%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SCT171+6 : TPTP v8.1.2. Released v5.3.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n022.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 14:12:25 EDT 2023

% Result   : Theorem 0.82s 1.26s
% Output   : Proof 0.82s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.27/0.27  % Problem    : SCT171+6 : TPTP v8.1.2. Released v5.3.0.
% 0.27/0.28  % Command    : do_cvc5 %s %d
% 0.27/0.48  % Computer : n022.cluster.edu
% 0.27/0.48  % Model    : x86_64 x86_64
% 0.27/0.48  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.27/0.48  % Memory   : 8042.1875MB
% 0.27/0.48  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.27/0.49  % CPULimit   : 300
% 0.27/0.49  % WCLimit    : 300
% 0.27/0.49  % DateTime   : Thu Aug 24 14:57:41 EDT 2023
% 0.27/0.49  % CPUTime    : 
% 0.33/0.76  %----Proving TF0_NAR, FOF, or CNF
% 0.82/1.26  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.D5sNO2UtPa/cvc5---1.0.5_31407.p...
% 0.82/1.26  ------- get file name : TPTP file name is SCT171+6
% 0.82/1.26  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_31407.smt2...
% 0.82/1.26  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.82/1.26  % SZS status Theorem for SCT171+6
% 0.82/1.26  % SZS output start Proof for SCT171+6
% 0.82/1.26  (
% 0.82/1.26  (let ((_let_1 (tptp.product_prod tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun tptp.arrow_660593299e_indi _let_2))) (let ((_let_4 (tptp.product_Pair tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt))) (let ((_let_5 (tptp.fun tptp.arrow_490897120le_alt _let_1))) (let ((_let_6 (tptp.hAPP tptp.arrow_490897120le_alt _let_5 _let_4 tptp.c))) (let ((_let_7 (tptp.member _let_1))) (let ((_let_8 (tptp.fun _let_2 tptp.bool))) (let ((_let_9 (tptp.hAPP _let_1 _let_8 _let_7 (tptp.hAPP tptp.arrow_490897120le_alt _let_1 _let_6 tptp.d)))) (let ((_let_10 (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_9 (tptp.hAPP _let_3 _let_2 tptp.f tptp.p))))) (let ((_let_11 (not _let_10))) (let ((_let_12 (tptp.fun tptp.arrow_660593299e_indi tptp.bool))) (let ((_let_13 (tptp.top_top _let_12))) (let ((_let_14 (tptp.hAPP _let_12 tptp.nat (tptp.finite_card tptp.arrow_660593299e_indi) _let_13))) (let ((_let_15 (tptp.zero_zero tptp.nat))) (let ((_let_16 (tptp.fun tptp.nat tptp.bool))) (let ((_let_17 (tptp.fun tptp.nat _let_16))) (let ((_let_18 (tptp.fun tptp.arrow_660593299e_indi tptp.nat))) (let ((_let_19 (tptp.one_one tptp.nat))) (let ((_let_20 (tptp.fun tptp.product_unit tptp.bool))) (let ((_let_21 (tptp.fun tptp.arrow_660593299e_indi _let_8))) (let ((_let_22 (tptp.fun _let_3 tptp.bool))) (let ((_let_23 (tptp.fun tptp.nat tptp.nat))) (let ((_let_24 (tptp.ord_less tptp.nat))) (let ((_let_25 (tptp.combb tptp.nat _let_16 tptp.arrow_660593299e_indi))) (let ((_let_26 (tptp.fun tptp.arrow_660593299e_indi _let_16))) (let ((_let_27 (tptp.fun _let_18 _let_26))) (let ((_let_28 (tptp.combc tptp.arrow_660593299e_indi tptp.nat tptp.bool))) (let ((_let_29 (tptp.fun tptp.nat _let_12))) (let ((_let_30 (tptp.hAPP _let_26 _let_29 _let_28 (tptp.hAPP _let_18 _let_26 (tptp.hAPP _let_17 _let_27 _let_25 _let_24) tptp.h)))) (let ((_let_31 (tptp.fun _let_2 _let_2))) (let ((_let_32 (tptp.fun _let_2 _let_31))) (let ((_let_33 (tptp.fun tptp.arrow_660593299e_indi _let_32))) (let ((_let_34 (tptp.hAPP (tptp.fun tptp.bool _let_32) (tptp.fun _let_12 _let_33) (tptp.combb tptp.bool _let_32 tptp.arrow_660593299e_indi) (tptp.if _let_2)))) (let ((_let_35 (tptp.combc tptp.arrow_660593299e_indi _let_2 _let_31))) (let ((_let_36 (tptp.fun tptp.arrow_660593299e_indi _let_31))) (let ((_let_37 (tptp.fun _let_2 _let_36))) (let ((_let_38 (tptp.combc tptp.arrow_660593299e_indi _let_2 _let_2))) (let ((_let_39 (tptp.fun _let_2 _let_3))) (let ((_let_40 (tptp.hAPP _let_1 _let_8 _let_7 (tptp.hAPP tptp.arrow_490897120le_alt _let_1 (tptp.hAPP tptp.arrow_490897120le_alt _let_5 _let_4 tptp.a) tptp.b)))) (let ((_let_41 (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_40 (tptp.hAPP _let_3 _let_2 tptp.f (tptp.hAPP _let_2 _let_3 (tptp.hAPP _let_36 _let_39 _let_38 (tptp.hAPP _let_2 _let_36 (tptp.hAPP _let_33 _let_37 _let_35 (tptp.hAPP _let_12 _let_33 _let_34 (tptp.hAPP tptp.nat _let_12 _let_30 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_23 (tptp.plus_plus tptp.nat) tptp.n) _let_19)))) tptp.lab)) tptp.lba)))))) (let ((_let_42 (tptp.fun tptp.arrow_490897120le_alt _let_2))) (let ((_let_43 (tptp.combb _let_2 _let_42 tptp.arrow_660593299e_indi))) (let ((_let_44 (tptp.fun tptp.arrow_660593299e_indi _let_42))) (let ((_let_45 (tptp.fun _let_3 _let_44))) (let ((_let_46 (tptp.fun _let_2 _let_42))) (let ((_let_47 (tptp.combc tptp.arrow_660593299e_indi tptp.arrow_490897120le_alt _let_2))) (let ((_let_48 (tptp.fun tptp.arrow_490897120le_alt _let_3))) (let ((_let_49 (tptp.fun tptp.arrow_490897120le_alt _let_42))) (let ((_let_50 (tptp.fun tptp.arrow_660593299e_indi _let_49))) (let ((_let_51 (tptp.fun _let_2 _let_49))) (let ((_let_52 (tptp.combs tptp.arrow_660593299e_indi _let_2 _let_31))) (let ((_let_53 (tptp.fun _let_3 _let_36))) (let ((_let_54 (tptp.combs tptp.arrow_660593299e_indi _let_2 _let_2))) (let ((_let_55 (tptp.fun _let_3 _let_3))) (let ((_let_56 (tptp.hAPP _let_12 _let_33 _let_34 (tptp.hAPP tptp.nat _let_12 _let_30 tptp.n)))) (let ((_let_57 (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_36 _let_55 _let_54 (tptp.hAPP _let_3 _let_36 (tptp.hAPP _let_33 _let_53 _let_52 _let_56) (tptp.hAPP tptp.arrow_490897120le_alt _let_3 (tptp.hAPP _let_44 _let_48 _let_47 (tptp.hAPP _let_3 _let_44 (tptp.hAPP _let_46 _let_45 _let_43 tptp.arrow_1427655034_mktop) tptp.p)) tptp.e))) (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_36 _let_55 _let_54 (tptp.hAPP _let_3 _let_36 (tptp.hAPP _let_33 _let_53 _let_52 (tptp.hAPP _let_12 _let_33 _let_34 (tptp.hAPP tptp.nat _let_12 (tptp.hAPP _let_26 _let_29 _let_28 (tptp.hAPP _let_18 _let_26 (tptp.hAPP _let_17 _let_27 _let_25 (tptp.fequal tptp.nat)) tptp.h)) tptp.n))) (tptp.hAPP tptp.arrow_490897120le_alt _let_3 (tptp.hAPP _let_44 _let_48 _let_47 (tptp.hAPP tptp.arrow_490897120le_alt _let_44 (tptp.hAPP _let_50 (tptp.fun tptp.arrow_490897120le_alt _let_44) (tptp.combc tptp.arrow_660593299e_indi tptp.arrow_490897120le_alt _let_42) (tptp.hAPP _let_3 _let_50 (tptp.hAPP _let_51 (tptp.fun _let_3 _let_50) (tptp.combb _let_2 _let_49 tptp.arrow_660593299e_indi) tptp.arrow_14103264_above) tptp.p)) tptp.c)) tptp.e))) (tptp.hAPP tptp.arrow_490897120le_alt _let_3 (tptp.hAPP _let_44 _let_48 _let_47 (tptp.hAPP _let_3 _let_44 (tptp.hAPP _let_46 _let_45 _let_43 tptp.arrow_1278947948_mkbot) tptp.p)) tptp.e))))) (let ((_let_58 (tptp.hAPP _let_3 _let_2 tptp.f _let_57))) (let ((_let_59 (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 _let_8 _let_7 (tptp.hAPP tptp.arrow_490897120le_alt _let_1 _let_6 tptp.e)) _let_58)))) (let ((_let_60 (tptp.hAPP _let_1 _let_8 _let_7 (tptp.hAPP tptp.arrow_490897120le_alt _let_1 (tptp.hAPP tptp.arrow_490897120le_alt _let_5 _let_4 tptp.b) tptp.a)))) (let ((_let_61 (tptp.member _let_2))) (let ((_let_62 (tptp.fun _let_8 tptp.bool))) (let ((_let_63 (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 _let_8 _let_7 (tptp.hAPP tptp.arrow_490897120le_alt _let_1 (tptp.hAPP tptp.arrow_490897120le_alt _let_5 _let_4 tptp.e) tptp.d)) _let_58)))) (let ((_let_64 (tptp.fun _let_3 _let_8))) (let ((_let_65 (tptp.fun _let_3 _let_2))) (let ((_let_66 (tptp.fun _let_65 tptp.bool))) (let ((_let_67 (tptp.member _let_3))) (let ((_let_68 (tptp.fun _let_22 tptp.bool))) (let ((_let_69 (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_9 _let_58)))) (let ((_let_70 (= _let_10 _let_69))) (let ((_let_71 (tptp.fun tptp.nat tptp.arrow_660593299e_indi))) (let ((_let_72 (tptp.fun tptp.bool tptp.bool))) (let ((_let_73 (tptp.fun tptp.bool _let_72))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (ASSUME :args (_let_11)) (MACRO_RESOLUTION_TRUST (REORDERING (EQUIV_ELIM1 (SYMM (ASSUME :args (_let_70)))) :args ((or _let_10 (not _let_69)))) (ASSUME :args (_let_69)) :args (_let_10 false _let_69)) :args (false false _let_10)) :args ((= (tptp.ti _let_66 tptp.arrow_2037941124le_IIA) tptp.arrow_2037941124le_IIA) (= (tptp.ti _let_8 tptp.arrow_2064824852le_Lin) tptp.arrow_2064824852le_Lin) (= (tptp.ti _let_22 tptp.arrow_1111136790e_Prof) tptp.arrow_1111136790e_Prof) (= (tptp.ti _let_51 tptp.arrow_14103264_above) tptp.arrow_14103264_above) (= (tptp.ti _let_51 tptp.arrow_1322701812_below) tptp.arrow_1322701812_below) (= (tptp.ti (tptp.fun _let_65 _let_12) tptp.arrow_218898985ctator) tptp.arrow_218898985ctator) (= (tptp.ti _let_46 tptp.arrow_1278947948_mkbot) tptp.arrow_1278947948_mkbot) (= (tptp.ti _let_46 tptp.arrow_1427655034_mktop) tptp.arrow_1427655034_mktop) (= (tptp.ti _let_66 tptp.arrow_831799591nimity) tptp.arrow_831799591nimity) (forall ((X_b $$unsorted) (X_c $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.combb X_b X_c X_a))) (= (tptp.ti (tptp.fun (tptp.fun X_b X_c) (tptp.fun (tptp.fun X_a X_b) (tptp.fun X_a X_c))) _let_1) _let_1))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted)) (let ((_let_1 (tptp.combc X_a X_b X_c))) (= (tptp.ti (tptp.fun (tptp.fun X_a (tptp.fun X_b X_c)) (tptp.fun X_b (tptp.fun X_a X_c))) _let_1) _let_1))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.combi X_a))) (= (tptp.ti (tptp.fun X_a X_a) _let_1) _let_1))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (let ((_let_1 (tptp.combk X_a X_b))) (= (tptp.ti (tptp.fun X_a (tptp.fun X_b X_a)) _let_1) _let_1))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted)) (let ((_let_1 (tptp.combs X_a X_b X_c))) (= (tptp.ti (tptp.fun (tptp.fun X_a (tptp.fun X_b X_c)) (tptp.fun (tptp.fun X_a X_b) (tptp.fun X_a X_c))) _let_1) _let_1))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.finite_card X_a))) (= (tptp.ti (tptp.fun (tptp.fun X_a tptp.bool) tptp.nat) _let_1) _let_1))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.finite_finite_1 X_b))) (= (tptp.ti (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) _let_1) _let_1))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.finite_fold_image tptp.nat X_a))) (= (tptp.ti (tptp.fun (tptp.fun tptp.nat (tptp.fun tptp.nat tptp.nat)) (tptp.fun (tptp.fun X_a tptp.nat) (tptp.fun tptp.nat (tptp.fun (tptp.fun X_a tptp.bool) tptp.nat)))) _let_1) _let_1))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (let ((_let_1 (tptp.finite908156982e_idem X_a X_b))) (= (tptp.ti (tptp.fun (tptp.fun X_a (tptp.fun X_a X_a)) (tptp.fun X_a (tptp.fun (tptp.fun X_b X_a) (tptp.fun (tptp.fun (tptp.fun X_b tptp.bool) X_a) tptp.bool)))) _let_1) _let_1))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (let ((_let_1 (tptp.in_rel X_a X_b))) (= (tptp.ti (tptp.fun (tptp.fun (tptp.product_prod X_a X_b) tptp.bool) (tptp.fun X_a (tptp.fun X_b tptp.bool))) _let_1) _let_1))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (let ((_let_1 (tptp.inj_on X_a X_b))) (= (tptp.ti (tptp.fun (tptp.fun X_a X_b) (tptp.fun (tptp.fun X_a tptp.bool) tptp.bool)) _let_1) _let_1))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (let ((_let_1 (tptp.pi X_a X_b))) (= (tptp.ti (tptp.fun (tptp.fun X_a tptp.bool) (tptp.fun (tptp.fun X_a (tptp.fun X_b tptp.bool)) (tptp.fun (tptp.fun X_a X_b) tptp.bool))) _let_1) _let_1))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (=> (tptp.one X_a) (= (tptp.ti X_a _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (=> (tptp.monoid_add X_a) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a X_a)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (=> (tptp.ab_semigroup_add X_a) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a X_a)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (=> (tptp.cancel_semigroup_add X_a) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a X_a)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (=> (tptp.zero X_a) (= (tptp.ti X_a _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.undefined X_a))) (= (tptp.ti X_a _let_1) _let_1))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (let ((_let_1 (tptp.hilbert_inv_into X_a X_b))) (= (tptp.ti (tptp.fun (tptp.fun X_a tptp.bool) (tptp.fun (tptp.fun X_a X_b) (tptp.fun X_b X_a))) _let_1) _let_1))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.if X_a))) (= (tptp.ti (tptp.fun tptp.bool (tptp.fun X_a (tptp.fun X_a X_a))) _let_1) _let_1))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.ring_1_Ints X_a))) (=> (tptp.ring_1 X_a) (= (tptp.ti (tptp.fun X_a tptp.bool) _let_1) _let_1)))) (= (tptp.ti _let_23 tptp.suc) tptp.suc) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (=> (tptp.ord X_a) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a tptp.bool)) _let_1) _let_1)))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_b))) (=> (tptp.ord X_b) (= (tptp.ti (tptp.fun X_b (tptp.fun X_b tptp.bool)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.top_top X_a))) (=> (tptp.top X_a) (= (tptp.ti X_a _let_1) _let_1)))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (let ((_let_1 (tptp.product_Pair X_a X_b))) (= (tptp.ti (tptp.fun X_a (tptp.fun X_b (tptp.product_prod X_a X_b))) _let_1) _let_1))) (forall ((X_b $$unsorted) (X_c $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.product_prod_rec X_b X_c X_a))) (= (tptp.ti (tptp.fun (tptp.fun X_b (tptp.fun X_c X_a)) (tptp.fun (tptp.product_prod X_b X_c) X_a)) _let_1) _let_1))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.ord_atLeastLessThan X_a))) (=> (tptp.linorder X_a) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a (tptp.fun X_a tptp.bool))) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.collect X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (= (tptp.ti (tptp.fun _let_2 _let_2) _let_1) _let_1)))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.image X_b X_a))) (= (tptp.ti (tptp.fun (tptp.fun X_b X_a) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_a tptp.bool))) _let_1) _let_1))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (let ((_let_1 (tptp.sum_Plus X_a X_b))) (= (tptp.ti (tptp.fun (tptp.fun X_a tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun (tptp.sum_sum X_a X_b) tptp.bool))) _let_1) _let_1))) (= (tptp.ti tptp.bool tptp.fFalse) tptp.fFalse) (= (tptp.ti _let_72 tptp.fNot) tptp.fNot) (= (tptp.ti tptp.bool tptp.fTrue) tptp.fTrue) (= (tptp.ti _let_73 tptp.fconj) tptp.fconj) (= (tptp.ti _let_73 tptp.fdisj) tptp.fdisj) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.fequal X_a))) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a tptp.bool)) _let_1) _let_1))) (forall ((X_a $$unsorted) (X_c $$unsorted) (B_1_1 $$unsorted) (B_2_1 $$unsorted)) (= (tptp.hAPP X_a X_c (tptp.ti (tptp.fun X_a X_c) B_1_1) B_2_1) (tptp.hAPP X_a X_c B_1_1 B_2_1))) (forall ((X_a $$unsorted) (X_c $$unsorted) (B_1_1 $$unsorted) (B_2_1 $$unsorted)) (= (tptp.hAPP X_a X_c B_1_1 (tptp.ti X_a B_2_1)) (tptp.hAPP X_a X_c B_1_1 B_2_1))) (forall ((X_c $$unsorted) (X_a $$unsorted) (B_1_1 $$unsorted) (B_2_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a X_c B_1_1 B_2_1))) (= (tptp.ti X_c _let_1) _let_1))) (forall ((B_1_1 $$unsorted)) (= (tptp.hBOOL (tptp.ti tptp.bool B_1_1)) (tptp.hBOOL B_1_1))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.member X_a))) (= (tptp.ti (tptp.fun X_a (tptp.fun (tptp.fun X_a tptp.bool) tptp.bool)) _let_1) _let_1))) (= (tptp.ti _let_65 tptp.f) tptp.f) (= (tptp.ti _let_2 tptp.lab) tptp.lab) (= (tptp.ti _let_2 tptp.lba) tptp.lba) (= (tptp.ti _let_3 tptp.p) tptp.p) (= (tptp.ti tptp.arrow_490897120le_alt tptp.a) tptp.a) (= (tptp.ti tptp.arrow_490897120le_alt tptp.b) tptp.b) (= (tptp.ti tptp.arrow_490897120le_alt tptp.c) tptp.c) (= (tptp.ti tptp.arrow_490897120le_alt tptp.d) tptp.d) (= (tptp.ti tptp.arrow_490897120le_alt tptp.e) tptp.e) (= (tptp.ti _let_18 tptp.h) tptp.h) (= (tptp.ti tptp.nat tptp.n) tptp.n) (tptp.hBOOL (tptp.hAPP _let_65 tptp.bool tptp.arrow_2037941124le_IIA tptp.f)) (tptp.hBOOL (tptp.hAPP _let_65 tptp.bool tptp.arrow_831799591nimity tptp.f)) (not (= tptp.c tptp.d)) (tptp.hBOOL (tptp.hAPP _let_22 tptp.bool (tptp.hAPP _let_3 _let_68 _let_67 tptp.p) tptp.arrow_1111136790e_Prof)) (forall ((X_1 $$unsorted) (Y_2 $$unsorted) (L_3 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) (tptp.hAPP tptp.arrow_490897120le_alt _let_1 (tptp.hAPP tptp.arrow_490897120le_alt (tptp.fun tptp.arrow_490897120le_alt _let_1) (tptp.product_Pair tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt) X_1) Y_2)))) (let ((_let_4 (tptp.ti tptp.arrow_490897120le_alt Z))) (let ((_let_5 (tptp.ti tptp.arrow_490897120le_alt X_1))) (let ((_let_6 (= _let_5 _let_4))) (let ((_let_7 (tptp.ti tptp.arrow_490897120le_alt Y_2))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 (tptp.hAPP tptp.arrow_490897120le_alt _let_2 (tptp.hAPP _let_2 (tptp.fun tptp.arrow_490897120le_alt _let_2) tptp.arrow_1278947948_mkbot L_3) Z))) (and (not (= _let_7 _let_4)) (=> _let_6 (not (= _let_5 _let_7))) (=> (not _let_6) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 L_3))))))))))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted) (L_3 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) (tptp.hAPP tptp.arrow_490897120le_alt _let_1 (tptp.hAPP tptp.arrow_490897120le_alt (tptp.fun tptp.arrow_490897120le_alt _let_1) (tptp.product_Pair tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt) X_1) Y_2)))) (let ((_let_4 (tptp.ti tptp.arrow_490897120le_alt Z))) (let ((_let_5 (tptp.ti tptp.arrow_490897120le_alt Y_2))) (let ((_let_6 (= _let_5 _let_4))) (let ((_let_7 (tptp.ti tptp.arrow_490897120le_alt X_1))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 (tptp.hAPP tptp.arrow_490897120le_alt _let_2 (tptp.hAPP _let_2 (tptp.fun tptp.arrow_490897120le_alt _let_2) tptp.arrow_1427655034_mktop L_3) Z))) (and (not (= _let_7 _let_4)) (=> _let_6 (not (= _let_7 _let_5))) (=> (not _let_6) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 L_3))))))))))))) (forall ((P_1 $$unsorted) (Pa $$unsorted) (A_5 $$unsorted) (B_3 $$unsorted) (Aa $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun tptp.arrow_660593299e_indi _let_2))) (let ((_let_4 (tptp.product_Pair tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt))) (let ((_let_5 (tptp.fun tptp.arrow_490897120le_alt _let_1))) (let ((_let_6 (tptp.member _let_1))) (let ((_let_7 (tptp.fun _let_2 tptp.bool))) (let ((_let_8 (tptp.member _let_3))) (let ((_let_9 (tptp.fun _let_3 tptp.bool))) (let ((_let_10 (tptp.fun _let_9 tptp.bool))) (let ((_let_11 (tptp.ti tptp.arrow_490897120le_alt A_5))) (let ((_let_12 (tptp.ti tptp.arrow_490897120le_alt Ba))) (let ((_let_13 (tptp.ti tptp.arrow_490897120le_alt B_3))) (let ((_let_14 (tptp.ti tptp.arrow_490897120le_alt Aa))) (=> (not (= _let_14 _let_12)) (=> (not (= _let_11 _let_13)) (=> (not (= _let_14 _let_13)) (=> (not (= _let_12 _let_11)) (=> (tptp.hBOOL (tptp.hAPP _let_9 tptp.bool (tptp.hAPP _let_3 _let_10 _let_8 Pa) tptp.arrow_1111136790e_Prof)) (=> (tptp.hBOOL (tptp.hAPP _let_9 tptp.bool (tptp.hAPP _let_3 _let_10 _let_8 P_1) tptp.arrow_1111136790e_Prof)) (=> (forall ((I_2 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.product_Pair tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt))) (let ((_let_4 (tptp.fun tptp.arrow_490897120le_alt _let_1))) (let ((_let_5 (tptp.member _let_1))) (let ((_let_6 (tptp.fun _let_2 tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 _let_6 _let_5 (tptp.hAPP tptp.arrow_490897120le_alt _let_1 (tptp.hAPP tptp.arrow_490897120le_alt _let_4 _let_3 Aa) Ba)) (tptp.hAPP tptp.arrow_660593299e_indi _let_2 Pa I_2))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 _let_6 _let_5 (tptp.hAPP tptp.arrow_490897120le_alt _let_1 (tptp.hAPP tptp.arrow_490897120le_alt _let_4 _let_3 A_5) B_3)) (tptp.hAPP tptp.arrow_660593299e_indi _let_2 P_1 I_2))))))))))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 _let_7 _let_6 (tptp.hAPP tptp.arrow_490897120le_alt _let_1 (tptp.hAPP tptp.arrow_490897120le_alt _let_5 _let_4 Aa) Ba)) (tptp.hAPP _let_3 _let_2 tptp.f Pa))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 _let_7 _let_6 (tptp.hAPP tptp.arrow_490897120le_alt _let_1 (tptp.hAPP tptp.arrow_490897120le_alt _let_5 _let_4 A_5) B_3)) (tptp.hAPP _let_3 _let_2 tptp.f P_1)))))))))))))))))))))))))) (forall ((P_1 $$unsorted) (Pa $$unsorted) (A_5 $$unsorted) (B_3 $$unsorted) (Aa $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun tptp.arrow_660593299e_indi _let_2))) (let ((_let_4 (tptp.product_Pair tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt))) (let ((_let_5 (tptp.fun tptp.arrow_490897120le_alt _let_1))) (let ((_let_6 (tptp.member _let_1))) (let ((_let_7 (tptp.fun _let_2 tptp.bool))) (let ((_let_8 (tptp.member _let_3))) (let ((_let_9 (tptp.fun _let_3 tptp.bool))) (let ((_let_10 (tptp.fun _let_9 tptp.bool))) (let ((_let_11 (tptp.ti tptp.arrow_490897120le_alt A_5))) (let ((_let_12 (tptp.ti tptp.arrow_490897120le_alt Ba))) (let ((_let_13 (tptp.ti tptp.arrow_490897120le_alt B_3))) (let ((_let_14 (tptp.ti tptp.arrow_490897120le_alt Aa))) (=> (not (= _let_14 _let_12)) (=> (not (= _let_11 _let_13)) (=> (not (= _let_14 _let_13)) (=> (not (= _let_12 _let_11)) (=> (tptp.hBOOL (tptp.hAPP _let_9 tptp.bool (tptp.hAPP _let_3 _let_10 _let_8 Pa) tptp.arrow_1111136790e_Prof)) (=> (tptp.hBOOL (tptp.hAPP _let_9 tptp.bool (tptp.hAPP _let_3 _let_10 _let_8 P_1) tptp.arrow_1111136790e_Prof)) (=> (forall ((I_2 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.product_Pair tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt))) (let ((_let_4 (tptp.fun tptp.arrow_490897120le_alt _let_1))) (let ((_let_5 (tptp.member _let_1))) (let ((_let_6 (tptp.fun _let_2 tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 _let_6 _let_5 (tptp.hAPP tptp.arrow_490897120le_alt _let_1 (tptp.hAPP tptp.arrow_490897120le_alt _let_4 _let_3 Aa) Ba)) (tptp.hAPP tptp.arrow_660593299e_indi _let_2 Pa I_2))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 _let_6 _let_5 (tptp.hAPP tptp.arrow_490897120le_alt _let_1 (tptp.hAPP tptp.arrow_490897120le_alt _let_4 _let_3 A_5) B_3)) (tptp.hAPP tptp.arrow_660593299e_indi _let_2 P_1 I_2))))))))))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 _let_7 _let_6 (tptp.hAPP tptp.arrow_490897120le_alt _let_1 (tptp.hAPP tptp.arrow_490897120le_alt _let_5 _let_4 Aa) Ba)) (tptp.hAPP _let_3 _let_2 tptp.f Pa))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 _let_7 _let_6 (tptp.hAPP tptp.arrow_490897120le_alt _let_1 (tptp.hAPP tptp.arrow_490897120le_alt _let_5 _let_4 A_5) B_3)) (tptp.hAPP _let_3 _let_2 tptp.f P_1)))))))))))))))))))))))))) (forall ((P_1 $$unsorted) (Pa $$unsorted) (Ca $$unsorted) (Aa $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun tptp.arrow_660593299e_indi _let_2))) (let ((_let_4 (tptp.product_Pair tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt))) (let ((_let_5 (tptp.fun tptp.arrow_490897120le_alt _let_1))) (let ((_let_6 (tptp.member _let_1))) (let ((_let_7 (tptp.fun _let_2 tptp.bool))) (let ((_let_8 (tptp.member _let_3))) (let ((_let_9 (tptp.fun _let_3 tptp.bool))) (let ((_let_10 (tptp.fun _let_9 tptp.bool))) (let ((_let_11 (tptp.ti tptp.arrow_490897120le_alt Ca))) (let ((_let_12 (tptp.ti tptp.arrow_490897120le_alt Aa))) (let ((_let_13 (tptp.ti tptp.arrow_490897120le_alt Ba))) (=> (not (= _let_12 _let_13)) (=> (not (= _let_13 _let_11)) (=> (not (= _let_12 _let_11)) (=> (tptp.hBOOL (tptp.hAPP _let_9 tptp.bool (tptp.hAPP _let_3 _let_10 _let_8 Pa) tptp.arrow_1111136790e_Prof)) (=> (tptp.hBOOL (tptp.hAPP _let_9 tptp.bool (tptp.hAPP _let_3 _let_10 _let_8 P_1) tptp.arrow_1111136790e_Prof)) (=> (forall ((I_2 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.product_Pair tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt))) (let ((_let_4 (tptp.fun tptp.arrow_490897120le_alt _let_1))) (let ((_let_5 (tptp.member _let_1))) (let ((_let_6 (tptp.fun _let_2 tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 _let_6 _let_5 (tptp.hAPP tptp.arrow_490897120le_alt _let_1 (tptp.hAPP tptp.arrow_490897120le_alt _let_4 _let_3 Aa) Ba)) (tptp.hAPP tptp.arrow_660593299e_indi _let_2 Pa I_2))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 _let_6 _let_5 (tptp.hAPP tptp.arrow_490897120le_alt _let_1 (tptp.hAPP tptp.arrow_490897120le_alt _let_4 _let_3 Ba) Ca)) (tptp.hAPP tptp.arrow_660593299e_indi _let_2 P_1 I_2))))))))))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 _let_7 _let_6 (tptp.hAPP tptp.arrow_490897120le_alt _let_1 (tptp.hAPP tptp.arrow_490897120le_alt _let_5 _let_4 Aa) Ba)) (tptp.hAPP _let_3 _let_2 tptp.f Pa))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 _let_7 _let_6 (tptp.hAPP tptp.arrow_490897120le_alt _let_1 (tptp.hAPP tptp.arrow_490897120le_alt _let_5 _let_4 Ba) Ca)) (tptp.hAPP _let_3 _let_2 tptp.f P_1)))))))))))))))))))))))) (forall ((P_1 $$unsorted) (Pa $$unsorted) (A_5 $$unsorted) (B_3 $$unsorted) (Aa $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun tptp.arrow_660593299e_indi _let_2))) (let ((_let_4 (tptp.product_Pair tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt))) (let ((_let_5 (tptp.fun tptp.arrow_490897120le_alt _let_1))) (let ((_let_6 (tptp.member _let_1))) (let ((_let_7 (tptp.fun _let_2 tptp.bool))) (let ((_let_8 (tptp.member _let_3))) (let ((_let_9 (tptp.fun _let_3 tptp.bool))) (let ((_let_10 (tptp.fun _let_9 tptp.bool))) (=> (not (= (tptp.ti tptp.arrow_490897120le_alt Aa) (tptp.ti tptp.arrow_490897120le_alt Ba))) (=> (not (= (tptp.ti tptp.arrow_490897120le_alt A_5) (tptp.ti tptp.arrow_490897120le_alt B_3))) (=> (tptp.hBOOL (tptp.hAPP _let_9 tptp.bool (tptp.hAPP _let_3 _let_10 _let_8 Pa) tptp.arrow_1111136790e_Prof)) (=> (tptp.hBOOL (tptp.hAPP _let_9 tptp.bool (tptp.hAPP _let_3 _let_10 _let_8 P_1) tptp.arrow_1111136790e_Prof)) (=> (forall ((I_2 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.product_Pair tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt))) (let ((_let_4 (tptp.fun tptp.arrow_490897120le_alt _let_1))) (let ((_let_5 (tptp.member _let_1))) (let ((_let_6 (tptp.fun _let_2 tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 _let_6 _let_5 (tptp.hAPP tptp.arrow_490897120le_alt _let_1 (tptp.hAPP tptp.arrow_490897120le_alt _let_4 _let_3 Aa) Ba)) (tptp.hAPP tptp.arrow_660593299e_indi _let_2 Pa I_2))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 _let_6 _let_5 (tptp.hAPP tptp.arrow_490897120le_alt _let_1 (tptp.hAPP tptp.arrow_490897120le_alt _let_4 _let_3 A_5) B_3)) (tptp.hAPP tptp.arrow_660593299e_indi _let_2 P_1 I_2))))))))))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 _let_7 _let_6 (tptp.hAPP tptp.arrow_490897120le_alt _let_1 (tptp.hAPP tptp.arrow_490897120le_alt _let_5 _let_4 Aa) Ba)) (tptp.hAPP _let_3 _let_2 tptp.f Pa))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 _let_7 _let_6 (tptp.hAPP tptp.arrow_490897120le_alt _let_1 (tptp.hAPP tptp.arrow_490897120le_alt _let_5 _let_4 A_5) B_3)) (tptp.hAPP _let_3 _let_2 tptp.f P_1)))))))))))))))))))) (forall ((P_1 $$unsorted) (Pa $$unsorted) (Aa $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun tptp.arrow_660593299e_indi _let_2))) (let ((_let_4 (tptp.product_Pair tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt))) (let ((_let_5 (tptp.fun tptp.arrow_490897120le_alt _let_1))) (let ((_let_6 (tptp.member _let_1))) (let ((_let_7 (tptp.fun _let_2 tptp.bool))) (let ((_let_8 (tptp.member _let_3))) (let ((_let_9 (tptp.fun _let_3 tptp.bool))) (let ((_let_10 (tptp.fun _let_9 tptp.bool))) (=> (not (= (tptp.ti tptp.arrow_490897120le_alt Aa) (tptp.ti tptp.arrow_490897120le_alt Ba))) (=> (tptp.hBOOL (tptp.hAPP _let_9 tptp.bool (tptp.hAPP _let_3 _let_10 _let_8 Pa) tptp.arrow_1111136790e_Prof)) (=> (tptp.hBOOL (tptp.hAPP _let_9 tptp.bool (tptp.hAPP _let_3 _let_10 _let_8 P_1) tptp.arrow_1111136790e_Prof)) (=> (forall ((I_2 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.product_Pair tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt))) (let ((_let_4 (tptp.fun tptp.arrow_490897120le_alt _let_1))) (let ((_let_5 (tptp.member _let_1))) (let ((_let_6 (tptp.fun _let_2 tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 _let_6 _let_5 (tptp.hAPP tptp.arrow_490897120le_alt _let_1 (tptp.hAPP tptp.arrow_490897120le_alt _let_4 _let_3 Aa) Ba)) (tptp.hAPP tptp.arrow_660593299e_indi _let_2 Pa I_2))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 _let_6 _let_5 (tptp.hAPP tptp.arrow_490897120le_alt _let_1 (tptp.hAPP tptp.arrow_490897120le_alt _let_4 _let_3 Ba) Aa)) (tptp.hAPP tptp.arrow_660593299e_indi _let_2 P_1 I_2))))))))))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 _let_7 _let_6 (tptp.hAPP tptp.arrow_490897120le_alt _let_1 (tptp.hAPP tptp.arrow_490897120le_alt _let_5 _let_4 Aa) Ba)) (tptp.hAPP _let_3 _let_2 tptp.f Pa))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 _let_7 _let_6 (tptp.hAPP tptp.arrow_490897120le_alt _let_1 (tptp.hAPP tptp.arrow_490897120le_alt _let_5 _let_4 Ba) Aa)) (tptp.hAPP _let_3 _let_2 tptp.f P_1))))))))))))))))))) (forall ((I_2 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.arrow_660593299e_indi _let_2 tptp.p I_2))) (let ((_let_4 (tptp.fun tptp.arrow_490897120le_alt _let_2))) (let ((_let_5 (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) (tptp.hAPP tptp.arrow_490897120le_alt _let_1 (tptp.hAPP tptp.arrow_490897120le_alt (tptp.fun tptp.arrow_490897120le_alt _let_1) (tptp.product_Pair tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt) tptp.c) tptp.d)))) (let ((_let_6 (tptp.hAPP tptp.arrow_660593299e_indi tptp.nat tptp.h I_2))) (let ((_let_7 (= _let_6 tptp.n))) (let ((_let_8 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) _let_6) tptp.n)))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_5 _let_3)) (and (=> _let_8 (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_5 (tptp.hAPP tptp.arrow_490897120le_alt _let_2 (tptp.hAPP _let_2 _let_4 tptp.arrow_1427655034_mktop _let_3) tptp.e)))) (=> (not _let_8) (and (=> _let_7 (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_5 (tptp.hAPP tptp.arrow_490897120le_alt _let_2 (tptp.hAPP tptp.arrow_490897120le_alt _let_4 (tptp.hAPP _let_2 (tptp.fun tptp.arrow_490897120le_alt _let_4) tptp.arrow_14103264_above _let_3) tptp.c) tptp.e)))) (=> (not _let_7) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_5 (tptp.hAPP tptp.arrow_490897120le_alt _let_2 (tptp.hAPP _let_2 _let_4 tptp.arrow_1278947948_mkbot _let_3) tptp.e))))))))))))))))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_9 (tptp.hAPP tptp.arrow_660593299e_indi _let_2 tptp.p (tptp.hAPP tptp.nat tptp.arrow_660593299e_indi (tptp.hAPP _let_18 _let_71 (tptp.hAPP _let_12 (tptp.fun _let_18 _let_71) (tptp.hilbert_inv_into tptp.arrow_660593299e_indi tptp.nat) _let_13) tptp.h) tptp.n)))) _let_69 _let_70 (forall ((X_a $$unsorted) (X_b $$unsorted) (Pa $$unsorted)) (= (forall ((X1 $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.product_prod X_a X_b) tptp.bool Pa X1))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_b))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa (tptp.hAPP X_b _let_1 (tptp.hAPP X_a (tptp.fun X_b _let_1) (tptp.product_Pair X_a X_b) A_3) B_2))))))) (tptp.hBOOL (tptp.hAPP _let_22 tptp.bool (tptp.hAPP _let_3 _let_68 _let_67 _let_57) tptp.arrow_1111136790e_Prof)) _let_59 _let_63 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_16 _let_24 tptp.n) _let_14)) (tptp.hBOOL (tptp.hAPP _let_12 tptp.bool (tptp.hAPP _let_18 (tptp.fun _let_12 tptp.bool) (tptp.inj_on tptp.arrow_660593299e_indi tptp.nat) tptp.h) _let_13)) (forall ((X_b $$unsorted) (X_a $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted) (A_6 $$unsorted) (B_4 $$unsorted)) (let ((_let_1 (tptp.product_Pair X_a X_b))) (let ((_let_2 (tptp.product_prod X_a X_b))) (let ((_let_3 (tptp.fun X_b _let_2))) (=> (= (tptp.hAPP X_b _let_2 (tptp.hAPP X_a _let_3 _let_1 A_2) B_1) (tptp.hAPP X_b _let_2 (tptp.hAPP X_a _let_3 _let_1 A_6) B_4)) (not (=> (= (tptp.ti X_a A_2) (tptp.ti X_a A_6)) (not (= (tptp.ti X_b B_1) (tptp.ti X_b B_4)))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (Aa $$unsorted) (Ba $$unsorted) (A_5 $$unsorted) (B_3 $$unsorted)) (let ((_let_1 (tptp.product_Pair X_a X_b))) (let ((_let_2 (tptp.product_prod X_a X_b))) (let ((_let_3 (tptp.fun X_b _let_2))) (= (= (tptp.hAPP X_b _let_2 (tptp.hAPP X_a _let_3 _let_1 Aa) Ba) (tptp.hAPP X_b _let_2 (tptp.hAPP X_a _let_3 _let_1 A_5) B_3)) (and (= (tptp.ti X_a Aa) (tptp.ti X_a A_5)) (= (tptp.ti X_b Ba) (tptp.ti X_b B_3)))))))) (forall ((Fa $$unsorted)) (let ((_let_1 (tptp.fun (tptp.product_prod tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt) tptp.bool))) (= (tptp.hBOOL (tptp.hAPP (tptp.fun (tptp.fun tptp.arrow_660593299e_indi _let_1) _let_1) tptp.bool tptp.arrow_2037941124le_IIA Fa)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.arrow_660593299e_indi (tptp.fun (tptp.product_prod tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt) tptp.bool)))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) X_2) tptp.arrow_1111136790e_Prof)) (forall ((Xa $$unsorted)) (let ((_let_1 (tptp.fun tptp.arrow_660593299e_indi (tptp.fun (tptp.product_prod tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt) tptp.bool)))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) Xa) tptp.arrow_1111136790e_Prof)) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun tptp.arrow_660593299e_indi _let_2))) (let ((_let_4 (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) (tptp.hAPP tptp.arrow_490897120le_alt _let_1 (tptp.hAPP tptp.arrow_490897120le_alt (tptp.fun tptp.arrow_490897120le_alt _let_1) (tptp.product_Pair tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt) A_3) B_2)))) (=> (forall ((I_2 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) (tptp.hAPP tptp.arrow_490897120le_alt _let_1 (tptp.hAPP tptp.arrow_490897120le_alt (tptp.fun tptp.arrow_490897120le_alt _let_1) (tptp.product_Pair tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt) A_3) B_2)))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 (tptp.hAPP tptp.arrow_660593299e_indi _let_2 X_2 I_2))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 (tptp.hAPP tptp.arrow_660593299e_indi _let_2 Xa I_2)))))))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_4 (tptp.hAPP _let_3 _let_2 Fa X_2))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_4 (tptp.hAPP _let_3 _let_2 Fa Xa))))))))))))))))))))) (forall ((Fa $$unsorted)) (let ((_let_1 (tptp.fun (tptp.product_prod tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt) tptp.bool))) (= (tptp.hBOOL (tptp.hAPP (tptp.fun (tptp.fun tptp.arrow_660593299e_indi _let_1) _let_1) tptp.bool tptp.arrow_831799591nimity Fa)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.arrow_660593299e_indi (tptp.fun (tptp.product_prod tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt) tptp.bool)))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) X_2) tptp.arrow_1111136790e_Prof)) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (forall ((I_2 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) (tptp.hAPP tptp.arrow_490897120le_alt _let_1 (tptp.hAPP tptp.arrow_490897120le_alt (tptp.fun tptp.arrow_490897120le_alt _let_1) (tptp.product_Pair tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt) A_3) B_2)) (tptp.hAPP tptp.arrow_660593299e_indi _let_2 X_2 I_2)))))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) (tptp.hAPP tptp.arrow_490897120le_alt _let_1 (tptp.hAPP tptp.arrow_490897120le_alt (tptp.fun tptp.arrow_490897120le_alt _let_1) (tptp.product_Pair tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt) A_3) B_2)) (tptp.hAPP (tptp.fun tptp.arrow_660593299e_indi _let_2) _let_2 Fa X_2)))))))))))))) (forall ((X_a $$unsorted) (X_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.top_top (tptp.fun X_a tptp.bool)) X_1))) (forall ((X_a $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_1) (tptp.top_top _let_1))))) (forall ((X_a $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_1) (tptp.top_top _let_1))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (X_a $$unsorted) (F1 $$unsorted) (Aa $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.fun X_c X_a))) (let ((_let_2 (tptp.product_prod X_b X_c))) (= (tptp.hAPP _let_2 X_a (tptp.hAPP (tptp.fun X_b _let_1) (tptp.fun _let_2 X_a) (tptp.product_prod_rec X_b X_c X_a) F1) (tptp.hAPP X_c _let_2 (tptp.hAPP X_b (tptp.fun X_c _let_2) (tptp.product_Pair X_b X_c) Aa) Ba)) (tptp.hAPP X_c X_a (tptp.hAPP X_b _let_1 F1 Aa) Ba))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (tptp.top X_a) (forall ((X_1 $$unsorted)) (= (tptp.hAPP X_b X_a (tptp.top_top (tptp.fun X_b X_a)) X_1) (tptp.top_top X_a))))) (forall ((X_a $$unsorted)) (=> (tptp.top X_a) (forall ((A_2 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.top_top X_a)) A_2)))))) (forall ((X_a $$unsorted)) (=> (tptp.top X_a) (forall ((Aa $$unsorted)) (let ((_let_1 (tptp.top_top X_a))) (= (not (= (tptp.ti X_a Aa) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) Aa) _let_1))))))) (tptp.hBOOL (tptp.hAPP _let_66 tptp.bool (tptp.hAPP _let_65 (tptp.fun _let_66 tptp.bool) (tptp.member _let_65) tptp.f) (tptp.hAPP _let_64 _let_66 (tptp.hAPP _let_22 (tptp.fun _let_64 _let_66) (tptp.pi _let_3 _let_2) tptp.arrow_1111136790e_Prof) (tptp.hAPP _let_8 _let_64 (tptp.combk _let_8 _let_3) tptp.arrow_2064824852le_Lin)))) (= _let_63 (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_60 (tptp.hAPP _let_3 _let_2 tptp.f (tptp.hAPP _let_2 _let_3 (tptp.hAPP _let_36 _let_39 _let_38 (tptp.hAPP _let_2 _let_36 (tptp.hAPP _let_33 _let_37 _let_35 _let_56) tptp.lab)) tptp.lba))))) (tptp.hBOOL (tptp.hAPP _let_8 tptp.bool (tptp.hAPP _let_2 _let_62 _let_61 tptp.lab) tptp.arrow_2064824852le_Lin)) (tptp.hBOOL (tptp.hAPP _let_8 tptp.bool (tptp.hAPP _let_2 _let_62 _let_61 tptp.lba) tptp.arrow_2064824852le_Lin)) (not (= tptp.a tptp.b)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_40 tptp.lab)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_60 tptp.lba)) (not (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_40 tptp.lba))) (not (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_60 tptp.lab))) (forall ((Na $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.arrow_660593299e_indi _let_1))) (let ((_let_3 (tptp.fun tptp.arrow_660593299e_indi tptp.nat))) (let ((_let_4 (tptp.fun tptp.arrow_660593299e_indi tptp.bool))) (let ((_let_5 (tptp.fun (tptp.product_prod tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt) tptp.bool))) (let ((_let_6 (tptp.fun _let_5 _let_5))) (let ((_let_7 (tptp.fun _let_5 _let_6))) (let ((_let_8 (tptp.fun tptp.arrow_660593299e_indi _let_7))) (let ((_let_9 (tptp.fun tptp.arrow_660593299e_indi _let_6))) (let ((_let_10 (tptp.fun tptp.arrow_660593299e_indi _let_5))) (let ((_let_11 (tptp.fun _let_10 tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_11 tptp.bool (tptp.hAPP _let_10 (tptp.fun _let_11 tptp.bool) (tptp.member _let_10) (tptp.hAPP _let_5 _let_10 (tptp.hAPP _let_9 (tptp.fun _let_5 _let_10) (tptp.combc tptp.arrow_660593299e_indi _let_5 _let_5) (tptp.hAPP _let_5 _let_9 (tptp.hAPP _let_8 (tptp.fun _let_5 _let_9) (tptp.combc tptp.arrow_660593299e_indi _let_5 _let_6) (tptp.hAPP _let_4 _let_8 (tptp.hAPP (tptp.fun tptp.bool _let_7) (tptp.fun _let_4 _let_8) (tptp.combb tptp.bool _let_7 tptp.arrow_660593299e_indi) (tptp.if _let_5)) (tptp.hAPP tptp.nat _let_4 (tptp.hAPP _let_2 (tptp.fun tptp.nat _let_4) (tptp.combc tptp.arrow_660593299e_indi tptp.nat tptp.bool) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun tptp.nat _let_1) (tptp.fun _let_3 _let_2) (tptp.combb tptp.nat _let_1 tptp.arrow_660593299e_indi) (tptp.ord_less tptp.nat)) tptp.h)) Na))) tptp.lab)) tptp.lba)) tptp.arrow_1111136790e_Prof)))))))))))))) (not (forall ((Lab $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 _let_3 (tptp.member _let_1) (tptp.hAPP tptp.arrow_490897120le_alt _let_1 (tptp.hAPP tptp.arrow_490897120le_alt (tptp.fun tptp.arrow_490897120le_alt _let_1) (tptp.product_Pair tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt) tptp.a) tptp.b)) Lab)) (not (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_3 tptp.bool) (tptp.member _let_2) Lab) tptp.arrow_2064824852le_Lin))))))))) (not (forall ((Lba $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 _let_3 (tptp.member _let_1) (tptp.hAPP tptp.arrow_490897120le_alt _let_1 (tptp.hAPP tptp.arrow_490897120le_alt (tptp.fun tptp.arrow_490897120le_alt _let_1) (tptp.product_Pair tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt) tptp.b) tptp.a)) Lba)) (not (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_3 tptp.bool) (tptp.member _let_2) Lba) tptp.arrow_2064824852le_Lin))))))))) (forall ((I_2 $$unsorted)) (let ((_let_1 (tptp.product_Pair tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt))) (let ((_let_2 (tptp.product_prod tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt))) (let ((_let_3 (tptp.fun tptp.arrow_490897120le_alt _let_2))) (let ((_let_4 (tptp.member _let_2))) (let ((_let_5 (tptp.fun _let_2 tptp.bool))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (let ((_let_7 (tptp.hAPP _let_2 _let_6 _let_4 (tptp.hAPP tptp.arrow_490897120le_alt _let_2 (tptp.hAPP tptp.arrow_490897120le_alt _let_3 _let_1 tptp.b) tptp.a)))) (let ((_let_8 (tptp.hAPP tptp.arrow_660593299e_indi tptp.nat tptp.h I_2))) (let ((_let_9 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) _let_8) tptp.n)))) (let ((_let_10 (not _let_9))) (let ((_let_11 (tptp.hAPP tptp.arrow_660593299e_indi _let_5 tptp.p I_2))) (let ((_let_12 (tptp.fun tptp.arrow_490897120le_alt _let_5))) (let ((_let_13 (tptp.hAPP _let_2 _let_6 _let_4 (tptp.hAPP tptp.arrow_490897120le_alt _let_2 (tptp.hAPP tptp.arrow_490897120le_alt _let_3 _let_1 tptp.e) tptp.d)))) (let ((_let_14 (= _let_8 tptp.n))) (= (and (=> _let_9 (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool _let_13 (tptp.hAPP tptp.arrow_490897120le_alt _let_5 (tptp.hAPP _let_5 _let_12 tptp.arrow_1427655034_mktop _let_11) tptp.e)))) (=> _let_10 (and (=> _let_14 (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool _let_13 (tptp.hAPP tptp.arrow_490897120le_alt _let_5 (tptp.hAPP tptp.arrow_490897120le_alt _let_12 (tptp.hAPP _let_5 (tptp.fun tptp.arrow_490897120le_alt _let_12) tptp.arrow_14103264_above _let_11) tptp.c) tptp.e)))) (=> (not _let_14) (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool _let_13 (tptp.hAPP tptp.arrow_490897120le_alt _let_5 (tptp.hAPP _let_5 _let_12 tptp.arrow_1278947948_mkbot _let_11) tptp.e))))))) (and (=> _let_9 (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool _let_7 tptp.lab))) (=> _let_10 (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool _let_7 tptp.lba)))))))))))))))))))) (forall ((M $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.arrow_660593299e_indi _let_1))) (let ((_let_3 (tptp.fun tptp.arrow_660593299e_indi tptp.nat))) (let ((_let_4 (tptp.fun tptp.arrow_660593299e_indi tptp.bool))) (let ((_let_5 (tptp.product_prod tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (let ((_let_7 (tptp.fun _let_6 _let_6))) (let ((_let_8 (tptp.fun _let_6 _let_7))) (let ((_let_9 (tptp.fun tptp.arrow_660593299e_indi _let_8))) (let ((_let_10 (tptp.fun tptp.arrow_660593299e_indi _let_7))) (let ((_let_11 (tptp.fun tptp.arrow_660593299e_indi _let_6))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) M) tptp.n)) (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP _let_5 (tptp.fun _let_6 tptp.bool) (tptp.member _let_5) (tptp.hAPP tptp.arrow_490897120le_alt _let_5 (tptp.hAPP tptp.arrow_490897120le_alt (tptp.fun tptp.arrow_490897120le_alt _let_5) (tptp.product_Pair tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt) tptp.b) tptp.a)) (tptp.hAPP _let_11 _let_6 tptp.f (tptp.hAPP _let_6 _let_11 (tptp.hAPP _let_10 (tptp.fun _let_6 _let_11) (tptp.combc tptp.arrow_660593299e_indi _let_6 _let_6) (tptp.hAPP _let_6 _let_10 (tptp.hAPP _let_9 (tptp.fun _let_6 _let_10) (tptp.combc tptp.arrow_660593299e_indi _let_6 _let_7) (tptp.hAPP _let_4 _let_9 (tptp.hAPP (tptp.fun tptp.bool _let_8) (tptp.fun _let_4 _let_9) (tptp.combb tptp.bool _let_8 tptp.arrow_660593299e_indi) (tptp.if _let_6)) (tptp.hAPP tptp.nat _let_4 (tptp.hAPP _let_2 (tptp.fun tptp.nat _let_4) (tptp.combc tptp.arrow_660593299e_indi tptp.nat tptp.bool) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun tptp.nat _let_1) (tptp.fun _let_3 _let_2) (tptp.combb tptp.nat _let_1 tptp.arrow_660593299e_indi) (tptp.ord_less tptp.nat)) tptp.h)) M))) tptp.lab)) tptp.lba))))))))))))))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted) (L_3 $$unsorted)) (let ((_let_1 (tptp.product_Pair tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt))) (let ((_let_2 (tptp.product_prod tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt))) (let ((_let_3 (tptp.fun tptp.arrow_490897120le_alt _let_2))) (let ((_let_4 (tptp.member _let_2))) (let ((_let_5 (tptp.fun _let_2 tptp.bool))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP _let_5 (tptp.fun _let_6 tptp.bool) (tptp.member _let_5) L_3) tptp.arrow_2064824852le_Lin)) (=> (not (= (tptp.ti tptp.arrow_490897120le_alt X_1) (tptp.ti tptp.arrow_490897120le_alt Y_2))) (= (not (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP _let_2 _let_6 _let_4 (tptp.hAPP tptp.arrow_490897120le_alt _let_2 (tptp.hAPP tptp.arrow_490897120le_alt _let_3 _let_1 X_1) Y_2)) L_3))) (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP _let_2 _let_6 _let_4 (tptp.hAPP tptp.arrow_490897120le_alt _let_2 (tptp.hAPP tptp.arrow_490897120le_alt _let_3 _let_1 Y_2) X_1)) L_3)))))))))))) (forall ((Aa $$unsorted) (Ba $$unsorted) (L_3 $$unsorted)) (let ((_let_1 (tptp.product_Pair tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt))) (let ((_let_2 (tptp.product_prod tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt))) (let ((_let_3 (tptp.fun tptp.arrow_490897120le_alt _let_2))) (let ((_let_4 (tptp.member _let_2))) (let ((_let_5 (tptp.fun _let_2 tptp.bool))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP _let_5 (tptp.fun _let_6 tptp.bool) (tptp.member _let_5) L_3) tptp.arrow_2064824852le_Lin)) (=> (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP _let_2 _let_6 _let_4 (tptp.hAPP tptp.arrow_490897120le_alt _let_2 (tptp.hAPP tptp.arrow_490897120le_alt _let_3 _let_1 Aa) Ba)) L_3)) (not (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP _let_2 _let_6 _let_4 (tptp.hAPP tptp.arrow_490897120le_alt _let_2 (tptp.hAPP tptp.arrow_490897120le_alt _let_3 _let_1 Ba) Aa)) L_3)))))))))))) (forall ((X_1 $$unsorted) (L_3 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.product_prod tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt) tptp.bool))) (let ((_let_2 (tptp.member _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_1 _let_4 _let_2 L_3) tptp.arrow_2064824852le_Lin)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_1 _let_4 _let_2 (tptp.hAPP tptp.arrow_490897120le_alt _let_1 (tptp.hAPP _let_1 (tptp.fun tptp.arrow_490897120le_alt _let_1) tptp.arrow_1427655034_mktop L_3) X_1)) tptp.arrow_2064824852le_Lin)))))))) (forall ((X_1 $$unsorted) (L_3 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.product_prod tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt) tptp.bool))) (let ((_let_2 (tptp.member _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_1 _let_4 _let_2 L_3) tptp.arrow_2064824852le_Lin)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_1 _let_4 _let_2 (tptp.hAPP tptp.arrow_490897120le_alt _let_1 (tptp.hAPP _let_1 (tptp.fun tptp.arrow_490897120le_alt _let_1) tptp.arrow_1278947948_mkbot L_3) X_1)) tptp.arrow_2064824852le_Lin)))))))) (forall ((L_3 $$unsorted) (X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.product_prod tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt) tptp.bool))) (let ((_let_2 (tptp.fun tptp.arrow_490897120le_alt _let_1))) (let ((_let_3 (tptp.member _let_1))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (not (= (tptp.ti tptp.arrow_490897120le_alt X_1) (tptp.ti tptp.arrow_490897120le_alt Y_2))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP _let_1 _let_5 _let_3 L_3) tptp.arrow_2064824852le_Lin)) (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP _let_1 _let_5 _let_3 (tptp.hAPP tptp.arrow_490897120le_alt _let_1 (tptp.hAPP tptp.arrow_490897120le_alt _let_2 (tptp.hAPP _let_1 (tptp.fun tptp.arrow_490897120le_alt _let_2) tptp.arrow_14103264_above L_3) X_1) Y_2)) tptp.arrow_2064824852le_Lin)))))))))) (forall ((L_3 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.product_prod tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt) tptp.bool))) (let ((_let_2 (tptp.fun tptp.arrow_660593299e_indi _let_1))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_4 tptp.bool) (tptp.member _let_1) L_3) tptp.arrow_2064824852le_Lin)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_3 tptp.bool) (tptp.member _let_2) (tptp.hAPP _let_1 _let_2 (tptp.combk _let_1 tptp.arrow_660593299e_indi) L_3)) tptp.arrow_1111136790e_Prof)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X) Y))) (=> (not (= (tptp.ti X_a X) (tptp.ti X_a Y))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X))))))))) (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X) Y)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((Z_1 $$unsorted) (Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 Z_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 X)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((Z_1 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 X))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 Y)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) Z_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 Z_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((C $$unsorted) (B_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B_1) A_2)) (=> (= (tptp.ti X_a B_1) (tptp.ti X_a C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 C) A_2))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ord X_a) (forall ((C $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) A_2))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B_1)) (=> (= B_1 C) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 C)))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((C $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) C))) (=> (= (tptp.ti X_a A_2) (tptp.ti X_a B_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_2)))))))) (forall ((X_a $$unsorted)) (=> (tptp.ord X_a) (forall ((C $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (= A_2 B_1) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B_1) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_2) C))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((B_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B_1) A_2)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_2) B_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_2) B_1)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B_1) A_2))))))))) (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((Pa $$unsorted) (X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X_1) Y_2)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y_2) X_1)) (tptp.hBOOL Pa)))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) X) Y)) (not (= (tptp.ti X_a Y) (tptp.ti X_a X))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) X) Y)) (not (= (tptp.ti X_a X) (tptp.ti X_a Y))))))) (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X) Y)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X))))))))) (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X) Y)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) X) Y)) (not (= (tptp.ti X_a X) (tptp.ti X_a Y))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (not (= (tptp.ti X_a X) (tptp.ti X_a Y))) (=> (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X) Y))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((Y_2 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y_2) X_1))) (= (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X_1) Y_2))) (= (tptp.ti X_a X_1) (tptp.ti X_a Y_2))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (or (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X) Y)) (= (tptp.ti X_a X) (tptp.ti X_a Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (= (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X_1) Y_2))) (or (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y_2) X_1)) (= (tptp.ti X_a X_1) (tptp.ti X_a Y_2))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (= (not (= (tptp.ti X_a X_1) (tptp.ti X_a Y_2))) (or (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X_1) Y_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y_2) X_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((X $$unsorted)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) X) X)))))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (= (tptp.top_top _let_1) (tptp.hAPP _let_1 _let_1 (tptp.collect X_a) (tptp.hAPP tptp.bool _let_1 (tptp.combk tptp.bool X_a) tptp.fTrue))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (F $$unsorted) (G $$unsorted)) (let ((_let_1 (tptp.fun X_a X_b))) (=> (forall ((X_2 $$unsorted)) (= (tptp.hAPP X_a X_b F X_2) (tptp.hAPP X_a X_b G X_2))) (= (tptp.ti _let_1 F) (tptp.ti _let_1 G))))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_1) A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool A_1 X_1))))) (forall ((X_a $$unsorted) (Pa $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (= (tptp.hAPP _let_1 _let_1 (tptp.collect X_a) Pa) (tptp.ti _let_1 Pa)))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted) (L_3 $$unsorted) (Aa $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.product_Pair tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt))) (let ((_let_2 (tptp.product_prod tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt))) (let ((_let_3 (tptp.fun tptp.arrow_490897120le_alt _let_2))) (let ((_let_4 (tptp.hAPP tptp.arrow_490897120le_alt _let_3 _let_1 X_1))) (let ((_let_5 (tptp.member _let_2))) (let ((_let_6 (tptp.fun _let_2 tptp.bool))) (let ((_let_7 (tptp.fun _let_6 tptp.bool))) (let ((_let_8 (tptp.hAPP _let_2 _let_7 _let_5 (tptp.hAPP tptp.arrow_490897120le_alt _let_2 _let_4 Y_2)))) (let ((_let_9 (tptp.ti tptp.arrow_490897120le_alt Ba))) (let ((_let_10 (tptp.ti tptp.arrow_490897120le_alt Y_2))) (let ((_let_11 (= _let_10 _let_9))) (let ((_let_12 (tptp.ti tptp.arrow_490897120le_alt Aa))) (let ((_let_13 (tptp.ti tptp.arrow_490897120le_alt X_1))) (let ((_let_14 (= _let_13 _let_9))) (let ((_let_15 (tptp.fun tptp.arrow_490897120le_alt _let_6))) (=> (not (= _let_12 _let_9)) (=> (tptp.hBOOL (tptp.hAPP _let_7 tptp.bool (tptp.hAPP _let_6 (tptp.fun _let_7 tptp.bool) (tptp.member _let_6) L_3) tptp.arrow_2064824852le_Lin)) (= (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool _let_8 (tptp.hAPP tptp.arrow_490897120le_alt _let_6 (tptp.hAPP tptp.arrow_490897120le_alt _let_15 (tptp.hAPP _let_6 (tptp.fun tptp.arrow_490897120le_alt _let_15) tptp.arrow_14103264_above L_3) Aa) Ba))) (and (not (= _let_13 _let_10)) (=> _let_14 (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP _let_2 _let_7 _let_5 (tptp.hAPP tptp.arrow_490897120le_alt _let_2 (tptp.hAPP tptp.arrow_490897120le_alt _let_3 _let_1 Aa) Y_2)) L_3))) (=> (not _let_14) (and (=> _let_11 (or (= _let_13 _let_12) (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP _let_2 _let_7 _let_5 (tptp.hAPP tptp.arrow_490897120le_alt _let_2 _let_4 Aa)) L_3)))) (=> (not _let_11) (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool _let_8 L_3))))))))))))))))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (S_1 $$unsorted) (R_1 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.product_prod X_a X_b) tptp.bool))) (= (forall ((X_2 $$unsorted) (Xa $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) (tptp.hAPP X_b _let_1 (tptp.hAPP X_a (tptp.fun X_b _let_1) (tptp.product_Pair X_a X_b) X_2) Xa)))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 R_1)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 S_1))))))) (= (tptp.ti _let_1 R_1) (tptp.ti _let_1 S_1))))) _let_41 (= _let_59 _let_41) (forall ((I_2 $$unsorted)) (let ((_let_1 (tptp.product_Pair tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt))) (let ((_let_2 (tptp.product_prod tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt))) (let ((_let_3 (tptp.fun tptp.arrow_490897120le_alt _let_2))) (let ((_let_4 (tptp.member _let_2))) (let ((_let_5 (tptp.fun _let_2 tptp.bool))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (let ((_let_7 (tptp.hAPP _let_2 _let_6 _let_4 (tptp.hAPP tptp.arrow_490897120le_alt _let_2 (tptp.hAPP tptp.arrow_490897120le_alt _let_3 _let_1 tptp.a) tptp.b)))) (let ((_let_8 (tptp.hAPP tptp.arrow_660593299e_indi tptp.nat tptp.h I_2))) (let ((_let_9 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) _let_8))) (let ((_let_10 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_9 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) tptp.n) (tptp.one_one tptp.nat)))))) (let ((_let_11 (tptp.hAPP tptp.arrow_660593299e_indi _let_5 tptp.p I_2))) (let ((_let_12 (tptp.fun tptp.arrow_490897120le_alt _let_5))) (let ((_let_13 (tptp.hAPP _let_2 _let_6 _let_4 (tptp.hAPP tptp.arrow_490897120le_alt _let_2 (tptp.hAPP tptp.arrow_490897120le_alt _let_3 _let_1 tptp.c) tptp.e)))) (let ((_let_14 (= _let_8 tptp.n))) (let ((_let_15 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_9 tptp.n)))) (= (and (=> _let_15 (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool _let_13 (tptp.hAPP tptp.arrow_490897120le_alt _let_5 (tptp.hAPP _let_5 _let_12 tptp.arrow_1427655034_mktop _let_11) tptp.e)))) (=> (not _let_15) (and (=> _let_14 (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool _let_13 (tptp.hAPP tptp.arrow_490897120le_alt _let_5 (tptp.hAPP tptp.arrow_490897120le_alt _let_12 (tptp.hAPP _let_5 (tptp.fun tptp.arrow_490897120le_alt _let_12) tptp.arrow_14103264_above _let_11) tptp.c) tptp.e)))) (=> (not _let_14) (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool _let_13 (tptp.hAPP tptp.arrow_490897120le_alt _let_5 (tptp.hAPP _let_5 _let_12 tptp.arrow_1278947948_mkbot _let_11) tptp.e))))))) (and (=> _let_10 (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool _let_7 tptp.lab))) (=> (not _let_10) (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool _let_7 tptp.lba))))))))))))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_1 $$unsorted) (Y_2 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.top_top _let_1))) (let ((_let_3 (tptp.fun X_b X_a))) (let ((_let_4 (tptp.fun X_a X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_4 (tptp.fun _let_1 tptp.bool) (tptp.inj_on X_a X_b) F) _let_2)) (=> (= (tptp.hAPP X_a X_b F X_1) (tptp.ti X_b Y_2)) (= (tptp.hAPP X_b X_a (tptp.hAPP _let_4 _let_3 (tptp.hAPP _let_1 (tptp.fun _let_4 _let_3) (tptp.hilbert_inv_into X_a X_b) _let_2) F) Y_2) (tptp.ti X_a X_1))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_1 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.top_top _let_1))) (let ((_let_3 (tptp.fun X_b X_a))) (let ((_let_4 (tptp.fun X_a X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_4 (tptp.fun _let_1 tptp.bool) (tptp.inj_on X_a X_b) F) _let_2)) (= (tptp.hAPP X_b X_a (tptp.hAPP _let_4 _let_3 (tptp.hAPP _let_1 (tptp.fun _let_4 _let_3) (tptp.hilbert_inv_into X_a X_b) _let_2) F) (tptp.hAPP X_a X_b F X_1)) (tptp.ti X_a X_1)))))))) (forall ((I_1 $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.fun (tptp.product_prod tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt) tptp.bool))) (let ((_let_2 (tptp.fun tptp.arrow_660593299e_indi _let_1))) (let ((_let_3 (tptp.fun _let_2 _let_1))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (let ((_let_6 (tptp.fun _let_3 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP _let_3 (tptp.fun _let_6 tptp.bool) (tptp.member _let_3) Fa) (tptp.hAPP _let_5 _let_6 (tptp.hAPP (tptp.fun _let_2 tptp.bool) (tptp.fun _let_5 _let_6) (tptp.pi _let_2 _let_1) tptp.arrow_1111136790e_Prof) (tptp.hAPP _let_4 _let_5 (tptp.combk _let_4 _let_2) tptp.arrow_2064824852le_Lin)))) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.arrow_660593299e_indi (tptp.fun (tptp.product_prod tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt) tptp.bool)))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) X_2) tptp.arrow_1111136790e_Prof)) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) (tptp.hAPP tptp.arrow_490897120le_alt _let_1 (tptp.hAPP tptp.arrow_490897120le_alt (tptp.fun tptp.arrow_490897120le_alt _let_1) (tptp.product_Pair tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt) A_3) B_2)))) (=> (not (= (tptp.ti tptp.arrow_490897120le_alt A_3) (tptp.ti tptp.arrow_490897120le_alt B_2))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 (tptp.hAPP tptp.arrow_660593299e_indi _let_2 X_2 I_1))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 (tptp.hAPP (tptp.fun tptp.arrow_660593299e_indi _let_2) _let_2 Fa X_2))))))))))))) (tptp.hBOOL (tptp.hAPP tptp.arrow_660593299e_indi tptp.bool (tptp.hAPP _let_3 (tptp.fun tptp.arrow_660593299e_indi tptp.bool) tptp.arrow_218898985ctator Fa) I_1))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_1 $$unsorted) (F $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun X_a X_b))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.fun X_a _let_2))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP _let_3 (tptp.fun _let_4 tptp.bool) (tptp.member _let_3) F) (tptp.hAPP _let_5 _let_4 (tptp.hAPP _let_1 (tptp.fun _let_5 _let_4) (tptp.pi X_a X_b) A_1) B))) (=> (not (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_b (tptp.fun _let_2 tptp.bool) (tptp.member X_b) (tptp.hAPP X_a X_b F X_1)) (tptp.hAPP X_a _let_2 B X_1)))) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_1) A_1))))))))))) (forall ((Aa $$unsorted) (Ba $$unsorted)) (=> (not (= (tptp.ti tptp.arrow_490897120le_alt Aa) (tptp.ti tptp.arrow_490897120le_alt Ba))) (exists ((X_2 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (and (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_3 tptp.bool) (tptp.member _let_2) X_2) tptp.arrow_2064824852le_Lin)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 _let_3 (tptp.member _let_1) (tptp.hAPP tptp.arrow_490897120le_alt _let_1 (tptp.hAPP tptp.arrow_490897120le_alt (tptp.fun tptp.arrow_490897120le_alt _let_1) (tptp.product_Pair tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt) Aa) Ba)) X_2))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.fun X_a X_b) tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun X_a _let_2))) (= (tptp.hAPP _let_3 _let_1 (tptp.hAPP (tptp.fun X_a tptp.bool) (tptp.fun _let_3 _let_1) (tptp.pi X_a X_b) A_1) (tptp.hAPP _let_2 _let_3 (tptp.combk _let_2 X_a) (tptp.top_top _let_2))) (tptp.top_top _let_1)))))) (forall ((X_c $$unsorted) (X_a $$unsorted) (X_b $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.top_top _let_1))) (let ((_let_3 (tptp.fun X_c X_b))) (let ((_let_4 (tptp.fun X_a _let_3))) (let ((_let_5 (tptp.fun X_a X_b))) (let ((_let_6 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_5 _let_6 (tptp.inj_on X_a X_b) F) _let_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_4 _let_6 (tptp.inj_on X_a _let_3) (tptp.hAPP _let_5 _let_4 (tptp.hAPP (tptp.fun X_b _let_3) (tptp.fun _let_5 _let_4) (tptp.combb X_b _let_3 X_a) (tptp.combk X_b X_c)) F)) _let_2)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((X $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X) X))))) (exists ((N $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.fun tptp.arrow_660593299e_indi _let_2))) (let ((_let_4 (tptp.fun tptp.arrow_660593299e_indi tptp.nat))) (let ((_let_5 (tptp.fun tptp.arrow_660593299e_indi tptp.bool))) (let ((_let_6 (tptp.product_prod tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt))) (let ((_let_7 (tptp.fun _let_6 tptp.bool))) (let ((_let_8 (tptp.fun _let_7 _let_7))) (let ((_let_9 (tptp.fun _let_7 _let_8))) (let ((_let_10 (tptp.fun tptp.arrow_660593299e_indi _let_9))) (let ((_let_11 (tptp.fun tptp.arrow_660593299e_indi _let_8))) (let ((_let_12 (tptp.fun tptp.arrow_660593299e_indi _let_7))) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 N) (tptp.hAPP _let_5 tptp.nat (tptp.finite_card tptp.arrow_660593299e_indi) (tptp.top_top _let_5)))) (forall ((M $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.arrow_660593299e_indi _let_1))) (let ((_let_3 (tptp.fun tptp.arrow_660593299e_indi tptp.nat))) (let ((_let_4 (tptp.fun tptp.arrow_660593299e_indi tptp.bool))) (let ((_let_5 (tptp.product_prod tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (let ((_let_7 (tptp.fun _let_6 _let_6))) (let ((_let_8 (tptp.fun _let_6 _let_7))) (let ((_let_9 (tptp.fun tptp.arrow_660593299e_indi _let_8))) (let ((_let_10 (tptp.fun tptp.arrow_660593299e_indi _let_7))) (let ((_let_11 (tptp.fun tptp.arrow_660593299e_indi _let_6))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) M) N)) (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP _let_5 (tptp.fun _let_6 tptp.bool) (tptp.member _let_5) (tptp.hAPP tptp.arrow_490897120le_alt _let_5 (tptp.hAPP tptp.arrow_490897120le_alt (tptp.fun tptp.arrow_490897120le_alt _let_5) (tptp.product_Pair tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt) tptp.b) tptp.a)) (tptp.hAPP _let_11 _let_6 tptp.f (tptp.hAPP _let_6 _let_11 (tptp.hAPP _let_10 (tptp.fun _let_6 _let_11) (tptp.combc tptp.arrow_660593299e_indi _let_6 _let_6) (tptp.hAPP _let_6 _let_10 (tptp.hAPP _let_9 (tptp.fun _let_6 _let_10) (tptp.combc tptp.arrow_660593299e_indi _let_6 _let_7) (tptp.hAPP _let_4 _let_9 (tptp.hAPP (tptp.fun tptp.bool _let_8) (tptp.fun _let_4 _let_9) (tptp.combb tptp.bool _let_8 tptp.arrow_660593299e_indi) (tptp.if _let_6)) (tptp.hAPP tptp.nat _let_4 (tptp.hAPP _let_2 (tptp.fun tptp.nat _let_4) (tptp.combc tptp.arrow_660593299e_indi tptp.nat tptp.bool) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun tptp.nat _let_1) (tptp.fun _let_3 _let_2) (tptp.combb tptp.nat _let_1 tptp.arrow_660593299e_indi) (tptp.ord_less tptp.nat)) tptp.h)) M))) tptp.lab)) tptp.lba))))))))))))))))) (tptp.hBOOL (tptp.hAPP _let_7 tptp.bool (tptp.hAPP _let_6 (tptp.fun _let_7 tptp.bool) (tptp.member _let_6) (tptp.hAPP tptp.arrow_490897120le_alt _let_6 (tptp.hAPP tptp.arrow_490897120le_alt (tptp.fun tptp.arrow_490897120le_alt _let_6) (tptp.product_Pair tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt) tptp.a) tptp.b)) (tptp.hAPP _let_12 _let_7 tptp.f (tptp.hAPP _let_7 _let_12 (tptp.hAPP _let_11 (tptp.fun _let_7 _let_12) (tptp.combc tptp.arrow_660593299e_indi _let_7 _let_7) (tptp.hAPP _let_7 _let_11 (tptp.hAPP _let_10 (tptp.fun _let_7 _let_11) (tptp.combc tptp.arrow_660593299e_indi _let_7 _let_8) (tptp.hAPP _let_5 _let_10 (tptp.hAPP (tptp.fun tptp.bool _let_9) (tptp.fun _let_5 _let_10) (tptp.combb tptp.bool _let_9 tptp.arrow_660593299e_indi) (tptp.if _let_7)) (tptp.hAPP tptp.nat _let_5 (tptp.hAPP _let_3 (tptp.fun tptp.nat _let_5) (tptp.combc tptp.arrow_660593299e_indi tptp.nat tptp.bool) (tptp.hAPP _let_4 _let_3 (tptp.hAPP (tptp.fun tptp.nat _let_2) (tptp.fun _let_4 _let_3) (tptp.combb tptp.nat _let_2 tptp.arrow_660593299e_indi) _let_1) tptp.h)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) N) (tptp.one_one tptp.nat))))) tptp.lab)) tptp.lba)))))))))))))))))) (not (forall ((N $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.fun tptp.arrow_660593299e_indi _let_2))) (let ((_let_4 (tptp.fun tptp.arrow_660593299e_indi tptp.nat))) (let ((_let_5 (tptp.fun tptp.arrow_660593299e_indi tptp.bool))) (let ((_let_6 (tptp.product_prod tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt))) (let ((_let_7 (tptp.fun _let_6 tptp.bool))) (let ((_let_8 (tptp.fun _let_7 _let_7))) (let ((_let_9 (tptp.fun _let_7 _let_8))) (let ((_let_10 (tptp.fun tptp.arrow_660593299e_indi _let_9))) (let ((_let_11 (tptp.fun tptp.arrow_660593299e_indi _let_8))) (let ((_let_12 (tptp.fun tptp.arrow_660593299e_indi _let_7))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 N) (tptp.hAPP _let_5 tptp.nat (tptp.finite_card tptp.arrow_660593299e_indi) (tptp.top_top _let_5)))) (=> (forall ((M $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.arrow_660593299e_indi _let_1))) (let ((_let_3 (tptp.fun tptp.arrow_660593299e_indi tptp.nat))) (let ((_let_4 (tptp.fun tptp.arrow_660593299e_indi tptp.bool))) (let ((_let_5 (tptp.product_prod tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (let ((_let_7 (tptp.fun _let_6 _let_6))) (let ((_let_8 (tptp.fun _let_6 _let_7))) (let ((_let_9 (tptp.fun tptp.arrow_660593299e_indi _let_8))) (let ((_let_10 (tptp.fun tptp.arrow_660593299e_indi _let_7))) (let ((_let_11 (tptp.fun tptp.arrow_660593299e_indi _let_6))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) M) N)) (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP _let_5 (tptp.fun _let_6 tptp.bool) (tptp.member _let_5) (tptp.hAPP tptp.arrow_490897120le_alt _let_5 (tptp.hAPP tptp.arrow_490897120le_alt (tptp.fun tptp.arrow_490897120le_alt _let_5) (tptp.product_Pair tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt) tptp.b) tptp.a)) (tptp.hAPP _let_11 _let_6 tptp.f (tptp.hAPP _let_6 _let_11 (tptp.hAPP _let_10 (tptp.fun _let_6 _let_11) (tptp.combc tptp.arrow_660593299e_indi _let_6 _let_6) (tptp.hAPP _let_6 _let_10 (tptp.hAPP _let_9 (tptp.fun _let_6 _let_10) (tptp.combc tptp.arrow_660593299e_indi _let_6 _let_7) (tptp.hAPP _let_4 _let_9 (tptp.hAPP (tptp.fun tptp.bool _let_8) (tptp.fun _let_4 _let_9) (tptp.combb tptp.bool _let_8 tptp.arrow_660593299e_indi) (tptp.if _let_6)) (tptp.hAPP tptp.nat _let_4 (tptp.hAPP _let_2 (tptp.fun tptp.nat _let_4) (tptp.combc tptp.arrow_660593299e_indi tptp.nat tptp.bool) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun tptp.nat _let_1) (tptp.fun _let_3 _let_2) (tptp.combb tptp.nat _let_1 tptp.arrow_660593299e_indi) (tptp.ord_less tptp.nat)) tptp.h)) M))) tptp.lab)) tptp.lba))))))))))))))))) (not (tptp.hBOOL (tptp.hAPP _let_7 tptp.bool (tptp.hAPP _let_6 (tptp.fun _let_7 tptp.bool) (tptp.member _let_6) (tptp.hAPP tptp.arrow_490897120le_alt _let_6 (tptp.hAPP tptp.arrow_490897120le_alt (tptp.fun tptp.arrow_490897120le_alt _let_6) (tptp.product_Pair tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt) tptp.a) tptp.b)) (tptp.hAPP _let_12 _let_7 tptp.f (tptp.hAPP _let_7 _let_12 (tptp.hAPP _let_11 (tptp.fun _let_7 _let_12) (tptp.combc tptp.arrow_660593299e_indi _let_7 _let_7) (tptp.hAPP _let_7 _let_11 (tptp.hAPP _let_10 (tptp.fun _let_7 _let_11) (tptp.combc tptp.arrow_660593299e_indi _let_7 _let_8) (tptp.hAPP _let_5 _let_10 (tptp.hAPP (tptp.fun tptp.bool _let_9) (tptp.fun _let_5 _let_10) (tptp.combb tptp.bool _let_9 tptp.arrow_660593299e_indi) (tptp.if _let_7)) (tptp.hAPP tptp.nat _let_5 (tptp.hAPP _let_3 (tptp.fun tptp.nat _let_5) (tptp.combc tptp.arrow_660593299e_indi tptp.nat tptp.bool) (tptp.hAPP _let_4 _let_3 (tptp.hAPP (tptp.fun tptp.nat _let_2) (tptp.fun _let_4 _let_3) (tptp.combb tptp.nat _let_2 tptp.arrow_660593299e_indi) _let_1) tptp.h)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) N) (tptp.one_one tptp.nat))))) tptp.lab)) tptp.lba))))))))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X) Y))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X)))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.ord X_b) (forall ((X_1 $$unsorted) (F $$unsorted) (G $$unsorted)) (let ((_let_1 (tptp.fun X_a X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) F) G)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) (tptp.hAPP X_a X_b F X_1)) (tptp.hAPP X_a X_b G X_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((Z_1 $$unsorted) (Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 Z_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 X)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X) Y)) (= (tptp.ti X_a X) (tptp.ti X_a Y))))))))) (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((Z_1 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 X))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 Y)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) Z_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 Z_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X) Y)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X)) (= (tptp.ti X_a X) (tptp.ti X_a Y))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((C $$unsorted) (B_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B_1) A_2)) (=> (= (tptp.ti X_a B_1) (tptp.ti X_a C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 C) A_2))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ord X_a) (forall ((C $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) A_2))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B_1)) (=> (= B_1 C) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 C)))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((C $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) C))) (=> (= (tptp.ti X_a A_2) (tptp.ti X_a B_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_2)))))))) (forall ((X_a $$unsorted)) (=> (tptp.ord X_a) (forall ((C $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (= A_2 B_1) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B_1) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_2) C))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((Y_2 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y_2) X_1)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X_1) Y_2)) (= (tptp.ti X_a X_1) (tptp.ti X_a Y_2))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.ord X_b) (forall ((X_1 $$unsorted) (F $$unsorted) (G $$unsorted)) (let ((_let_1 (tptp.fun X_a X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) F) G)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) (tptp.hAPP X_a X_b F X_1)) (tptp.hAPP X_a X_b G X_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (=> (= X Y) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X) Y)))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (= (= (tptp.ti X_a X_1) (tptp.ti X_a Y_2)) (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X_1) Y_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y_2) X_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (or (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X) Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X)))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.ord X_b) (forall ((F $$unsorted) (G $$unsorted)) (let ((_let_1 (tptp.fun X_a X_b))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) F) G)) (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) (tptp.hAPP X_a X_b F X_2)) (tptp.hAPP X_a X_b G X_2))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (= (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) X_1) Y_2))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) Y_2) X_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (= (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) X_1) Y_2))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) Y_2) X_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (or (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) X) Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) Y) X))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) X_1) Y_2)) (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) X_1) Y_2)) (not (= (tptp.ti X_a X_1) (tptp.ti X_a Y_2))))))))) (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less