat_bool F) (tptp.pi_nat_bool A (tptp.hAPP_f1579826888l_bool tptp.cOMBK_623810489ol_nat B)))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) A)) (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.hAPP_b1787118453l_bool tptp.member_bool (tptp.hAPP_nat_bool F X_2)) B))))) (forall ((X_2 tptp.nat) (F tptp.fun_nat_Product_unit) (A tptp.fun_nat_bool) (B tptp.fun_Pr1643180309t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f537623936l_bool (tptp.hAPP_f1598887207l_bool tptp.member1024687843t_unit F) (tptp.pi_nat_Product_unit A (tptp.hAPP_f1539020360t_bool tptp.cOMBK_649751363ol_nat B)))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) A)) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_P607165281l_bool tptp.member_Product_unit (tptp.hAPP_n633340360t_unit F X_2)) B))))) (forall ((X_2 tptp.arrow_856714788e_indi) (F tptp.fun_Ar338949104le_alt) (A tptp.fun_Ar1809396326i_bool) (B tptp.fun_Pr2067565481t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1754488902l_bool (tptp.hAPP_f766019597l_bool tptp.member387840963le_alt F) (tptp.pi_Arr1460528004le_alt A (tptp.hAPP_f480276746t_bool tptp.cOMBK_1650320063e_indi B)))) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_A1597696899l_bool tptp.member1479139729e_indi X_2) A)) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_A899858958le_alt F X_2)) B))))) (forall ((X_2 tptp.bool) (F tptp.fun_bo1682907689le_alt) (A tptp.fun_bool_bool) (B tptp.fun_Pr2067565481t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1620711039l_bool (tptp.hAPP_f334747853l_bool tptp.member684813948le_alt F) (tptp.pi_boo7125949le_alt A (tptp.hAPP_f1723896209t_bool tptp.cOMBK_5056120l_bool B)))) (=> (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.hAPP_b1787118453l_bool tptp.member_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_b2094455111le_alt F X_2)) B))))) (forall ((X_2 tptp.product_unit) (F tptp.fun_Pr2090226719le_alt) (A tptp.fun_Pr1643180309t_bool) (B tptp.fun_Pr2067565481t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f684683381l_bool (tptp.hAPP_f41367117l_bool tptp.member869664626le_alt F) (tptp.pi_Pro1820940723le_alt A (tptp.hAPP_f15777819t_bool tptp.cOMBK_681766254t_unit B)))) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_P607165281l_bool tptp.member_Product_unit X_2) A)) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_P396106045le_alt F X_2)) B))))) (forall ((X_2 tptp.arrow_856714788e_indi) (F tptp.fun_Ar624010239t_bool) (A tptp.fun_Ar1809396326i_bool) (B tptp.fun_fu3835832l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f826064725l_bool (tptp.hAPP_f1364091725l_bool tptp.member1124505298t_bool F) (tptp.pi_Arr2025169427t_bool A (tptp.hAPP_f1352816552l_bool tptp.cOMBK_1255579598e_indi B)))) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_A1597696899l_bool tptp.member1479139729e_indi X_2) A)) (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f1225332775l_bool tptp.member933336803t_bool (tptp.hAPP_A2107398813t_bool F X_2)) B))))) (forall ((X_2 tptp.bool) (F tptp.fun_bo1476023096t_bool) (A tptp.fun_bool_bool) (B tptp.fun_fu3835832l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1605957262l_bool (tptp.hAPP_f1525863565l_bool tptp.member344984203t_bool F) (tptp.pi_boo347863884t_bool A (tptp.hAPP_f1322579375l_bool tptp.cOMBK_317366791l_bool B)))) (=> (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.hAPP_b1787118453l_bool tptp.member_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f1225332775l_bool tptp.member933336803t_bool (tptp.hAPP_b489616086t_bool F X_2)) B))))) (forall ((X_2 tptp.product_unit) (F tptp.fun_Pr1531194158t_bool) (A tptp.fun_Pr1643180309t_bool) (B tptp.fun_fu3835832l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1851324036l_bool (tptp.hAPP_f1974966541l_bool tptp.member364267905t_bool F) (tptp.pi_Pro782712642t_bool A (tptp.hAPP_f1482764601l_bool tptp.cOMBK_708287485t_unit B)))) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_P607165281l_bool tptp.member_Product_unit X_2) A)) (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f1225332775l_bool tptp.member933336803t_bool (tptp.hAPP_P913627340t_bool F X_2)) B))))) (forall ((X_2 tptp.arrow_856714788e_indi) (F tptp.fun_Ar286530093t_bool) (A tptp.fun_Ar1809396326i_bool) (B tptp.fun_fu2098777574l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f686820739l_bool (tptp.hAPP_f692361165l_bool tptp.member785631232t_bool F) (tptp.pi_Arr687740481t_bool A (tptp.hAPP_f258290692l_bool tptp.cOMBK_1514079484e_indi B)))) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_A1597696899l_bool tptp.member1479139729e_indi X_2) A)) (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f1714503811l_bool tptp.member173038353t_bool (tptp.hAPP_A1378093259t_bool F X_2)) B))))) (forall ((X_2 tptp.bool) (F tptp.fun_bo559790694t_bool) (A tptp.fun_bool_bool) (B tptp.fun_fu2098777574l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1211446716l_bool (tptp.hAPP_f1134773005l_bool tptp.member1782492345t_bool F) (tptp.pi_boo769613946t_bool A (tptp.hAPP_f369767947l_bool tptp.cOMBK_2030738485l_bool B)))) (=> (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.hAPP_b1787118453l_bool tptp.member_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f1714503811l_bool tptp.member173038353t_bool (tptp.hAPP_b1029214724t_bool F X_2)) B))))) (forall ((X_2 tptp.product_unit) (F tptp.fun_Pr2016729180t_bool) (A tptp.fun_Pr1643180309t_bool) (B tptp.fun_fu2098777574l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f2068478898l_bool (tptp.hAPP_f1883507597l_bool tptp.member480326063t_bool F) (tptp.pi_Pro1533274736t_bool A (tptp.hAPP_f956752277l_bool tptp.cOMBK_1075760171t_unit B)))) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_P607165281l_bool tptp.member_Product_unit X_2) A)) (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f1714503811l_bool tptp.member173038353t_bool (tptp.hAPP_P1858715130t_bool F X_2)) B))))) (forall ((X_2 tptp.bool) (F tptp.fun_bo1431306493t_bool) (A tptp.fun_bool_bool) (B tptp.fun_fu638310559l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f398210311l_bool (tptp.hAPP_f416878261l_bool tptp.member1133581546t_bool F) (tptp.pi_boo1111177555t_bool A (tptp.hAPP_f86272063l_bool tptp.cOMBK_650639032l_bool B)))) (=> (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.hAPP_b1787118453l_bool tptp.member_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1482930381l_bool tptp.member1069471740t_bool (tptp.hAPP_b128655177t_bool F X_2)) B))))) (forall ((X_2 tptp.product_unit) (F tptp.fun_Pr1887398791t_bool) (A tptp.fun_Pr1643180309t_bool) (B tptp.fun_fu638310559l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1426814865l_bool (tptp.hAPP_f1942212041l_bool tptp.member803887220t_bool F) (tptp.pi_Pro1290680285t_bool A (tptp.hAPP_f502523701l_bool tptp.cOMBK_1521810862t_unit B)))) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_P607165281l_bool tptp.member_Product_unit X_2) A)) (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1482930381l_bool tptp.member1069471740t_bool (tptp.hAPP_P1914371027t_bool F X_2)) B))))) (forall ((X_2 tptp.arrow_856714788e_indi) (F tptp.fun_Ar671024215di_nat) (A tptp.fun_Ar1809396326i_bool) (B tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f225240161l_bool (tptp.hAPP_f677301097l_bool tptp.member1502495556di_nat F) (tptp.pi_Arr1233262509di_nat A (tptp.hAPP_f1132083526t_bool tptp.cOMBK_833041760e_indi B)))) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_A1597696899l_bool tptp.member1479139729e_indi X_2) A)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat (tptp.hAPP_A376526755di_nat F X_2)) B))))) (forall ((X_2 tptp.bool) (F tptp.fun_bool_nat) (A tptp.fun_bool_bool) (B tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f67777128l_bool (tptp.hAPP_f144393719l_bool tptp.member_fun_bool_nat F) (tptp.pi_bool_nat A (tptp.hAPP_f1247925759t_bool tptp.cOMBK_1034797721l_bool B)))) (=> (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.hAPP_b1787118453l_bool tptp.member_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat (tptp.hAPP_bool_nat F X_2)) B))))) (forall ((X_2 tptp.product_unit) (F tptp.fun_Product_unit_nat) (A tptp.fun_Pr1643180309t_bool) (B tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f339859954l_bool (tptp.hAPP_f1950626059l_bool tptp.member87760213it_nat F) (tptp.pi_Product_unit_nat A (tptp.hAPP_f1212412661t_bool tptp.cOMBK_356206223t_unit B)))) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_P607165281l_bool tptp.member_Product_unit X_2) A)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat (tptp.hAPP_P426034740it_nat F X_2)) B))))) (forall ((X_2 tptp.fun_Ar274636406t_bool) (F tptp.fun_fu2114379172t_bool) (A tptp.fun_fu3835832l_bool) (B tptp.fun_fu638310559l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f1714503811l_bool tptp.member173038353t_bool F) (tptp.pi_fun1746584570t_bool A (tptp.hAPP_f1104294872l_bool tptp.cOMBK_1701906001t_bool B)))) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f1225332775l_bool tptp.member933336803t_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1482930381l_bool tptp.member1069471740t_bool (tptp.hAPP_f2008608496t_bool F X_2)) B))))) (forall ((X_2 tptp.arrow_856714788e_indi) (F tptp.fun_Ar274636406t_bool) (A tptp.fun_Ar1809396326i_bool) (B tptp.fun_fu638310559l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f1225332775l_bool tptp.member933336803t_bool F) (tptp.pi_Arr959578316t_bool A (tptp.hAPP_f1717907078l_bool tptp.cOMBK_1520063231e_indi B)))) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_A1597696899l_bool tptp.member1479139729e_indi X_2) A)) (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1482930381l_bool tptp.member1069471740t_bool (tptp.hAPP_A1646126530t_bool F X_2)) B))))) (forall ((X_2 tptp.arrow_856714788e_indi) (Y_2 tptp.arrow_856714788e_indi) (F tptp.fun_Ar671024215di_nat)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.inj_on1960344199di_nat F) tptp.top_to788185952i_bool)) (= (= (tptp.hAPP_A376526755di_nat F X_2) (tptp.hAPP_A376526755di_nat F Y_2)) (= X_2 Y_2)))) (forall ((X_2 tptp.nat) (Y_2 tptp.nat) (F tptp.fun_nat_nat)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.inj_on_nat_nat F) tptp.top_top_fun_nat_bool)) (= (= (tptp.hAPP_nat_nat F X_2) (tptp.hAPP_nat_nat F Y_2)) (= X_2 Y_2)))) (forall ((X_2 tptp.arrow_856714788e_indi) (Y_2 tptp.arrow_856714788e_indi) (F tptp.fun_Ar671024215di_nat)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.inj_on1960344199di_nat F) tptp.top_to788185952i_bool)) (=> (= (tptp.hAPP_A376526755di_nat F X_2) (tptp.hAPP_A376526755di_nat F Y_2)) (= X_2 Y_2)))) (forall ((X_2 tptp.nat) (Y_2 tptp.nat) (F tptp.fun_nat_nat)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.inj_on_nat_nat F) tptp.top_top_fun_nat_bool)) (=> (= (tptp.hAPP_nat_nat F X_2) (tptp.hAPP_nat_nat F Y_2)) (= X_2 Y_2)))) (forall ((X_2 tptp.arrow_856714788e_indi) (F tptp.fun_Ar671024215di_nat) (A tptp.fun_Ar1809396326i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.inj_on1960344199di_nat F) A)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_A1597696899l_bool tptp.member1479139729e_indi X_2) A)) (= (tptp.hAPP_n1937165849e_indi (tptp.hilber1580028780di_nat A F) (tptp.hAPP_A376526755di_nat F X_2)) X_2)))) (forall ((X_2 tptp.nat) (F tptp.fun_nat_nat) (A tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.inj_on_nat_nat F) A)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) A)) (= (tptp.hAPP_nat_nat (tptp.hilber195283148at_nat A F) (tptp.hAPP_nat_nat F X_2)) X_2)))) (forall ((Y_2 tptp.nat) (X_2 tptp.arrow_856714788e_indi) (F tptp.fun_Ar671024215di_nat) (A tptp.fun_Ar1809396326i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.inj_on1960344199di_nat F) A)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_A1597696899l_bool tptp.member1479139729e_indi X_2) A)) (=> (= (tptp.hAPP_A376526755di_nat F X_2) Y_2) (= (tptp.hAPP_n1937165849e_indi (tptp.hilber1580028780di_nat A F) Y_2) X_2))))) (forall ((Y_2 tptp.nat) (X_2 tptp.nat) (F tptp.fun_nat_nat) (A tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.inj_on_nat_nat F) A)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) A)) (=> (= (tptp.hAPP_nat_nat F X_2) Y_2) (= (tptp.hAPP_nat_nat (tptp.hilber195283148at_nat A F) Y_2) X_2))))) (forall ((F tptp.fun_Pr1509342064e_indi) (B tptp.fun_Pr895221296i_bool) (A tptp.fun_Pr2067565481t_bool)) (=> (forall ((X_1 tptp.produc472769767le_alt)) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt X_1) A)) (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_A1597696899l_bool tptp.member1479139729e_indi (tptp.hAPP_P276596750e_indi F X_1)) (tptp.hAPP_P1859429372i_bool B X_1))))) (tptp.hBOOL (tptp.hAPP_f2124588998l_bool (tptp.hAPP_f1187850253l_bool tptp.member1558233923e_indi F) (tptp.pi_Pro837265796e_indi A B))))) (forall ((F tptp.fun_Pr376858015t_unit) (B tptp.fun_Pr1069395679t_bool) (A tptp.fun_Pr2067565481t_bool)) (=> (forall ((X_1 tptp.produc472769767le_alt)) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt X_1) A)) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_P607165281l_bool tptp.member_Product_unit (tptp.hAPP_P1069491261t_unit F X_1)) (tptp.hAPP_P2037731755t_bool B X_1))))) (tptp.hBOOL (tptp.hAPP_f1159856629l_bool (tptp.hAPP_f1700632141l_bool tptp.member1303779570t_unit F) (tptp.pi_Pro346842291t_unit A B))))) (forall ((F tptp.fun_fu1929591039e_indi) (B tptp.fun_fu223278561i_bool) (A tptp.fun_fu3835832l_bool)) (=> (forall ((X_1 tptp.fun_Ar274636406t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f1225332775l_bool tptp.member933336803t_bool X_1) A)) (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_A1597696899l_bool tptp.member1479139729e_indi (tptp.hAPP_f602741661e_indi F X_1)) (tptp.hAPP_f391644589i_bool B X_1))))) (tptp.hBOOL (tptp.hAPP_f665932885l_bool (tptp.hAPP_f430646093l_bool tptp.member282602450e_indi F) (tptp.pi_fun520512275e_indi A B))))) (forall ((F tptp.fun_fu3835832l_bool) (B tptp.fun_fu916327706l_bool) (A tptp.fun_fu3835832l_bool)) (=> (forall ((X_1 tptp.fun_Ar274636406t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f1225332775l_bool tptp.member933336803t_bool X_1) A)) (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.hAPP_b1787118453l_bool tptp.member_bool (tptp.hAPP_f995490902l_bool F X_1)) (tptp.hAPP_f1676084198l_bool B X_1))))) (tptp.hBOOL (tptp.hAPP_f1867557646l_bool (tptp.hAPP_f1048573069l_bool tptp.member1020280587l_bool F) (tptp.pi_fun853738700l_bool A B))))) (forall ((F tptp.fun_fu1023022254t_unit) (B tptp.fun_fu1734317328t_bool) (A tptp.fun_fu3835832l_bool)) (=> (forall ((X_1 tptp.fun_Ar274636406t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f1225332775l_bool tptp.member933336803t_bool X_1) A)) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_P607165281l_bool tptp.member_Product_unit (tptp.hAPP_f1775626572t_unit F X_1)) (tptp.hAPP_f1438163420t_bool B X_1))))) (tptp.hBOOL (tptp.hAPP_f115957764l_bool (tptp.hAPP_f1184790797l_bool tptp.member2003579649t_unit F) (tptp.pi_fun1644711874t_unit A B))))) (forall ((F tptp.fun_fu748153389e_indi) (B tptp.fun_fu2109152051i_bool) (A tptp.fun_fu2098777574l_bool)) (=> (forall ((X_1 tptp.fun_fu2114379172t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f1714503811l_bool tptp.member173038353t_bool X_1) A)) (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_A1597696899l_bool tptp.member1479139729e_indi (tptp.hAPP_f350323403e_indi F X_1)) (tptp.hAPP_f399308031i_bool B X_1))))) (tptp.hBOOL (tptp.hAPP_f2350467l_bool (tptp.hAPP_f1411422157l_bool tptp.member1247254528e_indi F) (tptp.pi_fun1807454273e_indi A B))))) (forall ((F tptp.fun_fu2098777574l_bool) (B tptp.fun_fu1522163052l_bool) (A tptp.fun_fu2098777574l_bool)) (=> (forall ((X_1 tptp.fun_fu2114379172t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f1714503811l_bool tptp.member173038353t_bool X_1) A)) (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.hAPP_b1787118453l_bool tptp.member_bool (tptp.hAPP_f1572141188l_bool F X_1)) (tptp.hAPP_f414129720l_bool B X_1))))) (tptp.hBOOL (tptp.hAPP_f2047920444l_bool (tptp.hAPP_f59810573l_bool tptp.member1173995577l_bool F) (tptp.pi_fun1312540410l_bool A B))))) (forall ((F tptp.fun_fu1480298716t_unit) (B tptp.fun_fu1143287650t_bool) (A tptp.fun_fu2098777574l_bool)) (=> (forall ((X_1 tptp.fun_fu2114379172t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f1714503811l_bool tptp.member173038353t_bool X_1) A)) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_P607165281l_bool tptp.member_Product_unit (tptp.hAPP_f1865816954t_unit F X_1)) (tptp.hAPP_f151782958t_bool B X_1))))) (tptp.hBOOL (tptp.hAPP_f92582962l_bool (tptp.hAPP_f1494690701l_bool tptp.member2091379247t_unit F) (tptp.pi_fun1540376560t_unit A B))))) (forall ((F tptp.fun_fu562005862e_indi) (B tptp.fun_fu2142850746i_bool) (A tptp.fun_fu638310559l_bool)) (=> (forall ((X_1 tptp.fun_Pr2067565481t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1482930381l_bool tptp.member1069471740t_bool X_1) A)) (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_A1597696899l_bool tptp.member1479139729e_indi (tptp.hAPP_f9587896e_indi F X_1)) (tptp.hAPP_f2010315474i_bool B X_1))))) (tptp.hBOOL (tptp.hAPP_f679138160l_bool (tptp.hAPP_f1006969351l_bool tptp.member1220706259e_indi F) (tptp.pi_fun1470523330e_indi A B))))) (forall ((F tptp.fun_fu638310559l_bool) (B tptp.fun_fu237781875l_bool) (A tptp.fun_fu638310559l_bool)) (=> (forall ((X_1 tptp.fun_Pr2067565481t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1482930381l_bool tptp.member1069471740t_bool X_1) A)) (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.hAPP_b1787118453l_bool tptp.member_bool (tptp.hAPP_f52567537l_bool F X_1)) (tptp.hAPP_f463104139l_bool B X_1))))) (tptp.hBOOL (tptp.hAPP_f1686510249l_bool (tptp.hAPP_f1930590713l_bool tptp.member340585612l_bool F) (tptp.pi_fun1035089915l_bool A B))))) (forall ((F tptp.fun_fu665686165t_unit) (B tptp.fun_fu643686505t_bool) (A tptp.fun_fu638310559l_bool)) (=> (forall ((X_1 tptp.fun_Pr2067565481t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1482930381l_bool tptp.member1069471740t_bool X_1) A)) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_P607165281l_bool tptp.member_Product_unit (tptp.hAPP_f801675751t_unit F X_1)) (tptp.hAPP_f1400551297t_bool B X_1))))) (tptp.hBOOL (tptp.hAPP_f1478188703l_bool (tptp.hAPP_f1329172965l_bool tptp.member1729658242t_unit F) (tptp.pi_fun177985009t_unit A B))))) (forall ((F tptp.fun_na699243463e_indi) (B tptp.fun_na2037635353i_bool) (A tptp.fun_nat_bool)) (=> (forall ((X_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)) (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_A1597696899l_bool tptp.member1479139729e_indi (tptp.hAPP_n1937165849e_indi F X_1)) (tptp.hAPP_n34002993i_bool B X_1))))) (tptp.hBOOL (tptp.hAPP_f736267217l_bool (tptp.hAPP_f707406409l_bool tptp.member1530714804e_indi F) (tptp.pi_nat646417955e_indi A B))))) (forall ((F tptp.fun_nat_bool) (B tptp.fun_na1469252690l_bool) (A tptp.fun_nat_bool)) (=> (forall ((X_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)) (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.hAPP_b1787118453l_bool tptp.member_bool (tptp.hAPP_nat_bool F X_1)) (tptp.hAPP_n1006566506l_bool B X_1))))) (tptp.hBOOL (tptp.hAPP_f1637334154l_bool (tptp.hAPP_f1951378235l_bool tptp.member_fun_nat_bool F) (tptp.pi_nat_bool A B))))) (forall ((F tptp.fun_nat_Product_unit) (B tptp.fun_na1041622088t_bool) (A tptp.fun_nat_bool)) (=> (forall ((X_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_P607165281l_bool tptp.member_Product_unit (tptp.hAPP_n633340360t_unit F X_1)) (tptp.hAPP_n454528608t_bool B X_1))))) (tptp.hBOOL (tptp.hAPP_f537623936l_bool (tptp.hAPP_f1598887207l_bool tptp.member1024687843t_unit F) (tptp.pi_nat_Product_unit A B))))) (forall ((F tptp.fun_Ar338949104le_alt) (B tptp.fun_Ar274636406t_bool) (A tptp.fun_Ar1809396326i_bool)) (=> (forall ((X_1 tptp.arrow_856714788e_indi)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_A1597696899l_bool tptp.member1479139729e_indi X_1) A)) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_A899858958le_alt F X_1)) (tptp.hAPP_A1646126530t_bool B X_1))))) (tptp.hBOOL (tptp.hAPP_f1754488902l_bool (tptp.hAPP_f766019597l_bool tptp.member387840963le_alt F) (tptp.pi_Arr1460528004le_alt A B))))) (forall ((F tptp.fun_bo1682907689le_alt) (B tptp.fun_bo1431306493t_bool) (A tptp.fun_bool_bool)) (=> (forall ((X_1 tptp.bool)) (=> (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.hAPP_b1787118453l_bool tptp.member_bool X_1) A)) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_b2094455111le_alt F X_1)) (tptp.hAPP_b128655177t_bool B X_1))))) (tptp.hBOOL (tptp.hAPP_f1620711039l_bool (tptp.hAPP_f334747853l_bool tptp.member684813948le_alt F) (tptp.pi_boo7125949le_alt A B))))) (forall ((F tptp.fun_Pr2090226719le_alt) (B tptp.fun_Pr1887398791t_bool) (A tptp.fun_Pr1643180309t_bool)) (=> (forall ((X_1 tptp.product_unit)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_P607165281l_bool tptp.member_Product_unit X_1) A)) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt (tptp.hAPP_P396106045le_alt F X_1)) (tptp.hAPP_P1914371027t_bool B X_1))))) (tptp.hBOOL (tptp.hAPP_f684683381l_bool (tptp.hAPP_f41367117l_bool tptp.member869664626le_alt F) (tptp.pi_Pro1820940723le_alt A B))))) (forall ((F tptp.fun_Ar624010239t_bool) (B tptp.fun_Ar1998664965l_bool) (A tptp.fun_Ar1809396326i_bool)) (=> (forall ((X_1 tptp.arrow_856714788e_indi)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_A1597696899l_bool tptp.member1479139729e_indi X_1) A)) (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f1225332775l_bool tptp.member933336803t_bool (tptp.hAPP_A2107398813t_bool F X_1)) (tptp.hAPP_A1411662545l_bool B X_1))))) (tptp.hBOOL (tptp.hAPP_f826064725l_bool (tptp.hAPP_f1364091725l_bool tptp.member1124505298t_bool F) (tptp.pi_Arr2025169427t_bool A B))))) (forall ((F tptp.fun_bo1476023096t_bool) (B tptp.fun_bo2107365004l_bool) (A tptp.fun_bool_bool)) (=> (forall ((X_1 tptp.bool)) (=> (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.hAPP_b1787118453l_bool tptp.member_bool X_1) A)) (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f1225332775l_bool tptp.member933336803t_bool (tptp.hAPP_b489616086t_bool F X_1)) (tptp.hAPP_b1078573912l_bool B X_1))))) (tptp.hBOOL (tptp.hAPP_f1605957262l_bool (tptp.hAPP_f1525863565l_bool tptp.member344984203t_bool F) (tptp.pi_boo347863884t_bool A B))))) (forall ((F tptp.fun_Pr1531194158t_bool) (B tptp.fun_Pr537467670l_bool) (A tptp.fun_Pr1643180309t_bool)) (=> (forall ((X_1 tptp.product_unit)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_P607165281l_bool tptp.member_Product_unit X_1) A)) (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f1225332775l_bool tptp.member933336803t_bool (tptp.hAPP_P913627340t_bool F X_1)) (tptp.hAPP_P284783074l_bool B X_1))))) (tptp.hBOOL (tptp.hAPP_f1851324036l_bool (tptp.hAPP_f1974966541l_bool tptp.member364267905t_bool F) (tptp.pi_Pro782712642t_bool A B))))) (forall ((F tptp.fun_Ar286530093t_bool) (B tptp.fun_Ar1321653811l_bool) (A tptp.fun_Ar1809396326i_bool)) (=> (forall ((X_1 tptp.arrow_856714788e_indi)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_A1597696899l_bool tptp.member1479139729e_indi X_1) A)) (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f1714503811l_bool tptp.member173038353t_bool (tptp.hAPP_A1378093259t_bool F X_1)) (tptp.hAPP_A2084592127l_bool B X_1))))) (tptp.hBOOL (tptp.hAPP_f686820739l_bool (tptp.hAPP_f692361165l_bool tptp.member785631232t_bool F) (tptp.pi_Arr687740481t_bool A B))))) (forall ((F tptp.fun_bo559790694t_bool) (B tptp.fun_bo1445676730l_bool) (A tptp.fun_bool_bool)) (=> (forall ((X_1 tptp.bool)) (=> (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.hAPP_b1787118453l_bool tptp.member_bool X_1) A)) (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f1714503811l_bool tptp.member173038353t_bool (tptp.hAPP_b1029214724t_bool F X_1)) (tptp.hAPP_b1777246598l_bool B X_1))))) (tptp.hBOOL (tptp.hAPP_f1211446716l_bool (tptp.hAPP_f1134773005l_bool tptp.member1782492345t_bool F) (tptp.pi_boo769613946t_bool A B))))) (forall ((F tptp.fun_Pr2016729180t_bool) (B tptp.fun_Pr151242052l_bool) (A tptp.fun_Pr1643180309t_bool)) (=> (forall ((X_1 tptp.product_unit)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_P607165281l_bool tptp.member_Product_unit X_1) A)) (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f1714503811l_bool tptp.member173038353t_bool (tptp.hAPP_P1858715130t_bool F X_1)) (tptp.hAPP_P283873808l_bool B X_1))))) (tptp.hBOOL (tptp.hAPP_f2068478898l_bool (tptp.hAPP_f1883507597l_bool tptp.member480326063t_bool F) (tptp.pi_Pro1533274736t_bool A B))))) (forall ((F tptp.fun_bo1431306493t_bool) (B tptp.fun_bo377688929l_bool) (A tptp.fun_bool_bool)) (=> (forall ((X_1 tptp.bool)) (=> (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.hAPP_b1787118453l_bool tptp.member_bool X_1) A)) (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1482930381l_bool tptp.member1069471740t_bool (tptp.hAPP_b128655177t_bool F X_1)) (tptp.hAPP_b1272691967l_bool B X_1))))) (tptp.hBOOL (tptp.hAPP_f398210311l_bool (tptp.hAPP_f416878261l_bool tptp.member1133581546t_bool F) (tptp.pi_boo1111177555t_bool A B))))) (forall ((F tptp.fun_Pr1887398791t_bool) (B tptp.fun_Pr1791323223l_bool) (A tptp.fun_Pr1643180309t_bool)) (=> (forall ((X_1 tptp.product_unit)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_P607165281l_bool tptp.member_Product_unit X_1) A)) (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1482930381l_bool tptp.member1069471740t_bool (tptp.hAPP_P1914371027t_bool F X_1)) (tptp.hAPP_P754918389l_bool B X_1))))) (tptp.hBOOL (tptp.hAPP_f1426814865l_bool (tptp.hAPP_f1942212041l_bool tptp.member803887220t_bool F) (tptp.pi_Pro1290680285t_bool A B))))) (forall ((F tptp.fun_Ar671024215di_nat) (B tptp.fun_Ar603939593t_bool) (A tptp.fun_Ar1809396326i_bool)) (=> (forall ((X_1 tptp.arrow_856714788e_indi)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_A1597696899l_bool tptp.member1479139729e_indi X_1) A)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat (tptp.hAPP_A376526755di_nat F X_1)) (tptp.hAPP_A1686943911t_bool B X_1))))) (tptp.hBOOL (tptp.hAPP_f225240161l_bool (tptp.hAPP_f677301097l_bool tptp.member1502495556di_nat F) (tptp.pi_Arr1233262509di_nat A B))))) (forall ((F tptp.fun_bool_nat) (B tptp.fun_bo1570548802t_bool) (A tptp.fun_bool_bool)) (=> (forall ((X_1 tptp.bool)) (=> (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.hAPP_b1787118453l_bool tptp.member_bool X_1) A)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat (tptp.hAPP_bool_nat F X_1)) (tptp.hAPP_b1013836512t_bool B X_1))))) (tptp.hBOOL (tptp.hAPP_f67777128l_bool (tptp.hAPP_f144393719l_bool tptp.member_fun_bool_nat F) (tptp.pi_bool_nat A B))))) (forall ((F tptp.fun_Product_unit_nat) (B tptp.fun_Pr1029464120t_bool) (A tptp.fun_Pr1643180309t_bool)) (=> (forall ((X_1 tptp.product_unit)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_P607165281l_bool tptp.member_Product_unit X_1) A)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat (tptp.hAPP_P426034740it_nat F X_1)) (tptp.hAPP_P32877782t_bool B X_1))))) (tptp.hBOOL (tptp.hAPP_f339859954l_bool (tptp.hAPP_f1950626059l_bool tptp.member87760213it_nat F) (tptp.pi_Product_unit_nat A B))))) (forall ((F tptp.fun_Pr2067565481t_bool) (B tptp.fun_Pr1780397033l_bool) (A tptp.fun_Pr2067565481t_bool)) (=> (forall ((X_1 tptp.produc472769767le_alt)) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt X_1) A)) (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.hAPP_b1787118453l_bool tptp.member_bool (tptp.hAPP_P1178790471t_bool F X_1)) (tptp.hAPP_P1103642805l_bool B X_1))))) (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1482930381l_bool tptp.member1069471740t_bool F) (tptp.pi_Pro1238944957t_bool A B))))) (forall ((F tptp.fun_fu2114379172t_bool) (B tptp.fun_fu1863781882l_bool) (A tptp.fun_fu3835832l_bool)) (=> (forall ((X_1 tptp.fun_Ar274636406t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f1225332775l_bool tptp.member933336803t_bool X_1) A)) (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1482930381l_bool tptp.member1069471740t_bool (tptp.hAPP_f2008608496t_bool F X_1)) (tptp.hAPP_f1915815064l_bool B X_1))))) (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f1714503811l_bool tptp.member173038353t_bool F) (tptp.pi_fun1746584570t_bool A B))))) (forall ((F tptp.fun_Ar274636406t_bool) (B