X_a) X_1) Y_2)) (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X_1) Y_2)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y_2) X_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) X_1) Y_2)) (or (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) X_1) Y_2)) (= (tptp.ti X_a X_1) (tptp.ti X_a Y_2)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) X) Y))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) Y) X))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) Y) X))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) X) Y))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) X_1) Y_2))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) X_1) Y_2)) (= (tptp.ti X_a X_1) (tptp.ti X_a Y_2)))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (not (= (tptp.ti X_a A_2) (tptp.ti X_a B_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) A_2) B_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) A_2) B_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (not (= (tptp.ti X_a A_2) (tptp.ti X_a B_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) B_1) A_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) B_1) A_2)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) Y) X)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) X) Y)))))))) (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) X) Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) X) Y))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) X_1) Y_2)) (= (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) X_1) Y_2))) (= (tptp.ti X_a X_1) (tptp.ti X_a Y_2)))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) X) Y)) (or (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) X) Y)) (= (tptp.ti X_a X) (tptp.ti X_a Y)))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) A_2) B_1)) (=> (not (= (tptp.ti X_a A_2) (tptp.ti X_a B_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) A_2) B_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((B_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) B_1) A_2)) (=> (not (= (tptp.ti X_a A_2) (tptp.ti X_a B_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) B_1) A_2)))))))) (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((Z_1 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) X))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_2 Y)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) Y) Z_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_2 Z_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((Z_1 $$unsorted) (Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) Z_1) Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Z_1) X))))))))) (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((Z_1 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) X) Y)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) Z_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X) Z_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((Z_1 $$unsorted) (Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) Z_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) Y) X)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_2 Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_2 X))))))))) (forall ((X_a $$unsorted)) (=> (tptp.top X_a) (forall ((A_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) A_2) (tptp.top_top X_a)))))) (forall ((X_a $$unsorted)) (=> (tptp.top X_a) (forall ((Aa $$unsorted)) (let ((_let_1 (tptp.top_top X_a))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) _let_1) Aa)) (= (tptp.ti X_a Aa) _let_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.top X_a) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.top_top X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) _let_1) A_2)) (= (tptp.ti X_a A_2) _let_1)))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun _let_1 tptp.bool) (tptp.inj_on X_a X_b) F) A_1)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) A_1)) (forall ((Xa $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) Xa) A_1)) (=> (= (tptp.hAPP X_a X_b F X_2) (tptp.hAPP X_a X_b F Xa)) (= (tptp.ti X_a X_2) (tptp.ti X_a Xa)))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_1 $$unsorted) (Y_2 $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.member X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP (tptp.fun X_a X_b) _let_3 (tptp.inj_on X_a X_b) F) A_1)) (=> (not (= (tptp.ti X_a X_1) (tptp.ti X_a Y_2))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a _let_3 _let_1 X_1) A_1)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a _let_3 _let_1 Y_2) A_1)) (not (= (tptp.hAPP X_a X_b F X_1) (tptp.hAPP X_a X_b F Y_2))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (Y_2 $$unsorted) (X_1 $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.member X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP (tptp.fun X_a X_b) _let_3 (tptp.inj_on X_a X_b) F) A_1)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a _let_3 _let_1 X_1) A_1)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a _let_3 _let_1 Y_2) A_1)) (= (= (tptp.hAPP X_a X_b F X_1) (tptp.hAPP X_a X_b F Y_2)) (= (tptp.ti X_a X_1) (tptp.ti X_a Y_2)))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_1 $$unsorted) (Y_2 $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.member X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP (tptp.fun X_a X_b) _let_3 (tptp.inj_on X_a X_b) F) A_1)) (=> (= (tptp.hAPP X_a X_b F X_1) (tptp.hAPP X_a X_b F Y_2)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a _let_3 _let_1 X_1) A_1)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a _let_3 _let_1 Y_2) A_1)) (= (tptp.ti X_a X_1) (tptp.ti X_a Y_2)))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_1 $$unsorted) (F $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.fun X_a X_b))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.fun X_a _let_1))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP _let_3 (tptp.fun _let_4 tptp.bool) (tptp.member _let_3) F) (tptp.hAPP _let_5 _let_4 (tptp.hAPP _let_2 (tptp.fun _let_5 _let_4) (tptp.pi X_a X_b) A_1) B))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a (tptp.fun _let_2 tptp.bool) (tptp.member X_a) X_1) A_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) (tptp.hAPP X_a X_b F X_1)) (tptp.hAPP X_a _let_1 B X_1))))))))))) (= tptp.arrow_1111136790e_Prof (tptp.hAPP _let_21 _let_22 (tptp.hAPP _let_12 (tptp.fun _let_21 _let_22) (tptp.pi tptp.arrow_660593299e_indi _let_2) _let_13) (tptp.hAPP _let_8 _let_21 (tptp.combk _let_8 tptp.arrow_660593299e_indi) tptp.arrow_2064824852le_Lin))) (forall ((X_a $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP (tptp.fun X_a X_a) (tptp.fun _let_1 tptp.bool) (tptp.inj_on X_a X_a) (tptp.combi X_a)) A_1)))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_1 $$unsorted) (F $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.fun X_a _let_1))) (let ((_let_4 (tptp.fun X_a X_b))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP _let_4 (tptp.fun _let_5 tptp.bool) (tptp.member _let_4) F) (tptp.hAPP _let_3 _let_5 (tptp.hAPP _let_2 (tptp.fun _let_3 _let_5) (tptp.pi X_a X_b) A_1) (tptp.hAPP _let_1 _let_3 (tptp.combk _let_1 X_a) B)))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a (tptp.fun _let_2 tptp.bool) (tptp.member X_a) X_1) A_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) (tptp.hAPP X_a X_b F X_1)) B)))))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun X_a _let_1))) (let ((_let_3 (tptp.fun X_a X_a))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP _let_3 (tptp.fun _let_4 tptp.bool) (tptp.member _let_3) (tptp.combi X_a)) (tptp.hAPP _let_2 _let_4 (tptp.hAPP _let_1 (tptp.fun _let_2 _let_4) (tptp.pi X_a X_a) A_1) (tptp.hAPP _let_1 _let_2 (tptp.combk _let_1 X_a) A_1))))))))) (forall ((Fa $$unsorted) (I_1 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.product_prod tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt) tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.arrow_660593299e_indi tptp.bool (tptp.hAPP (tptp.fun (tptp.fun tptp.arrow_660593299e_indi _let_1) _let_1) (tptp.fun tptp.arrow_660593299e_indi tptp.bool) tptp.arrow_218898985ctator Fa) I_1)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.product_prod tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt) tptp.bool))) (let ((_let_2 (tptp.fun tptp.arrow_660593299e_indi _let_1))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_3 tptp.bool) (tptp.member _let_2) X_2) tptp.arrow_1111136790e_Prof)) (= (tptp.hAPP _let_2 _let_1 Fa X_2) (tptp.hAPP tptp.arrow_660593299e_indi _let_1 X_2 I_1)))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_1 $$unsorted) (Y_2 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun _let_1 tptp.bool) (tptp.inj_on X_a X_b) F) (tptp.top_top _let_1))) (= (= (tptp.hAPP X_a X_b F X_1) (tptp.hAPP X_a X_b F Y_2)) (= (tptp.ti X_a X_1) (tptp.ti X_a Y_2)))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_1 $$unsorted) (Y_2 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun _let_1 tptp.bool) (tptp.inj_on X_a X_b) F) (tptp.top_top _let_1))) (=> (= (tptp.hAPP X_a X_b F X_1) (tptp.hAPP X_a X_b F Y_2)) (= (tptp.ti X_a X_1) (tptp.ti X_a Y_2)))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_1 $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b X_a))) (let ((_let_2 (tptp.fun X_a X_b))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 _let_4 (tptp.inj_on X_a X_b) F) A_1)) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_a _let_4 (tptp.member X_a) X_1) A_1)) (= (tptp.hAPP X_b X_a (tptp.hAPP _let_2 _let_1 (tptp.hAPP _let_3 (tptp.fun _let_2 _let_1) (tptp.hilbert_inv_into X_a X_b) A_1) F) (tptp.hAPP X_a X_b F X_1)) (tptp.ti X_a X_1))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (Y_2 $$unsorted) (X_1 $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b X_a))) (let ((_let_2 (tptp.fun X_a X_b))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 _let_4 (tptp.inj_on X_a X_b) F) A_1)) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_a _let_4 (tptp.member X_a) X_1) A_1)) (=> (= (tptp.hAPP X_a X_b F X_1) (tptp.ti X_b Y_2)) (= (tptp.hAPP X_b X_a (tptp.hAPP _let_2 _let_1 (tptp.hAPP _let_3 (tptp.fun _let_2 _let_1) (tptp.hilbert_inv_into X_a X_b) A_1) F) Y_2) (tptp.ti X_a X_1)))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F $$unsorted) (B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun X_a (tptp.fun X_b tptp.bool)))) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a (tptp.fun _let_2 tptp.bool) (tptp.member X_a) X_2) A_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) (tptp.hAPP X_a X_b F X_2)) (tptp.hAPP X_a _let_1 B X_2))))))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) F) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun X_a tptp.bool) (tptp.fun _let_3 _let_2) (tptp.pi X_a X_b) A_1) B)))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (G $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun X_b X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.top_top _let_2))) (let ((_let_4 (tptp.fun X_a X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_4 (tptp.fun _let_2 tptp.bool) (tptp.inj_on X_a X_b) F) _let_3)) (=> (forall ((X_2 $$unsorted)) (= (tptp.hAPP X_a X_b F (tptp.hAPP X_b X_a G X_2)) (tptp.ti X_b X_2))) (= (tptp.hAPP _let_4 _let_1 (tptp.hAPP _let_2 (tptp.fun _let_4 _let_1) (tptp.hilbert_inv_into X_a X_b) _let_3) F) (tptp.ti _let_1 G))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((A_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) A_2) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_2) (tptp.one_one X_a))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere223160158up_add X_a) (forall ((C $$unsorted) (D $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 A_2) B_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 (tptp.ord_less_eq X_a) C) D)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_2) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B_1) D)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere223160158up_add X_a) (forall ((C $$unsorted) (D $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 (tptp.ord_less_eq X_a) A_2) B_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 C) D)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_2) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B_1) D)))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (forall ((X_2 $$unsorted) (Y_3 $$unsorted)) (=> (= (tptp.hAPP X_a X_b F X_2) (tptp.hAPP X_a X_b F Y_3)) (= (tptp.ti X_a X_2) (tptp.ti X_a Y_3)))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun _let_1 tptp.bool) (tptp.inj_on X_a X_b) F) (tptp.top_top _let_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.dense_linorder X_a) (forall ((Z_1 $$unsorted) (Y $$unsorted)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) X_2) Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) X_2) Z_1))))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) Y) Z_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.dense_linorder X_a) (forall ((Z_1 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) X) Y)) (=> (forall ((W $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.ord_less X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 _let_2 X) W)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 _let_2 W) Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) W) Z_1))))))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) Y) Z_1)))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.ord X_b) (forall ((F $$unsorted) (G $$unsorted)) (let ((_let_1 (tptp.fun X_a X_b))) (let ((_let_2 (tptp.ord_less_eq _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 (tptp.ord_less _let_1) F) G)) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 F) G)) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 G) F))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (B $$unsorted) (A_4 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.pi X_a X_b))) (let ((_let_2 (tptp.fun (tptp.fun X_a X_b) tptp.bool))) (let ((_let_3 (tptp.fun X_a (tptp.fun X_b tptp.bool)))) (let ((_let_4 (tptp.fun _let_3 _let_2))) (let ((_let_5 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP _let_5 (tptp.fun _let_5 tptp.bool) (tptp.ord_less_eq _let_5) A_4) A_1)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) (tptp.hAPP _let_3 _let_2 (tptp.hAPP _let_5 _let_4 _let_1 A_1) B)) (tptp.hAPP _let_3 _let_2 (tptp.hAPP _let_5 _let_4 _let_1 A_4) B)))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (R_1 $$unsorted) (S_1 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.fun X_b _let_3))) (let ((_let_5 (tptp.fun X_b _let_1))) (let ((_let_6 (tptp.fun _let_5 _let_4))) (let ((_let_7 (tptp.fun X_a _let_4))) (let ((_let_8 (tptp.fun X_a _let_5))) (let ((_let_9 (tptp.fun X_b tptp.bool))) (let ((_let_10 (tptp.fun _let_2 _let_9))) (let ((_let_11 (tptp.fun X_a _let_10))) (let ((_let_12 (tptp.fun X_a _let_9))) (let ((_let_13 (tptp.hAPP _let_11 (tptp.fun _let_2 _let_12) (tptp.combc X_a _let_2 _let_9) (tptp.hAPP _let_7 _let_11 (tptp.hAPP (tptp.fun _let_4 _let_10) (tptp.fun _let_7 _let_11) (tptp.combb _let_4 _let_10 X_a) (tptp.combc X_b _let_2 tptp.bool)) (tptp.hAPP _let_8 _let_7 (tptp.hAPP _let_6 (tptp.fun _let_8 _let_7) (tptp.combb _let_5 _let_4 X_a) (tptp.hAPP (tptp.fun _let_1 _let_3) _let_6 (tptp.combb _let_1 _let_3 X_b) (tptp.member _let_1))) (tptp.product_Pair X_a X_b)))))) (= (tptp.hBOOL (tptp.hAPP _let_12 tptp.bool (tptp.hAPP _let_12 (tptp.fun _let_12 tptp.bool) (tptp.ord_less_eq _let_12) (tptp.hAPP _let_2 _let_12 _let_13 R_1)) (tptp.hAPP _let_2 _let_12 _let_13 S_1))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 _let_3 (tptp.ord_less_eq _let_2) R_1) S_1))))))))))))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) A_1) (tptp.top_top _let_1))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (A_1 $$unsorted) (F $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP (tptp.fun X_a X_b) _let_2 (tptp.inj_on X_a X_b) F))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 B)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_1) B)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 A_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (not (= (tptp.ti X_a X) (tptp.ti X_a Y))) (=> (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X) Y))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X))))))))) (forall ((X_a $$unsorted)) (=> (tptp.cancel_semigroup_add X_a) (forall ((B_1 $$unsorted) (A_2 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (=> (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B_1) A_2) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 C) A_2)) (= (tptp.ti X_a B_1) (tptp.ti X_a C)))))))) (forall ((X_a $$unsorted)) (=> (tptp.cancel146912293up_add X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_2))) (=> (= (tptp.hAPP X_a X_a _let_1 B_1) (tptp.hAPP X_a X_a _let_1 C)) (= (tptp.ti X_a B_1) (tptp.ti X_a C))))))) (forall ((X_a $$unsorted)) (=> (tptp.cancel_semigroup_add X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_2))) (=> (= (tptp.hAPP X_a X_a _let_1 B_1) (tptp.hAPP X_a X_a _let_1 C)) (= (tptp.ti X_a B_1) (tptp.ti X_a C))))))) (forall ((X_a $$unsorted)) (=> (tptp.cancel_semigroup_add X_a) (forall ((Ba $$unsorted) (Aa $$unsorted) (Ca $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (= (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Ba) Aa) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Ca) Aa)) (= (tptp.ti X_a Ba) (tptp.ti X_a Ca)))))))) (forall ((X_a $$unsorted)) (=> (tptp.cancel_semigroup_add X_a) (forall ((Aa $$unsorted) (Ba $$unsorted) (Ca $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) Aa))) (= (= (tptp.hAPP X_a X_a _let_1 Ba) (tptp.hAPP X_a X_a _let_1 Ca)) (= (tptp.ti X_a Ba) (tptp.ti X_a Ca))))))) (forall ((X_a $$unsorted)) (=> (tptp.ab_semigroup_add X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 A_2))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 B_1)) C) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B_1) C))))))))) (forall ((X_a $$unsorted)) (=> (tptp.one X_a) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (let ((_let_2 (tptp.ti X_a X_1))) (= (= _let_1 _let_2) (= _let_2 _let_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere236663937imp_le X_a) (forall ((C $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) C))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 A_2)) (tptp.hAPP X_a X_a _let_3 B_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_2) B_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere236663937imp_le X_a) (forall ((A_2 $$unsorted) (C $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.plus_plus X_a))) (let ((_let_4 (tptp.fun X_a X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 A_2) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 