tptp.fun_Ar1474557608l_bool) (A tptp.fun_Ar1809396326i_bool)) (=> (forall ((X_1 tptp.arrow_856714788e_indi)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_A1597696899l_bool tptp.member1479139729e_indi X_1) A)) (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1482930381l_bool tptp.member1069471740t_bool (tptp.hAPP_A1646126530t_bool F X_1)) (tptp.hAPP_A897398598l_bool B X_1))))) (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f1225332775l_bool tptp.member933336803t_bool F) (tptp.pi_Arr959578316t_bool A B))))) (forall ((G tptp.fun_na699243463e_indi) (F tptp.fun_Ar671024215di_nat)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.inj_on1960344199di_nat F) tptp.top_to788185952i_bool)) (=> (forall ((X_1 tptp.nat)) (= (tptp.hAPP_A376526755di_nat F (tptp.hAPP_n1937165849e_indi G X_1)) X_1)) (= (tptp.hilber1580028780di_nat tptp.top_to788185952i_bool F) G)))) (forall ((G tptp.fun_nat_nat) (F tptp.fun_nat_nat)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.inj_on_nat_nat F) tptp.top_top_fun_nat_bool)) (=> (forall ((X_1 tptp.nat)) (= (tptp.hAPP_nat_nat F (tptp.hAPP_nat_nat G X_1)) X_1)) (= (tptp.hilber195283148at_nat tptp.top_top_fun_nat_bool F) G)))) (forall ((A_18 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_18) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_18) tptp.one_one_nat)))) (forall ((C_16 tptp.nat) (D_3 tptp.nat) (A_17 tptp.nat) (B_16 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_17) B_16)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat C_16) D_3)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_17) C_16)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat B_16) D_3)))))) (forall ((C_15 tptp.nat) (D_2 tptp.nat) (A_16 tptp.nat) (B_15 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_16) B_15)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat C_15) D_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_16) C_15)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat B_15) D_2)))))) (forall ((F tptp.fun_Ar671024215di_nat)) (=> (forall ((X_1 tptp.arrow_856714788e_indi) (Y_1 tptp.arrow_856714788e_indi)) (=> (= (tptp.hAPP_A376526755di_nat F X_1) (tptp.hAPP_A376526755di_nat F Y_1)) (= X_1 Y_1))) (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.inj_on1960344199di_nat F) tptp.top_to788185952i_bool)))) (forall ((F tptp.fun_nat_nat)) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (= (tptp.hAPP_nat_nat F X_1) (tptp.hAPP_nat_nat F Y_1)) (= X_1 Y_1))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.inj_on_nat_nat F) tptp.top_top_fun_nat_bool)))) (forall ((Ca tptp.fun_nat_bool) (F tptp.fun_fu821463397t_bool) (Ba tptp.fun_nat_bool) (Aa tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool Ba) Aa)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Ca) (tptp.hAPP_f800510211t_bool F Ba))) (=> (forall ((X_1 tptp.fun_nat_bool) (Y_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool (tptp.hAPP_f800510211t_bool F Y_1)) (tptp.hAPP_f800510211t_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool Ca) (tptp.hAPP_f800510211t_bool F Aa))))))) (forall ((Ca tptp.fun_nat_bool) (F tptp.fun_fu988033326t_bool) (Ba tptp.fun_Pr1643180309t_bool) (Aa tptp.fun_Pr1643180309t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool Ba) Aa)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Ca) (tptp.hAPP_f543204480t_bool F Ba))) (=> (forall ((X_1 tptp.fun_Pr1643180309t_bool) (Y_1 tptp.fun_Pr1643180309t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool (tptp.hAPP_f543204480t_bool F Y_1)) (tptp.hAPP_f543204480t_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool Ca) (tptp.hAPP_f543204480t_bool F Aa))))))) (forall ((Ca tptp.fun_nat_bool) (F tptp.fun_fu1254370943t_bool) (Ba tptp.fun_Ar1809396326i_bool) (Aa tptp.fun_Ar1809396326i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool Ba) Aa)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Ca) (tptp.hAPP_f622418129t_bool F Ba))) (=> (forall ((X_1 tptp.fun_Ar1809396326i_bool) (Y_1 tptp.fun_Ar1809396326i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool (tptp.hAPP_f622418129t_bool F Y_1)) (tptp.hAPP_f622418129t_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool Ca) (tptp.hAPP_f622418129t_bool F Aa))))))) (forall ((Ca tptp.fun_nat_bool) (F tptp.fun_nat_fun_nat_bool) (Ba tptp.nat) (Aa tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ba) Aa)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Ca) (tptp.hAPP_n1699378549t_bool F Ba))) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool (tptp.hAPP_n1699378549t_bool F Y_1)) (tptp.hAPP_n1699378549t_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool Ca) (tptp.hAPP_n1699378549t_bool F Aa))))))) (forall ((Ca tptp.fun_Pr1643180309t_bool) (F tptp.fun_na1041622088t_bool) (Ba tptp.nat) (Aa tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ba) Aa)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool Ca) (tptp.hAPP_n454528608t_bool F Ba))) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool (tptp.hAPP_n454528608t_bool F Y_1)) (tptp.hAPP_n454528608t_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool Ca) (tptp.hAPP_n454528608t_bool F Aa))))))) (forall ((Ca tptp.fun_Ar1809396326i_bool) (F tptp.fun_na2037635353i_bool) (Ba tptp.nat) (Aa tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ba) Aa)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool Ca) (tptp.hAPP_n34002993i_bool F Ba))) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool (tptp.hAPP_n34002993i_bool F Y_1)) (tptp.hAPP_n34002993i_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool Ca) (tptp.hAPP_n34002993i_bool F Aa))))))) (forall ((Ca tptp.fun_fu638310559l_bool) (F tptp.fun_na144630978l_bool) (Ba tptp.nat) (Aa tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ba) Aa)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool Ca) (tptp.hAPP_n1134275860l_bool F Ba))) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1727358153l_bool (tptp.hAPP_n1134275860l_bool F Y_1)) (tptp.hAPP_n1134275860l_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1727358153l_bool Ca) (tptp.hAPP_n1134275860l_bool F Aa))))))) (forall ((Ca tptp.fun_fu2098777574l_bool) (F tptp.fun_na138495129l_bool) (Ba tptp.nat) (Aa tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ba) Aa)) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool Ca) (tptp.hAPP_n1555388849l_bool F Ba))) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le119247420l_bool (tptp.hAPP_n1555388849l_bool F Y_1)) (tptp.hAPP_n1555388849l_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le119247420l_bool Ca) (tptp.hAPP_n1555388849l_bool F Aa))))))) (forall ((Ca tptp.fun_fu3835832l_bool) (F tptp.fun_na6909291l_bool) (Ba tptp.nat) (Aa tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ba) Aa)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool Ca) (tptp.hAPP_n2125602947l_bool F Ba))) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1959568910l_bool (tptp.hAPP_n2125602947l_bool F Y_1)) (tptp.hAPP_n2125602947l_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1959568910l_bool Ca) (tptp.hAPP_n2125602947l_bool F Aa))))))) (forall ((Ca tptp.fun_Pr2067565481t_bool) (F tptp.fun_na998785244t_bool) (Ba tptp.nat) (Aa tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ba) Aa)) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool Ca) (tptp.hAPP_n1161265524t_bool F Ba))) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1478665215t_bool (tptp.hAPP_n1161265524t_bool F Y_1)) (tptp.hAPP_n1161265524t_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1478665215t_bool Ca) (tptp.hAPP_n1161265524t_bool F Aa))))))) (forall ((Ca tptp.bool) (F tptp.fun_nat_bool) (Ba tptp.nat) (Aa tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ba) Aa)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Ca) (tptp.hAPP_nat_bool F Ba))) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_bool (tptp.hAPP_nat_bool F Y_1)) (tptp.hAPP_nat_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_bool Ca) (tptp.hAPP_nat_bool F Aa))))))) (forall ((Ca tptp.fun_Ar331856045t_bool) (F tptp.fun_na300967376t_bool) (Ba tptp.nat) (Aa tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ba) Aa)) (=> (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool Ca) (tptp.hAPP_n1312530466t_bool F Ba))) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le19409623t_bool (tptp.hAPP_n1312530466t_bool F Y_1)) (tptp.hAPP_n1312530466t_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le19409623t_bool Ca) (tptp.hAPP_n1312530466t_bool F Aa))))))) (forall ((Ca tptp.nat) (F tptp.fun_fun_nat_bool_nat) (Ba tptp.fun_nat_bool) (Aa tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool Ba) Aa)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ca) (tptp.hAPP_f22106695ol_nat F Ba))) (=> (forall ((X_1 tptp.fun_nat_bool) (Y_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_f22106695ol_nat F Y_1)) (tptp.hAPP_f22106695ol_nat F X_1))))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ca) (tptp.hAPP_f22106695ol_nat F Aa))))))) (forall ((Ca tptp.nat) (F tptp.fun_fu572628082ol_nat) (Ba tptp.fun_Pr1643180309t_bool) (Aa tptp.fun_Pr1643180309t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool Ba) Aa)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ca) (tptp.hAPP_f2030293770ol_nat F Ba))) (=> (forall ((X_1 tptp.fun_Pr1643180309t_bool) (Y_1 tptp.fun_Pr1643180309t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_f2030293770ol_nat F Y_1)) (tptp.hAPP_f2030293770ol_nat F X_1))))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ca) (tptp.hAPP_f2030293770ol_nat F Aa))))))) (forall ((Ca tptp.nat) (F tptp.fun_fu1603738721ol_nat) (Ba tptp.fun_Ar1809396326i_bool) (Aa tptp.fun_Ar1809396326i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool Ba) Aa)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ca) (tptp.hAPP_f846027769ol_nat F Ba))) (=> (forall ((X_1 tptp.fun_Ar1809396326i_bool) (Y_1 tptp.fun_Ar1809396326i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_f846027769ol_nat F Y_1)) (tptp.hAPP_f846027769ol_nat F X_1))))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ca) (tptp.hAPP_f846027769ol_nat F Aa))))))) (forall ((Ca tptp.fun_nat_bool) (F tptp.fun_nat_fun_nat_bool) (Ba tptp.nat) (Aa tptp.nat)) (let ((_let_1 (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool Ca))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ba) Aa)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_n1699378549t_bool F Ba))) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_n1699378549t_bool F Y_1)) (tptp.hAPP_n1699378549t_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_n1699378549t_bool F Aa)))))))) (forall ((Ca tptp.fun_Pr1643180309t_bool) (F tptp.fun_na1041622088t_bool) (Ba tptp.nat) (Aa tptp.nat)) (let ((_let_1 (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool Ca))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ba) Aa)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool _let_1 (tptp.hAPP_n454528608t_bool F Ba))) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool (tptp.hAPP_n454528608t_bool F Y_1)) (tptp.hAPP_n454528608t_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool _let_1 (tptp.hAPP_n454528608t_bool F Aa)))))))) (forall ((Ca tptp.fun_Ar1809396326i_bool) (F tptp.fun_na2037635353i_bool) (Ba tptp.nat) (Aa tptp.nat)) (let ((_let_1 (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool Ca))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ba) Aa)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool _let_1 (tptp.hAPP_n34002993i_bool F Ba))) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool (tptp.hAPP_n34002993i_bool F Y_1)) (tptp.hAPP_n34002993i_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f584385070l_bool _let_1 (tptp.hAPP_n34002993i_bool F Aa)))))))) (forall ((Ca tptp.fun_fu638310559l_bool) (F tptp.fun_na144630978l_bool) (Ba tptp.nat) (Aa tptp.nat)) (let ((_let_1 (tptp.hAPP_f1722316607l_bool tptp.ord_le1727358153l_bool Ca))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ba) Aa)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool _let_1 (tptp.hAPP_n1134275860l_bool F Ba))) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool (tptp.hAPP_n1134275860l_bool F Y_1)) (tptp.hAPP_n1134275860l_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f182583295l_bool _let_1 (tptp.hAPP_n1134275860l_bool F Aa)))))))) (forall ((Ca tptp.fun_fu2098777574l_bool) (F tptp.fun_na138495129l_bool) (Ba tptp.nat) (Aa tptp.nat)) (let ((_let_1 (tptp.hAPP_f916323245l_bool tptp.ord_le119247420l_bool Ca))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ba) Aa)) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool _let_1 (tptp.hAPP_n1555388849l_bool F Ba))) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool (tptp.hAPP_n1555388849l_bool F Y_1)) (tptp.hAPP_n1555388849l_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f975209902l_bool _let_1 (tptp.hAPP_n1555388849l_bool F Aa)))))))) (forall ((Ca tptp.fun_fu3835832l_bool) (F tptp.fun_na6909291l_bool) (Ba tptp.nat) (Aa tptp.nat)) (let ((_let_1 (tptp.hAPP_f585353809l_bool tptp.ord_le1959568910l_bool Ca))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ba) Aa)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool _let_1 (tptp.hAPP_n2125602947l_bool F Ba))) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool (tptp.hAPP_n2125602947l_bool F Y_1)) (tptp.hAPP_n2125602947l_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f73423488l_bool _let_1 (tptp.hAPP_n2125602947l_bool F Aa)))))))) (forall ((Ca tptp.fun_Pr2067565481t_bool) (F tptp.fun_na998785244t_bool) (Ba tptp.nat) (Aa tptp.nat)) (let ((_let_1 (tptp.hAPP_f930900275l_bool tptp.ord_le1478665215t_bool Ca))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ba) Aa)) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_1 (tptp.hAPP_n1161265524t_bool F Ba))) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool (tptp.hAPP_n1161265524t_bool F Y_1)) (tptp.hAPP_n1161265524t_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_1 (tptp.hAPP_n1161265524t_bool F Aa)))))))) (forall ((Ca tptp.bool) (F tptp.fun_nat_bool) (Ba tptp.nat) (Aa tptp.nat)) (let ((_let_1 (tptp.hAPP_b589554111l_bool tptp.ord_less_bool Ca))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ba) Aa)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 (tptp.hAPP_nat_bool F Ba))) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_nat_bool F Y_1)) (tptp.hAPP_nat_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 (tptp.hAPP_nat_bool F Aa)))))))) (forall ((Ca tptp.fun_Ar331856045t_bool) (F tptp.fun_na300967376t_bool) (Ba tptp.nat) (Aa tptp.nat)) (let ((_let_1 (tptp.hAPP_f1055587775l_bool tptp.ord_le19409623t_bool Ca))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ba) Aa)) (=> (tptp.hBOOL (tptp.hAPP_f1452856589l_bool _let_1 (tptp.hAPP_n1312530466t_bool F Ba))) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool (tptp.hAPP_n1312530466t_bool F Y_1)) (tptp.hAPP_n1312530466t_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f1452856589l_bool _let_1 (tptp.hAPP_n1312530466t_bool F Aa)))))))) (forall ((Ca tptp.fun_nat_bool) (F tptp.fun_fu821463397t_bool) (Ba tptp.fun_nat_bool) (Aa tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool Ca))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Ba) Aa)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f800510211t_bool F Ba))) (=> (forall ((X_1 tptp.fun_nat_bool) (Y_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_f800510211t_bool F Y_1)) (tptp.hAPP_f800510211t_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f800510211t_bool F Aa)))))))) (forall ((Ca tptp.fun_Pr1643180309t_bool) (F tptp.fun_fu1096920966t_bool) (Ba tptp.fun_nat_bool) (Aa tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool Ca))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Ba) Aa)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool _let_1 (tptp.hAPP_f1061584978t_bool F Ba))) (=> (forall ((X_1 tptp.fun_nat_bool) (Y_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool (tptp.hAPP_f1061584978t_bool F Y_1)) (tptp.hAPP_f1061584978t_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool _let_1 (tptp.hAPP_f1061584978t_bool F Aa)))))))) (forall ((Ca tptp.fun_Ar1809396326i_bool) (F tptp.fun_fu1415967063i_bool) (Ba tptp.fun_nat_bool) (Aa tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool Ca))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Ba) Aa)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool _let_1 (tptp.hAPP_f1992344867i_bool F Ba))) (=> (forall ((X_1 tptp.fun_nat_bool) (Y_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool (tptp.hAPP_f1992344867i_bool F Y_1)) (tptp.hAPP_f1992344867i_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f584385070l_bool _let_1 (tptp.hAPP_f1992344867i_bool F Aa)))))))) (forall ((Ca tptp.fun_fu638310559l_bool) (F tptp.fun_fu1182412548l_bool) (Ba tptp.fun_nat_bool) (Aa tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f1722316607l_bool tptp.ord_le1727358153l_bool Ca))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Ba) Aa)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool _let_1 (tptp.hAPP_f229466530l_bool F Ba))) (=> (forall ((X_1 tptp.fun_nat_bool) (Y_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool (tptp.hAPP_f229466530l_bool F Y_1)) (tptp.hAPP_f229466530l_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f182583295l_bool _let_1 (tptp.hAPP_f229466530l_bool F Aa)))))))) (forall ((Ca tptp.fun_fu2098777574l_bool) (F tptp.fun_fu1927280855l_bool) (Ba tptp.fun_nat_bool) (Aa tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f916323245l_bool tptp.ord_le119247420l_bool Ca))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Ba) Aa)) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool _let_1 (tptp.hAPP_f561646243l_bool F Ba))) (=> (forall ((X_1 tptp.fun_nat_bool) (Y_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool (tptp.hAPP_f561646243l_bool F Y_1)) (tptp.hAPP_f561646243l_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f975209902l_bool _let_1 (tptp.hAPP_f561646243l_bool F Aa)))))))) (forall ((Ca tptp.fun_fu3835832l_bool) (F tptp.fun_fu138597289l_bool) (Ba tptp.fun_nat_bool) (Aa tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f585353809l_bool tptp.ord_le1959568910l_bool Ca))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Ba) Aa)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool _let_1 (tptp.hAPP_f256405365l_bool F Ba))) (=> (forall ((X_1 tptp.fun_nat_bool) (Y_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool (tptp.hAPP_f256405365l_bool F Y_1)) (tptp.hAPP_f256405365l_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f73423488l_bool _let_1 (tptp.hAPP_f256405365l_bool F Aa)))))))) (forall ((Ca tptp.fun_Pr2067565481t_bool) (F tptp.fun_fu1778022682t_bool) (Ba tptp.fun_nat_bool) (Aa tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f930900275l_bool tptp.ord_le1478665215t_bool Ca))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Ba) Aa)) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_1 (tptp.hAPP_f1472089702t_bool F Ba))) (=> (forall ((X_1 tptp.fun_nat_bool) (Y_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool (tptp.hAPP_f1472089702t_bool F Y_1)) (tptp.hAPP_f1472089702t_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_1 (tptp.hAPP_f1472089702t_bool F Aa)))))))) (forall ((Ca tptp.bool) (F tptp.fun_fu425979586l_bool) (Ba tptp.fun_nat_bool) (Aa tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_b589554111l_bool tptp.ord_less_bool Ca))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Ba) Aa)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 (tptp.hAPP_f54304608l_bool F Ba))) (=> (forall ((X_1 tptp.fun_nat_bool) (Y_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_f54304608l_bool F Y_1)) (tptp.hAPP_f54304608l_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 (tptp.hAPP_f54304608l_bool F Aa)))))))) (forall ((Ca tptp.fun_Ar331856045t_bool) (F tptp.fun_fu221658642t_bool) (Ba tptp.fun_nat_bool) (Aa tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f1055587775l_bool tptp.ord_le19409623t_bool Ca))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Ba) Aa)) (=> (tptp.hBOOL (tptp.hAPP_f1452856589l_bool _let_1 (tptp.hAPP_f1635284656t_bool F Ba))) (=> (forall ((X_1 tptp.fun_nat_bool) (Y_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool (tptp.hAPP_f1635284656t_bool F Y_1)) (tptp.hAPP_f1635284656t_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f1452856589l_bool _let_1 (tptp.hAPP_f1635284656t_bool F Aa)))))))) (forall ((Ca tptp.fun_nat_bool) (F tptp.fun_fu1632756612t_bool) (Ba tptp.fun_fu638310559l_bool) (Aa tptp.fun_fu638310559l_bool)) (let ((_let_1 (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool Ca))) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool Ba) Aa)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f2063587362t_bool F Ba))) (=> (forall ((X_1 tptp.fun_fu638310559l_bool) (Y_1 tptp.fun_fu638310559l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_f2063587362t_bool F Y_1)) (tptp.hAPP_f2063587362t_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f2063587362t_bool F Aa)))))))) (forall ((Ca tptp.fun_nat_bool) (F tptp.fun_fu309681663t_bool) (Ba tptp.fun_fu2098777574l_bool) (Aa tptp.fun_fu2098777574l_bool)) (let ((_let_1 (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool Ca))) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool Ba) Aa)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f1705385041t_bool F Ba))) (=> (forall ((X_1 tptp.fun_fu2098777574l_bool) (Y_1 tptp.fun_fu2098777574l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_f1705385041t_bool F Y_1)) (tptp.hAPP_f1705385041t_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f1705385041t_bool F Aa)))))))) (forall ((Ca tptp.fun_nat_bool) (F tptp.fun_fu1078872017t_bool) (Ba tptp.fun_fu3835832l_bool) (Aa tptp.fun_fu3835832l_bool)) (let ((_let_1 (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool Ca))) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool Ba) Aa)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f743717923t_bool F Ba))) (=> (forall ((X_1 tptp.fun_fu3835832l_bool) (Y_1 tptp.fun_fu3835832l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_f743717923t_bool F Y_1)) (tptp.hAPP_f743717923t_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f743717923t_bool F Aa)))))))) (forall ((Ca tptp.fun_nat_bool) (F tptp.fun_fu477456066t_bool) (Ba tptp.fun_Pr2067565481t_bool) (Aa tptp.fun_Pr2067565481t_bool)) (let ((_let_1 (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool Ca))) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool Ba) Aa)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f703394068t_bool F Ba))) (=> (forall ((X_1 tptp.fun_Pr2067565481t_bool) (Y_1 tptp.fun_Pr2067565481t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_f703394068t_bool F Y_1)) (tptp.hAPP_f703394068t_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f703394068t_bool F Aa)))))))) (forall ((Ca tptp.fun_nat_bool) (F tptp.fun_bo1570548802t_bool) (Ba tptp.bool) (Aa tptp.bool)) (let ((_let_1 (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool Ca))) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Ba) Aa)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_b1013836512t_bool F Ba))) (=> (forall ((X_1 tptp.bool) (Y_1 tptp.bool)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_b1013836512t_bool F Y_1)) (tptp.hAPP_b1013836512t_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_b1013836512t_bool F Aa)))))))) (forall ((Ca tptp.fun_nat_bool) (F tptp.fun_fu1254370943t_bool) (Ba tptp.fun_Ar1809396326i_bool) (Aa tptp.fun_Ar1809396326i_bool)) (let ((_let_1 (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool Ca))) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool Ba) Aa)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f622418129t_bool F Ba))) (=> (forall ((X_1 tptp.fun_Ar1809396326i_bool) (Y_1 tptp.fun_Ar1809396326i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_f622418129t_bool F Y_1)) (tptp.hAPP_f622418129t_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f622418129t_bool F Aa)))))))) (forall ((Ca tptp.fun_nat_bool) (F tptp.fun_fu988033326t_bool) (Ba tptp.fun_Pr1643180309t_bool) (Aa tptp.fun_Pr1643180309t_bool)) (let ((_let_1 (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool Ca))) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool Ba) Aa)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f543204480t_bool F Ba))) (=> (forall ((X_1 tptp.fun_Pr1643180309t_bool) (Y_1 tptp.fun_Pr1643180309t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_f543204480t_bool F Y_1)) (tptp.hAPP_f543204480t_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f543204480t_bool F Aa)))))))) (forall ((Ca tptp.fun_nat_bool) (F tptp.fun_fu1869722514t_bool) (Ba tptp.fun_Ar331856045t_bool) (Aa tptp.fun_Ar331856045t_bool)) (let ((_let_1 (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool Ca))) (=> (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool Ba) Aa)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f1691234864t_bool F Ba))) (=> (forall ((X_1 tptp.fun_Ar331856045t_bool) (Y_1 tptp.fun_Ar331856045t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_f1691234864t_bool F Y_1)) (tptp.hAPP_f1691234864t_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f1691234864t_bool F Aa)))))))) (forall ((Ca tptp.nat) (F tptp.fun_fu955147676ol_nat) (Ba tptp.fun_fu638310559l_bool) (Aa tptp.fun_fu638310559l_bool)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ca))) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool Ba) Aa)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_f1487854056ol_nat F Ba))) (=> (forall ((X_1 tptp.fun_fu638310559l_bool) (Y_1 tptp.fun_fu638310559l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f1487854056ol_nat F Y_1)) (tptp.hAPP_f1487854056ol_nat F X_1))))) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_f1487854056ol_nat F Aa)))))))) (forall ((Ca tptp.nat) (F tptp.fun_fu859131105ol_nat) (Ba tptp.fun_fu2098777574l_bool) (Aa tptp.fun_fu2098777574l_bool)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ca))) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool Ba) Aa)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_f1049163897ol_nat F Ba))) (=> (forall ((X_1 tptp.fun_fu2098777574l_bool) (Y_1 tptp.fun_fu2098777574l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f1049163897ol_nat F Y_1)) (tptp.hAPP_f1049163897ol_nat F X_1))))) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_f1049163897ol_nat F Aa)))))))) (forall ((Ca tptp.nat) (F tptp.fun_fu777705871ol_nat) (Ba tptp.fun_fu3835832l_bool) (Aa tptp.fun_fu3835832l_bool)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ca))) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool Ba) Aa)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_f602722087ol_nat F Ba))) (=> (forall ((X_1 tptp.fun_fu3835832l_bool) (Y_1 tptp.fun_fu3835832l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f602722087ol_nat F Y_1)) (tptp.hAPP_f602722087ol_nat F X_1))))) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_f602722087ol_nat F Aa)))))))) (forall ((Ca tptp.nat) (F tptp.fun_fu841105374ol_nat) (Ba tptp.fun_Pr2067565481t_bool) (Aa tptp.fun_Pr2067565481t_bool)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ca))) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool Ba) Aa)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_f1842225014ol_nat F Ba))) (=> (forall ((X_1 tptp.fun_Pr2067565481t_bool) (Y_1 tptp.fun_Pr2067565481t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f1842225014ol_nat F Y_1)) (tptp.hAPP_f1842225014ol_nat F X_1))))) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_f1842225014ol_nat F Aa)))))))) (forall ((Ca tptp.nat) (F tptp.fun_bool_nat) (Ba tptp.bool) (Aa tptp.bool)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ca))) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Ba) Aa)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_bool_nat F Ba))) (=> (forall ((X_1 tptp.bool) (Y_1 tptp.bool)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_bool_nat F Y_1)) (tptp.hAPP_bool_nat F X_1))))) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_bool_nat F Aa)))))))) (forall ((Ca tptp.nat) (F tptp.fun_fu1603738721ol_nat) (Ba tptp.fun_Ar1809396326i_bool) (Aa tptp.fun_Ar1809396326i_bool)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ca))) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool Ba) Aa)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_f846027769ol_nat F Ba))) (=> (forall ((X_1 tptp.fun_Ar1809396326i_bool) (Y_1 tptp.fun_Ar1809396326i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f846027769ol_nat F Y_1)) (tptp.hAPP_f846027769ol_nat F X_1))))) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_f846027769ol_nat F Aa)))))))) (forall ((Ca tptp.nat) (F tptp.fun_fu572628082ol_nat) (Ba tptp.fun_Pr1643180309t_bool) (Aa tptp.fun_Pr1643180309t_bool)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ca))) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool Ba) Aa)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_f2030293770ol_nat F Ba))) (=> (forall ((X_1 tptp.fun_Pr1643180309t_bool) (Y_1 tptp.fun_Pr1643180309t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f2030293770ol_nat F Y_1)) (tptp.hAPP_f2030293770ol_nat F X_1))))) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_f2030293770ol_nat F Aa)))))))) (forall ((Ca tptp.nat) (F tptp.fun_fu1677555470ol_nat) (Ba tptp.fun_Ar331856045t_bool) (Aa tptp.fun_Ar331856045t_bool)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ca))) (=> (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool Ba) Aa)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_f1403773274ol_nat F Ba))) (=> (forall ((X_1 tptp.fun_Ar331856045t_bool) (Y_1 tptp.fun_Ar331856045t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f1403773274ol_nat F Y_1)) (tptp.hAPP_f1403773274ol_nat F X_1))))) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_f1403773274ol_nat F Aa)))))))) (forall ((F tptp.fun_Pr1643180309t_bool) (G tptp.fun_Pr1643180309t_bool)) (= (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool F) G)) (and (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool F) G)) (not (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool G) F)))))) (forall ((F tptp.fun_Ar1809396326i_bool) (G tptp.fun_Ar1809396326i_bool)) (= (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool F) G)) (and (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool F) G)) (not (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool G) F)))))) (forall ((F tptp.fun_fu638310559l_bool) (G tptp.fun_fu638310559l_bool)) (= (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1727358153l_bool F) G)) (and (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool F) G)) (not (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool G) F)))))) (forall ((F tptp.fun_fu2098777574l_bool) (G tptp.fun_fu2098777574l_bool)) (= (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le119247420l_bool F) G)) (and (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool F) G)) (not (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool G) F)))))) (forall ((F tptp.fun_fu3835832l_bool) (G tptp.fun_fu3835832l_bool)) (= (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1959568910l_bool F) G)) (and (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool F) G)) (not (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool G) F)))))) (forall ((F tptp.fun_Pr2067565481t_bool) (G tptp.fun_Pr2067565481t_bool)) (= (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1478665215t_bool F) G)) (and (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool F) G)) (not (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool G) F)))))) (forall ((F tptp.fun_Ar331856045t_bool) (G tptp.fun_Ar331856045t_bool)) (= (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le19409623t_bool F) G)) (and (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool F) G)) (not (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool G) F)))))) (forall ((F tptp.fun_nat_bool) (G tptp.fun_nat_bool)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool F) G)) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool F) G)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool G) F)))))) (forall ((B tptp.fun_Pr1780397033l_bool) (A_15 tptp.fun_Pr2067565481t_bool) (A tptp.fun_Pr2067565481t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool A_15) A)) (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool (tptp.pi_Pro1238944957t_bool A B)) (tptp.pi_Pro1238944957t_bool A_15 B))))) (forall ((B tptp.fun_fu1863781882l_bool) (A_15 tptp.fun_fu3835832l_bool) (A tptp.fun_fu3835832l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool A_15) A)) (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool (tptp.pi_fun1746584570t_bool A B)) (tptp.pi_fun1746584570t_bool A_15 B))))) (forall ((B tptp.fun_Ar1474557608l_bool) (A_15 tptp.fun_Ar1809396326i_bool) (A tptp.fun_Ar1809396326i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool A_15) A)) (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool (tptp.pi_Arr959578316t_bool A B)) (tptp.pi_Arr959578316t_bool A_15 B))))) (forall ((R_1 tptp.fun_Pr2067565481t_bool) (S_1 tptp.fun_Pr2067565481t_bool)) (let ((_let_1 (tptp.hAPP_f1081591777t_bool tptp.cOMBC_557453916t_bool (tptp.hAPP_f105674721t_bool (tptp.cOMBB_652885079le_alt tptp.cOMBC_395465908l_bool) (tptp.hAPP_f184584489l_bool (tptp.cOMBB_1575576719le_alt (tptp.cOMBB_1660064607le_alt tptp.member1333168212le_alt)) tptp.produc1590937303le_alt))))) (= (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool (tptp.hAPP_f449303873t_bool _let_1 R_1)) (tptp.hAPP_f449303873t_bool _let_1 S_1))) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool R_1) S_1))))) (forall ((A tptp.fun_fu638310559l_bool)) (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool A) tptp.top_to1312956197l_bool))) (forall ((A tptp.fun_fu3835832l_bool)) (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool A) tptp.top_to553140914l_bool))) (forall ((A tptp.fun_fu2098777574l_bool)) (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool A) tptp.top_to827110112l_bool))) (forall ((A tptp.fun_Pr2067565481t_bool)) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool A) tptp.top_to1138392227t_bool))) (forall ((A tptp.fun_Ar1809396326i_bool)) (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool A) tptp.top_to788185952i_bool))) (forall ((A tptp.fun_nat_bool)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) tptp.top_top_fun_nat_bool))) (forall ((A tptp.fun_Pr1643180309t_bool)) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool A) tptp.top_to1257323279t_bool))) (forall ((A tptp.fun_Ar1809396326i_bool) (F tptp.fun_Ar671024215di_nat) (B tptp.fun_Ar1809396326i_bool)) (let ((_let_1 (tptp.inj_on1960344199di_nat F))) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool _let_1 B)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool A) B)) (tptp.hBOOL (tptp.hAPP_f584385070l_bool _let_1 A)))))) (forall ((A tptp.fun_nat_bool) (F tptp.fun_nat_nat) (B tptp.fun_nat_bool)) (let ((_let_1 (tptp.inj_on_nat_nat F))) (=> (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)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 A)))))) (forall ((B_14 tptp.nat) (A_14 tptp.nat) (C_14 tptp.nat)) (=> (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat B_14) A_14) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat C_14) A_14)) (= B_14 C_14))) (forall ((A_13 tptp.nat) (B_13 tptp.nat) (C_13 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_13))) (=> (= (tptp.hAPP_nat_nat _let_1 B_13) (tptp.hAPP_nat_nat _let_1 C_13)) (= B_13 C_13)))) (forall ((A_12 tptp.nat) (B_12 tptp.nat) (C_12 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_12))) (=> (= (tptp.hAPP_nat_nat _let_1 B_12) (tptp.hAPP_nat_nat _let_1 C_12)) (= B_12 C_12)))) (forall ((Ba tptp.nat) (Aa tptp.nat) (Ca tptp.nat)) (= (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Ba) Aa) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Ca) Aa)) (= Ba Ca))) (forall ((Aa tptp.nat) (Ba tptp.nat) (Ca tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Aa))) (= (= (tptp.hAPP_nat_nat _let_1 Ba) (tptp.hAPP_nat_nat _let_1 Ca)) (= Ba Ca)))) (forall ((A_11 tptp.nat) (B_11 tptp.nat) (C_11 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_11))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 B_11)) C_11) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat B_11) C_11))))) (forall ((X_2 tptp.nat)) (= (= tptp.one_one_nat X_2) (= X_2 tptp.one_one_nat))) (forall ((C_10 tptp.nat) (A_10 tptp.nat) (B_10 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat C_10))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 A_10)) (tptp.hAPP_nat_nat _let_1 B_10))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_10) B_10))))) (forall ((A_9 tptp.nat) (C_9 tptp.nat) (B_9 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_9) C_9)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat B_9) C_9))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_9) B_9)))) (forall ((C_8 tptp.nat) (D_1 tptp.nat) (A_8 tptp.nat) (B_8 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_8) B_8)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat C_8) D_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_8) C_8)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat B_8) D_1)))))) (forall ((C_7 tptp.nat) (A_7 tptp.nat) (B_7 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat C_7))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_7) B_7)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 A_7)) (tptp.hAPP_nat_nat _let_1 B_7)))))) (forall ((C_6 tptp.nat) (A_6 tptp.nat) (B_6 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_6) B_6)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_6) C_6)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat B_6) C_6))))) (forall ((Ca tptp.nat) (Aa tptp.nat) (Ba tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Ca))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 Aa)) (tptp.hAPP_nat_nat _let_1 Ba))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Aa) Ba))))) (forall ((Aa tptp.nat) (Ca tptp.nat) (Ba tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Aa) Ca)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Ba) Ca))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Aa) Ba)))) (forall ((C_5 tptp.nat) (A_5 tptp.nat) (B_5 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat C_5))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 A_5)) (tptp.hAPP_nat_nat _let_1 B_5))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_5) B_5))))) (forall ((A_4 tptp.nat) (C_4 tptp.nat) (B_4 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_4) C_4)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat B_4) C_4))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_4) B_4)))) (forall ((C_3 tptp.nat) (D tptp.nat) (A_3 tptp.nat) (B_3 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_3) B_3)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat C_3) D)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_3) C_3)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat B_3) D)))))) (forall ((C_2 tptp.nat) (A_2 tptp.nat) (B_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat C_2))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_2) B_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 A_2)) (tptp.hAPP_nat_nat _let_1 B_2)))))) (forall ((C_1 tptp.nat) (A_1 tptp.nat) (B_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_1) B_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_1) C_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat B_1) C_1))))) (forall ((Ca tptp.nat) (Aa tptp.nat) (Ba tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Ca))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 Aa)) (tptp.hAPP_nat_nat _let_1 Ba))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Aa) Ba))))) (forall ((Aa tptp.nat) (Ca tptp.nat) (Ba tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Aa) Ca)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Ba) Ca))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Aa) Ba)))) (forall ((F tptp.fun_fu638310559l_bool) (G tptp.fun_fu638310559l_bool)) (=> (forall ((X_1 tptp.fun_Pr2067565481t_bool)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_f52567537l_bool F X_1)) (tptp.hAPP_f52567537l_bool G X_1)))) (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool F) G)))) (forall ((F tptp.fun_fu2098777574l_bool) (G tptp.fun_fu2098777574l_bool)) (=> (forall ((X_1 tptp.fun_fu2114379172t_bool)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_f1572141188l_bool F X_1)) (tptp.hAPP_f1572141188l_bool G X_1)))) (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool F) G)))) (forall ((F tptp.fun_fu3835832l_bool) (G tptp.fun_fu3835832l_bool)) (=> (forall ((X_1 tptp.fun_Ar274636406t_bool)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_f995490902l_bool F X_1)) (tptp.hAPP_f995490902l_bool G X_1)))) (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool F) G)))) (forall ((F tptp.fun_Pr2067565481t_bool) (G tptp.fun_Pr2067565481t_bool)) (=> (forall ((X_1 tptp.produc472769767le_alt)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_P1178790471t_bool F X_1)) (tptp.hAPP_P1178790471t_bool G X_1)))) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool F) G)))) (forall ((F tptp.fun_Ar1809396326i_bool) (G tptp.fun_Ar1809396326i_bool)) (=> (forall ((X_1 tptp.arrow_856714788e_indi)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_A997847300i_bool F X_1)) (tptp.hAPP_A997847300i_bool G X_1)))) (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool F) G)))) (forall ((F tptp.fun_Pr1643180309t_bool) (G tptp.fun_Pr1643180309t_bool)) (=> (forall ((X_1 tptp.product_unit)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_P1676879539t_bool F X_1)) (tptp.hAPP_P1676879539t_bool G X_1)))) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool F) G)))) (forall ((F tptp.fun_Ar331856045t_bool) (G tptp.fun_Ar331856045t_bool)) (=> (forall ((X_1 tptp.arrow_1893660431le_alt)) (tptp.hBOOL (tptp.hAPP_f739344229l_bool (tptp.hAPP_f1549168575l_bool tptp.ord_le1779845435t_bool (tptp.hAPP_A2063800319t_bool F X_1)) (tptp.hAPP_A2063800319t_bool G X_1)))) (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool F) G)))) (forall ((F tptp.fun_nat_bool) (G tptp.fun_nat_bool)) (=> (forall ((X_1 tptp.nat)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_nat_bool F X_1)) (tptp.hAPP_nat_bool G X_1)))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool F) G)))) (forall ((Ca tptp.fun_nat_bool) (F tptp.fun_fu821463397t_bool) (Ba tptp.fun_nat_bool) (Aa tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_f800510211t_bool F Ba)) Aa)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool Ca) Ba)) (=> (forall ((X_1 tptp.fun_nat_bool) (Y_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool (tptp.hAPP_f800510211t_bool F Y_1)) (tptp.hAPP_f800510211t_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool (tptp.hAPP_f800510211t_bool F Ca)) Aa)))))) (forall ((Ca tptp.fun_Pr1643180309t_bool) (F tptp.fun_fu988033326t_bool) (Ba tptp.fun_Pr1643180309t_bool) (Aa tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_f543204480t_bool F Ba)) Aa)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool Ca) Ba)) (=> (forall ((X_1 tptp.fun_Pr1643180309t_bool) (Y_1 tptp.fun_Pr1643180309t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool (tptp.hAPP_f543204480t_bool F Y_1)) (tptp.hAPP_f543204480t_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool (tptp.hAPP_f543204480t_bool F Ca)) Aa)))))) (forall ((Ca tptp.fun_Ar1809396326i_bool) (F tptp.fun_fu1254370943t_bool) (Ba tptp.fun_Ar1809396326i_bool) (Aa tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_f622418129t_bool F Ba)) Aa)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool Ca) Ba)) (=> (forall ((X_1 tptp.fun_Ar1809396326i_bool) (Y_1 tptp.fun_Ar1809396326i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool (tptp.hAPP_f622418129t_bool F Y_1)) (tptp.hAPP_f622418129t_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool (tptp.hAPP_f622418129t_bool F Ca)) Aa)))))) (forall ((Ca tptp.nat) (F tptp.fun_nat_fun_nat_bool) (Ba tptp.nat) (Aa tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_n1699378549t_bool F Ba)) Aa)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ca) Ba)) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool (tptp.hAPP_n1699378549t_bool F Y_1)) (tptp.hAPP_n1699378549t_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool (tptp.hAPP_n1699378549t_bool F Ca)) Aa)))))) (forall ((Ca tptp.nat) (F tptp.fun_na1041622088t_bool) (Ba tptp.nat) (Aa tptp.fun_Pr1643180309t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool (tptp.hAPP_n454528608t_bool F Ba)) Aa)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ca) Ba)) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool (tptp.hAPP_n454528608t_bool F Y_1)) (tptp.hAPP_n454528608t_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool (tptp.hAPP_n454528608t_bool F Ca)) Aa)))))) (forall ((Ca tptp.nat) (F tptp.fun_na2037635353i_bool) (Ba tptp.nat) (Aa tptp.fun_Ar1809396326i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool (tptp.hAPP_n34002993i_bool F Ba)) Aa)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ca) Ba)) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool (tptp.hAPP_n34002993i_bool F Y_1)) (tptp.hAPP_n34002993i_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool (tptp.hAPP_n34002993i_bool F Ca)) Aa)))))) (forall ((Ca tptp.nat) (F tptp.fun_na144630978l_bool) (Ba tptp.nat) (Aa tptp.fun_fu638310559l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool (tptp.hAPP_n1134275860l_bool F Ba)) Aa)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ca) Ba)) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1727358153l_bool (tptp.hAPP_n1134275860l_bool F Y_1)) (tptp.hAPP_n1134275860l_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1727358153l_bool (tptp.hAPP_n1134275860l_bool F Ca)) Aa)))))) (forall ((Ca tptp.nat) (F tptp.fun_na138495129l_bool) (Ba tptp.nat) (Aa tptp.fun_fu2098777574l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool (tptp.hAPP_n1555388849l_bool F Ba)) Aa)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ca) Ba)) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le119247420l_bool (tptp.hAPP_n1555388849l_bool F Y_1)) (tptp.hAPP_n1555388849l_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le119247420l_bool (tptp.hAPP_n1555388849l_bool F Ca)) Aa)))))) (forall ((Ca tptp.nat) (F tptp.fun_na6909291l_bool) (Ba tptp.nat) (Aa tptp.fun_fu3835832l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool (tptp.hAPP_n2125602947l_bool F Ba)) Aa)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ca) Ba)) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1959568910l_bool (tptp.hAPP_n2125602947l_bool F Y_1)) (tptp.hAPP_n2125602947l_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1959568910l_bool (tptp.hAPP_n2125602947l_bool F Ca)) Aa)))))) (forall ((Ca tptp.nat) (F tptp.fun_na998785244t_bool) (Ba tptp.nat) (Aa tptp.fun_Pr2067565481t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool (tptp.hAPP_n1161265524t_bool F Ba)) Aa)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ca) Ba)) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1478665215t_bool (tptp.hAPP_n1161265524t_bool F Y_1)) (tptp.hAPP_n1161265524t_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1478665215t_bool (tptp.hAPP_n1161265524t_bool F Ca)) Aa)))))) (forall ((Ca tptp.nat) (F tptp.fun_nat_bool) (Ba tptp.nat) (Aa tptp.bool)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_nat_bool F Ba)) Aa)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ca) Ba)) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_bool (tptp.hAPP_nat_bool F Y_1)) (tptp.hAPP_nat_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_bool (tptp.hAPP_nat_bool F Ca)) Aa)))))) (forall ((Ca tptp.nat) (F tptp.fun_na300967376t_bool) (Ba tptp.nat) (Aa tptp.fun_Ar331856045t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool (tptp.hAPP_n1312530466t_bool F Ba)) Aa)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ca) Ba)) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le19409623t_bool (tptp.hAPP_n1312530466t_bool F Y_1)) (tptp.hAPP_n1312530466t_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le19409623t_bool (tptp.hAPP_n1312530466t_bool F Ca)) Aa)))))) (forall ((Ca tptp.fun_nat_bool) (F tptp.fun_fun_nat_bool_nat) (Ba tptp.fun_nat_bool) (Aa tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f22106695ol_nat F Ba)) Aa)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool Ca) Ba)) (=> (forall ((X_1 tptp.fun_nat_bool) (Y_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_f22106695ol_nat F Y_1)) (tptp.hAPP_f22106695ol_nat F X_1))))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_f22106695ol_nat F Ca)) Aa)))))) (forall ((Ca tptp.fun_Pr1643180309t_bool) (F tptp.fun_fu572628082ol_nat) (Ba tptp.fun_Pr1643180309t_bool) (Aa tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f2030293770ol_nat F Ba)) Aa)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool Ca) Ba)) (=> (forall ((X_1 tptp.fun_Pr1643180309t_bool) (Y_1 tptp.fun_Pr1643180309t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_f2030293770ol_nat F Y_1)) (tptp.hAPP_f2030293770ol_nat F X_1))))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_f2030293770ol_nat F Ca)) Aa)))))) (forall ((Ca tptp.fun_Ar1809396326i_bool) (F tptp.fun_fu1603738721ol_nat) (Ba tptp.fun_Ar1809396326i_bool) (Aa tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f846027769ol_nat F Ba)) Aa)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool Ca) Ba)) (=> (forall ((X_1 tptp.fun_Ar1809396326i_bool) (Y_1 tptp.fun_Ar1809396326i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_f846027769ol_nat F Y_1)) (tptp.hAPP_f846027769ol_nat F X_1))))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_f846027769ol_nat F Ca)) Aa)))))) (forall ((Ca tptp.nat) (F tptp.fun_nat_fun_nat_bool) (Ba tptp.nat) (Aa tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool (tptp.hAPP_n1699378549t_bool F Ba)) Aa)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ca) Ba)) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_n1699378549t_bool F Y_1)) (tptp.hAPP_n1699378549t_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool (tptp.hAPP_n1699378549t_bool F Ca)) Aa)))))) (forall ((Ca tptp.nat) (F tptp.fun_na1041622088t_bool) (Ba tptp.nat) (Aa tptp.fun_Pr1643180309t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool (tptp.hAPP_n454528608t_bool F Ba)) Aa)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ca) Ba)) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool (tptp.hAPP_n454528608t_bool F Y_1)) (tptp.hAPP_n454528608t_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool (tptp.hAPP_n454528608t_bool F Ca)) Aa)))))) (forall ((Ca tptp.nat) (F tptp.fun_na2037635353i_bool) (Ba tptp.nat) (Aa tptp.fun_Ar1809396326i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool (tptp.hAPP_n34002993i_bool F Ba)) Aa)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ca) Ba)) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool (tptp.hAPP_n34002993i_bool F Y_1)) (tptp.hAPP_n34002993i_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool (tptp.hAPP_n34002993i_bool F Ca)) Aa)))))) (forall ((Ca tptp.nat) (F tptp.fun_na144630978l_bool) (Ba tptp.nat) (Aa tptp.fun_fu638310559l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1727358153l_bool (tptp.hAPP_n1134275860l_bool F Ba)) Aa)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ca) Ba)) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool (tptp.hAPP_n1134275860l_bool F Y_1)) (tptp.hAPP_n1134275860l_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1727358153l_bool (tptp.hAPP_n1134275860l_bool F Ca)) Aa)))))) (forall ((Ca tptp.nat) (F tptp.fun_na138495129l_bool) (Ba tptp.nat) (Aa tptp.fun_fu2098777574l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le119247420l_bool (tptp.hAPP_n1555388849l_bool F Ba)) Aa)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ca) Ba)) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool (tptp.hAPP_n1555388849l_bool F Y_1)) (tptp.hAPP_n1555388849l_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le119247420l_bool (tptp.hAPP_n1555388849l_bool F Ca)) Aa)))))) (forall ((Ca tptp.nat) (F tptp.fun_na6909291l_bool) (Ba tptp.nat) (Aa tptp.fun_fu3835832l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1959568910l_bool (tptp.hAPP_n2125602947l_bool F Ba)) Aa)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ca) Ba)) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool (tptp.hAPP_n2125602947l_bool F Y_1)) (tptp.hAPP_n2125602947l_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1959568910l_bool (tptp.hAPP_n2125602947l_bool F Ca)) Aa)))))) (forall ((Ca tptp.nat) (F tptp.fun_na998785244t_bool) (Ba tptp.nat) (Aa tptp.fun_Pr2067565481t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1478665215t_bool (tptp.hAPP_n1161265524t_bool F Ba)) Aa)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ca) Ba)) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool (tptp.hAPP_n1161265524t_bool F Y_1)) (tptp.hAPP_n1161265524t_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1478665215t_bool (tptp.hAPP_n1161265524t_bool F Ca)) Aa)))))) (forall ((Ca tptp.nat) (F tptp.fun_nat_bool) (Ba tptp.nat) (Aa tptp.bool)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_bool (tptp.hAPP_nat_bool F Ba)) Aa)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ca) Ba)) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_nat_bool F Y_1)) (tptp.hAPP_nat_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_bool (tptp.hAPP_nat_bool F Ca)) Aa)))))) (forall ((Ca tptp.nat) (F tptp.fun_na300967376t_bool) (Ba tptp.nat) (Aa tptp.fun_Ar331856045t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le19409623t_bool (tptp.hAPP_n1312530466t_bool F Ba)) Aa)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ca) Ba)) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool (tptp.hAPP_n1312530466t_bool F Y_1)) (tptp.hAPP_n1312530466t_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le19409623t_bool (tptp.hAPP_n1312530466t_bool F Ca)) Aa)))))) (forall ((Ca tptp.fun_nat_bool) (F tptp.fun_fu821463397t_bool) (Ba tptp.fun_nat_bool) (Aa tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool (tptp.hAPP_f800510211t_bool F Ba)) Aa)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Ca) Ba)) (=> (forall ((X_1 tptp.fun_nat_bool) (Y_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_f800510211t_bool F Y_1)) (tptp.hAPP_f800510211t_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool (tptp.hAPP_f800510211t_bool F Ca)) Aa)))))) (forall ((Ca tptp.fun_nat_bool) (F tptp.fun_fu1096920966t_bool) (Ba tptp.fun_nat_bool) (Aa tptp.fun_Pr1643180309t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool (tptp.hAPP_f1061584978t_bool F Ba)) Aa)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Ca) Ba)) (=> (forall ((X_1 tptp.fun_nat_bool) (Y_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool (tptp.hAPP_f1061584978t_bool F Y_1)) (tptp.hAPP_f1061584978t_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool (tptp.hAPP_f1061584978t_bool F Ca)) Aa)))))) (forall ((Ca tptp.fun_nat_bool) (F tptp.fun_fu1415967063i_bool) (Ba tptp.fun_nat_bool) (Aa tptp.fun_Ar1809396326i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool (tptp.hAPP_f1992344867i_bool F Ba)) Aa)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Ca) Ba)) (=> (forall ((X_1 tptp.fun_nat_bool) (Y_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool (tptp.hAPP_f1992344867i_bool F Y_1)) (tptp.hAPP_f1992344867i_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool (tptp.hAPP_f1992344867i_bool F Ca)) Aa)))))) (forall ((Ca tptp.fun_nat_bool) (F tptp.fun_fu1182412548l_bool) (Ba tptp.fun_nat_bool) (Aa tptp.fun_fu638310559l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1727358153l_bool (tptp.hAPP_f229466530l_bool F Ba)) Aa)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Ca) Ba)) (=> (forall ((X_1 tptp.fun_nat_bool) (Y_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool (tptp.hAPP_f229466530l_bool F Y_1)) (tptp.hAPP_f229466530l_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1727358153l_bool (tptp.hAPP_f229466530l_bool F Ca)) Aa)))))) (forall ((Ca tptp.fun_nat_bool) (F tptp.fun_fu1927280855l_bool) (Ba tptp.fun_nat_bool) (Aa tptp.fun_fu2098777574l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le119247420l_bool (tptp.hAPP_f561646243l_bool F