B_1) C))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_2) B_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere779506340up_add X_a) (forall ((C $$unsorted) (D $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less_eq X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 A_2) B_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 C) D)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_2) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B_1) D)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere779506340up_add X_a) (forall ((C $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) C))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_2) B_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 A_2)) (tptp.hAPP X_a X_a _let_1 B_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere779506340up_add X_a) (forall ((C $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less_eq X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 A_2) B_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_2) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B_1) C))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere236663937imp_le X_a) (forall ((Ca $$unsorted) (Aa $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) Ca))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 Aa)) (tptp.hAPP X_a X_a _let_3 Ba))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Aa) Ba))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere236663937imp_le X_a) (forall ((Aa $$unsorted) (Ca $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.plus_plus X_a))) (let ((_let_4 (tptp.fun X_a X_a))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 Aa) Ca)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 Ba) Ca))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Aa) Ba)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere236663937imp_le X_a) (forall ((C $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) C))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 A_2)) (tptp.hAPP X_a X_a _let_3 B_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_2) B_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere236663937imp_le X_a) (forall ((A_2 $$unsorted) (C $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.plus_plus X_a))) (let ((_let_4 (tptp.fun X_a X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 A_2) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 B_1) C))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_2) B_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere223160158up_add X_a) (forall ((C $$unsorted) (D $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 A_2) B_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 C) D)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_2) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B_1) D)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere223160158up_add X_a) (forall ((C $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) C))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_2) B_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 A_2)) (tptp.hAPP X_a X_a _let_1 B_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere223160158up_add X_a) (forall ((C $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 A_2) B_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_2) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B_1) C))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere236663937imp_le X_a) (forall ((Ca $$unsorted) (Aa $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) Ca))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 Aa)) (tptp.hAPP X_a X_a _let_3 Ba))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Aa) Ba))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere236663937imp_le X_a) (forall ((Aa $$unsorted) (Ca $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.plus_plus X_a))) (let ((_let_4 (tptp.fun X_a X_a))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 Aa) Ca)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 Ba) Ca))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Aa) Ba)))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.ord X_b) (forall ((F $$unsorted) (G $$unsorted)) (let ((_let_1 (tptp.fun X_a X_b))) (=> (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) (tptp.hAPP X_a X_b F X_2)) (tptp.hAPP X_a X_b G X_2)))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) F) G))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (and (tptp.order X_a) (tptp.ord X_b)) (forall ((Ca $$unsorted) (F $$unsorted) (Ba $$unsorted) (Aa $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) (tptp.hAPP X_b X_a F Ba)) Aa)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) Ca) Ba)) (=> (forall ((X_2 $$unsorted) (Y_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) Y_3) X_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.hAPP X_b X_a F Y_3)) (tptp.hAPP X_b X_a F X_2))))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) (tptp.hAPP X_b X_a F Ca)) Aa))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (and (tptp.order X_a) (tptp.order X_b)) (forall ((Ca $$unsorted) (F $$unsorted) (Ba $$unsorted) (Aa $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_b X_a F Ba)) Aa)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) Ca) Ba)) (=> (forall ((X_2 $$unsorted) (Y_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) Y_3) X_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP X_b X_a F Y_3)) (tptp.hAPP X_b X_a F X_2))))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_b X_a F Ca)) Aa)))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (and (tptp.order X_b) (tptp.order X_a)) (forall ((Ca $$unsorted) (Aa $$unsorted) (F $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) Aa) (tptp.hAPP X_b X_a F Ba))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) Ba) Ca)) (=> (forall ((X_2 $$unsorted) (Y_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) X_2) Y_3)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.hAPP X_b X_a F X_2)) (tptp.hAPP X_b X_a F Y_3))))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) Aa) (tptp.hAPP X_b X_a F Ca)))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (and (tptp.order X_b) (tptp.order X_a)) (forall ((Ca $$unsorted) (Aa $$unsorted) (F $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) Aa))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_b X_a F Ba))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) Ba) Ca)) (=> (forall ((X_2 $$unsorted) (Y_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) X_2) Y_3)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP X_b X_a F X_2)) (tptp.hAPP X_b X_a F Y_3))))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_b X_a F Ca)))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (and (tptp.order X_b) (tptp.order X_a)) (forall ((F $$unsorted) (Ca $$unsorted) (Aa $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.ord_less X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) Aa) Ba)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 (tptp.hAPP X_a X_b F Ba)) Ca)) (=> (forall ((X_2 $$unsorted) (Y_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X_2) Y_3)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b 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(tptp.hAPP _let_1 tptp.bool _let_3 B)))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less _let_1) A_1) B)) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_1) B)) (not (= (tptp.ti _let_1 A_1) (tptp.ti _let_1 B)))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_1) B)) (or (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less _let_1) A_1) B)) (= (tptp.ti _let_1 A_1) (tptp.ti _let_1 B))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less _let_1) A_1) B)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_1) B)))))) (forall ((X_a $$unsorted) (C_1 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP _let_1 _let_2 (tptp.ord_less _let_1) A_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 B)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) B) C_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 C_1)))))))) (forall ((X_a $$unsorted) (C_1 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.ord_less _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 (tptp.ord_less_eq _let_1) A_1) B)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 B) C_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 A_1) C_1)))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (Q_1 $$unsorted) (Pa $$unsorted) (X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a _let_1))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_a _let_1 Pa X_1) Y_2)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) Pa) Q_1)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_a _let_1 Q_1 X_1) Y_2))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.ord_less_eq _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (=> (= (tptp.ti _let_1 A_1) (tptp.ti _let_1 B)) (not (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 A_1) B)) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 B) A_1)))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_1 $$unsorted) (Y_2 $$unsorted) (Pa $$unsorted) (Q_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a _let_1))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) Pa) Q_1)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_a _let_1 Pa X_1) Y_2)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_a _let_1 Q_1 X_1) Y_2))))))) (forall ((X_a $$unsorted) (C_1 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.ord_less_eq _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.hAPP _let_1 _let_3 _let_2 A_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_4 B)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 B) C_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_4 C_1))))))))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 (tptp.member X_a) X_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_1) B)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 A_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 B)))))))) (forall ((X_a $$unsorted) (B $$unsorted) (X_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 (tptp.member X_a) X_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 A_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_1) B)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 B)))))))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (Pa $$unsorted) (Q_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) Pa) Q_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa X_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool Q_1 X_1)))))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 (tptp.member X_a) X_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_1) B)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 A_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 B)))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (= (tptp.ti _let_1 A_1) (tptp.ti _let_1 B)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) B) A_1))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (= (tptp.ti _let_1 A_1) (tptp.ti _let_1 B)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) A_1) B))))) (forall ((X_a $$unsorted) (Q_1 $$unsorted) (Pa $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa X_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) Pa) Q_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool Q_1 X_1)))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.ord_less_eq _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (= (tptp.ti _let_1 A_1) (tptp.ti _let_1 B)) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 A_1) B)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 B) A_1)))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) A_1) A_1)))) (forall ((X_a $$unsorted) (R_1 $$unsorted) (S_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.ord_less_eq _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.hAPP (tptp.fun X_a _let_3) (tptp.fun _let_1 _let_1) (tptp.combc X_a _let_1 tptp.bool) (tptp.member X_a)))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 (tptp.hAPP _let_1 _let_1 _let_4 R_1)) (tptp.hAPP _let_1 _let_1 _let_4 S_1))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 R_1) S_1)))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (Q_1 $$unsorted) (Pa $$unsorted)) (let ((_let_1 (tptp.fun X_a (tptp.fun X_b tptp.bool)))) (=> (forall ((X_2 $$unsorted) (Y_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_a _let_1 Pa X_2) Y_3)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_a _let_1 Q_1 X_2) Y_3))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) Pa) Q_1))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (B $$unsorted) (C_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.fun X_a X_b) tptp.bool))) (let ((_let_2 (tptp.fun X_a (tptp.fun X_b tptp.bool)))) (let ((_let_3 (tptp.hAPP (tptp.fun X_a tptp.bool) (tptp.fun _let_2 _let_1) (tptp.pi X_a X_b) A_1))) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a (tptp.fun _let_2 tptp.bool) (tptp.member X_a) X_2) A_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) (tptp.hAPP X_a _let_1 B X_2)) (tptp.hAPP X_a _let_1 C_1 X_2))))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) (tptp.hAPP _let_2 _let_1 _let_3 B)) (tptp.hAPP _let_2 _let_1 _let_3 C_1)))))))) (forall ((X_a $$unsorted) (B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B)))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) A_1) B))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (and (tptp.order X_a) (tptp.order X_b)) (forall ((Ca $$unsorted) (F $$unsorted) (Ba $$unsorted) (Aa $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) Ba) Aa)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less_eq X_b) Ca) (tptp.hAPP X_a X_b F Ba))) (=> (forall ((X_2 $$unsorted) (Y_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) Y_3) X_2)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) (tptp.hAPP X_a X_b F Y_3)) (tptp.hAPP X_a X_b F X_2))))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less X_b) Ca) (tptp.hAPP X_a X_b F Aa)))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (and (tptp.order X_a) (tptp.order X_b)) (forall ((Ca $$unsorted) (F $$unsorted) (Ba $$unsorted) (Aa $$unsorted)) (let ((_let_1 (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) Ca))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) Ba) Aa)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool _let_1 (tptp.hAPP X_a X_b F Ba))) (=> (forall ((X_2 $$unsorted) (Y_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) Y_3) X_2)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) (tptp.hAPP X_a X_b F Y_3)) (tptp.hAPP X_a X_b F X_2))))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool _let_1 (tptp.hAPP X_a X_b F Aa)))))))))) (forall ((X_a $$unsorted) (Ca $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 (tptp.member X_a) Ca))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less _let_1) A_1) B)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 A_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 B)))))))) (forall ((X_a $$unsorted) (C_1 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.ord_less _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.hAPP _let_1 _let_3 _let_2 A_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_4 B)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 B) C_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_4 C_1))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (and (tptp.order X_b) (tptp.order X_a)) (forall ((F $$unsorted) (Ca $$unsorted) (Aa $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) Aa) Ba)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less_eq X_b) (tptp.hAPP X_a X_b F Ba)) Ca)) (=> (forall ((X_2 $$unsorted) (Y_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) X_2) Y_3)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) (tptp.hAPP X_a X_b F X_2)) (tptp.hAPP X_a X_b F Y_3))))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less X_b) (tptp.hAPP X_a X_b F Aa)) Ca))))))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted) (L_3 $$unsorted) (Aa $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.product_Pair tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt))) (let ((_let_2 (tptp.product_prod tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt))) (let ((_let_3 (tptp.fun tptp.arrow_490897120le_alt _let_2))) (let ((_let_4 (tptp.hAPP tptp.arrow_490897120le_alt _let_3 _let_1 X_1))) (let ((_let_5 (tptp.member _let_2))) (let ((_let_6 (tptp.fun _let_2 tptp.bool))) (let ((_let_7 (tptp.fun _let_6 tptp.bool))) (let ((_let_8 (tptp.hAPP _let_2 _let_7 _let_5 (tptp.hAPP tptp.arrow_490897120le_alt _let_2 _let_4 Y_2)))) (let ((_let_9 (tptp.ti tptp.arrow_490897120le_alt Aa))) (let ((_let_10 (tptp.ti tptp.arrow_490897120le_alt X_1))) (let ((_let_11 (= _let_10 _let_9))) (let ((_let_12 (tptp.ti tptp.arrow_490897120le_alt Ba))) (let ((_let_13 (tptp.ti tptp.arrow_490897120le_alt Y_2))) (let ((_let_14 (= _let_13 _let_9))) (let ((_let_15 (tptp.fun tptp.arrow_490897120le_alt _let_6))) (=> (not (= _let_9 _let_12)) (=> (tptp.hBOOL (tptp.hAPP _let_7 tptp.bool (tptp.hAPP _let_6 (tptp.fun _let_7 tptp.bool) (tptp.member _let_6) L_3) tptp.arrow_2064824852le_Lin)) (= (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool _let_8 (tptp.hAPP tptp.arrow_490897120le_alt _let_6 (tptp.hAPP tptp.arrow_490897120le_alt _let_15 (tptp.hAPP _let_6 (tptp.fun tptp.arrow_490897120le_alt _let_15) tptp.arrow_1322701812_below L_3) Aa) Ba))) (and (not (= _let_10 _let_13)) (=> _let_14 (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP _let_2 _let_7 _let_5 (tptp.hAPP tptp.arrow_490897120le_alt _let_2 _let_4 Ba)) L_3))) (=> (not _let_14) (and (=> _let_11 (or (= _let_13 _let_12) (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP _let_2 _let_7 _let_5 (tptp.hAPP tptp.arrow_490897120le_alt _let_2 (tptp.hAPP tptp.arrow_490897120le_alt _let_3 _let_1 Ba) Y_2)) L_3)))) (=> (not _let_11) (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool _let_8 L_3))))))))))))))))))))))))) (forall ((M_3 $$unsorted) (K_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M_3) K_1)) N_1)) (not (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M_3) N_1)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 K_1) N_1))))))))) (forall ((M_3 $$unsorted) (K_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M_3) K_1)) N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M_3) N_1)))))) (forall ((M_3 $$unsorted) (K_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M_3) K_1)) N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 K_1) N_1)))))) (forall ((N_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N_1) N_1)))) (forall ((M_2 $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (not (= M_2 Na)) (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M_2) Na)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Na) M_2))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (not (= X Y)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 X) Y))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Y) X))))))) (forall ((N_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N_1) N_1)))) (forall ((N_1 $$unsorted) (M_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N_1) M_3)) (not (= M_3 N_1)))) (forall ((S $$unsorted) (T_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) S) T_3)) (not (= S T_3)))) (forall ((Pa $$unsorted) (M_2 $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 Pa Na) M_2)))) (let ((_let_3 (tptp.ord_less tptp.nat))) (=> (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 _let_3 M_2) Na)) _let_2) (=> (=> (= M_2 Na) _let_2) (=> (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 _let_3 Na) M_2)) _let_2) _let_2))))))) (forall ((M_3 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M_3) N_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 N_1) M_3))))) (forall ((X $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 X))) (let ((_let_4 (tptp.hAPP tptp.nat _let_2 _let_1 Y))) (= (tptp.hAPP tptp.nat tptp.nat _let_3 (tptp.hAPP tptp.nat tptp.nat _let_4 Z_1)) (tptp.hAPP tptp.nat tptp.nat _let_4 (tptp.hAPP tptp.nat tptp.nat _let_3 Z_1)))))))) (forall ((M_3 $$unsorted) (N_1 $$unsorted) (K_1 $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 M_3))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 N_1)) K_1) (tptp.hAPP tptp.nat tptp.nat _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 N_1) K_1))))))) (forall ((K $$unsorted) (M_2 $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) K))) (= (= (tptp.hAPP tptp.nat tptp.nat _let_1 M_2) (tptp.hAPP tptp.nat tptp.nat _let_1 Na)) (= M_2 Na)))) (forall ((M_2 $$unsorted) (K $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M_2) K) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 Na) K)) (= M_2 Na))))) (forall ((N_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N_1) N_1))) (forall ((M_3 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M_3) N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 N_1) M_3)))))) (forall ((M_3 $$unsorted) (N_1 $$unsorted)) (=> (= M_3 N_1) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M_3) N_1)))) (forall ((K_1 $$unsorted) (I $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 I))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 J_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 J_2) K_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 K_1)))))))) (forall ((M_3 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M_3) N_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 N_1) M_3)) (= M_3 N_1)))))) (forall ((L_3 $$unsorted) (X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.product_prod tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt) tptp.bool))) (let ((_let_2 (tptp.fun tptp.arrow_490897120le_alt _let_1))) (let ((_let_3 (tptp.member _let_1))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (not (= (tptp.ti tptp.arrow_490897120le_alt X_1) (tptp.ti tptp.arrow_490897120le_alt Y_2))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP _let_1 _let_5 _let_3 L_3) tptp.arrow_2064824852le_Lin)) (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP _let_1 _let_5 _let_3 (tptp.hAPP tptp.arrow_490897120le_alt _let_1 (tptp.hAPP tptp.arrow_490897120le_alt _let_2 (tptp.hAPP _let_1 (tptp.fun tptp.arrow_490897120le_alt _let_2) tptp.arrow_1322701812_below L_3) X_1) Y_2)) tptp.arrow_2064824852le_Lin)))))))))) (forall ((K $$unsorted) (N_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_3 tptp.bool) (tptp.inj_on tptp.nat tptp.nat) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc tptp.nat tptp.nat tptp.nat) (tptp.plus_plus tptp.nat)) K)) N_3)))))) (forall ((I $$unsorted) (J_2 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) I) J_2)) I)))) (forall ((J_2 $$unsorted) (I $$unsorted)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) J_2) I)) I)))) (forall ((K $$unsorted) (M_2 $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) K))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 M_2)) (tptp.hAPP tptp.nat tptp.nat _let_3 Na))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M_2) Na))))))) (forall ((M_3 $$unsorted) (I $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 J_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) J_2) M_3)))))) (forall ((M_3 $$unsorted) (I $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 J_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M_3) J_2)))))) (forall ((K_1 $$unsorted) (I $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.ord_less tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 I) J_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 I) K_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 J_2) K_1))))))))) (forall ((K_1 $$unsorted) (L_2 $$unsorted) (I $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.ord_less tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 I) J_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 K_1) L_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 I) K_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 J_2) L_2)))))))))) (forall ((M_3 $$unsorted) (N_1 $$unsorted) (K_1 $$unsorted) (L_2 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.plus_plus tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 K_1) L_2)) (=> (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_4 _let_3 M_3) L_2) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_4 _let_3 K_1) N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M_3) N_1))))))))) (forall ((I $$unsorted) (J_2 $$unsorted) (K_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) I) J_2)) K_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 I) K_1)))))) (forall ((M_2 $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) M_2) Na)) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) M_2) Na)) (not (= M_2 Na)))))) (forall ((M_2 $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) M_2) Na)) (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) M_2) Na)) (= M_2 Na))))) (forall ((M_3 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) M_3) N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) M_3) N_1))))) (forall ((M_3 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) M_3) N_1)) (=> (not (= M_3 N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) M_3) N_1)))))) (forall ((M_3 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) M_3) N_1)) (= M_3 N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) M_3) N_1))))) (forall ((N_1 $$unsorted) (M_3 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M_3) N_1)))) (forall ((N_1 $$unsorted) (M_3 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) N_1) M_3)))) (forall ((M_2 $$unsorted) (Na $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M_2) Na)) (exists ((K_2 $$unsorted)) (= Na (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M_2) K_2))))) (forall ((K $$unsorted) (M_2 $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) K))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 M_2)) (tptp.hAPP tptp.nat tptp.nat _let_3 Na))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M_2) Na))))))) (forall ((M_3 $$unsorted) (I $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) I))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 J_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) J_2) M_3)))))) (forall ((M_3 $$unsorted) (I $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) I))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 J_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M_3) J_2)))))) (forall ((K_1 $$unsorted) (I $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.ord_less_eq tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 I) J_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 I) K_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 J_2) K_1))))))))) (forall ((K_1 $$unsorted) (L_2 $$unsorted) (I $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.ord_less_eq tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 I) J_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 K_1) L_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 I) K_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 J_2) L_2)))))))))) (forall ((M_2 $$unsorted) (K $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (=> (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat F M)) (tptp.hAPP tptp.nat tptp.nat F N))))))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat F M_2)) K)) (tptp.hAPP tptp.nat tptp.nat F (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M_2) K)))))))) (forall ((I_1 $$unsorted) (J_1 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (forall ((I_2 $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 I_2) J)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat F I_2)) (tptp.hAPP tptp.nat tptp.nat F J))))))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 I_1) J_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat F I_1)) (tptp.hAPP tptp.nat tptp.nat F J_1)))))))) (forall ((Z_1 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) X))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) Y) Z_1)))))) (forall ((Y $$unsorted) (X $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) X))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 Z_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) Y) Z_1)))))) (forall ((Y $$unsorted) (X $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) X))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 Z_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) Y) Z_1)))))) (forall ((Z_1 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) X))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) Y) Z_1)))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) X) Y)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) X) Y))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (R_1 $$unsorted) (X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_a _let_3 (tptp.hAPP _let_2 (tptp.fun X_a _let_3) (tptp.in_rel X_a X_b) R_1) X_1) Y_2)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) (tptp.hAPP X_b _let_1 (tptp.hAPP X_a (tptp.fun X_b _let_1) (tptp.product_Pair X_a X_b) X_1) Y_2)) R_1))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F $$unsorted) (B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a _let_1))) (let ((_let_3 (tptp.fun X_a X_b))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a (tptp.fun _let_2 tptp.bool) (tptp.member X_a) X_2) A_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) (tptp.hAPP X_a X_b F X_2)) B)))))) (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP _let_3 (tptp.fun _let_4 tptp.bool) (tptp.member _let_3) F) (tptp.hAPP _let_2 _let_4 (tptp.hAPP (tptp.fun X_a tptp.bool) (tptp.fun _let_2 _let_4) (tptp.pi X_a X_b) A_1) (tptp.hAPP _let_1 _let_2 (tptp.combk _let_1 X_a) B)))))))))) (exists ((L_1 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.product_prod tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt) tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) L_1) tptp.arrow_2064824852le_Lin))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (B $$unsorted) (F $$unsorted) (G $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun X_a (tptp.fun X_b tptp.bool)))) (let ((_let_4 (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun X_a tptp.bool) (tptp.fun _let_3 _let_2) (tptp.pi X_a X_b) A_1) B))) (let ((_let_5 (tptp.member _let_1))) (let ((_let_6 (tptp.fun _let_2 tptp.bool))) (=> (forall ((W $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) W) A_1)) (= (tptp.hAPP X_a X_b F W) (tptp.hAPP X_a X_b G W))))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 _let_6 _let_5 F) _let_4)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 _let_6 _let_5 G) _let_4))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F $$unsorted) (B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun X_a (tptp.fun X_b tptp.bool)))) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a (tptp.fun _let_2 tptp.bool) (tptp.member X_a) X_2) A_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) (tptp.hAPP X_a X_b F X_2)) (tptp.hAPP X_a _let_1 B X_2))))))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) F) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun X_a tptp.bool) (tptp.fun _let_3 _let_2) (tptp.pi X_a X_b) A_1) B)))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (F $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.fun X_a X_b))) (let ((_let_4 (tptp.fun X_a _let_1))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP _let_3 (tptp.fun _let_5 tptp.bool) (tptp.member _let_3) F) (tptp.hAPP _let_4 _let_5 (tptp.hAPP _let_2 (tptp.fun _let_4 _let_5) (tptp.pi X_a X_b) A_1) (tptp.hAPP _let_1 _let_4 (tptp.combk _let_1 X_a) B)))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_3 (tptp.fun _let_2 tptp.bool) (tptp.inj_on X_a X_b) F) A_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) B)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP _let_2 tptp.nat (tptp.finite_card X_a) A_1)) (tptp.hAPP _let_1 tptp.nat (tptp.finite_card X_b) B)))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (forall ((X_2 $$unsorted) (Y_3 $$unsorted)) (let ((_let_1 (tptp.member X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a _let_3 _let_1 X_2) A_1)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a _let_3 _let_1 Y_3) A_1)) (=> (= (tptp.hAPP X_a X_b F X_2) (tptp.hAPP X_a X_b F Y_3)) (= (tptp.ti X_a X_2) (tptp.ti X_a Y_3))))))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun _let_1 tptp.bool) (tptp.inj_on X_a X_b) F) A_1))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F $$unsorted) (G $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.inj_on X_a X_b))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.fun X_a X_b))) (=> (forall ((A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) A_3) A_1)) (= (tptp.hAPP X_a X_b F A_3) (tptp.hAPP X_a X_b G A_3))))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_4 _let_3 _let_1 F) A_1)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_4 _let_3 _let_1 G) A_1))))))))) (tptp.hBOOL (tptp.hAPP _let_12 tptp.bool (tptp.finite_finite_1 tptp.arrow_660593299e_indi) _let_13)) (forall ((X_a $$unsorted) (X_b $$unsorted) (G $$unsorted) (F $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.fun X_b X_a))) (let ((_let_4 (tptp.fun X_b _let_2))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (let ((_let_6 (tptp.fun X_a X_b))) (let ((_let_7 (tptp.fun X_a _let_1))) (let ((_let_8 (tptp.fun _let_6 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_8 tptp.bool (tptp.hAPP _let_6 (tptp.fun _let_8 tptp.bool) (tptp.member _let_6) F) (tptp.hAPP _let_7 _let_8 (tptp.hAPP _let_2 (tptp.fun _let_7 _let_8) (tptp.pi X_a X_b) A_1) (tptp.hAPP _let_1 _let_7 (tptp.combk _let_1 X_a) B)))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_6 (tptp.fun _let_2 tptp.bool) (tptp.inj_on X_a X_b) F) A_1)) (=> (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP _let_3 (tptp.fun _let_5 tptp.bool) (tptp.member _let_3) G) (tptp.hAPP _let_4 _let_5 (tptp.hAPP _let_1 (tptp.fun _let_4 _let_5) (tptp.pi X_b X_a) B) (tptp.hAPP _let_2 _let_4 (tptp.combk _let_2 X_b) A_1)))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_3 (tptp.fun _let_1 tptp.bool) (tptp.inj_on X_b X_a) G) B)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_a) A_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) B)) (= (tptp.hAPP _let_2 tptp.nat (tptp.finite_card X_a) A_1) (tptp.hAPP _let_1 tptp.nat (tptp.finite_card X_b) B))))))))))))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun _let_1 _let_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) A_1)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 _let_1) (tptp.hAPP _let_2 _let_2 (tptp.collect _let_1) (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_3 _let_3 (tptp.combc _let_1 _let_1 tptp.bool) (tptp.ord_less_eq _let_1)) A_1))))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.finite_card X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) B)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_1) B)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP _let_1 tptp.nat _let_3 A_1)) (tptp.hAPP _let_1 tptp.nat _let_3 B))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less _let_1) A_1) B))))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.finite_card X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_a) B)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less _let_2) A_1) B)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP _let_2 tptp.nat _let_1 A_1)) (tptp.hAPP _let_2 tptp.nat _let_1 B)))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.finite_card X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_a) B)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) A_1) B)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP _let_2 tptp.nat _let_1 A_1)) (tptp.hAPP _let_2 tptp.nat _let_1 B)))))))) (forall ((X_a $$unsorted) (Q_1 $$unsorted) (Pa $$unsorted)) (let ((_let_1 (tptp.fun tptp.bool tptp.bool))) (let ((_let_2 (tptp.fun X_a _let_1))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.collect X_a))) (let ((_let_5 (tptp.finite_finite_1 X_a))) (=> (or (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool _let_5 (tptp.hAPP _let_3 _let_3 _let_4 Pa))) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool _let_5 (tptp.hAPP _let_3 _let_3 _let_4 Q_1)))) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool _let_5 (tptp.hAPP _let_3 _let_3 _let_4 (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_2 (tptp.fun _let_3 _let_3) (tptp.combs X_a tptp.bool tptp.bool) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun tptp.bool _let_1) (tptp.fun _let_3 _let_2) (tptp.combb tptp.bool _let_1 X_a) tptp.fconj) Pa)) Q_1))))))))))) (forall ((K $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 tptp.nat) (tptp.hAPP _let_1 _let_1 (tptp.collect tptp.nat) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc tptp.nat tptp.nat tptp.bool) (tptp.ord_less tptp.nat)) K))))))) (forall ((K $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 tptp.nat) (tptp.hAPP _let_1 _let_1 (tptp.collect tptp.nat) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc tptp.nat tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat)) K))))))) (forall ((X_a $$unsorted)) (=> (tptp.finite_finite X_a) (forall ((A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_a