Ba)) Aa)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Ca) Ba)) (=> (forall ((X_1 tptp.fun_nat_bool) (Y_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool (tptp.hAPP_f561646243l_bool F Y_1)) (tptp.hAPP_f561646243l_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le119247420l_bool (tptp.hAPP_f561646243l_bool F Ca)) Aa)))))) (forall ((Ca tptp.fun_nat_bool) (F tptp.fun_fu138597289l_bool) (Ba tptp.fun_nat_bool) (Aa tptp.fun_fu3835832l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1959568910l_bool (tptp.hAPP_f256405365l_bool F Ba)) Aa)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Ca) Ba)) (=> (forall ((X_1 tptp.fun_nat_bool) (Y_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool (tptp.hAPP_f256405365l_bool F Y_1)) (tptp.hAPP_f256405365l_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1959568910l_bool (tptp.hAPP_f256405365l_bool F Ca)) Aa)))))) (forall ((Ca tptp.fun_nat_bool) (F tptp.fun_fu1778022682t_bool) (Ba tptp.fun_nat_bool) (Aa tptp.fun_Pr2067565481t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1478665215t_bool (tptp.hAPP_f1472089702t_bool F Ba)) Aa)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Ca) Ba)) (=> (forall ((X_1 tptp.fun_nat_bool) (Y_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool (tptp.hAPP_f1472089702t_bool F Y_1)) (tptp.hAPP_f1472089702t_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1478665215t_bool (tptp.hAPP_f1472089702t_bool F Ca)) Aa)))))) (forall ((Ca tptp.fun_nat_bool) (F tptp.fun_fu425979586l_bool) (Ba tptp.fun_nat_bool) (Aa tptp.bool)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_bool (tptp.hAPP_f54304608l_bool F Ba)) Aa)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Ca) Ba)) (=> (forall ((X_1 tptp.fun_nat_bool) (Y_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_f54304608l_bool F Y_1)) (tptp.hAPP_f54304608l_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_bool (tptp.hAPP_f54304608l_bool F Ca)) Aa)))))) (forall ((Ca tptp.fun_nat_bool) (F tptp.fun_fu221658642t_bool) (Ba tptp.fun_nat_bool) (Aa tptp.fun_Ar331856045t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le19409623t_bool (tptp.hAPP_f1635284656t_bool F Ba)) Aa)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Ca) Ba)) (=> (forall ((X_1 tptp.fun_nat_bool) (Y_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool (tptp.hAPP_f1635284656t_bool F Y_1)) (tptp.hAPP_f1635284656t_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le19409623t_bool (tptp.hAPP_f1635284656t_bool F Ca)) Aa)))))) (forall ((Ca tptp.fun_fu638310559l_bool) (F tptp.fun_fu1632756612t_bool) (Ba tptp.fun_fu638310559l_bool) (Aa tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool (tptp.hAPP_f2063587362t_bool F Ba)) Aa)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool Ca) Ba)) (=> (forall ((X_1 tptp.fun_fu638310559l_bool) (Y_1 tptp.fun_fu638310559l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_f2063587362t_bool F Y_1)) (tptp.hAPP_f2063587362t_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool (tptp.hAPP_f2063587362t_bool F Ca)) Aa)))))) (forall ((Ca tptp.fun_fu2098777574l_bool) (F tptp.fun_fu309681663t_bool) (Ba tptp.fun_fu2098777574l_bool) (Aa tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool (tptp.hAPP_f1705385041t_bool F Ba)) Aa)) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool Ca) Ba)) (=> (forall ((X_1 tptp.fun_fu2098777574l_bool) (Y_1 tptp.fun_fu2098777574l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_f1705385041t_bool F Y_1)) (tptp.hAPP_f1705385041t_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool (tptp.hAPP_f1705385041t_bool F Ca)) Aa)))))) (forall ((Ca tptp.fun_fu3835832l_bool) (F tptp.fun_fu1078872017t_bool) (Ba tptp.fun_fu3835832l_bool) (Aa tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool (tptp.hAPP_f743717923t_bool F Ba)) Aa)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool Ca) Ba)) (=> (forall ((X_1 tptp.fun_fu3835832l_bool) (Y_1 tptp.fun_fu3835832l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_f743717923t_bool F Y_1)) (tptp.hAPP_f743717923t_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool (tptp.hAPP_f743717923t_bool F Ca)) Aa)))))) (forall ((Ca tptp.fun_Pr2067565481t_bool) (F tptp.fun_fu477456066t_bool) (Ba tptp.fun_Pr2067565481t_bool) (Aa tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool (tptp.hAPP_f703394068t_bool F Ba)) Aa)) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool Ca) Ba)) (=> (forall ((X_1 tptp.fun_Pr2067565481t_bool) (Y_1 tptp.fun_Pr2067565481t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_f703394068t_bool F Y_1)) (tptp.hAPP_f703394068t_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool (tptp.hAPP_f703394068t_bool F Ca)) Aa)))))) (forall ((Ca tptp.bool) (F tptp.fun_bo1570548802t_bool) (Ba tptp.bool) (Aa tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool (tptp.hAPP_b1013836512t_bool F Ba)) Aa)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Ca) Ba)) (=> (forall ((X_1 tptp.bool) (Y_1 tptp.bool)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_b1013836512t_bool F Y_1)) (tptp.hAPP_b1013836512t_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool (tptp.hAPP_b1013836512t_bool F Ca)) Aa)))))) (forall ((Ca tptp.fun_Ar1809396326i_bool) (F tptp.fun_fu1254370943t_bool) (Ba tptp.fun_Ar1809396326i_bool) (Aa tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool (tptp.hAPP_f622418129t_bool F Ba)) Aa)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool Ca) Ba)) (=> (forall ((X_1 tptp.fun_Ar1809396326i_bool) (Y_1 tptp.fun_Ar1809396326i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_f622418129t_bool F Y_1)) (tptp.hAPP_f622418129t_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool (tptp.hAPP_f622418129t_bool F Ca)) Aa)))))) (forall ((Ca tptp.fun_Pr1643180309t_bool) (F tptp.fun_fu988033326t_bool) (Ba tptp.fun_Pr1643180309t_bool) (Aa tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool (tptp.hAPP_f543204480t_bool F Ba)) Aa)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool Ca) Ba)) (=> (forall ((X_1 tptp.fun_Pr1643180309t_bool) (Y_1 tptp.fun_Pr1643180309t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_f543204480t_bool F Y_1)) (tptp.hAPP_f543204480t_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool (tptp.hAPP_f543204480t_bool F Ca)) Aa)))))) (forall ((Ca tptp.fun_Ar331856045t_bool) (F tptp.fun_fu1869722514t_bool) (Ba tptp.fun_Ar331856045t_bool) (Aa tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool (tptp.hAPP_f1691234864t_bool F Ba)) Aa)) (=> (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool Ca) Ba)) (=> (forall ((X_1 tptp.fun_Ar331856045t_bool) (Y_1 tptp.fun_Ar331856045t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_f1691234864t_bool F Y_1)) (tptp.hAPP_f1691234864t_bool F X_1))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool (tptp.hAPP_f1691234864t_bool F Ca)) Aa)))))) (forall ((Ca tptp.fun_fu638310559l_bool) (F tptp.fun_fu955147676ol_nat) (Ba tptp.fun_fu638310559l_bool) (Aa tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_f1487854056ol_nat F Ba)) Aa)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool Ca) Ba)) (=> (forall ((X_1 tptp.fun_fu638310559l_bool) (Y_1 tptp.fun_fu638310559l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f1487854056ol_nat F Y_1)) (tptp.hAPP_f1487854056ol_nat F X_1))))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_f1487854056ol_nat F Ca)) Aa)))))) (forall ((Ca tptp.fun_fu2098777574l_bool) (F tptp.fun_fu859131105ol_nat) (Ba tptp.fun_fu2098777574l_bool) (Aa tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_f1049163897ol_nat F Ba)) Aa)) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool Ca) Ba)) (=> (forall ((X_1 tptp.fun_fu2098777574l_bool) (Y_1 tptp.fun_fu2098777574l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f1049163897ol_nat F Y_1)) (tptp.hAPP_f1049163897ol_nat F X_1))))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_f1049163897ol_nat F Ca)) Aa)))))) (forall ((Ca tptp.fun_fu3835832l_bool) (F tptp.fun_fu777705871ol_nat) (Ba tptp.fun_fu3835832l_bool) (Aa tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_f602722087ol_nat F Ba)) Aa)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool Ca) Ba)) (=> (forall ((X_1 tptp.fun_fu3835832l_bool) (Y_1 tptp.fun_fu3835832l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f602722087ol_nat F Y_1)) (tptp.hAPP_f602722087ol_nat F X_1))))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_f602722087ol_nat F Ca)) Aa)))))) (forall ((Ca tptp.fun_Pr2067565481t_bool) (F tptp.fun_fu841105374ol_nat) (Ba tptp.fun_Pr2067565481t_bool) (Aa tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_f1842225014ol_nat F Ba)) Aa)) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool Ca) Ba)) (=> (forall ((X_1 tptp.fun_Pr2067565481t_bool) (Y_1 tptp.fun_Pr2067565481t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f1842225014ol_nat F Y_1)) (tptp.hAPP_f1842225014ol_nat F X_1))))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_f1842225014ol_nat F Ca)) Aa)))))) (forall ((Ca tptp.bool) (F tptp.fun_bool_nat) (Ba tptp.bool) (Aa tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_bool_nat F Ba)) Aa)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Ca) Ba)) (=> (forall ((X_1 tptp.bool) (Y_1 tptp.bool)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_bool_nat F Y_1)) (tptp.hAPP_bool_nat F X_1))))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_bool_nat F Ca)) Aa)))))) (forall ((Ca tptp.fun_Ar1809396326i_bool) (F tptp.fun_fu1603738721ol_nat) (Ba tptp.fun_Ar1809396326i_bool) (Aa tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_f846027769ol_nat F Ba)) Aa)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool Ca) Ba)) (=> (forall ((X_1 tptp.fun_Ar1809396326i_bool) (Y_1 tptp.fun_Ar1809396326i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f846027769ol_nat F Y_1)) (tptp.hAPP_f846027769ol_nat F X_1))))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_f846027769ol_nat F Ca)) Aa)))))) (forall ((Ca tptp.fun_Pr1643180309t_bool) (F tptp.fun_fu572628082ol_nat) (Ba tptp.fun_Pr1643180309t_bool) (Aa tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_f2030293770ol_nat F Ba)) Aa)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool Ca) Ba)) (=> (forall ((X_1 tptp.fun_Pr1643180309t_bool) (Y_1 tptp.fun_Pr1643180309t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f2030293770ol_nat F Y_1)) (tptp.hAPP_f2030293770ol_nat F X_1))))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_f2030293770ol_nat F Ca)) Aa)))))) (forall ((Ca tptp.fun_Ar331856045t_bool) (F tptp.fun_fu1677555470ol_nat) (Ba tptp.fun_Ar331856045t_bool) (Aa tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_f1403773274ol_nat F Ba)) Aa)) (=> (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool Ca) Ba)) (=> (forall ((X_1 tptp.fun_Ar331856045t_bool) (Y_1 tptp.fun_Ar331856045t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool Y_1) X_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f1403773274ol_nat F Y_1)) (tptp.hAPP_f1403773274ol_nat F X_1))))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_f1403773274ol_nat F Ca)) Aa)))))) (forall ((Ca tptp.fun_nat_bool) (Aa tptp.fun_nat_bool) (F tptp.fun_fu821463397t_bool) (Ba tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Aa) (tptp.hAPP_f800510211t_bool F Ba))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool Ba) Ca)) (=> (forall ((X_1 tptp.fun_nat_bool) (Y_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool (tptp.hAPP_f800510211t_bool F X_1)) (tptp.hAPP_f800510211t_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool Aa) (tptp.hAPP_f800510211t_bool F Ca))))))) (forall ((Ca tptp.fun_Pr1643180309t_bool) (Aa tptp.fun_nat_bool) (F tptp.fun_fu988033326t_bool) (Ba tptp.fun_Pr1643180309t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Aa) (tptp.hAPP_f543204480t_bool F Ba))) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool Ba) Ca)) (=> (forall ((X_1 tptp.fun_Pr1643180309t_bool) (Y_1 tptp.fun_Pr1643180309t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool (tptp.hAPP_f543204480t_bool F X_1)) (tptp.hAPP_f543204480t_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool Aa) (tptp.hAPP_f543204480t_bool F Ca))))))) (forall ((Ca tptp.fun_Ar1809396326i_bool) (Aa tptp.fun_nat_bool) (F tptp.fun_fu1254370943t_bool) (Ba tptp.fun_Ar1809396326i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Aa) (tptp.hAPP_f622418129t_bool F Ba))) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool Ba) Ca)) (=> (forall ((X_1 tptp.fun_Ar1809396326i_bool) (Y_1 tptp.fun_Ar1809396326i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool (tptp.hAPP_f622418129t_bool F X_1)) (tptp.hAPP_f622418129t_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool Aa) (tptp.hAPP_f622418129t_bool F Ca))))))) (forall ((Ca tptp.nat) (Aa tptp.fun_nat_bool) (F tptp.fun_nat_fun_nat_bool) (Ba tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Aa) (tptp.hAPP_n1699378549t_bool F Ba))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ba) Ca)) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool (tptp.hAPP_n1699378549t_bool F X_1)) (tptp.hAPP_n1699378549t_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool Aa) (tptp.hAPP_n1699378549t_bool F Ca))))))) (forall ((Ca tptp.nat) (Aa tptp.fun_Pr1643180309t_bool) (F tptp.fun_na1041622088t_bool) (Ba tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool Aa) (tptp.hAPP_n454528608t_bool F Ba))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ba) Ca)) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool (tptp.hAPP_n454528608t_bool F X_1)) (tptp.hAPP_n454528608t_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool Aa) (tptp.hAPP_n454528608t_bool F Ca))))))) (forall ((Ca tptp.nat) (Aa tptp.fun_Ar1809396326i_bool) (F tptp.fun_na2037635353i_bool) (Ba tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool Aa) (tptp.hAPP_n34002993i_bool F Ba))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ba) Ca)) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool (tptp.hAPP_n34002993i_bool F X_1)) (tptp.hAPP_n34002993i_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool Aa) (tptp.hAPP_n34002993i_bool F Ca))))))) (forall ((Ca tptp.nat) (Aa tptp.fun_fu638310559l_bool) (F tptp.fun_na144630978l_bool) (Ba tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool Aa) (tptp.hAPP_n1134275860l_bool F Ba))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ba) Ca)) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1727358153l_bool (tptp.hAPP_n1134275860l_bool F X_1)) (tptp.hAPP_n1134275860l_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1727358153l_bool Aa) (tptp.hAPP_n1134275860l_bool F Ca))))))) (forall ((Ca tptp.nat) (Aa tptp.fun_fu2098777574l_bool) (F tptp.fun_na138495129l_bool) (Ba tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool Aa) (tptp.hAPP_n1555388849l_bool F Ba))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ba) Ca)) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le119247420l_bool (tptp.hAPP_n1555388849l_bool F X_1)) (tptp.hAPP_n1555388849l_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le119247420l_bool Aa) (tptp.hAPP_n1555388849l_bool F Ca))))))) (forall ((Ca tptp.nat) (Aa tptp.fun_fu3835832l_bool) (F tptp.fun_na6909291l_bool) (Ba tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool Aa) (tptp.hAPP_n2125602947l_bool F Ba))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ba) Ca)) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1959568910l_bool (tptp.hAPP_n2125602947l_bool F X_1)) (tptp.hAPP_n2125602947l_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1959568910l_bool Aa) (tptp.hAPP_n2125602947l_bool F Ca))))))) (forall ((Ca tptp.nat) (Aa tptp.fun_Pr2067565481t_bool) (F tptp.fun_na998785244t_bool) (Ba tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool Aa) (tptp.hAPP_n1161265524t_bool F Ba))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ba) Ca)) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1478665215t_bool (tptp.hAPP_n1161265524t_bool F X_1)) (tptp.hAPP_n1161265524t_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1478665215t_bool Aa) (tptp.hAPP_n1161265524t_bool F Ca))))))) (forall ((Ca tptp.nat) (Aa tptp.bool) (F tptp.fun_nat_bool) (Ba tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Aa) (tptp.hAPP_nat_bool F Ba))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ba) Ca)) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_bool (tptp.hAPP_nat_bool F X_1)) (tptp.hAPP_nat_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_bool Aa) (tptp.hAPP_nat_bool F Ca))))))) (forall ((Ca tptp.nat) (Aa tptp.fun_Ar331856045t_bool) (F tptp.fun_na300967376t_bool) (Ba tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool Aa) (tptp.hAPP_n1312530466t_bool F Ba))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ba) Ca)) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le19409623t_bool (tptp.hAPP_n1312530466t_bool F X_1)) (tptp.hAPP_n1312530466t_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le19409623t_bool Aa) (tptp.hAPP_n1312530466t_bool F Ca))))))) (forall ((Ca tptp.fun_nat_bool) (Aa tptp.nat) (F tptp.fun_fun_nat_bool_nat) (Ba tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Aa) (tptp.hAPP_f22106695ol_nat F Ba))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool Ba) Ca)) (=> (forall ((X_1 tptp.fun_nat_bool) (Y_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_f22106695ol_nat F X_1)) (tptp.hAPP_f22106695ol_nat F Y_1))))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Aa) (tptp.hAPP_f22106695ol_nat F Ca))))))) (forall ((Ca tptp.fun_Pr1643180309t_bool) (Aa tptp.nat) (F tptp.fun_fu572628082ol_nat) (Ba tptp.fun_Pr1643180309t_bool)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Aa) (tptp.hAPP_f2030293770ol_nat F Ba))) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool Ba) Ca)) (=> (forall ((X_1 tptp.fun_Pr1643180309t_bool) (Y_1 tptp.fun_Pr1643180309t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_f2030293770ol_nat F X_1)) (tptp.hAPP_f2030293770ol_nat F Y_1))))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Aa) (tptp.hAPP_f2030293770ol_nat F Ca))))))) (forall ((Ca tptp.fun_Ar1809396326i_bool) (Aa tptp.nat) (F tptp.fun_fu1603738721ol_nat) (Ba tptp.fun_Ar1809396326i_bool)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Aa) (tptp.hAPP_f846027769ol_nat F Ba))) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool Ba) Ca)) (=> (forall ((X_1 tptp.fun_Ar1809396326i_bool) (Y_1 tptp.fun_Ar1809396326i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_f846027769ol_nat F X_1)) (tptp.hAPP_f846027769ol_nat F Y_1))))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Aa) (tptp.hAPP_f846027769ol_nat F Ca))))))) (forall ((Ca tptp.nat) (Aa tptp.fun_nat_bool) (F tptp.fun_nat_fun_nat_bool) (Ba tptp.nat)) (let ((_let_1 (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool Aa))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_n1699378549t_bool F Ba))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ba) Ca)) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_n1699378549t_bool F X_1)) (tptp.hAPP_n1699378549t_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_n1699378549t_bool F Ca)))))))) (forall ((Ca tptp.nat) (Aa tptp.fun_Pr1643180309t_bool) (F tptp.fun_na1041622088t_bool) (Ba tptp.nat)) (let ((_let_1 (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool Aa))) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool _let_1 (tptp.hAPP_n454528608t_bool F Ba))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ba) Ca)) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool (tptp.hAPP_n454528608t_bool F X_1)) (tptp.hAPP_n454528608t_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool _let_1 (tptp.hAPP_n454528608t_bool F Ca)))))))) (forall ((Ca tptp.nat) (Aa tptp.fun_Ar1809396326i_bool) (F tptp.fun_na2037635353i_bool) (Ba tptp.nat)) (let ((_let_1 (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool Aa))) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool _let_1 (tptp.hAPP_n34002993i_bool F Ba))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ba) Ca)) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool (tptp.hAPP_n34002993i_bool F X_1)) (tptp.hAPP_n34002993i_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f584385070l_bool _let_1 (tptp.hAPP_n34002993i_bool F Ca)))))))) (forall ((Ca tptp.nat) (Aa tptp.fun_fu638310559l_bool) (F tptp.fun_na144630978l_bool) (Ba tptp.nat)) (let ((_let_1 (tptp.hAPP_f1722316607l_bool tptp.ord_le1727358153l_bool Aa))) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool _let_1 (tptp.hAPP_n1134275860l_bool F Ba))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ba) Ca)) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool (tptp.hAPP_n1134275860l_bool F X_1)) (tptp.hAPP_n1134275860l_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f182583295l_bool _let_1 (tptp.hAPP_n1134275860l_bool F Ca)))))))) (forall ((Ca tptp.nat) (Aa tptp.fun_fu2098777574l_bool) (F tptp.fun_na138495129l_bool) (Ba tptp.nat)) (let ((_let_1 (tptp.hAPP_f916323245l_bool tptp.ord_le119247420l_bool Aa))) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool _let_1 (tptp.hAPP_n1555388849l_bool F Ba))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ba) Ca)) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool (tptp.hAPP_n1555388849l_bool F X_1)) (tptp.hAPP_n1555388849l_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f975209902l_bool _let_1 (tptp.hAPP_n1555388849l_bool F Ca)))))))) (forall ((Ca tptp.nat) (Aa tptp.fun_fu3835832l_bool) (F tptp.fun_na6909291l_bool) (Ba tptp.nat)) (let ((_let_1 (tptp.hAPP_f585353809l_bool tptp.ord_le1959568910l_bool Aa))) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool _let_1 (tptp.hAPP_n2125602947l_bool F Ba))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ba) Ca)) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool (tptp.hAPP_n2125602947l_bool F X_1)) (tptp.hAPP_n2125602947l_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f73423488l_bool _let_1 (tptp.hAPP_n2125602947l_bool F Ca)))))))) (forall ((Ca tptp.nat) (Aa tptp.fun_Pr2067565481t_bool) (F tptp.fun_na998785244t_bool) (Ba tptp.nat)) (let ((_let_1 (tptp.hAPP_f930900275l_bool tptp.ord_le1478665215t_bool Aa))) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_1 (tptp.hAPP_n1161265524t_bool F Ba))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ba) Ca)) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool (tptp.hAPP_n1161265524t_bool F X_1)) (tptp.hAPP_n1161265524t_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_1 (tptp.hAPP_n1161265524t_bool F Ca)))))))) (forall ((Ca tptp.nat) (Aa tptp.bool) (F tptp.fun_nat_bool) (Ba tptp.nat)) (let ((_let_1 (tptp.hAPP_b589554111l_bool tptp.ord_less_bool Aa))) (=> (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 (tptp.hAPP_nat_bool F Ba))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ba) Ca)) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_nat_bool F X_1)) (tptp.hAPP_nat_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 (tptp.hAPP_nat_bool F Ca)))))))) (forall ((Ca tptp.nat) (Aa tptp.fun_Ar331856045t_bool) (F tptp.fun_na300967376t_bool) (Ba tptp.nat)) (let ((_let_1 (tptp.hAPP_f1055587775l_bool tptp.ord_le19409623t_bool Aa))) (=> (tptp.hBOOL (tptp.hAPP_f1452856589l_bool _let_1 (tptp.hAPP_n1312530466t_bool F Ba))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ba) Ca)) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool (tptp.hAPP_n1312530466t_bool F X_1)) (tptp.hAPP_n1312530466t_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f1452856589l_bool _let_1 (tptp.hAPP_n1312530466t_bool F Ca)))))))) (forall ((Ca tptp.fun_nat_bool) (Aa tptp.fun_nat_bool) (F tptp.fun_fu821463397t_bool) (Ba tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool Aa))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f800510211t_bool F Ba))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Ba) Ca)) (=> (forall ((X_1 tptp.fun_nat_bool) (Y_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_f800510211t_bool F X_1)) (tptp.hAPP_f800510211t_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f800510211t_bool F Ca)))))))) (forall ((Ca tptp.fun_nat_bool) (Aa tptp.fun_Pr1643180309t_bool) (F tptp.fun_fu1096920966t_bool) (Ba tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool Aa))) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool _let_1 (tptp.hAPP_f1061584978t_bool F Ba))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Ba) Ca)) (=> (forall ((X_1 tptp.fun_nat_bool) (Y_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool (tptp.hAPP_f1061584978t_bool F X_1)) (tptp.hAPP_f1061584978t_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool _let_1 (tptp.hAPP_f1061584978t_bool F Ca)))))))) (forall ((Ca tptp.fun_nat_bool) (Aa tptp.fun_Ar1809396326i_bool) (F tptp.fun_fu1415967063i_bool) (Ba tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool Aa))) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool _let_1 (tptp.hAPP_f1992344867i_bool F Ba))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Ba) Ca)) (=> (forall ((X_1 tptp.fun_nat_bool) (Y_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool (tptp.hAPP_f1992344867i_bool F X_1)) (tptp.hAPP_f1992344867i_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f584385070l_bool _let_1 (tptp.hAPP_f1992344867i_bool F Ca)))))))) (forall ((Ca tptp.fun_nat_bool) (Aa tptp.fun_fu638310559l_bool) (F tptp.fun_fu1182412548l_bool) (Ba tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f1722316607l_bool tptp.ord_le1727358153l_bool Aa))) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool _let_1 (tptp.hAPP_f229466530l_bool F Ba))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Ba) Ca)) (=> (forall ((X_1 tptp.fun_nat_bool) (Y_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool (tptp.hAPP_f229466530l_bool F X_1)) (tptp.hAPP_f229466530l_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f182583295l_bool _let_1 (tptp.hAPP_f229466530l_bool F Ca)))))))) (forall ((Ca tptp.fun_nat_bool) (Aa tptp.fun_fu2098777574l_bool) (F tptp.fun_fu1927280855l_bool) (Ba tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f916323245l_bool tptp.ord_le119247420l_bool Aa))) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool _let_1 (tptp.hAPP_f561646243l_bool F Ba))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Ba) Ca)) (=> (forall ((X_1 tptp.fun_nat_bool) (Y_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool (tptp.hAPP_f561646243l_bool F X_1)) (tptp.hAPP_f561646243l_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f975209902l_bool _let_1 (tptp.hAPP_f561646243l_bool F Ca)))))))) (forall ((Ca tptp.fun_nat_bool) (Aa tptp.fun_fu3835832l_bool) (F tptp.fun_fu138597289l_bool) (Ba tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f585353809l_bool tptp.ord_le1959568910l_bool Aa))) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool _let_1 (tptp.hAPP_f256405365l_bool F Ba))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Ba) Ca)) (=> (forall ((X_1 tptp.fun_nat_bool) (Y_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool (tptp.hAPP_f256405365l_bool F X_1)) (tptp.hAPP_f256405365l_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f73423488l_bool _let_1 (tptp.hAPP_f256405365l_bool F Ca)))))))) (forall ((Ca tptp.fun_nat_bool) (Aa tptp.fun_Pr2067565481t_bool) (F tptp.fun_fu1778022682t_bool) (Ba tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f930900275l_bool tptp.ord_le1478665215t_bool Aa))) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_1 (tptp.hAPP_f1472089702t_bool F Ba))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Ba) Ca)) (=> (forall ((X_1 tptp.fun_nat_bool) (Y_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool (tptp.hAPP_f1472089702t_bool F X_1)) (tptp.hAPP_f1472089702t_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_1 (tptp.hAPP_f1472089702t_bool F Ca)))))))) (forall ((Ca tptp.fun_nat_bool) (Aa tptp.bool) (F tptp.fun_fu425979586l_bool) (Ba tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_b589554111l_bool tptp.ord_less_bool Aa))) (=> (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 (tptp.hAPP_f54304608l_bool F Ba))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Ba) Ca)) (=> (forall ((X_1 tptp.fun_nat_bool) (Y_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_f54304608l_bool F X_1)) (tptp.hAPP_f54304608l_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 (tptp.hAPP_f54304608l_bool F Ca)))))))) (forall ((Ca tptp.fun_nat_bool) (Aa tptp.fun_Ar331856045t_bool) (F tptp.fun_fu221658642t_bool) (Ba tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f1055587775l_bool tptp.ord_le19409623t_bool Aa))) (=> (tptp.hBOOL (tptp.hAPP_f1452856589l_bool _let_1 (tptp.hAPP_f1635284656t_bool F Ba))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Ba) Ca)) (=> (forall ((X_1 tptp.fun_nat_bool) (Y_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool (tptp.hAPP_f1635284656t_bool F X_1)) (tptp.hAPP_f1635284656t_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f1452856589l_bool _let_1 (tptp.hAPP_f1635284656t_bool F Ca)))))))) (forall ((Ca tptp.fun_fu638310559l_bool) (Aa tptp.fun_nat_bool) (F tptp.fun_fu1632756612t_bool) (Ba tptp.fun_fu638310559l_bool)) (let ((_let_1 (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool Aa))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f2063587362t_bool F Ba))) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool Ba) Ca)) (=> (forall ((X_1 tptp.fun_fu638310559l_bool) (Y_1 tptp.fun_fu638310559l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_f2063587362t_bool F X_1)) (tptp.hAPP_f2063587362t_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f2063587362t_bool F Ca)))))))) (forall ((Ca tptp.fun_fu2098777574l_bool) (Aa tptp.fun_nat_bool) (F tptp.fun_fu309681663t_bool) (Ba tptp.fun_fu2098777574l_bool)) (let ((_let_1 (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool Aa))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f1705385041t_bool F Ba))) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool Ba) Ca)) (=> (forall ((X_1 tptp.fun_fu2098777574l_bool) (Y_1 tptp.fun_fu2098777574l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_f1705385041t_bool F X_1)) (tptp.hAPP_f1705385041t_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f1705385041t_bool F Ca)))))))) (forall ((Ca tptp.fun_fu3835832l_bool) (Aa tptp.fun_nat_bool) (F tptp.fun_fu1078872017t_bool) (Ba tptp.fun_fu3835832l_bool)) (let ((_let_1 (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool Aa))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f743717923t_bool F Ba))) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool Ba) Ca)) (=> (forall ((X_1 tptp.fun_fu3835832l_bool) (Y_1 tptp.fun_fu3835832l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_f743717923t_bool F X_1)) (tptp.hAPP_f743717923t_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f743717923t_bool F Ca)))))))) (forall ((Ca tptp.fun_Pr2067565481t_bool) (Aa tptp.fun_nat_bool) (F tptp.fun_fu477456066t_bool) (Ba tptp.fun_Pr2067565481t_bool)) (let ((_let_1 (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool Aa))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f703394068t_bool F Ba))) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool Ba) Ca)) (=> (forall ((X_1 tptp.fun_Pr2067565481t_bool) (Y_1 tptp.fun_Pr2067565481t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_f703394068t_bool F X_1)) (tptp.hAPP_f703394068t_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f703394068t_bool F Ca)))))))) (forall ((Ca tptp.bool) (Aa tptp.fun_nat_bool) (F tptp.fun_bo1570548802t_bool) (Ba tptp.bool)) (let ((_let_1 (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool Aa))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_b1013836512t_bool F Ba))) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Ba) Ca)) (=> (forall ((X_1 tptp.bool) (Y_1 tptp.bool)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_b1013836512t_bool F X_1)) (tptp.hAPP_b1013836512t_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_b1013836512t_bool F Ca)))))))) (forall ((Ca tptp.fun_Ar1809396326i_bool) (Aa tptp.fun_nat_bool) (F tptp.fun_fu1254370943t_bool) (Ba tptp.fun_Ar1809396326i_bool)) (let ((_let_1 (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool Aa))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f622418129t_bool F Ba))) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool Ba) Ca)) (=> (forall ((X_1 tptp.fun_Ar1809396326i_bool) (Y_1 tptp.fun_Ar1809396326i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_f622418129t_bool F X_1)) (tptp.hAPP_f622418129t_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f622418129t_bool F Ca)))))))) (forall ((Ca tptp.fun_Pr1643180309t_bool) (Aa tptp.fun_nat_bool) (F tptp.fun_fu988033326t_bool) (Ba tptp.fun_Pr1643180309t_bool)) (let ((_let_1 (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool Aa))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f543204480t_bool F Ba))) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool Ba) Ca)) (=> (forall ((X_1 tptp.fun_Pr1643180309t_bool) (Y_1 tptp.fun_Pr1643180309t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_f543204480t_bool F X_1)) (tptp.hAPP_f543204480t_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f543204480t_bool F Ca)))))))) (forall ((Ca tptp.fun_Ar331856045t_bool) (Aa tptp.fun_nat_bool) (F tptp.fun_fu1869722514t_bool) (Ba tptp.fun_Ar331856045t_bool)) (let ((_let_1 (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool Aa))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f1691234864t_bool F Ba))) (=> (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool Ba) Ca)) (=> (forall ((X_1 tptp.fun_Ar331856045t_bool) (Y_1 tptp.fun_Ar331856045t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_f1691234864t_bool F X_1)) (tptp.hAPP_f1691234864t_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f1691234864t_bool F Ca)))))))) (forall ((Ca tptp.fun_fu638310559l_bool) (Aa tptp.nat) (F tptp.fun_fu955147676ol_nat) (Ba tptp.fun_fu638310559l_bool)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Aa))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_f1487854056ol_nat F Ba))) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool Ba) Ca)) (=> (forall ((X_1 tptp.fun_fu638310559l_bool) (Y_1 tptp.fun_fu638310559l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f1487854056ol_nat F X_1)) (tptp.hAPP_f1487854056ol_nat F Y_1))))) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_f1487854056ol_nat F Ca)))))))) (forall ((Ca tptp.fun_fu2098777574l_bool) (Aa tptp.nat) (F tptp.fun_fu859131105ol_nat) (Ba tptp.fun_fu2098777574l_bool)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Aa))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_f1049163897ol_nat F Ba))) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool Ba) Ca)) (=> (forall ((X_1 tptp.fun_fu2098777574l_bool) (Y_1 tptp.fun_fu2098777574l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f1049163897ol_nat F X_1)) (tptp.hAPP_f1049163897ol_nat F Y_1))))) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_f1049163897ol_nat F Ca)))))))) (forall ((Ca tptp.fun_fu3835832l_bool) (Aa tptp.nat) (F tptp.fun_fu777705871ol_nat) (Ba tptp.fun_fu3835832l_bool)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Aa))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_f602722087ol_nat F Ba))) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool Ba) Ca)) (=> (forall ((X_1 tptp.fun_fu3835832l_bool) (Y_1 tptp.fun_fu3835832l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f602722087ol_nat F X_1)) (tptp.hAPP_f602722087ol_nat F Y_1))))) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_f602722087ol_nat F Ca)))))))) (forall ((Ca tptp.fun_Pr2067565481t_bool) (Aa tptp.nat) (F tptp.fun_fu841105374ol_nat) (Ba tptp.fun_Pr2067565481t_bool)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Aa))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_f1842225014ol_nat F Ba))) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool Ba) Ca)) (=> (forall ((X_1 tptp.fun_Pr2067565481t_bool) (Y_1 tptp.fun_Pr2067565481t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f1842225014ol_nat F X_1)) (tptp.hAPP_f1842225014ol_nat F Y_1))))) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_f1842225014ol_nat F Ca)))))))) (forall ((Ca tptp.bool) (Aa tptp.nat) (F tptp.fun_bool_nat) (Ba tptp.bool)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Aa))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_bool_nat F Ba))) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Ba) Ca)) (=> (forall ((X_1 tptp.bool) (Y_1 tptp.bool)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_bool_nat F X_1)) (tptp.hAPP_bool_nat F Y_1))))) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_bool_nat F Ca)))))))) (forall ((Ca tptp.fun_Ar1809396326i_bool) (Aa tptp.nat) (F tptp.fun_fu1603738721ol_nat) (Ba tptp.fun_Ar1809396326i_bool)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Aa))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_f846027769ol_nat F Ba))) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool Ba) Ca)) (=> (forall ((X_1 tptp.fun_Ar1809396326i_bool) (Y_1 tptp.fun_Ar1809396326i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f846027769ol_nat F X_1)) (tptp.hAPP_f846027769ol_nat F Y_1))))) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_f846027769ol_nat F Ca)))))))) (forall ((Ca tptp.fun_Pr1643180309t_bool) (Aa tptp.nat) (F tptp.fun_fu572628082ol_nat) (Ba tptp.fun_Pr1643180309t_bool)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Aa))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_f2030293770ol_nat F Ba))) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool Ba) Ca)) (=> (forall ((X_1 tptp.fun_Pr1643180309t_bool) (Y_1 tptp.fun_Pr1643180309t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f2030293770ol_nat F X_1)) (tptp.hAPP_f2030293770ol_nat F Y_1))))) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_f2030293770ol_nat F Ca)))))))) (forall ((Ca tptp.fun_Ar331856045t_bool) (Aa tptp.nat) (F tptp.fun_fu1677555470ol_nat) (Ba tptp.fun_Ar331856045t_bool)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Aa))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_f1403773274ol_nat F Ba))) (=> (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool Ba) Ca)) (=> (forall ((X_1 tptp.fun_Ar331856045t_bool) (Y_1 tptp.fun_Ar331856045t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f1403773274ol_nat F X_1)) (tptp.hAPP_f1403773274ol_nat F Y_1))))) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_f1403773274ol_nat F Ca)))))))) (forall ((F tptp.fun_nat_fun_nat_bool) (Ca tptp.fun_nat_bool) (Aa tptp.nat) (Ba tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Aa) Ba)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool (tptp.hAPP_n1699378549t_bool F Ba)) Ca)) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_n1699378549t_bool F X_1)) (tptp.hAPP_n1699378549t_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool (tptp.hAPP_n1699378549t_bool F Aa)) Ca)))))) (forall ((F tptp.fun_na1041622088t_bool) (Ca tptp.fun_Pr1643180309t_bool) (Aa tptp.nat) (Ba tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Aa) Ba)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool (tptp.hAPP_n454528608t_bool F Ba)) Ca)) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool (tptp.hAPP_n454528608t_bool F X_1)) (tptp.hAPP_n454528608t_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool (tptp.hAPP_n454528608t_bool F Aa)) Ca)))))) (forall ((F tptp.fun_na2037635353i_bool) (Ca tptp.fun_Ar1809396326i_bool) (Aa tptp.nat) (Ba tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Aa) Ba)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool (tptp.hAPP_n34002993i_bool F Ba)) Ca)) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool (tptp.hAPP_n34002993i_bool F X_1)) (tptp.hAPP_n34002993i_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool (tptp.hAPP_n34002993i_bool F Aa)) Ca)))))) (forall ((F tptp.fun_na144630978l_bool) (Ca tptp.fun_fu638310559l_bool) (Aa tptp.nat) (Ba tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Aa) Ba)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1727358153l_bool (tptp.hAPP_n1134275860l_bool F Ba)) Ca)) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool (tptp.hAPP_n1134275860l_bool F X_1)) (tptp.hAPP_n1134275860l_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1727358153l_bool (tptp.hAPP_n1134275860l_bool F Aa)) Ca)))))) (forall ((F tptp.fun_na138495129l_bool) (Ca tptp.fun_fu2098777574l_bool) (Aa tptp.nat) (Ba tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Aa) Ba)) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le119247420l_bool (tptp.hAPP_n1555388849l_bool F Ba)) Ca)) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool (tptp.hAPP_n1555388849l_bool F X_1)) (tptp.hAPP_n1555388849l_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le119247420l_bool (tptp.hAPP_n1555388849l_bool F Aa)) Ca)))))) (forall ((F tptp.fun_na6909291l_bool) (Ca tptp.fun_fu3835832l_bool) (Aa tptp.nat) (Ba tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Aa) Ba)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1959568910l_bool (tptp.hAPP_n2125602947l_bool F Ba)) Ca)) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool (tptp.hAPP_n2125602947l_bool F X_1)) (tptp.hAPP_n2125602947l_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1959568910l_bool (tptp.hAPP_n2125602947l_bool F Aa)) Ca)))))) (forall ((F tptp.fun_na998785244t_bool) (Ca tptp.fun_Pr2067565481t_bool) (Aa tptp.nat) (Ba tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Aa) Ba)) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1478665215t_bool (tptp.hAPP_n1161265524t_bool F Ba)) Ca)) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool (tptp.hAPP_n1161265524t_bool F X_1)) (tptp.hAPP_n1161265524t_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1478665215t_bool (tptp.hAPP_n1161265524t_bool F Aa)) Ca)))))) (forall ((F tptp.fun_nat_bool) (Ca tptp.bool) (Aa tptp.nat) (Ba tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Aa) Ba)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_bool (tptp.hAPP_nat_bool F Ba)) Ca)) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_nat_bool F X_1)) (tptp.hAPP_nat_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_bool (tptp.hAPP_nat_bool F Aa)) Ca)))))) (forall ((F tptp.fun_na300967376t_bool) (Ca tptp.fun_Ar331856045t_bool) (Aa tptp.nat) (Ba tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Aa) Ba)) (=> (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le19409623t_bool (tptp.hAPP_n1312530466t_bool F Ba)) Ca)) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool (tptp.hAPP_n1312530466t_bool F X_1)) (tptp.hAPP_n1312530466t_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le19409623t_bool (tptp.hAPP_n1312530466t_bool F Aa)) Ca)))))) (forall ((F tptp.fun_fu821463397t_bool) (Ca tptp.fun_nat_bool) (Aa tptp.fun_nat_bool) (Ba tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Aa) Ba)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool (tptp.hAPP_f800510211t_bool F Ba)) Ca)) (=> (forall ((X_1 tptp.fun_nat_bool) (Y_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_f800510211t_bool F X_1)) (tptp.hAPP_f800510211t_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool (tptp.hAPP_f800510211t_bool F Aa)) Ca)))))) (forall ((F tptp.fun_fu1096920966t_bool) (Ca tptp.fun_Pr1643180309t_bool) (Aa tptp.fun_nat_bool) (Ba tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Aa) Ba)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool (tptp.hAPP_f1061584978t_bool F Ba)) Ca)) (=> (forall ((X_1 tptp.fun_nat_bool) (Y_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool (tptp.hAPP_f1061584978t_bool F X_1)) (tptp.hAPP_f1061584978t_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool (tptp.hAPP_f1061584978t_bool F Aa)) Ca)))))) (forall ((F tptp.fun_fu1415967063i_bool) (Ca tptp.fun_Ar1809396326i_bool) (Aa tptp.fun_nat_bool) (Ba tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Aa) Ba)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool (tptp.hAPP_f1992344867i_bool F Ba)) Ca)) (=> (forall ((X_1 tptp.fun_nat_bool) (Y_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool (tptp.hAPP_f1992344867i_bool F X_1)) (tptp.hAPP_f1992344867i_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool (tptp.hAPP_f1992344867i_bool F Aa)) Ca)))))) (forall ((F tptp.fun_fu1182412548l_bool) (Ca tptp.fun_fu638310559l_bool) (Aa tptp.fun_nat_bool) (Ba tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Aa) Ba)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1727358153l_bool (tptp.hAPP_f229466530l_bool F Ba)) Ca)) (=> (forall ((X_1 tptp.fun_nat_bool) (Y_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool (tptp.hAPP_f229466530l_bool F X_1)) (tptp.hAPP_f229466530l_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1727358153l_bool (tptp.hAPP_f229466530l_bool F Aa)) Ca)))))) (forall ((F tptp.fun_fu1927280855l_bool) (Ca tptp.fun_fu2098777574l_bool) (Aa tptp.fun_nat_bool) (Ba tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Aa) Ba)) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le119247420l_bool (tptp.hAPP_f561646243l_bool F Ba)) Ca)) (=> (forall ((X_1 tptp.fun_nat_bool) (Y_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool (tptp.hAPP_f561646243l_bool F X_1)) (tptp.hAPP_f561646243l_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le119247420l_bool (tptp.hAPP_f561646243l_bool F Aa)) Ca)))))) (forall ((F tptp.fun_fu138597289l_bool) (Ca tptp.fun_fu3835832l_bool) (Aa tptp.fun_nat_bool) (Ba tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Aa) Ba)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1959568910l_bool (tptp.hAPP_f256405365l_bool F Ba)) Ca)) (=> (forall ((X_1 tptp.fun_nat_bool) (Y_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool (tptp.hAPP_f256405365l_bool F X_1)) (tptp.hAPP_f256405365l_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1959568910l_bool (tptp.hAPP_f256405365l_bool F Aa)) Ca)))))) (forall ((F tptp.fun_fu1778022682t_bool) (Ca tptp.fun_Pr2067565481t_bool) (Aa tptp.fun_nat_bool) (Ba tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Aa) Ba)) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1478665215t_bool (tptp.hAPP_f1472089702t_bool F Ba)) Ca)) (=> (forall ((X_1 tptp.fun_nat_bool) (Y_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool (tptp.hAPP_f1472089702t_bool F X_1)) (tptp.hAPP_f1472089702t_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1478665215t_bool (tptp.hAPP_f1472089702t_bool F Aa)) Ca)))))) (forall ((F tptp.fun_fu425979586l_bool) (Ca tptp.bool) (Aa tptp.fun_nat_bool) (Ba tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Aa) Ba)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_bool (tptp.hAPP_f54304608l_bool F Ba)) Ca)) (=> (forall ((X_1 tptp.fun_nat_bool) (Y_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_f54304608l_bool F X_1)) (tptp.hAPP_f54304608l_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_bool (tptp.hAPP_f54304608l_bool F Aa)) Ca)))))) (forall ((F tptp.fun_fu221658642t_bool) (Ca tptp.fun_Ar331856045t_bool) (Aa tptp.fun_nat_bool) (Ba tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Aa) Ba)) (=> (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le19409623t_bool (tptp.hAPP_f1635284656t_bool F Ba)) Ca)) (=> (forall ((X_1 tptp.fun_nat_bool) (Y_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool (tptp.hAPP_f1635284656t_bool F X_1)) (tptp.hAPP_f1635284656t_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le19409623t_bool (tptp.hAPP_f1635284656t_bool F Aa)) Ca)))))) (forall ((F tptp.fun_fu1632756612t_bool) (Ca tptp.fun_nat_bool) (Aa tptp.fun_fu638310559l_bool) (Ba tptp.fun_fu638310559l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool Aa) Ba)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool (tptp.hAPP_f2063587362t_bool F Ba)) Ca)) (=> (forall ((X_1 tptp.fun_fu638310559l_bool) (Y_1 tptp.fun_fu638310559l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_f2063587362t_bool F X_1)) (tptp.hAPP_f2063587362t_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool (tptp.hAPP_f2063587362t_bool F Aa)) Ca)))))) (forall ((F tptp.fun_fu309681663t_bool) (Ca tptp.fun_nat_bool) (Aa tptp.fun_fu2098777574l_bool) (Ba tptp.fun_fu2098777574l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool Aa) Ba)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool (tptp.hAPP_f1705385041t_bool F Ba)) Ca)) (=> (forall ((X_1 tptp.fun_fu2098777574l_bool) (Y_1 tptp.fun_fu2098777574l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_f1705385041t_bool F X_1)) (tptp.hAPP_f1705385041t_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool (tptp.hAPP_f1705385041t_bool F Aa)) Ca)))))) (forall ((F tptp.fun_fu1078872017t_bool) (Ca tptp.fun_nat_bool) (Aa tptp.fun_fu3835832l_bool) (Ba tptp.fun_fu3835832l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool Aa) Ba)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool (tptp.hAPP_f743717923t_bool F Ba)) Ca)) (=> (forall ((X_1 tptp.fun_fu3835832l_bool) (Y_1 tptp.fun_fu3835832l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_f743717923t_bool F X_1)) (tptp.hAPP_f743717923t_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool (tptp.hAPP_f743717923t_bool F Aa)) Ca)))))) (forall ((F tptp.fun_fu477456066t_bool) (Ca tptp.fun_nat_bool) (Aa tptp.fun_Pr2067565481t_bool) (Ba tptp.fun_Pr2067565481t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool Aa) Ba)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool (tptp.hAPP_f703394068t_bool F Ba)) Ca)) (=> (forall ((X_1 tptp.fun_Pr2067565481t_bool) (Y_1 tptp.fun_Pr2067565481t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_f703394068t_bool F X_1)) (tptp.hAPP_f703394068t_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool (tptp.hAPP_f703394068t_bool F Aa)) Ca)))))) (forall ((F tptp.fun_bo1570548802t_bool) (Ca tptp.fun_nat_bool) (Aa tptp.bool) (Ba tptp.bool)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Aa) Ba)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool (tptp.hAPP_b1013836512t_bool F Ba)) Ca)) (=> (forall ((X_1 tptp.bool) (Y_1 tptp.bool)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_b1013836512t_bool F X_1)) (tptp.hAPP_b1013836512t_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool (tptp.hAPP_b1013836512t_bool F Aa)) Ca)))))) (forall ((F tptp.fun_fu1254370943t_bool) (Ca tptp.fun_nat_bool) (Aa tptp.fun_Ar1809396326i_bool) (Ba tptp.fun_Ar1809396326i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool Aa) Ba)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool (tptp.hAPP_f622418129t_bool F Ba)) Ca)) (=> (forall ((X_1 tptp.fun_Ar1809396326i_bool) (Y_1 tptp.fun_Ar1809396326i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_f622418129t_bool F X_1)) (tptp.hAPP_f622418129t_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool (tptp.hAPP_f622418129t_bool F Aa)) Ca)))))) (forall ((F tptp.fun_fu988033326t_bool) (Ca tptp.fun_nat_bool) (Aa tptp.fun_Pr1643180309t_bool) (Ba tptp.fun_Pr1643180309t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool Aa) Ba)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool (tptp.hAPP_f543204480t_bool F Ba)) Ca)) (=> (forall ((X_1 tptp.fun_Pr1643180309t_bool) (Y_1 tptp.fun_Pr1643180309t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_f543204480t_bool F X_1)) (tptp.hAPP_f543204480t_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool (tptp.hAPP_f543204480t_bool F Aa)) Ca)))))) (forall ((F tptp.fun_fu1869722514t_bool) (Ca tptp.fun_nat_bool) (Aa tptp.fun_Ar331856045t_bool) (Ba tptp.fun_Ar331856045t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool Aa) Ba)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool (tptp.hAPP_f1691234864t_bool F Ba)) Ca)) (=> (forall ((X_1 tptp.fun_Ar331856045t_bool) (Y_1 tptp.fun_Ar331856045t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_f1691234864t_bool F X_1)) (tptp.hAPP_f1691234864t_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool (tptp.hAPP_f1691234864t_bool F Aa)) Ca)))))) (forall ((F tptp.fun_fu955147676ol_nat) (Ca tptp.nat) (Aa tptp.fun_fu638310559l_bool) (Ba tptp.fun_fu638310559l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool Aa) Ba)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_f1487854056ol_nat F Ba)) Ca)) (=> (forall ((X_1 tptp.fun_fu638310559l_bool) (Y_1 tptp.fun_fu638310559l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f1487854056ol_nat F X_1)) (tptp.hAPP_f1487854056ol_nat F Y_1))))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_f1487854056ol_nat F Aa)) Ca)))))) (forall ((F tptp.fun_fu859131105ol_nat) (Ca tptp.nat) (Aa tptp.fun_fu2098777574l_bool) (Ba tptp.fun_fu2098777574l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool Aa) Ba)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_f1049163897ol_nat F Ba)) Ca)) (=> (forall ((X_1 tptp.fun_fu2098777574l_bool) (Y_1 tptp.fun_fu2098777574l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f1049163897ol_nat F X_1)) (tptp.hAPP_f1049163897ol_nat F Y_1))))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_f1049163897ol_nat F Aa)) Ca)))))) (forall ((F tptp.fun_fu777705871ol_nat) (Ca tptp.nat) (Aa tptp.fun_fu3835832l_bool) (Ba tptp.fun_fu3835832l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool Aa) Ba)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_f602722087ol_nat F Ba)) Ca)) (=> (forall ((X_1 tptp.fun_fu3835832l_bool) (Y_1 tptp.fun_fu3835832l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f602722087ol_nat F X_1)) (tptp.hAPP_f602722087ol_nat F Y_1))))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_f602722087ol_nat F Aa)) Ca)))))) (forall ((F tptp.fun_fu841105374ol_nat) (Ca tptp.nat) (Aa tptp.fun_Pr2067565481t_bool) (Ba tptp.fun_Pr2067565481t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool Aa) Ba)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_f1842225014ol_nat F Ba)) Ca)) (=> (forall ((X_1 tptp.fun_Pr2067565481t_bool) (Y_1 tptp.fun_Pr2067565481t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f1842225014ol_nat F X_1)) (tptp.hAPP_f1842225014ol_nat F Y_1))))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_f1842225014ol_nat F Aa)) Ca)))))) (forall ((F tptp.fun_bool_nat) (Ca tptp.nat) (Aa tptp.bool) (Ba tptp.bool)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Aa) Ba)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_bool_nat F Ba)) Ca)) (=> (forall ((X_1 tptp.bool) (Y_1 tptp.bool)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_bool_nat F X_1)) (tptp.hAPP_bool_nat F Y_1))))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_bool_nat F Aa)) Ca)))))) (forall ((F tptp.fun_fu1603738721ol_nat) (Ca tptp.nat) (Aa tptp.fun_Ar1809396326i_bool) (Ba tptp.fun_Ar1809396326i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool Aa) Ba)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_f846027769ol_nat F Ba)) Ca)) (=> (forall ((X_1 tptp.fun_Ar1809396326i_bool) (Y_1 tptp.fun_Ar1809396326i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f846027769ol_nat F X_1)) (tptp.hAPP_f846027769ol_nat F Y_1))))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_f846027769ol_nat F Aa)) Ca)))))) (forall ((F tptp.fun_fu572628082ol_nat) (Ca tptp.nat) (Aa tptp.fun_Pr1643180309t_bool) (Ba tptp.fun_Pr1643180309t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool Aa) Ba)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_f2030293770ol_nat F Ba)) Ca)) (=> (forall ((X_1 tptp.fun_Pr1643180309t_bool) (Y_1 tptp.fun_Pr1643180309t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f2030293770ol_nat F X_1)) (tptp.hAPP_f2030293770ol_nat F Y_1))))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_f2030293770ol_nat F Aa)) Ca)))))) (forall ((F tptp.fun_fu1677555470ol_nat) (Ca tptp.nat) (Aa tptp.fun_Ar331856045t_bool) (Ba tptp.fun_Ar331856045t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool Aa) Ba)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_f1403773274ol_nat F Ba)) Ca)) (=> (forall ((X_1 tptp.fun_Ar331856045t_bool) (Y_1 tptp.fun_Ar331856045t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f1403773274ol_nat F X_1)) (tptp.hAPP_f1403773274ol_nat F Y_1))))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_f1403773274ol_nat F Aa)) Ca)))))) (forall ((F tptp.fun_fu821463397t_bool) (Ca tptp.fun_nat_bool) (Aa tptp.fun_nat_bool) (Ba tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool Aa) Ba)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_f800510211t_bool F Ba)) Ca)) (=> (forall ((X_1 tptp.fun_nat_bool) (Y_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool (tptp.hAPP_f800510211t_bool F X_1)) (tptp.hAPP_f800510211t_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool (tptp.hAPP_f800510211t_bool F Aa)) Ca)))))) (forall ((F tptp.fun_fu988033326t_bool) (Ca tptp.fun_nat_bool) (Aa tptp.fun_Pr1643180309t_bool) (Ba tptp.fun_Pr1643180309t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool Aa) Ba)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_f543204480t_bool F Ba)) Ca)) (=> (forall ((X_1 tptp.fun_Pr1643180309t_bool) (Y_1 tptp.fun_Pr1643180309t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool (tptp.hAPP_f543204480t_bool F X_1)) (tptp.hAPP_f543204480t_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool (tptp.hAPP_f543204480t_bool F Aa)) Ca)))))) (forall ((F tptp.fun_fu1254370943t_bool) (Ca tptp.fun_nat_bool) (Aa tptp.fun_Ar1809396326i_bool) (Ba tptp.fun_Ar1809396326i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool Aa) Ba)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_f622418129t_bool F Ba)) Ca)) (=> (forall ((X_1 tptp.fun_Ar1809396326i_bool) (Y_1 tptp.fun_Ar1809396326i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool (tptp.hAPP_f622418129t_bool F X_1)) (tptp.hAPP_f622418129t_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool (tptp.hAPP_f622418129t_bool F Aa)) Ca)))))) (forall ((F tptp.fun_nat_fun_nat_bool) (Ca tptp.fun_nat_bool) (Aa tptp.nat) (Ba tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Aa) Ba)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_n1699378549t_bool F Ba)) Ca)) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool (tptp.hAPP_n1699378549t_bool F X_1)) (tptp.hAPP_n1699378549t_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool (tptp.hAPP_n1699378549t_bool F Aa)) Ca)))))) (forall ((F tptp.fun_na1041622088t_bool) (Ca tptp.fun_Pr1643180309t_bool) (Aa tptp.nat) (Ba tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Aa) Ba)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool (tptp.hAPP_n454528608t_bool F Ba)) Ca)) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool (tptp.hAPP_n454528608t_bool F X_1)) (tptp.hAPP_n454528608t_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool (tptp.hAPP_n454528608t_bool F Aa)) Ca)))))) (forall ((F tptp.fun_na2037635353i_bool) (Ca tptp.fun_Ar1809396326i_bool) (Aa tptp.nat) (Ba tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Aa) Ba)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool (tptp.hAPP_n34002993i_bool F Ba)) Ca)) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool (tptp.hAPP_n34002993i_bool F X_1)) (tptp.hAPP_n34002993i_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool (tptp.hAPP_n34002993i_bool F Aa)) Ca)))))) (forall ((F tptp.fun_na144630978l_bool) (Ca tptp.fun_fu638310559l_bool) (Aa tptp.nat) (Ba tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Aa) Ba)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool (tptp.hAPP_n1134275860l_bool F Ba)) Ca)) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1727358153l_bool (tptp.hAPP_n1134275860l_bool F X_1)) (tptp.hAPP_n1134275860l_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1727358153l_bool (tptp.hAPP_n1134275860l_bool F Aa)) Ca)))))) (forall ((F tptp.fun_na138495129l_bool) (Ca tptp.fun_fu2098777574l_bool) (Aa tptp.nat) (Ba tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Aa) Ba)) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool (tptp.hAPP_n1555388849l_bool F Ba)) Ca)) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le119247420l_bool (tptp.hAPP_n1555388849l_bool F X_1)) (tptp.hAPP_n1555388849l_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le119247420l_bool (tptp.hAPP_n1555388849l_bool F Aa)) Ca)))))) (forall ((F tptp.fun_na6909291l_bool) (Ca tptp.fun_fu3835832l_bool) (Aa tptp.nat) (Ba tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Aa) Ba)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool (tptp.hAPP_n2125602947l_bool F Ba)) Ca)) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1959568910l_bool (tptp.hAPP_n2125602947l_bool F X_1)) (tptp.hAPP_n2125602947l_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1959568910l_bool (tptp.hAPP_n2125602947l_bool F Aa)) Ca)))))) (forall ((F tptp.fun_na998785244t_bool) (Ca tptp.fun_Pr2067565481t_bool) (Aa tptp.nat) (Ba tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Aa) Ba)) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool (tptp.hAPP_n1161265524t_bool F Ba)) Ca)) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1478665215t_bool (tptp.hAPP_n1161265524t_bool F X_1)) (tptp.hAPP_n1161265524t_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1478665215t_bool (tptp.hAPP_n1161265524t_bool F Aa)) Ca)))))) (forall ((F tptp.fun_nat_bool) (Ca tptp.bool) (Aa tptp.nat) (Ba tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Aa) Ba)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_nat_bool F Ba)) Ca)) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_bool (tptp.hAPP_nat_bool F X_1)) (tptp.hAPP_nat_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_bool (tptp.hAPP_nat_bool F Aa)) Ca)))))) (forall ((F tptp.fun_na300967376t_bool) (Ca tptp.fun_Ar331856045t_bool) (Aa tptp.nat) (Ba tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Aa) Ba)) (=> (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le172225251t_bool (tptp.hAPP_n1312530466t_bool F Ba)) Ca)) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le19409623t_bool (tptp.hAPP_n1312530466t_bool F X_1)) (tptp.hAPP_n1312530466t_bool F Y_1))))) (tptp.hBOOL (tptp.hAPP_f1452856589l_bool (tptp.hAPP_f1055587775l_bool tptp.ord_le19409623t_bool (tptp.hAPP_n1312530466t_bool F Aa)) Ca)))))) (forall ((F tptp.fun_fun_nat_bool_nat) (Ca tptp.nat) (Aa tptp.fun_nat_bool) (Ba tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool Aa) Ba)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f22106695ol_nat F Ba)) Ca)) (=> (forall ((X_1 tptp.fun_nat_bool) (Y_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_f22106695ol_nat F X_1)) (tptp.hAPP_f22106695ol_nat F Y_1))))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_f22106695ol_nat F Aa)) Ca)))))) (forall ((F tptp.fun_fu572628082ol_nat) (Ca tptp.nat) (Aa tptp.fun_Pr1643180309t_bool) (Ba tptp.fun_Pr1643180309t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool Aa) Ba)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f2030293770ol_nat F Ba)) Ca)) (=> (forall ((X_1 tptp.fun_Pr1643180309t_bool) (Y_1 tptp.fun_Pr1643180309t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_f2030293770ol_nat F X_1)) (tptp.hAPP_f2030293770ol_nat F Y_1))))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_f2030293770ol_nat F Aa)) Ca)))))) (forall ((F tptp.fun_fu1603738721ol_nat) (Ca tptp.nat) (Aa tptp.fun_Ar1809396326i_bool) (Ba tptp.fun_Ar1809396326i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool Aa) Ba)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f846027769ol_nat F Ba)) Ca)) (=> (forall ((X_1 tptp.fun_Ar1809396326i_bool) (Y_1 tptp.fun_Ar1809396326i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_f846027769ol_nat F X_1)) (tptp.hAPP_f846027769ol_nat F Y_1))))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_f846027769ol_nat F Aa)) Ca)))))) (forall ((M_2 tptp.nat) (K_2 tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_2) K_2)) N)) (not (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_2) N)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_2) N))))))) (forall ((A tptp.fun_fu638310559l_bool) (B tptp.fun_fu638310559l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool B) A)) (= A B)))) (forall ((A tptp.fun_fu2098777574l_bool) (B tptp.fun_fu2098777574l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool B) A)) (= A B)))) (forall ((A tptp.fun_fu3835832l_bool) (B tptp.fun_fu3835832l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool B) A)) (= A B)))) (forall ((A tptp.fun_Pr2067565481t_bool) (B tptp.fun_Pr2067565481t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool B) A)) (= A B)))) (forall ((A tptp.fun_Ar1809396326i_bool) (B tptp.fun_Ar1809396326i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool B) A)) (= A B)))) (forall ((A tptp.fun_Pr1643180309t_bool) (B tptp.fun_Pr1643180309t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool B) A)) (= A B)))) (forall ((A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool B) A)) (= A B)))) (forall ((Ca tptp.arrow_856714788e_indi) (A tptp.fun_Ar1809396326i_bool) (B tptp.fun_Ar1809396326i_bool)) (let ((_let_1 (tptp.hAPP_A1597696899l_bool tptp.member1479139729e_indi Ca))) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f584385070l_bool _let_1 B)))))) (forall ((Ca tptp.bool) (A tptp.fun_bool_bool) (B tptp.fun_bool_bool)) (let ((_let_1 (tptp.hAPP_b1787118453l_bool tptp.member_bool Ca))) (=> (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.hAPP_f612708895l_bool tptp.ord_le742797417l_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f387058535l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f387058535l_bool _let_1 B)))))) (forall ((Ca tptp.product_unit) (A tptp.fun_Pr1643180309t_bool) (B tptp.fun_Pr1643180309t_bool)) (let ((_let_1 (tptp.hAPP_P607165281l_bool tptp.member_Product_unit Ca))) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool _let_1 B)))))) (forall ((Ca tptp.produc472769767le_alt) (A tptp.fun_Pr2067565481t_bool) (B tptp.fun_Pr2067565481t_bool)) (let ((_let_1 (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt Ca))) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_1 B)))))) (forall ((Ca tptp.fun_Ar274636406t_bool) (A tptp.fun_fu3835832l_bool) (B tptp.fun_fu3835832l_bool)) (let ((_let_1 (tptp.hAPP_f1225332775l_bool tptp.member933336803t_bool Ca))) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f73423488l_bool _let_1 B)))))) (forall ((Ca tptp.fun_fu2114379172t_bool) (A tptp.fun_fu2098777574l_bool) (B tptp.fun_fu2098777574l_bool)) (let ((_let_1 (tptp.hAPP_f1714503811l_bool tptp.member173038353t_bool Ca))) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f975209902l_bool _let_1 B)))))) (forall ((Ca tptp.fun_Pr2067565481t_bool) (A tptp.fun_fu638310559l_bool) (B tptp.fun_fu638310559l_bool)) (let ((_let_1 (tptp.hAPP_f1482930381l_bool tptp.member1069471740t_bool Ca))) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f182583295l_bool _let_1 B)))))) (forall ((Ca tptp.nat) (A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat Ca))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B)))))) (forall ((A tptp.fun_Pr1643180309t_bool) (B tptp.fun_Pr1643180309t_bool)) (= (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool A) B)) (and (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool A) B)) (not (= A B))))) (forall ((A tptp.fun_Ar1809396326i_bool) (B tptp.fun_Ar1809396326i_bool)) (= (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool A) B)) (and (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool A) B)) (not (= A B))))) (forall ((A tptp.fun_fu638310559l_bool) (B tptp.fun_fu638310559l_bool)) (= (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1727358153l_bool A) B)) (and (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool A) B)) (not (= A B))))) (forall ((A tptp.fun_fu2098777574l_bool) (B tptp.fun_fu2098777574l_bool)) (= (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le119247420l_bool A) B)) (and (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool A) B)) (not (= A B))))) (forall ((A tptp.fun_fu3835832l_bool) (B tptp.fun_fu3835832l_bool)) (= (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1959568910l_bool A) B)) (and (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool A) B)) (not (= A B))))) (forall ((A tptp.fun_Pr2067565481t_bool) (B tptp.fun_Pr2067565481t_bool)) (= (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1478665215t_bool A) B)) (and (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool A) B)) (not (= A B))))) (forall ((A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool A) B)) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) B)) (not (= A B))))) (forall ((A tptp.fun_Pr1643180309t_bool) (B tptp.fun_Pr1643180309t_bool)) (= (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool A) B)) (or (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool A) B)) (= A B)))) (forall ((A tptp.fun_Ar1809396326i_bool) (B tptp.fun_Ar1809396326i_bool)) (= (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool A) B)) (or (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool A) B)) (= A B)))) (forall ((A tptp.fun_fu638310559l_bool) (B tptp.fun_fu638310559l_bool)) (= (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool A) B)) (or (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1727358153l_bool A) B)) (= A B)))) (forall ((A tptp.fun_fu2098777574l_bool) (B tptp.fun_fu2098777574l_bool)) (= (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool A) B)) (or (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le119247420l_bool A) B)) (= A B)))) (forall ((A tptp.fun_fu3835832l_bool) (B tptp.fun_fu3835832l_bool)) (= (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool A) B)) (or (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1959568910l_bool A) B)) (= A B)))) (forall ((A tptp.fun_Pr2067565481t_bool) (B tptp.fun_Pr2067565481t_bool)) (= (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool A) B)) (or (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1478665215t_bool A) B)) (= A B)))) (forall ((A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) B)) (or (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool A) B)) (= A B)))) (forall ((A tptp.fun_Pr1643180309t_bool) (B tptp.fun_Pr1643180309t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool A) B)) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool A) B)))) (forall ((A tptp.fun_Ar1809396326i_bool) (B tptp.fun_Ar1809396326i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool A) B)) (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool A) B)))) (forall ((A tptp.fun_fu638310559l_bool) (B tptp.fun_fu638310559l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1727358153l_bool A) B)) (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool A) B)))) (forall ((A tptp.fun_fu2098777574l_bool) (B tptp.fun_fu2098777574l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le119247420l_bool A) B)) (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool A) B)))) (forall ((A tptp.fun_fu3835832l_bool) (B tptp.fun_fu3835832l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1959568910l_bool A) B)) (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool A) B)))) (forall ((A tptp.fun_Pr2067565481t_bool) (B tptp.fun_Pr2067565481t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1478665215t_bool A) B)) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool A) B)))) (forall ((A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool A) B)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) B)))) (forall ((C tptp.fun_Pr1643180309t_bool) (A tptp.fun_Pr1643180309t_bool) (B tptp.fun_Pr1643180309t_bool)) (let ((_let_1 (tptp.hAPP_f272527115l_bool tptp.ord_le1976645739t_bool A))) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool _let_1 B)) (=> (tptp.hBOOL (tptp.hAPP_f2028818269l_bool (tptp.hAPP_f272527115l_bool tptp.ord_le1874503007t_bool B) C)) (tptp.hBOOL (tptp.hAPP_f2028818269l_bool _let_1 C)))))) (forall ((C tptp.fun_Ar1809396326i_bool) (A tptp.fun_Ar1809396326i_bool) (B tptp.fun_Ar1809396326i_bool)) (let ((_let_1 (tptp.hAPP_f731870893l_bool tptp.ord_le225487548i_bool A))) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool _let_1 B)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.hAPP_f731870893l_bool tptp.ord_le1609180592i_bool B) C)) (tptp.hBOOL (tptp.hAPP_f584385070l_bool _let_1 C)))))) (forall ((C tptp.fun_fu638310559l_bool) (A tptp.fun_fu638310559l_bool) (B tptp.fun_fu638310559l_bool)) (let ((_let_1 (tptp.hAPP_f1722316607l_bool tptp.ord_le1727358153l_bool A))) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool _let_1 B)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool B) C)) (tptp.hBOOL (tptp.hAPP_f182583295l_bool _let_1 C)))))) (forall ((C tptp.fun_fu2098777574l_bool) (A tptp.fun_fu2098777574l_bool) (B tptp.fun_fu2098777574l_bool)) (let ((_let_1 (tptp.hAPP_f916323245l_bool tptp.ord_le119247420l_bool A))) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool _let_1 B)) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool B) C)) (tptp.hBOOL (tptp.hAPP_f975209902l_bool _let_1 C)))))) (forall ((C tptp.fun_fu3835832l_bool) (A tptp.fun_fu3835832l_bool) (B tptp.fun_fu3835832l_bool)) (let ((_let_1 (tptp.hAPP_f585353809l_bool tptp.ord_le1959568910l_bool A))) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool _let_1 B)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool B) C)) (tptp.hBOOL (tptp.hAPP_f73423488l_bool _let_1 C)))))) (forall ((C tptp.fun_Pr2067565481t_bool) (A tptp.fun_Pr2067565481t_bool) (B tptp.fun_Pr2067565481t_bool)) (let ((_let_1 (tptp.hAPP_f930900275l_bool tptp.ord_le1478665215t_bool A))) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_1 B)) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool B) C)) (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_1 C)))))) (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_le382113706t_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_fu638310559l_bool) (A tptp.fun_fu638310559l_bool) (B tptp.fun_fu638310559l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1727358153l_bool B) C)) (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1727358153l_bool A) C))))) (forall ((C tptp.fun_fu2098777574l_bool) (A tptp.fun_fu2098777574l_bool) (B tptp.fun_fu2098777574l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le119247420l_bool B) C)) (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le119247420l_bool A) C))))) (forall ((C tptp.fun_fu3835832l_bool) (A tptp.fun_fu3835832l_bool) (B tptp.fun_fu3835832l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1959568910l_bool B) C)) (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1959568910l_bool A) C))))) (forall ((C tptp.fun_Pr2067565481t_bool) (A tptp.fun_Pr2067565481t_bool) (B tptp.fun_Pr2067565481t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1478665215t_bool B) C)) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1478665215t_bool A) C))))) (forall ((C tptp.fun_nat_bool) (A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool B) C)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool A) 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 ((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 ((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.fun_Pr2067565481t_bool) (A tptp.fun_fu638310559l_bool) (B tptp.fun_fu638310559l_bool)) (let ((_let_1 (tptp.hAPP_f1482930381l_bool tptp.member1069471740t_bool X_2))) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f182583295l_bool _let_1 B)))))) (forall ((X_2 tptp.fun_fu2114379172t_bool) (A tptp.fun_fu2098777574l_bool) (B tptp.fun_fu2098777574l_bool)) (let ((_let_1 (tptp.hAPP_f1714503811l_bool tptp.member173038353t_bool X_2))) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f975209902l_bool _let_1 B)))))) (forall ((X_2 tptp.fun_Ar274636406t_bool) (A tptp.fun_fu3835832l_bool) (B tptp.fun_fu3835832l_bool)) (let ((_let_1 (tptp.hAPP_f1225332775l_bool tptp.member933336803t_bool X_2))) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f73423488l_bool _let_1 B)))))) (forall ((X_2 tptp.produc472769767le_alt) (A tptp.fun_Pr2067565481t_bool) (B tptp.fun_Pr2067565481t_bool)) (let ((_let_1 (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt X_2))) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f52567537l_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_fu638310559l_bool) (X_2 tptp.fun_Pr2067565481t_bool) (A tptp.fun_fu638310559l_bool)) (let ((_let_1 (tptp.hAPP_f1482930381l_bool tptp.member1069471740t_bool X_2))) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool _let_1 A)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool A) B)) (tptp.hBOOL (tptp.hAPP_f182583295l_bool _let_1 B)))))) (forall ((B tptp.fun_fu2098777574l_bool) (X_2 tptp.fun_fu2114379172t_bool) (A tptp.fun_fu2098777574l_bool)) (let ((_let_1 (tptp.hAPP_f1714503811l_bool tptp.member173038353t_bool X_2))) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool _let_1 A)) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool A) B)) (tptp.hBOOL (tptp.hAPP_f975209902l_bool _let_1 B)))))) (forall ((B tptp.fun_fu3835832l_bool) (X_2 tptp.fun_Ar274636406t_bool) (A tptp.fun_fu3835832l_bool)) (let ((_let_1 (tptp.hAPP_f1225332775l_bool tptp.member933336803t_bool X_2))) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool _let_1 A)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool A) B)) (tptp.hBOOL (tptp.hAPP_f73423488l_bool _let_1 B)))))) (forall ((B tptp.fun_Pr2067565481t_bool) (X_2 tptp.produc472769767le_alt) (A tptp.fun_Pr2067565481t_bool)) (let ((_let_1 (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt X_2))) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_1 A)) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool A) B)) (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_1 B)))))) (forall ((X_2 tptp.nat) (Pa tptp.fun_nat_bool) (Q_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Pa) Q_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool Pa X_2)) (tptp.hBOOL (tptp.hAPP_nat_bool Q_1 X_2))))) (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.fun_Pr2067565481t_bool) (A tptp.fun_fu638310559l_bool) (B tptp.fun_fu638310559l_bool)) (let ((_let_1 (tptp.hAPP_f1482930381l_bool tptp.member1069471740t_bool X_2))) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f182583295l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f182583295l_bool _let_1 B)))))) (forall ((X_2 tptp.fun_fu2114379172t_bool) (A tptp.fun_fu2098777574l_bool) (B tptp.fun_fu2098777574l_bool)) (let ((_let_1 (tptp.hAPP_f1714503811l_bool tptp.member173038353t_bool X_2))) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f975209902l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f975209902l_bool _let_1 B)))))) (forall ((X_2 tptp.fun_Ar274636406t_bool) (A tptp.fun_fu3835832l_bool) (B tptp.fun_fu3835832l_bool)) (let ((_let_1 (tptp.hAPP_f1225332775l_bool tptp.member933336803t_bool X_2))) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f73423488l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f73423488l_bool _let_1 B)))))) (forall ((X_2 tptp.produc472769767le_alt) (A tptp.fun_Pr2067565481t_bool) (B tptp.fun_Pr2067565481t_bool)) (let ((_let_1 (tptp.hAPP_P38525833l_bool tptp.member1333168212le_alt X_2))) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f52567537l_bool _let_1 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_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 ((Q_1 tptp.fun_nat_bool) (Pa tptp.fun_nat_bool) (X_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool Pa X_2)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Pa) Q_1)) (tptp.hBOOL (tptp.hAPP_nat_bool Q_1 X_2))))) (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_nat_bool)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) A))) (forall ((R_1 tptp.fun_nat_bool) (S_1 tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f1722879237t_bool tptp.cOMBC_226598744l_bool tptp.member_nat))) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_f800510211t_bool _let_1 R_1)) (tptp.hAPP_f800510211t_bool _let_1 S_1))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool R_1) S_1))))) (forall ((R_1 tptp.fun_fu638310559l_bool) (S_1 tptp.fun_fu638310559l_bool)) (let ((_let_1 (tptp.hAPP_f1776355587l_bool tptp.cOMBC_2133093654l_bool tptp.member1069471740t_bool))) (= (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool (tptp.hAPP_f1060563265l_bool _let_1 R_1)) (tptp.hAPP_f1060563265l_bool _let_1 S_1))) (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1722316607l_bool tptp.ord_le1545885909l_bool R_1) S_1))))) (forall ((R_1 tptp.fun_fu2098777574l_bool) (S_1 tptp.fun_fu2098777574l_bool)) (let ((_let_1 (tptp.hAPP_f1169241965l_bool tptp.cOMBC_1209358050l_bool tptp.member173038353t_bool))) (= (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool (tptp.hAPP_f1181604821l_bool _let_1 R_1)) (tptp.hAPP_f1181604821l_bool _let_1 S_1))) (tptp.hBOOL (tptp.hAPP_f975209902l_bool (tptp.hAPP_f916323245l_bool tptp.ord_le1121695024l_bool R_1) S_1))))) (forall ((R_1 tptp.fun_fu3835832l_bool) (S_1 tptp.fun_fu3835832l_bool)) (let ((_let_1 (tptp.hAPP_f1760776521l_bool tptp.cOMBC_514203746l_bool tptp.member933336803t_bool))) (= (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool (tptp.hAPP_f819682389l_bool _let_1 R_1)) (tptp.hAPP_f819682389l_bool _let_1 S_1))) (tptp.hBOOL (tptp.hAPP_f73423488l_bool (tptp.hAPP_f585353809l_bool tptp.ord_le1099920642l_bool R_1) S_1))))) (forall ((R_1 tptp.fun_Pr2067565481t_bool) (S_1 tptp.fun_Pr2067565481t_bool)) (let ((_let_1 (tptp.hAPP_f1033183015t_bool tptp.cOMBC_593569186l_bool tptp.member1333168212le_alt))) (= (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool (tptp.hAPP_f1356305429t_bool _let_1 R_1)) (tptp.hAPP_f1356305429t_bool _let_1 S_1))) (tptp.hBOOL (tptp.hAPP_f52567537l_bool (tptp.hAPP_f930900275l_bool tptp.ord_le1577377523t_bool R_1) S_1))))) (forall ((N tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N) N)))) (forall ((M_1 tptp.nat) (Na tptp.nat)) (= (not (= M_1 Na)) (or (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_1) Na)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Na) M_1))))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (= X Y)) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X) Y))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Y) X))))) (forall ((N tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N) N)))) (forall ((N tptp.nat) (M_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N) M_2)) (not (= M_2 N)))) (forall ((S tptp.nat) (T tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat S) T)) (not (= S T)))) (forall ((Pa tptp.fun_nat_fun_nat_bool) (M_1 tptp.nat) (Na tptp.nat)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool Pa Na) M_1)))) (=> (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_1) Na)) _let_1) (=> (=> (= M_1 Na) _let_1) (=> (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Na) M_1)) _let_1) _let_1))))) (forall ((M_2 tptp.nat) (N tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_2) N) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat N) M_2))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat X))) (let ((_let_2 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Y))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat _let_2 Z)) (tptp.hAPP_nat_nat _let_2 (tptp.hAPP_nat_nat _let_1 Z)))))) (forall ((M_2 tptp.nat) (N tptp.nat) (K_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_2))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 N)) K_2) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat N) K_2))))) (forall ((K tptp.nat) (M_1 tptp.nat) (Na tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat K))) (= (= (tptp.hAPP_nat_nat _let_1 M_1) (tptp.hAPP_nat_nat _let_1 Na)) (= M_1 Na)))) (forall ((M_1 tptp.nat) (K tptp.nat) (Na tptp.nat)) (= (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_1) K) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Na) K)) (= M_1 Na))) (forall ((N tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N) N))) (forall ((M_2 tptp.nat) (N tptp.nat)) (or (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_2) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N) M_2)))) (forall ((M_2 tptp.nat) (N tptp.nat)) (=> (= M_2 N) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_2) N)))) (forall ((K_2 tptp.nat) (I_2 tptp.nat) (J_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_2))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 J_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat J_1) K_2)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 K_2)))))) (forall ((M_2 tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_2) N)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N) M_2)) (= M_2 N)))) (forall ((K tptp.nat) (N_2 tptp.fun_nat_bool)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.inj_on_nat_nat (tptp.hAPP_nat_fun_nat_nat (tptp.hAPP_f416620757at_nat tptp.cOMBC_nat_nat_nat tptp.plus_plus_nat) K)) N_2))) (forall ((I_2 tptp.nat) (J_1 tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I_2) J_1)) I_2)))) (forall ((J_1 tptp.nat) (I_2 tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat J_1) I_2)) I_2)))) (forall ((K tptp.nat) (M_1 tptp.nat) (Na tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat K))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 M_1)) (tptp.hAPP_nat_nat _let_1 Na))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_1) Na))))) (forall ((M_2 tptp.nat) (I_2 tptp.nat) (J_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_2))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 J_1)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat J_1) M_2)))))) (forall ((M_2 tptp.nat) (I_2 tptp.nat) (J_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_2))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 J_1)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_2) J_1)))))) (forall ((K_2 tptp.nat) (I_2 tptp.nat) (J_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_2) J_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I_2) K_2)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat J_1) K_2))))) (forall ((K_2 tptp.nat) (L_1 tptp.nat) (I_2 tptp.nat) (J_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_2) J_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat K_2) L_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I_2) K_2)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat J_1) L_1)))))) (forall ((M_2 tptp.nat) (N tptp.nat) (K_2 tptp.nat) (L_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat K_2) L_1)) (=> (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_2) L_1) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat K_2) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_2) N))))) (forall ((I_2 tptp.nat) (J_1 tptp.nat) (K_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I_2) J_1)) K_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_2) K_2)))) (forall ((M_1 tptp.nat) (Na tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_1) Na)) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_1) Na)) (not (= M_1 Na))))) (forall ((M_1 tptp.nat) (Na tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_1) Na)) (or (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_1) Na)) (= M_1 Na)))) (forall ((M_2 tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_2) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_2) N)))) (forall ((M_2 tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_2) N)) (=> (not (= M_2 N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_2) N))))) (forall ((M_2 tptp.nat) (N tptp.nat)) (=> (or (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_2) N)) (= M_2 N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_2) N)))) (forall ((N tptp.nat) (M_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_2) N)))) (forall ((N tptp.nat) (M_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat N) M_2)))) (forall ((M_1 tptp.nat) (Na tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_1) Na)) (exists ((K_1 tptp.nat)) (= Na (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_1) K_1))))) (forall ((K tptp.nat) (M_1 tptp.nat) (Na tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat K))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 M_1)) (tptp.hAPP_nat_nat _let_1 Na))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_1) Na))))) (forall ((M_2 tptp.nat) (I_2 tptp.nat) (J_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_2))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 J_1)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat J_1) M_2)))))) (forall ((M_2 tptp.nat) (I_2 tptp.nat) (J_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_2))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 J_1)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_2) J_1)))))) (forall ((K_2 tptp.nat) (I_2 tptp.nat) (J_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_2) J_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I_2) K_2)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat J_1) K_2))))) (forall ((K_2 tptp.nat) (L_1 tptp.nat) (I_2 tptp.nat) (J_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_2) J_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_2) L_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I_2) K_2)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat J_1) L_1)))))) (forall ((M_2 tptp.nat) (K_2 tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_2) K_2)) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_2) N)))) (forall ((M_2 tptp.nat) (K_2 tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_2) K_2)) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_2) N)))) (forall ((M_1 tptp.nat) (K tptp.nat) (F tptp.fun_nat_nat)) (=> (forall ((M tptp.nat) (N_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat F M)) (tptp.hAPP_nat_nat F N_1))))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat F M_1)) K)) (tptp.hAPP_nat_nat F (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_1) K)))))) (forall ((I tptp.nat) (J tptp.nat) (F tptp.fun_nat_nat)) (=> (forall ((I_1 tptp.nat) (J_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_1) J_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat F I_1)) (tptp.hAPP_nat_nat F J_2))))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I) J)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat F I)) (tptp.hAPP_nat_nat F J)))))) (forall ((Z tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Y) Z)))))) (forall ((Y tptp.nat) (X tptp.nat) (Z tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Z)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Y) Z)))))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X) Y)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X) Y)))) (forall ((Y tptp.nat) (X tptp.nat) (Z tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Z)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Y) Z)))))) (forall ((Z tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Y) Z)))))) (exists ((L_2 tptp.fun_Pr2067565481t_bool)) (tptp.hBOOL (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1482930381l_bool tptp.member1069471740t_bool L_2) tptp.arrow_1361987423le_Lin))) (tptp.hBOOL (tptp.hAPP_f584385070l_bool tptp.finite92092049e_indi tptp.top_to788185952i_bool)) (forall ((K tptp.nat)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.hAPP_f800510211t_bool tptp.collect_nat (tptp.hAPP_n1699378549t_bool (tptp.hAPP_f229349961t_bool tptp.cOMBC_nat_nat_bool tptp.ord_less_eq_nat) K))))) (forall ((K tptp.nat)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.hAPP_f800510211t_bool tptp.collect_nat (tptp.hAPP_n1699378549t_bool (tptp.hAPP_f229349961t_bool tptp.cOMBC_nat_nat_bool tptp.ord_less_nat) K))))) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat tptp.top_top_fun_nat_bool))) (= (tptp.hAPP_f2030293770ol_nat tptp.finite1949902593t_unit tptp.top_to1257323279t_bool) tptp.one_one_nat) (forall ((Na tptp.nat)) (= (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat (tptp.hAPP_f800510211t_bool tptp.collect_nat (tptp.hAPP_n1699378549t_bool (tptp.hAPP_f229349961t_bool tptp.cOMBC_nat_nat_bool tptp.ord_less_nat) Na))) Na)) (forall ((Pa tptp.fun_nat_bool) (I tptp.nat)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.hAPP_f800510211t_bool tptp.collect_nat (tptp.hAPP_f800510211t_bool (tptp.cOMBS_nat_bool_bool (tptp.hAPP_f1146629647l_bool (tptp.cOMBB_1015721476ol_nat tptp.fconj) Pa)) (tptp.hAPP_n1699378549t_bool (tptp.hAPP_f229349961t_bool tptp.cOMBC_nat_nat_bool tptp.ord_less_nat) I)))))) (forall ((N_2 tptp.fun_nat_bool)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat N_2)) (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_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_1) M))))))) (forall ((N_2 tptp.fun_nat_bool)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat N_2)) (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_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_1) M))))))) (forall ((U tptp.nat) (F tptp.fun_nat_nat)) (=> (forall ((N_1 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_1) (tptp.hAPP_nat_nat F N_1)))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.hAPP_f800510211t_bool tptp.collect_nat (tptp.hAPP_n1699378549t_bool (tptp.hAPP_f229349961t_bool tptp.cOMBC_nat_nat_bool (tptp.hAPP_f618557131t_bool (tptp.cOMBB_800536526ol_nat tptp.ord_less_eq_nat) F)) U)))))) (forall ((Na tptp.nat) (N_2 tptp.fun_nat_bool)) (=> (forall ((X_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) N_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_1) Na)))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat N_2)))) (forall ((N tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N) tptp.zero_zero_nat)))) (forall ((N tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) N))) (forall ((N tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N) tptp.zero_zero_nat)))) (forall ((Na tptp.nat)) (= (not (= Na tptp.zero_zero_nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) Na)))) (forall ((N tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N) tptp.zero_zero_nat)))) (forall ((M_2 tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_2) N)) (not (= N tptp.zero_zero_nat)))) (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N)))) (forall ((N tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat tptp.zero_zero_nat) N) N)) (forall ((M_2 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_2) tptp.zero_zero_nat) M_2)) (forall ((M_1 tptp.nat) (Na tptp.nat)) (= (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_1) Na) tptp.zero_zero_nat) (and (= M_1 tptp.zero_zero_nat) (= Na tptp.zero_zero_nat)))) (forall ((M_2 tptp.nat) (N tptp.nat)) (=> (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_2) N) M_2) (= N tptp.zero_zero_nat))) (forall ((Na tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Na) tptp.zero_zero_nat)) (= Na tptp.zero_zero_nat))) (forall ((N tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) N))) (forall ((M_1 tptp.nat) (Na tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat))) (= (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_1) Na))) (or (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M_1)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Na)))))) (forall ((Na tptp.nat) (Pa tptp.fun_nat_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool Pa tptp.zero_zero_nat))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool Pa Na)) (exists ((K_1 tptp.nat)) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat K_1) Na)) (forall ((I_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_1) K_1)) (not (tptp.hBOOL (tptp.hAPP_nat_bool Pa I_1))))) (tptp.hBOOL (tptp.hAPP_nat_bool Pa (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat K_1) tptp.one_one_nat)))))))) (forall ((Na tptp.nat) (Pa tptp.fun_nat_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool Pa tptp.zero_zero_nat))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool Pa Na)) (exists ((K_1 tptp.nat)) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_1) Na)) (forall ((I_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_1) K_1)) (not (tptp.hBOOL (tptp.hAPP_nat_bool Pa I_1))))) (tptp.hBOOL (tptp.hAPP_nat_bool Pa K_1))))))) (forall ((I_2 tptp.nat) (J_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_2) J_1)) (exists ((K_1 tptp.nat)) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K_1)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I_2) K_1) J_1))))) (forall ((N tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N) (tptp.hAPP_nat_nat tptp.suc N)))) (forall ((M_2 tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_2) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat tptp.suc M_2)) (tptp.hAPP_nat_nat tptp.suc N))))) (forall ((N tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.hAPP_nat_nat tptp.suc N)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (= (tptp.hAPP_nat_nat tptp.suc X) (tptp.hAPP_nat_nat tptp.suc Y)) (= X Y))) (forall ((Nat_5 tptp.nat) (Nat_4 tptp.nat)) (= (= (tptp.hAPP_nat_nat tptp.suc Nat_5) (tptp.hAPP_nat_nat tptp.suc Nat_4)) (= Nat_5 Nat_4))) (forall ((N tptp.nat)) (not (= (tptp.hAPP_nat_nat tptp.suc N) N))) (forall ((N tptp.nat)) (not (= N (tptp.hAPP_nat_nat tptp.suc N)))) (forall ((M_2 tptp.nat)) (not (= (tptp.hAPP_nat_nat tptp.suc M_2) tptp.zero_zero_nat))) (forall ((M_2 tptp.nat)) (not (= tptp.zero_zero_nat (tptp.hAPP_nat_nat tptp.suc M_2)))) (forall ((Nat_3 tptp.nat)) (not (= (tptp.hAPP_nat_nat tptp.suc Nat_3) tptp.zero_zero_nat))) (forall ((M_2 tptp.nat)) (not (= (tptp.hAPP_nat_nat tptp.suc M_2) tptp.zero_zero_nat))) (forall ((Nat_2 tptp.nat)) (not (= tptp.zero_zero_nat (tptp.hAPP_nat_nat tptp.suc Nat_2)))) (forall ((M_2 tptp.nat)) (not (= tptp.zero_zero_nat (tptp.hAPP_nat_nat tptp.suc M_2)))) (forall ((M_2 tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat tptp.suc M_2)) (tptp.hAPP_nat_nat tptp.suc N))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_2) N)))) (forall ((M_2 tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat tptp.suc M_2)) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_2) N)))) (forall ((M_2 tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_2))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat tptp.suc N))) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N))) (= M_2 N))))) (forall ((K_2 tptp.nat) (I_2 tptp.nat) (J_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_2) J_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat J_1) K_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat tptp.suc I_2)) K_2))))) (forall ((M_2 tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat tptp.suc M_2))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_2) N)) (=> (not (= _let_1 N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat _let_1) N)))))) (forall ((M_2 tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_2))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat tptp.suc N)))))) (forall ((N tptp.nat) (M_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N))) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M_2))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat tptp.suc M_2))) (= M_2 N))))) (forall ((Na tptp.nat) (M_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Na))) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M_1))) (= (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat tptp.suc M_1))) (= Na M_1))))) (forall ((M_1 tptp.nat) (Na tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat tptp.suc M_1)) (tptp.hAPP_nat_nat tptp.suc Na))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_1) Na)))) (forall ((M_1 tptp.nat) (Na tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_1))) (= (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat tptp.suc Na))) (or (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Na)) (= M_1 Na))))) (forall ((M_1 tptp.nat) (Na tptp.nat)) (= (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_1) Na))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Na) (tptp.hAPP_nat_nat tptp.suc M_1))))) (forall ((M_2 tptp.nat) (N tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat tptp.suc M_2)) N) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_2) (tptp.hAPP_nat_nat tptp.suc N)))) (forall ((M_2 tptp.nat) (N tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat tptp.suc M_2)) N) (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_2) N)))) (forall ((M_2 tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_2))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat tptp.suc N)) (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat _let_1 N))))) (forall ((M_2 tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat tptp.suc M_2)) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_2) N)))) (forall ((M_2 tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat tptp.suc N))) (let ((_let_2 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_2))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 _let_1)) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 N))) (= M_2 _let_1)))))) (forall ((M_2 tptp.nat) (N 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)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat tptp.suc N)))))) (forall ((Na 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 Na)) (tptp.hAPP_nat_nat tptp.suc M_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Na) M_1)))) (forall ((M_1 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_1))) (= (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 _let_1)) (or (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 Na)) (= M_1 _let_1)))))) (forall ((M_1 tptp.nat) (Na tptp.nat)) (= (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_1) Na))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat tptp.suc Na)) M_1)))) (forall ((N tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat tptp.suc N)) N)))) (forall ((N_2 tptp.fun_nat_bool)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.inj_on_nat_nat tptp.suc) N_2))) (forall ((Na tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) Na)) (exists ((M tptp.nat)) (= Na (tptp.hAPP_nat_nat tptp.suc M))))) (forall ((Na tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Na) (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat))) (= Na tptp.zero_zero_nat))) (forall ((M_1 tptp.nat) (Na tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_1) (tptp.hAPP_nat_nat tptp.suc Na))) (or (= M_1 tptp.zero_zero_nat) (exists ((J_2 tptp.nat)) (and (= M_1 (tptp.hAPP_nat_nat tptp.suc J_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat J_2) Na))))))) (forall ((M_1 tptp.nat) (Na tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat))) (= (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_1) Na) _let_1) (or (and (= M_1 _let_1) (= Na tptp.zero_zero_nat)) (and (= M_1 tptp.zero_zero_nat) (= Na _let_1)))))) (forall ((M_1 tptp.nat) (Na tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat))) (= (= _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_1) Na)) (or (and (= M_1 _let_1) (= Na tptp.zero_zero_nat)) (and (= M_1 tptp.zero_zero_nat) (= Na _let_1)))))) (forall ((I_2 tptp.nat) (M_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_2) (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I_2) M_2))))) (forall ((I_2 tptp.nat) (M_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_2) (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_2) I_2))))) (forall ((M_1 tptp.nat) (Na tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_1) Na)) (exists ((K_1 tptp.nat)) (= Na (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_1) K_1)))))) (forall ((Na tptp.nat) (M_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Na) M_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat tptp.suc Na)) M_1)))) (forall ((M_1 tptp.nat) (Na tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_1) (tptp.hAPP_nat_nat tptp.suc Na))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_1) Na)))) (forall ((M_1 tptp.nat) (Na tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat tptp.suc M_1)) Na)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_1) Na)))) (forall ((M_2 tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_2) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_2) (tptp.hAPP_nat_nat tptp.suc N))))) (forall ((M_2 tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_2) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat tptp.suc M_2)) N)))) (forall ((M_1 tptp.nat) (Na tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_1) Na)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Na) (tptp.hAPP_nat_nat tptp.suc M_1))) (= Na M_1)))) (forall ((M_2 tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat tptp.suc M_2)) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_2) N)))) (= tptp.one_one_nat (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat)) (forall ((X_1 tptp.nat)) (= (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_1) (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat tptp.suc X_1)))) (forall ((Na tptp.nat)) (= (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat (tptp.hAPP_f800510211t_bool tptp.collect_nat (tptp.hAPP_n1699378549t_bool (tptp.hAPP_f229349961t_bool tptp.cOMBC_nat_nat_bool tptp.ord_less_eq_nat) Na))) (tptp.hAPP_nat_nat tptp.suc Na))) (forall ((I tptp.nat) (M_4 tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f229349961t_bool tptp.cOMBC_nat_nat_bool tptp.ord_less_nat))) (let ((_let_2 (tptp.cOMBB_1015721476ol_nat tptp.fconj))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat tptp.zero_zero_nat) M_4)) (= (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat (tptp.hAPP_f800510211t_bool tptp.collect_nat (tptp.hAPP_f800510211t_bool (tptp.cOMBS_nat_bool_bool (tptp.hAPP_f1146629647l_bool _let_2 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1722879237t_bool tptp.cOMBC_226598744l_bool (tptp.hAPP_f66927821l_bool (tptp.cOMBB_1146692694ol_nat tptp.member_nat) tptp.suc)) M_4))) (tptp.hAPP_n1699378549t_bool _let_1 I))))) (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat (tptp.hAPP_f800510211t_bool tptp.collect_nat (tptp.hAPP_f800510211t_bool (tptp.cOMBS_nat_bool_bool (tptp.hAPP_f1146629647l_bool _let_2 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1722879237t_bool tptp.cOMBC_226598744l_bool tptp.member_nat) M_4))) (tptp.hAPP_n1699378549t_bool _let_1 (tptp.hAPP_nat_nat tptp.suc I)))))))))) (forall ((I tptp.nat) (M_4 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat tptp.zero_zero_nat) M_4)) (not (= (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat (tptp.hAPP_f800510211t_bool tptp.collect_nat (tptp.hAPP_f800510211t_bool (tptp.cOMBS_nat_bool_bool (tptp.hAPP_f1146629647l_bool (tptp.cOMBB_1015721476ol_nat tptp.fconj) (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1722879237t_bool tptp.cOMBC_226598744l_bool tptp.member_nat) M_4))) (tptp.hAPP_n1699378549t_bool (tptp.hAPP_f229349961t_bool tptp.cOMBC_nat_nat_bool tptp.ord_less_nat) (tptp.hAPP_nat_nat tptp.suc I))))) tptp.zero_zero_nat)))) (forall ((I tptp.nat) (M_4 tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f229349961t_bool tptp.cOMBC_nat_nat_bool tptp.ord_less_nat))) (let ((_let_2 (tptp.cOMBB_1015721476ol_nat tptp.fconj))) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat tptp.zero_zero_nat) M_4))) (= (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat (tptp.hAPP_f800510211t_bool tptp.collect_nat (tptp.hAPP_f800510211t_bool (tptp.cOMBS_nat_bool_bool (tptp.hAPP_f1146629647l_bool _let_2 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1722879237t_bool tptp.cOMBC_226598744l_bool (tptp.hAPP_f66927821l_bool (tptp.cOMBB_1146692694ol_nat tptp.member_nat) tptp.suc)) M_4))) (tptp.hAPP_n1699378549t_bool _let_1 I)))) (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat (tptp.hAPP_f800510211t_bool tptp.collect_nat (tptp.hAPP_f800510211t_bool (tptp.cOMBS_nat_bool_bool (tptp.hAPP_f1146629647l_bool _let_2 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1722879237t_bool tptp.cOMBC_226598744l_bool tptp.member_nat) M_4))) (tptp.hAPP_n1699378549t_bool _let_1 (tptp.hAPP_nat_nat tptp.suc I)))))))))) (forall ((Pa tptp.fun_nat_bool) (I tptp.nat) (J tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I) J)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool Pa J)) (=> (forall ((I_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_1) J)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool Pa (tptp.hAPP_nat_nat tptp.suc I_1))) (tptp.hBOOL (tptp.hAPP_nat_bool Pa I_1))))) (tptp.hBOOL (tptp.hAPP_nat_bool Pa I)))))) (forall ((M_2 tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_2) N)) (exists ((K_1 tptp.nat)) (= N (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_2) K_1)))))) (forall ((N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (exists ((M tptp.nat)) (= N (tptp.hAPP_nat_nat tptp.suc M))))) (forall ((N tptp.nat)) (= (tptp.hAPP_nat_nat tptp.suc N) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat N) tptp.one_one_nat))) (forall ((N tptp.nat)) (= (tptp.hAPP_nat_nat tptp.suc N) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat tptp.one_one_nat) N))) (forall ((N tptp.nat) (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 N)) M_3)) (exists ((M tptp.nat)) (= M_3 (tptp.hAPP_nat_nat tptp.suc M))))) (forall ((I_2 tptp.nat) (K_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_2) K_2)) (=> (not (= K_2 (tptp.hAPP_nat_nat tptp.suc I_2))) (not (forall ((J_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_2) J_2)) (not (= K_2 (tptp.hAPP_nat_nat tptp.suc J_2))))))))) (forall ((I_2 tptp.nat) (K_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat tptp.suc I_2)) K_2)) (not (forall ((J_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_2) J_2)) (not (= K_2 (tptp.hAPP_nat_nat tptp.suc J_2)))))))) (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (exists ((M tptp.nat)) (= N (tptp.hAPP_nat_nat tptp.suc M))))) (forall ((Y tptp.nat)) (=> (not (= Y tptp.zero_zero_nat)) (not (forall ((Nat_1 tptp.nat)) (not (= Y (tptp.hAPP_nat_nat tptp.suc Nat_1))))))) (forall ((Pa tptp.fun_nat_bool) (K tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool Pa K)) (=> (forall ((N_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool Pa (tptp.hAPP_nat_nat tptp.suc N_1))) (tptp.hBOOL (tptp.hAPP_nat_bool Pa N_1)))) (tptp.hBOOL (tptp.hAPP_nat_bool Pa tptp.zero_zero_nat))))) (forall ((Na tptp.nat) (Pa tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool Pa tptp.zero_zero_nat)) (=> (forall ((N_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool Pa N_1)) (tptp.hBOOL (tptp.hAPP_nat_bool Pa (tptp.hAPP_nat_nat tptp.suc N_1))))) (tptp.hBOOL (tptp.hAPP_nat_bool Pa Na))))) (= (tptp.hAPP_f622418129t_bool (tptp.image_1465793779di_nat tptp.h) tptp.top_to788185952i_bool) (tptp.hAPP_n1699378549t_bool (tptp.ord_at4362885an_nat tptp.zero_zero_nat) _let_5)) (forall ((L tptp.nat) (U tptp.nat)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.hAPP_n1699378549t_bool (tptp.ord_at4362885an_nat L) U)))) (not (forall ((H tptp.fun_Ar671024215di_nat)) (=> (tptp.hBOOL (tptp.hAPP_f584385070l_bool (tptp.inj_on1960344199di_nat H) tptp.top_to788185952i_bool)) (not (= (tptp.hAPP_f622418129t_bool (tptp.image_1465793779di_nat H) tptp.top_to788185952i_bool) (tptp.hAPP_n1699378549t_bool (tptp.ord_at4362885an_nat tptp.zero_zero_nat) (tptp.hAPP_f846027769ol_nat tptp.finite1672073426e_indi tptp.top_to788185952i_bool))))))) (forall ((A tptp.fun_nat_bool) (K tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool (tptp.ord_at4362885an_nat K) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat K) (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat A))))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) _let_1)) (= A _let_1)))) (forall ((I tptp.nat) (J tptp.nat)) (= (tptp.hAPP_f800510211t_bool (tptp.image_nat_nat tptp.suc) (tptp.hAPP_n1699378549t_bool (tptp.ord_at4362885an_nat I) J)) (tptp.hAPP_n1699378549t_bool (tptp.ord_at4362885an_nat (tptp.hAPP_nat_nat tptp.suc I)) (tptp.hAPP_nat_nat tptp.suc J)))) (forall ((K tptp.nat) (I tptp.nat) (J tptp.nat)) (= (tptp.hAPP_f800510211t_bool (tptp.image_nat_nat (tptp.hAPP_nat_fun_nat_nat (tptp.hAPP_f416620757at_nat tptp.cOMBC_nat_nat_nat tptp.plus_plus_nat) K)) (tptp.hAPP_n1699378549t_bool (tptp.ord_at4362885an_nat I) J)) (tptp.hAPP_n1699378549t_bool (tptp.ord_at4362885an_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I) K)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat J) K)))) (forall ((Pa tptp.fun_nat_bool) (Na tptp.nat)) (= (forall ((M tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) Na)) (tptp.hBOOL (tptp.hAPP_nat_bool Pa M)))) (forall ((X_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) (tptp.hAPP_n1699378549t_bool (tptp.ord_at4362885an_nat tptp.zero_zero_nat) Na))) (tptp.hBOOL (tptp.hAPP_nat_bool Pa X_1)))))) (forall ((Pa tptp.fun_nat_bool) (Na tptp.nat)) (= (exists ((M tptp.nat)) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) Na)) (tptp.hBOOL (tptp.hAPP_nat_bool Pa M)))) (exists ((X_1 tptp.nat)) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) (tptp.hAPP_n1699378549t_bool (tptp.ord_at4362885an_nat tptp.zero_zero_nat) Na))) (tptp.hBOOL (tptp.hAPP_nat_bool Pa X_1)))))) (= (tptp.hAPP_n1699378549t_bool tptp.ord_greaterThan_nat tptp.zero_zero_nat) (tptp.hAPP_f800510211t_bool (tptp.image_nat_nat tptp.suc) tptp.top_top_fun_nat_bool)) (forall ((M_1 tptp.nat) (Na tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat tptp.suc M_1)) Na)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_f800510211t_bool (tptp.nat_case_bool tptp.fFalse) (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_1)) Na)))) (forall ((L tptp.nat) (U tptp.nat)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.hAPP_n1699378549t_bool (tptp.ord_gr375877188st_nat L) U)))) (forall ((L tptp.nat) (U tptp.nat)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.hAPP_n1699378549t_bool (tptp.ord_gr660468384an_nat L) U)))) (forall ((L tptp.nat) (U tptp.nat)) (= (tptp.hAPP_n1699378549t_bool (tptp.ord_at4362885an_nat (tptp.hAPP_nat_nat tptp.suc L)) U) (tptp.hAPP_n1699378549t_bool (tptp.ord_gr660468384an_nat L) U))) (forall ((M_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_2) (tptp.hAPP_nat_nat (tptp.times_times_nat M_2) M_2)))) (forall ((M_2 tptp.nat)) (let ((_let_1 (tptp.times_times_nat M_2))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_2) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat _let_1 M_2)))))) (forall ((K_2 tptp.nat) (I_2 tptp.nat) (J_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_2) J_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.times_times_nat I_2) K_2)) (tptp.hAPP_nat_nat (tptp.times_times_nat J_1) K_2))))) (forall ((K_2 tptp.nat) (I_2 tptp.nat) (J_1 tptp.nat)) (let ((_let_1 (tptp.times_times_nat K_2))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_2) J_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 I_2)) (tptp.hAPP_nat_nat _let_1 J_1)))))) (forall ((K_2 tptp.nat) (L_1 tptp.nat) (I_2 tptp.nat) (J_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_2) J_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_2) L_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.times_times_nat I_2) K_2)) (tptp.hAPP_nat_nat (tptp.times_times_nat J_1) L_1)))))) (forall ((M_1 tptp.nat) (Na tptp.nat)) (= (= (tptp.hAPP_nat_nat (tptp.times_times_nat M_1) Na) tptp.one_one_nat) (and (= M_1 tptp.one_one_nat) (= Na tptp.one_one_nat)))) (forall ((N tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.times_times_nat N) tptp.one_one_nat) N)) (forall ((M_1 tptp.nat) (Na tptp.nat)) (= (= tptp.one_one_nat (tptp.hAPP_nat_nat (tptp.times_times_nat M_1) Na)) (and (= M_1 tptp.one_one_nat) (= Na tptp.one_one_nat)))) (forall ((N tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.times_times_nat tptp.one_one_nat) N) N)) (forall ((M_2 tptp.nat) (N tptp.nat) (K_2 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_2) N)) K_2) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat M_2) K_2)) (tptp.hAPP_nat_nat (tptp.times_times_nat N) K_2)))) (forall ((K_2 tptp.nat) (M_2 tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.times_times_nat K_2))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_2) N)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 M_2)) (tptp.hAPP_nat_nat _let_1 N))))) (forall ((K tptp.nat) (M_1 tptp.nat) (Na tptp.nat)) (let ((_let_1 (tptp.times_times_nat (tptp.hAPP_nat_nat tptp.suc K)))) (= (= (tptp.hAPP_nat_nat _let_1 M_1) (tptp.hAPP_nat_nat _let_1 Na)) (= M_1 Na)))) (forall ((M_1 tptp.nat) (K tptp.nat) (Na tptp.nat)) (= (= (tptp.hAPP_nat_nat (tptp.times_times_nat M_1) K) (tptp.hAPP_nat_nat (tptp.times_times_nat Na) K)) (or (= M_1 Na) (= K tptp.zero_zero_nat)))) (forall ((K tptp.nat) (M_1 tptp.nat) (Na tptp.nat)) (let ((_let_1 (tptp.times_times_nat K))) (= (= (tptp.hAPP_nat_nat _let_1 M_1) (tptp.hAPP_nat_nat _let_1 Na)) (or (= M_1 Na) (= K tptp.zero_zero_nat))))) (forall ((M_1 tptp.nat) (Na tptp.nat)) (= (= (tptp.hAPP_nat_nat (tptp.times_times_nat M_1) Na) tptp.zero_zero_nat) (or (= M_1 tptp.zero_zero_nat) (= Na tptp.zero_zero_nat)))) (forall ((M_2 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.times_times_nat M_2) tptp.zero_zero_nat) tptp.zero_zero_nat)) (forall ((N tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.times_times_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)) (forall ((M_1 tptp.nat) (Na tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat))) (= (= (tptp.hAPP_nat_nat (tptp.times_times_nat M_1) Na) _let_1) (and (= M_1 _let_1) (= Na _let_1))))) (forall ((K_2 tptp.nat) (I_2 tptp.nat) (J_1 tptp.nat)) (let ((_let_1 (tptp.times_times_nat K_2))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_2) J_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 I_2)) (tptp.hAPP_nat_nat _let_1 J_1))))))) (forall ((K_2 tptp.nat) (I_2 tptp.nat) (J_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_2) J_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.times_times_nat I_2) K_2)) (tptp.hAPP_nat_nat (tptp.times_times_nat J_1) K_2)))))) (forall ((M_1 tptp.nat) (K tptp.nat) (Na tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.times_times_nat M_1) K)) (tptp.hAPP_nat_nat (tptp.times_times_nat Na) K))) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_1) Na))))) (forall ((K tptp.nat) (M_1 tptp.nat) (Na tptp.nat)) (let ((_let_1 (tptp.times_times_nat K))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 M_1)) (tptp.hAPP_nat_nat _let_1 Na))) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_1) Na)))))) (forall ((M_1 tptp.nat) (Na tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat))) (= (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.times_times_nat M_1) Na))) (and (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M_1)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Na)))))) (forall ((K tptp.nat) (M_1 tptp.nat) (Na tptp.nat)) (let ((_let_1 (tptp.times_times_nat (tptp.hAPP_nat_nat tptp.suc K)))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 M_1)) (tptp.hAPP_nat_nat _let_1 Na))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_1) Na))))) (forall ((M_2 tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.times_times_nat M_2))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat tptp.suc N)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_2) (tptp.hAPP_nat_nat _let_1 N))))) (forall ((M_2 tptp.nat) (N tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat tptp.suc M_2)) N) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat N) (tptp.hAPP_nat_nat (tptp.times_times_nat M_2) N)))) (forall ((K tptp.nat) (M_1 tptp.nat) (Na tptp.nat)) (let ((_let_1 (tptp.times_times_nat (tptp.hAPP_nat_nat tptp.suc K)))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 M_1)) (tptp.hAPP_nat_nat _let_1 Na))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_1) Na))))) (forall ((M_2 tptp.nat) (N tptp.nat)) (=> (= M_2 (tptp.hAPP_nat_nat (tptp.times_times_nat M_2) N)) (or (= N tptp.one_one_nat) (= M_2 tptp.zero_zero_nat)))) (forall ((M_2 tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat)))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N) (tptp.hAPP_nat_nat (tptp.times_times_nat M_2) N))))))) (forall ((M_2 tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat)))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N) (tptp.hAPP_nat_nat (tptp.times_times_nat N) M_2))))))) (forall ((M_2 tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat)))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M_2)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.times_times_nat M_2) N))))))) (forall ((M_1 tptp.nat) (Na tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat)))) (= (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.times_times_nat M_1) Na))) (and (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M_1)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Na)))))) (forall ((M_1 tptp.nat) (K tptp.nat) (Na tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.times_times_nat M_1) K)) (tptp.hAPP_nat_nat (tptp.times_times_nat Na) K))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_1) Na))))) (forall ((K tptp.nat) (M_1 tptp.nat) (Na tptp.nat)) (let ((_let_1 (tptp.times_times_nat K))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 M_1)) (tptp.hAPP_nat_nat _let_1 Na))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_1) Na)))))) (forall ((M_2 tptp.nat) (N tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.times_times_nat M_2) N) (tptp.hAPP_nat_nat (tptp.times_times_nat N) M_2))) (forall ((M_2 tptp.nat) (N tptp.nat) (K_2 tptp.nat)) (let ((_let_1 (tptp.times_times_nat M_2))) (= (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat _let_1 N)) K_2) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.times_times_nat N) K_2))))) (forall ((M_1 tptp.nat) (Na tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.times_times_nat K))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 M_1)) (tptp.hAPP_nat_nat _let_1 Na))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_1) Na)))))) (forall ((M_1 tptp.nat) (Na tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.times_times_nat K))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 M_1)) (tptp.hAPP_nat_nat _let_1 Na))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_1) Na)))))) (forall ((M_1 tptp.nat) (Na tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.times_times_nat K))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (= (= (tptp.hAPP_nat_nat _let_1 M_1) (tptp.hAPP_nat_nat _let_1 Na)) (= M_1 Na))))) (forall ((K tptp.nat) (M_1 tptp.nat) (Na tptp.nat)) (let ((_let_1 (tptp.times_times_nat K))) (= (= (tptp.hAPP_nat_nat _let_1 M_1) (tptp.hAPP_nat_nat _let_1 Na)) (or (= K tptp.zero_zero_nat) (= M_1 Na))))) (forall ((I_2 tptp.nat) (U_1 tptp.nat) (J_1 tptp.nat) (K_2 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat I_2) U_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat J_1) U_1)) K_2)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I_2) J_1)) U_1)) K_2))) (forall ((Nat tptp.nat)) (= (tptp.hAPP_nat_nat tptp.nat_size (tptp.hAPP_nat_nat tptp.suc Nat)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat tptp.nat_size Nat)) (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat)))) (= (tptp.hAPP_nat_nat tptp.nat_size tptp.zero_zero_nat) tptp.zero_zero_nat) (forall ((Nat tptp.nat)) (= (tptp.hAPP_nat_nat tptp.size_size_nat (tptp.hAPP_nat_nat tptp.suc Nat)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat tptp.size_size_nat Nat)) (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat)))) (forall ((N tptp.nat)) (= (tptp.hAPP_nat_nat tptp.size_size_nat N) N)) (= (tptp.hAPP_nat_nat tptp.size_size_nat tptp.zero_zero_nat) tptp.zero_zero_nat) (forall ((F tptp.fun_nat_nat)) (=> (forall ((I_1 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat F (tptp.hAPP_nat_nat tptp.suc I_1))) (tptp.hAPP_nat_nat F I_1)))) (exists ((I_1 tptp.nat)) (forall ((K_1 tptp.nat)) (= (tptp.hAPP_nat_nat F (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I_1) K_1)) (tptp.hAPP_nat_nat F I_1)))))) (= (tptp.hAPP_bool_nat tptp.bool_size tptp.fTrue) tptp.zero_zero_nat) (= (tptp.hAPP_bool_nat tptp.bool_size tptp.fFalse) tptp.zero_zero_nat) (forall ((L tptp.nat) (U tptp.nat)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.hAPP_n1699378549t_bool (tptp.ord_at238088361st_nat L) U)))) (forall ((L tptp.nat) (U tptp.nat)) (= (tptp.hAPP_n1699378549t_bool (tptp.ord_at4362885an_nat L) (tptp.hAPP_nat_nat tptp.suc U)) (tptp.hAPP_n1699378549t_bool (tptp.ord_at238088361st_nat L) U))) (forall ((Pa tptp.fun_nat_bool) (Na tptp.nat)) (= (exists ((M tptp.nat)) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) Na)) (tptp.hBOOL (tptp.hAPP_nat_bool Pa M)))) (exists ((X_1 tptp.nat)) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) (tptp.hAPP_n1699378549t_bool (tptp.ord_at238088361st_nat tptp.zero_zero_nat) Na))) (tptp.hBOOL (tptp.hAPP_nat_bool Pa X_1)))))) (forall ((Pa tptp.fun_nat_bool) (Na tptp.nat)) (= (forall ((M tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) Na)) (tptp.hBOOL (tptp.hAPP_nat_bool Pa M)))) (forall ((X_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) (tptp.hAPP_n1699378549t_bool (tptp.ord_at238088361st_nat tptp.zero_zero_nat) Na))) (tptp.hBOOL (tptp.hAPP_nat_bool Pa X_1)))))) (forall ((I tptp.nat) (J tptp.nat)) (= (tptp.hAPP_f800510211t_bool (tptp.image_nat_nat tptp.suc) (tptp.hAPP_n1699378549t_bool (tptp.ord_at238088361st_nat I) J)) (tptp.hAPP_n1699378549t_bool (tptp.ord_at238088361st_nat (tptp.hAPP_nat_nat tptp.suc I)) (tptp.hAPP_nat_nat tptp.suc J)))) (forall ((L tptp.nat) (U tptp.nat)) (= (tptp.hAPP_n1699378549t_bool (tptp.ord_at238088361st_nat (tptp.hAPP_nat_nat tptp.suc L)) U) (tptp.hAPP_n1699378549t_bool (tptp.ord_gr375877188st_nat L) U))) (forall ((K tptp.nat) (I tptp.nat) (J tptp.nat)) (= (tptp.hAPP_f800510211t_bool (tptp.image_nat_nat (tptp.hAPP_nat_fun_nat_nat (tptp.hAPP_f416620757at_nat tptp.cOMBC_nat_nat_nat tptp.plus_plus_nat) K)) (tptp.hAPP_n1699378549t_bool (tptp.ord_at238088361st_nat I) J)) (tptp.hAPP_n1699378549t_bool (tptp.ord_at238088361st_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I) K)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat J) K)))) (forall ((K tptp.nat) (I tptp.nat) (J tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat J) K))) (let ((_let_2 (tptp.ord_at4362885an_nat I))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I) J)) (= (tptp.hAPP_n1699378549t_bool _let_2 _let_1) (tptp.hAPP_f800510211t_bool (tptp.semila465093516t_bool (tptp.hAPP_n1699378549t_bool _let_2 J)) (tptp.hAPP_n1699378549t_bool (tptp.ord_at4362885an_nat J) _let_1))))))) (= (tptp.hAPP_n1699378549t_bool tptp.ord_atLeast_nat tptp.zero_zero_nat) tptp.top_top_fun_nat_bool) (forall ((K tptp.nat)) (= (tptp.hAPP_n1699378549t_bool tptp.ord_atLeast_nat (tptp.hAPP_nat_nat tptp.suc K)) (tptp.hAPP_n1699378549t_bool tptp.ord_greaterThan_nat K))) (forall ((K tptp.nat) (F tptp.fun_nat_nat)) (let ((_let_1 (tptp.big_co387207925at_nat F))) (=> (= (tptp.hAPP_nat_nat F tptp.zero_zero_nat) tptp.zero_zero_nat) (= (tptp.hAPP_f22106695ol_nat _let_1 (tptp.hAPP_n1699378549t_bool (tptp.ord_at238088361st_nat (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat)) K)) (tptp.hAPP_f22106695ol_nat _let_1 (tptp.hAPP_n1699378549t_bool (tptp.ord_at238088361st_nat tptp.zero_zero_nat) K)))))) (tptp.hBOOL tptp.fTrue) (forall ((P tptp.bool)) (or (= P tptp.fTrue) (= P tptp.fFalse))) (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))) (not (tptp.hBOOL tptp.fFalse)) (forall ((P tptp.bool)) (or (= P tptp.fTrue) (= P tptp.fFalse))) (forall ((P tptp.nat)) (= (tptp.hAPP_nat_nat tptp.cOMBI_nat P) P)) (forall ((X tptp.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 ((P tptp.bool) (Q tptp.nat)) (= (tptp.hAPP_nat_bool (tptp.hAPP_b1013836512t_bool tptp.cOMBK_bool_nat P) Q) P)) (forall ((P tptp.bool) (Q tptp.product_unit)) (= (tptp.hAPP_P1676879539t_bool (tptp.hAPP_b1096750261t_bool tptp.cOMBK_790042732t_unit P) Q) P)) (forall ((P tptp.fun_nat_fun_nat_nat) (Q tptp.nat) (R tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat (tptp.hAPP_f416620757at_nat tptp.cOMBC_nat_nat_nat P) Q) R) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat P R) Q))) (forall ((P tptp.fun_nat_fun_nat_bool) (Q tptp.nat) (R tptp.nat)) (= (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool (tptp.hAPP_f229349961t_bool tptp.cOMBC_nat_nat_bool P) Q) R) (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool P R) Q))) (forall ((P tptp.fun_na1469252690l_bool) (Q tptp.fun_nat_bool) (R tptp.nat)) (= (tptp.hAPP_nat_bool (tptp.hAPP_f800510211t_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.nat)) (= (tptp.hAPP_n1006566506l_bool (tptp.hAPP_f1579826888l_bool tptp.cOMBK_623810489ol_nat P) Q) P)) (forall ((P tptp.fun_nat_bool) (Q tptp.bool)) (= (tptp.hAPP_b1013836512t_bool (tptp.hAPP_f1247925759t_bool tptp.cOMBK_1034797721l_bool P) Q) P)) (forall ((P tptp.bool) (Q tptp.arrow_856714788e_indi)) (= (tptp.hAPP_A997847300i_bool (tptp.hAPP_b549570054i_bool tptp.cOMBK_561380029e_indi P) Q) P)) (forall ((P tptp.fun_nat_bool) (Q tptp.product_unit)) (= (tptp.hAPP_P32877782t_bool (tptp.hAPP_f1212412661t_bool tptp.cOMBK_356206223t_unit P) Q) P)) (forall ((P tptp.fun_Pr1643180309t_bool) (Q tptp.nat)) (= (tptp.hAPP_n454528608t_bool (tptp.hAPP_f1539020360t_bool tptp.cOMBK_649751363ol_nat P) Q) P)) (forall ((P tptp.fun_nat_fun_nat_bool) (Q tptp.fun_nat_nat) (R tptp.nat)) (= (tptp.hAPP_n1699378549t_bool (tptp.hAPP_f618557131t_bool (tptp.cOMBB_800536526ol_nat P) Q) R) (tptp.hAPP_n1699378549t_bool P (tptp.hAPP_nat_nat 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.hAPP_f1722879237t_bool tptp.cOMBC_226598744l_bool P) Q) R) (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool P R) Q))) (forall ((P tptp.fun_bo1549164019l_bool) (Q tptp.fun_nat_bool) (R tptp.nat)) (= (tptp.hAPP_n1006566506l_bool (tptp.hAPP_f1146629647l_bool (tptp.cOMBB_1015721476ol_nat P) Q) R) (tptp.hAPP_b589554111l_bool P (tptp.hAPP_nat_bool Q R)))) (forall ((P tptp.fun_Ar603939593t_bool) (Q tptp.nat) (R tptp.arrow_856714788e_indi)) (= (tptp.hAPP_A997847300i_bool (tptp.hAPP_n34002993i_bool (tptp.hAPP_f721434149i_bool tptp.cOMBC_722552198t_bool P) Q) R) (tptp.hAPP_nat_bool (tptp.hAPP_A1686943911t_bool P R) Q))) (forall ((P tptp.fun_Ar1809396326i_bool) (Q tptp.nat)) (= (tptp.hAPP_n34002993i_bool (tptp.hAPP_f1549597448i_bool tptp.cOMBK_341987762ol_nat P) Q) P)) (forall ((P tptp.fun_nat_bool) (Q tptp.arrow_856714788e_indi)) (= (tptp.hAPP_A1686943911t_bool (tptp.hAPP_f1132083526t_bool tptp.cOMBK_833041760e_indi P) Q) P)) (forall ((P tptp.fun_na1436237685l_bool) (Q tptp.fun_nat_nat) (R tptp.nat)) (= (tptp.hAPP_n215258509l_bool (tptp.hAPP_f66927821l_bool (tptp.cOMBB_1146692694ol_nat P) Q) R) (tptp.hAPP_n215258509l_bool P (tptp.hAPP_nat_nat Q R)))) (forall ((P tptp.fun_nat_fun_nat_bool) (Q tptp.fun_Ar671024215di_nat) (R tptp.arrow_856714788e_indi)) (= (tptp.hAPP_A1686943911t_bool (tptp.hAPP_f966656047t_bool (tptp.cOMBB_1869811296e_indi P) Q) R) (tptp.hAPP_n1699378549t_bool P (tptp.hAPP_A376526755di_nat Q R)))) (forall ((P tptp.bool) (Q tptp.produc472769767le_alt)) (= (tptp.hAPP_P1178790471t_bool (tptp.hAPP_b128655177t_bool tptp.cOMBK_198697344le_alt P) Q) P)) (forall ((X tptp.fun_Pr2067565481t_bool) (Y tptp.fun_Pr2067565481t_bool)) (= (tptp.hAPP_f1356305429t_bool (tptp.hAPP_f1299954409t_bool (tptp.hAPP_b35146737t_bool tptp.if_fun523439385t_bool tptp.fTrue) X) Y) X)) (forall ((X tptp.fun_Pr2067565481t_bool) (Y tptp.fun_Pr2067565481t_bool)) (= (tptp.hAPP_f1356305429t_bool (tptp.hAPP_f1299954409t_bool (tptp.hAPP_b35146737t_bool tptp.if_fun523439385t_bool tptp.fFalse) X) Y) Y)) (forall ((P tptp.bool)) (or (= P tptp.fTrue) (= P tptp.fFalse))) (forall ((P tptp.bool) (Q tptp.fun_Pr2067565481t_bool)) (= (tptp.hAPP_f52567537l_bool (tptp.hAPP_b1272691967l_bool tptp.cOMBK_81143760t_bool P) Q) P)) (forall ((P tptp.fun_bool_bool) (Q tptp.produc472769767le_alt)) (= (tptp.hAPP_P1103642805l_bool (tptp.hAPP_f699791347l_bool tptp.cOMBK_138598520le_alt P) Q) P)) (forall ((P tptp.fun_Pr2067565481t_bool) (Q tptp.bool)) (= (tptp.hAPP_b128655177t_bool (tptp.hAPP_f1723896209t_bool tptp.cOMBK_5056120l_bool P) Q) P)) (forall ((P tptp.fun_Pr1643180309t_bool) (Q tptp.produc472769767le_alt)) (= (tptp.hAPP_P2037731755t_bool (tptp.hAPP_f723483871t_bool tptp.cOMBK_751896174le_alt P) Q) P)) (forall ((P tptp.fun_Pr2067565481t_bool) (Q tptp.product_unit)) (= (tptp.hAPP_P1914371027t_bool (tptp.hAPP_f15777819t_bool tptp.cOMBK_681766254t_unit P) Q) P)) (forall ((P tptp.fun_bool_bool) (Q tptp.fun_Pr2067565481t_bool)) (= (tptp.hAPP_f463104139l_bool (tptp.hAPP_f1713038057l_bool tptp.cOMBK_118864600t_bool P) Q) P)) (forall ((P tptp.fun_fu638310559l_bool) (Q tptp.bool)) (= (tptp.hAPP_b1272691967l_bool (tptp.hAPP_f86272063l_bool tptp.cOMBK_650639032l_bool P) Q) P)) (forall ((P tptp.fun_Ar1809396326i_bool) (Q tptp.produc472769767le_alt)) (= (tptp.hAPP_P1859429372i_bool (tptp.hAPP_f359069313i_bool tptp.cOMBK_1987648063le_alt P) Q) P)) (forall ((P tptp.fun_Pr2067565481t_bool) (Q tptp.arrow_856714788e_indi)) (= (tptp.hAPP_A1646126530t_bool (tptp.hAPP_f480276746t_bool tptp.cOMBK_1650320063e_indi P) Q) P)) (forall ((P tptp.fun_Pr1643180309t_bool) (Q tptp.fun_Pr2067565481t_bool)) (= (tptp.hAPP_f1400551297t_bool (tptp.hAPP_f168465001t_bool tptp.cOMBK_14887266t_bool P) Q) P)) (forall ((P tptp.fun_fu638310559l_bool) (Q tptp.product_unit)) (= (tptp.hAPP_P754918389l_bool (tptp.hAPP_f502523701l_bool tptp.cOMBK_1521810862t_unit P) Q) P)) (forall ((P tptp.fun_Ar339057223l_bool) (Q tptp.fun_Pr2067565481t_bool) (R tptp.arrow_1893660431le_alt)) (= (tptp.hAPP_A1748732503t_bool (tptp.hAPP_f234621849t_bool (tptp.hAPP_f1689397393t_bool tptp.cOMBC_395465908l_bool P) Q) R) (tptp.hAPP_f52567537l_bool (tptp.hAPP_A442239897l_bool P R) Q))) (forall ((P tptp.bool) (Q tptp.fun_Ar274636406t_bool)) (= (tptp.hAPP_f995490902l_bool (tptp.hAPP_b1078573912l_bool tptp.cOMBK_445086735t_bool P) Q) P)) (forall ((P tptp.fun_Ar1809396326i_bool) (Q tptp.fun_Pr2067565481t_bool)) (= (tptp.hAPP_f2010315474i_bool (tptp.hAPP_f1128827177i_bool tptp.cOMBK_814147665t_bool P) Q) P)) (forall ((P tptp.fun_fu638310559l_bool) (Q tptp.arrow_856714788e_indi)) (= (tptp.hAPP_A897398598l_bool (tptp.hAPP_f1717907078l_bool tptp.cOMBK_1520063231e_indi P) Q) P)) (forall ((P tptp.fun_bool_bool) (Q tptp.fun_Ar274636406t_bool)) (= (tptp.hAPP_f1676084198l_bool (tptp.hAPP_f1582869284l_bool tptp.cOMBK_542452487t_bool P) Q) P)) (forall ((P tptp.fun_fu3835832l_bool) (Q tptp.bool)) (= (tptp.hAPP_b1078573912l_bool (tptp.hAPP_f1322579375l_bool tptp.cOMBK_317366791l_bool P) Q) P)) (forall ((P tptp.fun_Ar64685412t_bool) (Q tptp.arrow_1893660431le_alt) (R tptp.arrow_856714788e_indi)) (= (tptp.hAPP_A1646126530t_bool (tptp.hAPP_A425126512t_bool (tptp.hAPP_f1631649925t_bool tptp.cOMBC_1417338747t_bool P) Q) R) (tptp.hAPP_A1601437999t_bool (tptp.hAPP_A1309733808t_bool P R) Q))) (forall ((P tptp.fun_Pr1643180309t_bool) (Q tptp.fun_Ar274636406t_bool)) (= (tptp.hAPP_f1438163420t_bool (tptp.hAPP_f134177552t_bool tptp.cOMBK_1220673277t_bool P) Q) P)) (forall ((P tptp.fun_fu3835832l_bool) (Q tptp.product_unit)) (= (tptp.hAPP_P284783074l_bool (tptp.hAPP_f1482764601l_bool tptp.cOMBK_708287485t_unit P) Q) P)) (forall ((P tptp.fun_Ar636018671t_bool) (Q tptp.fun_Pr2067565481t_bool) (R tptp.arrow_1893660431le_alt)) (= (tptp.hAPP_A2063800319t_bool (tptp.hAPP_f449303873t_bool (tptp.hAPP_f1081591777t_bool tptp.cOMBC_557453916t_bool P) Q) R) (tptp.hAPP_f234621849t_bool (tptp.hAPP_A656921921t_bool P R) Q))) (forall ((P tptp.fun_Pr1085078251l_bool) (Q tptp.fun_Pr2067565481t_bool) (R tptp.produc472769767le_alt)) (= (tptp.hAPP_P1178790471t_bool (tptp.hAPP_f1356305429t_bool (tptp.hAPP_f1033183015t_bool tptp.cOMBC_593569186l_bool P) Q) R) (tptp.hAPP_f52567537l_bool (tptp.hAPP_P38525833l_bool P R) Q))) (forall ((P tptp.fun_Ar1809396326i_bool) (Q tptp.fun_Ar274636406t_bool)) (= (tptp.hAPP_f391644589i_bool (tptp.hAPP_f2022065970i_bool tptp.cOMBK_818801614t_bool P) Q) P)) (forall ((P tptp.fun_fu3835832l_bool) (Q tptp.arrow_856714788e_indi)) (= (tptp.hAPP_A1411662545l_bool (tptp.hAPP_f1352816552l_bool tptp.cOMBK_1255579598e_indi P) Q) P)) (forall ((P tptp.fun_Ar290235730t_bool) (Q tptp.arrow_1893660431le_alt) (R tptp.arrow_856714788e_indi)) (= (tptp.hAPP_A1309733808t_bool (tptp.hAPP_A1889513822t_bool (tptp.hAPP_f2102110817t_bool tptp.cOMBC_1486904681t_bool P) Q) R) (tptp.hAPP_A1058422557t_bool (tptp.hAPP_A38124190t_bool P R) Q))) (forall ((P tptp.fun_fu864675765l_bool) (Q tptp.fun_fu638310559l_bool) (R tptp.fun_Pr2067565481t_bool)) (= (tptp.hAPP_f52567537l_bool (tptp.hAPP_f1060563265l_bool (tptp.hAPP_f1776355587l_bool tptp.cOMBC_2133093654l_bool P) Q) R) (tptp.hAPP_f182583295l_bool (tptp.hAPP_f1482930381l_bool P R) Q))) (forall ((P tptp.fun_Pr1085078251l_bool) (Q tptp.fun_Ar245737999le_alt) (R tptp.arrow_1893660431le_alt)) (= (tptp.hAPP_A442239897l_bool (tptp.hAPP_f1536341593l_bool (tptp.cOMBB_1660064607le_alt P) Q) R) (tptp.hAPP_P38525833l_bool P (tptp.hAPP_A1299015393le_alt Q R)))) (forall ((P tptp.fun_Ar516759882t_bool) (Q tptp.fun_Pr2067565481t_bool) (R tptp.arrow_856714788e_indi)) (= (tptp.hAPP_A1646126530t_bool (tptp.hAPP_f480276746t_bool (tptp.hAPP_f601594885t_bool tptp.cOMBC_750853729t_bool P) Q) R) (tptp.hAPP_f1356305429t_bool (tptp.hAPP_A834130326t_bool P R) Q))) (forall ((P tptp.fun_Ar516759882t_bool) (Q tptp.fun_Ar274636406t_bool) (R tptp.arrow_856714788e_indi)) (= (tptp.hAPP_A1646126530t_bool (tptp.hAPP_f1302887663t_bool (tptp.cOMBS_1181656689t_bool P) Q) R) (tptp.hAPP_f1356305429t_bool (tptp.hAPP_A834130326t_bool P R) (tptp.hAPP_A1646126530t_bool Q R)))) (forall ((P tptp.bool) (Q tptp.fun_fu2114379172t_bool)) (= (tptp.hAPP_f1572141188l_bool (tptp.hAPP_b1777246598l_bool tptp.cOMBK_1279003709t_bool P) Q) P)) (forall ((P tptp.fun_fu638310559l_bool) (Q tptp.fun_Ar274636406t_bool)) (= (tptp.hAPP_f1915815064l_bool (tptp.hAPP_f1104294872l_bool tptp.cOMBK_1701906001t_bool P) Q) P)) (forall ((P tptp.fun_bool_bool) (Q tptp.fun_fu2114379172t_bool)) (= (tptp.hAPP_f414129720l_bool (tptp.hAPP_f1152234870l_bool tptp.cOMBK_1770320693t_bool P) Q) P)) (forall ((P tptp.fun_fu2098777574l_bool) (Q tptp.bool)) (= (tptp.hAPP_b1777246598l_bool (tptp.hAPP_f369767947l_bool tptp.cOMBK_2030738485l_bool P) Q) P)) (forall ((P tptp.fun_fu1679793515t_bool) (Q tptp.fun_Ar274636406t_bool) (R tptp.arrow_856714788e_indi)) (= (tptp.hAPP_A1309733808t_bool (tptp.hAPP_f831214557t_bool (tptp.cOMBB_80760910e_indi P) Q) R) (tptp.hAPP_f1761571331t_bool P (tptp.hAPP_A1646126530t_bool Q R)))) (forall ((P tptp.fun_Pr1643180309t_bool) (Q tptp.fun_fu2114379172t_bool)) (= (tptp.hAPP_f151782958t_bool (tptp.hAPP_f1327693154t_bool tptp.cOMBK_1385893163t_bool P) Q) P)) (forall ((P tptp.fun_fu2098777574l_bool) (Q tptp.product_unit)) (= (tptp.hAPP_P283873808l_bool (tptp.hAPP_f956752277l_bool tptp.cOMBK_1075760171t_unit P) Q) P)) (forall ((P tptp.fun_Ar1809396326i_bool) (Q tptp.fun_fu2114379172t_bool)) (= (tptp.hAPP_f399308031i_bool (tptp.hAPP_f448050564i_bool tptp.cOMBK_443335420t_bool P) Q) P)) (forall ((P tptp.fun_fu2098777574l_bool) (Q tptp.arrow_856714788e_indi)) (= (tptp.hAPP_A2084592127l_bool (tptp.hAPP_f258290692l_bool tptp.cOMBK_1514079484e_indi P) Q) P)) (forall ((P tptp.fun_fu361117961l_bool) (Q tptp.fun_fu3835832l_bool) (R tptp.fun_Ar274636406t_bool)) (= (tptp.hAPP_f995490902l_bool (tptp.hAPP_f819682389l_bool (tptp.hAPP_f1760776521l_bool tptp.cOMBC_514203746l_bool P) Q) R) (tptp.hAPP_f73423488l_bool (tptp.hAPP_f1225332775l_bool P R) Q))) (forall ((P tptp.fun_fu1572237755l_bool) (Q tptp.fun_Ar2121501495le_alt) (R tptp.arrow_1893660431le_alt)) (= (tptp.hAPP_A1608658241l_bool (tptp.hAPP_f184584489l_bool (tptp.cOMBB_1575576719le_alt P) Q) R) (tptp.hAPP_f1536341593l_bool P (tptp.hAPP_A1146194953le_alt Q R)))) (forall ((P tptp.fun_fu1287834969t_bool) (Q tptp.fun_Ar274636406t_bool) (R tptp.arrow_856714788e_indi)) (= (tptp.hAPP_A38124190t_bool (tptp.hAPP_f1751344075t_bool (tptp.cOMBB_1876517692e_indi P) Q) R) (tptp.hAPP_f1550387441t_bool P (tptp.hAPP_A1646126530t_bool Q R)))) (forall ((P tptp.fun_Ar535288606t_bool) (Q tptp.fun_Pr2067565481t_bool) (R tptp.arrow_856714788e_indi)) (= (tptp.hAPP_A834130326t_bool (tptp.hAPP_f1344464862t_bool (tptp.hAPP_f1908974253t_bool tptp.cOMBC_156709173t_bool P) Q) R) (tptp.hAPP_f1299954409t_bool (tptp.hAPP_A1395684458t_bool P R) Q))) (forall ((P tptp.fun_Ar535288606t_bool) (Q tptp.fun_Ar274636406t_bool) (R tptp.arrow_856714788e_indi)) (= (tptp.hAPP_A834130326t_bool (tptp.hAPP_f1001205955t_bool (tptp.cOMBS_1925466437t_bool P) Q) R) (tptp.hAPP_f1299954409t_bool (tptp.hAPP_A1395684458t_bool P R) (tptp.hAPP_A1646126530t_bool Q R)))) (forall ((P tptp.fun_fu696673523t_bool) (Q tptp.fun_Ar1995913199l_bool) (R tptp.arrow_1893660431le_alt)) (= (tptp.hAPP_A656921921t_bool (tptp.hAPP_f105674721t_bool (tptp.cOMBB_652885079le_alt P) Q) R) (tptp.hAPP_f1689397393t_bool P (tptp.hAPP_A1608658241l_bool Q R)))) (forall ((P tptp.fun_bo1945492389t_bool) (Q tptp.fun_Ar1809396326i_bool) (R tptp.arrow_856714788e_indi)) (= (tptp.hAPP_A1395684458t_bool (tptp.hAPP_f668886383t_bool (tptp.cOMBB_1061985500e_indi P) Q) R) (tptp.hAPP_b35146737t_bool P (tptp.hAPP_A997847300i_bool Q R)))) (forall ((P tptp.fun_fu1383920485l_bool) (Q tptp.fun_fu2098777574l_bool) (R tptp.fun_fu2114379172t_bool)) (= (tptp.hAPP_f1572141188l_bool (tptp.hAPP_f1181604821l_bool (tptp.hAPP_f1169241965l_bool tptp.cOMBC_1209358050l_bool P) Q) R) (tptp.hAPP_f975209902l_bool (tptp.hAPP_f1714503811l_bool P R) Q))) _let_4 true))))))))))))))))))))
% 1.44/1.69 )
% 1.44/1.69 % SZS output end Proof for SCT171_3
% 1.44/1.69 % cvc5---1.0.5 exiting
% 1.44/1.70 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------