tptp.bool) tptp.bool (tptp.finite_finite_1 X_a) A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.finite_finite X_a) (forall ((A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_a tptp.bool) tptp.bool (tptp.finite_finite_1 X_a) A_1))))) (= (tptp.hAPP _let_20 tptp.nat (tptp.finite_card tptp.product_unit) (tptp.top_top _let_20)) _let_19) (forall ((X_a $$unsorted) (Pa $$unsorted) (Q_1 $$unsorted)) (let ((_let_1 (tptp.collect X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.finite_finite_1 X_a))) (let ((_let_4 (tptp.fun tptp.bool tptp.bool))) (let ((_let_5 (tptp.fun X_a _let_4))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 (tptp.hAPP _let_2 _let_2 _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_5 (tptp.fun _let_2 _let_2) (tptp.combs X_a tptp.bool tptp.bool) (tptp.hAPP _let_2 _let_5 (tptp.hAPP (tptp.fun tptp.bool _let_4) (tptp.fun _let_2 _let_5) (tptp.combb tptp.bool _let_4 X_a) tptp.fdisj) Pa)) Q_1)))) (and (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 (tptp.hAPP _let_2 _let_2 _let_1 Pa))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 (tptp.hAPP _let_2 _let_2 _let_1 Q_1))))))))))) (forall ((Na $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (= (tptp.hAPP _let_1 tptp.nat (tptp.finite_card tptp.nat) (tptp.hAPP _let_1 _let_1 (tptp.collect tptp.nat) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc tptp.nat tptp.nat tptp.bool) (tptp.ord_less tptp.nat)) Na))) Na)))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.finite_finite_1 X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) A_1) B)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 B)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 A_1))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.finite_finite_1 X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 B)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) A_1) B)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 A_1))))))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.finite_finite X_a) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) (tptp.top_top _let_1)))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun X_b tptp.bool))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.finite_finite_1 X_a) (tptp.top_top _let_4))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.finite_finite_1 X_b) (tptp.top_top _let_3))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 _let_1) (tptp.top_top _let_2)))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.sum_sum X_a X_b))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.finite_finite_1 _let_3) (tptp.top_top _let_4))) (and (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_a) (tptp.top_top _let_2))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) (tptp.top_top _let_1)))))))))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.option X_a))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.finite_finite_1 _let_2) (tptp.top_top _let_3))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) (tptp.top_top _let_1)))))))) (forall ((X_a $$unsorted) (Pa $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.finite_finite_1 X_a))) (let ((_let_3 (tptp.collect X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 _let_3 Pa))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 _let_3 (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun tptp.bool tptp.bool) (tptp.fun _let_1 _let_1) (tptp.combb tptp.bool tptp.bool X_a) tptp.fNot) Pa)))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.top_top _let_1))))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.top_top _let_1))) (let ((_let_3 (tptp.finite_card X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) _let_2)) (=> (= (tptp.hAPP _let_1 tptp.nat _let_3 A_1) (tptp.hAPP _let_1 tptp.nat _let_3 _let_2)) (= (tptp.ti _let_1 A_1) _let_2))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a X_b))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.finite_finite_1 _let_2) (tptp.top_top _let_3))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) (tptp.top_top _let_1)))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.finite_card X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) B)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) A_1) B)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP _let_1 tptp.nat _let_2 B)) (tptp.hAPP _let_1 tptp.nat _let_2 A_1))) (= (tptp.ti _let_1 A_1) (tptp.ti _let_1 B)))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.finite_finite_1 X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (not (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 (tptp.top_top _let_2)))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 A_1)) (exists ((A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) A_3) A_1)))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.sum_sum X_a X_b))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_a) A_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) B)) (= (tptp.hAPP _let_4 tptp.nat (tptp.finite_card _let_3) (tptp.hAPP _let_1 _let_4 (tptp.hAPP _let_2 (tptp.fun _let_1 _let_4) (tptp.sum_Plus X_a X_b) A_1) B)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) (tptp.hAPP _let_2 tptp.nat (tptp.finite_card X_a) A_1)) (tptp.hAPP _let_1 tptp.nat (tptp.finite_card X_b) B)))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (B $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Z $$unsorted) (G $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP _let_1 X_a Fa A_1))) (let ((_let_3 (tptp.fun X_a X_a))) (let ((_let_4 (tptp.fun _let_1 X_a))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (let ((_let_6 (tptp.fun X_b X_a))) (let ((_let_7 (tptp.fun _let_6 _let_5))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP _let_6 _let_5 (tptp.hAPP X_a _let_7 (tptp.hAPP (tptp.fun X_a _let_3) (tptp.fun X_a _let_7) (tptp.finite908156982e_idem X_a X_b) F) Z) G) Fa)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) B) A_1)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 F (tptp.hAPP _let_1 X_a Fa B)) _let_2) _let_2)))))))))))) (not (tptp.hBOOL (tptp.hAPP _let_16 tptp.bool (tptp.finite_finite_1 tptp.nat) (tptp.top_top _let_16)))) (forall ((X_b $$unsorted) (X_a $$unsorted) (X_1 $$unsorted) (F $$unsorted) (Z $$unsorted) (G $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.fun (tptp.fun X_b tptp.bool) X_a))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.fun X_b X_a))) (let ((_let_5 (tptp.fun _let_4 _let_3))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_4 _let_3 (tptp.hAPP X_a _let_5 (tptp.hAPP (tptp.fun X_a _let_1) (tptp.fun X_a _let_5) (tptp.finite908156982e_idem X_a X_b) F) Z) G) Fa)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 F X_1) X_1) (tptp.ti X_a X_1))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.sum_sum X_a X_b))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.finite_finite_1 _let_3) (tptp.hAPP _let_1 _let_4 (tptp.hAPP _let_2 (tptp.fun _let_1 _let_4) (tptp.sum_Plus X_a X_b) A_1) B))) (and (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_a) A_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) B))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.sum_sum X_a X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun X_b tptp.bool))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.finite_finite_1 X_a) A_1)) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.finite_finite_1 X_b) B)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 _let_1) (tptp.hAPP _let_3 _let_2 (tptp.hAPP _let_4 (tptp.fun _let_3 _let_2) (tptp.sum_Plus X_a X_b) A_1) B)))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.sum_sum X_a X_b))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.finite_finite_1 _let_2) (tptp.hAPP _let_4 _let_3 (tptp.hAPP _let_1 (tptp.fun _let_4 _let_3) (tptp.sum_Plus X_a X_b) A_1) B))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) A_1)))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.sum_sum X_a X_b))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.finite_finite_1 _let_2) (tptp.hAPP _let_1 _let_3 (tptp.hAPP (tptp.fun X_a tptp.bool) (tptp.fun _let_1 _let_3) (tptp.sum_Plus X_a X_b) A_1) B))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) B))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (X_1 $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Z $$unsorted) (G $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP _let_1 X_a Fa A_1))) (let ((_let_3 (tptp.fun X_a X_a))) (let ((_let_4 (tptp.fun _let_1 X_a))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (let ((_let_6 (tptp.fun X_b X_a))) (let ((_let_7 (tptp.fun _let_6 _let_5))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP _let_6 _let_5 (tptp.hAPP X_a _let_7 (tptp.hAPP (tptp.fun X_a _let_3) (tptp.fun X_a _let_7) (tptp.finite908156982e_idem X_a X_b) F) Z) G) Fa)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_1) A_1)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 F (tptp.hAPP X_b X_a G X_1)) _let_2) _let_2)))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.fun (tptp.sum_sum X_a X_b) tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (= (tptp.hAPP _let_2 _let_1 (tptp.hAPP _let_3 (tptp.fun _let_2 _let_1) (tptp.sum_Plus X_a X_b) (tptp.top_top _let_3)) (tptp.top_top _let_2)) (tptp.top_top _let_1)))))) (forall ((Pa $$unsorted) (I_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (let ((_let_3 (tptp.fun tptp.bool tptp.bool))) (let ((_let_4 (tptp.fun tptp.nat _let_3))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 tptp.nat) (tptp.hAPP _let_1 _let_1 (tptp.collect tptp.nat) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_4 (tptp.fun _let_1 _let_1) (tptp.combs tptp.nat tptp.bool tptp.bool) (tptp.hAPP _let_1 _let_4 (tptp.hAPP (tptp.fun tptp.bool _let_3) (tptp.fun _let_1 _let_4) (tptp.combb tptp.bool _let_3 tptp.nat) tptp.fconj) Pa)) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc tptp.nat tptp.nat tptp.bool) (tptp.ord_less tptp.nat)) I_1)))))))))) (forall ((N_3 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat tptp.bool) tptp.bool (tptp.finite_finite_1 tptp.nat) N_3)) (exists ((M $$unsorted)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.nat (tptp.fun _let_1 tptp.bool) (tptp.member tptp.nat) X_2) N_3)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) X_2) M)))))))) (forall ((N_3 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat tptp.bool) tptp.bool (tptp.finite_finite_1 tptp.nat) N_3)) (exists ((M $$unsorted)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.nat (tptp.fun _let_1 tptp.bool) (tptp.member tptp.nat) X_2) N_3)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) X_2) M)))))))) (forall ((U $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (let ((_let_3 (tptp.fun tptp.nat tptp.nat))) (=> (forall ((N $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N) (tptp.hAPP tptp.nat tptp.nat F N)))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 tptp.nat) (tptp.hAPP _let_1 _let_1 (tptp.collect tptp.nat) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc tptp.nat tptp.nat tptp.bool) (tptp.hAPP _let_3 _let_2 (tptp.hAPP _let_2 (tptp.fun _let_3 _let_2) (tptp.combb tptp.nat _let_1 tptp.nat) (tptp.ord_less_eq tptp.nat)) F)) U))))))))) (forall ((Na $$unsorted) (N_3 $$unsorted)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.nat (tptp.fun _let_1 tptp.bool) (tptp.member tptp.nat) X_2) N_3)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) X_2) Na))))) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat tptp.bool) tptp.bool (tptp.finite_finite_1 tptp.nat) N_3)))) (forall ((X_b $$unsorted) (X_a $$unsorted) (B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.sum_sum X_a X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun X_b tptp.bool))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (let ((_let_5 (tptp.hAPP _let_2 tptp.nat (tptp.finite_card _let_1) (tptp.hAPP _let_3 _let_2 (tptp.hAPP _let_4 (tptp.fun _let_3 _let_2) (tptp.sum_Plus X_a X_b) A_1) B)))) (let ((_let_6 (and (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.finite_finite_1 X_a) A_1)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.finite_finite_1 X_b) B))))) (and (=> _let_6 (= _let_5 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) (tptp.hAPP _let_4 tptp.nat (tptp.finite_card X_a) A_1)) (tptp.hAPP _let_3 tptp.nat (tptp.finite_card X_b) B)))) (=> (not _let_6) (= _let_5 (tptp.zero_zero tptp.nat))))))))))) (forall ((N_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N_1) (tptp.zero_zero tptp.nat))))) (forall ((N_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.zero_zero tptp.nat)) N_1))) (forall ((N_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (=> (not (= N_1 _let_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) _let_1) N_1))))) (forall ((M_3 $$unsorted) (N_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M_3) N_1)) (not (= N_1 (tptp.zero_zero tptp.nat))))) (forall ((N_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N_1) (tptp.zero_zero tptp.nat))))) (forall ((Na $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (= (not (= Na _let_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) _let_1) Na))))) (forall ((N_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N_1) (tptp.zero_zero tptp.nat))))) (forall ((N_1 $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) (tptp.zero_zero tptp.nat)) N_1) N_1)) (forall ((M_3 $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M_3) (tptp.zero_zero tptp.nat)) M_3)) (forall ((M_2 $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M_2) Na) _let_1) (and (= M_2 _let_1) (= Na _let_1))))) (forall ((M_3 $$unsorted) (N_1 $$unsorted)) (=> (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M_3) N_1) M_3) (= N_1 (tptp.zero_zero tptp.nat)))) (forall ((Na $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) Na) _let_1)) (= Na _let_1)))) (forall ((N_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.zero_zero tptp.nat)) N_1))) (forall ((X_a $$unsorted)) (=> (tptp.zero X_a) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ti X_a X_1))) (= (= _let_1 _let_2) (= _let_2 _let_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.zero_neq_one X_a) (not (= (tptp.zero_zero X_a) (tptp.one_one X_a))))) (forall ((X_a $$unsorted)) (=> (tptp.zero_neq_one X_a) (not (= (tptp.one_one X_a) (tptp.zero_zero X_a))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_monoid_add X_a) (forall ((A_2 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_2) (tptp.zero_zero X_a)) (tptp.ti X_a A_2))))) (forall ((X_a $$unsorted)) (=> (tptp.monoid_add X_a) (forall ((A_2 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_2) (tptp.zero_zero X_a)) (tptp.ti X_a A_2))))) (forall ((X_a $$unsorted)) (=> (tptp.linord219039673up_add X_a) (forall ((Aa $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (= _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) Aa) Aa)) (= (tptp.ti X_a Aa) _let_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_monoid_add X_a) (forall ((A_2 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) (tptp.zero_zero X_a)) A_2) (tptp.ti X_a A_2))))) (forall ((X_a $$unsorted)) (=> (tptp.monoid_add X_a) (forall ((A_2 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) (tptp.zero_zero X_a)) A_2) (tptp.ti X_a A_2))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_2) _let_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B_1) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_2) B_1)) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B_1 $$unsorted) (A_2 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 B_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.zero_zero X_a)) C)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 A_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_2) C))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B_1 $$unsorted) (C $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 B_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.zero_zero X_a)) A_2)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_2) C))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((Y_2 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) _let_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_2 X_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_2 Y_2)) (= (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) X_1) Y_2) _let_1) (and (= (tptp.ti X_a X_1) _let_1) (= (tptp.ti X_a Y_2) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_2)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_2) B_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord219039673up_add X_a) (forall ((Aa $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) Aa) Aa)) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 Aa) _let_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord219039673up_add X_a) (forall ((Aa $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) Aa) Aa))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 Aa))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_2) _let_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B_1) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_2) B_1)) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((B_1 $$unsorted) (C $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 B_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.zero_zero X_a)) A_2)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_2) C))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.zero_zero X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_2)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_2) B_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord219039673up_add X_a) (forall ((Aa $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) Aa) Aa)) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 Aa) _let_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord219039673up_add X_a) (forall ((Aa $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.zero_zero X_a)))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) Aa) Aa))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 Aa))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) (tptp.one_one X_a))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.one_one X_a)) (tptp.zero_zero X_a)))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.zero_zero X_a)) (tptp.one_one X_a))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.one_one X_a)) (tptp.zero_zero X_a)))))) (forall ((M_2 $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M_2) Na))) (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 M_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 Na)))))) (forall ((X_a $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) A_1))) (= (tptp.hAPP _let_1 tptp.nat (tptp.finite_card X_a) A_1) (tptp.zero_zero tptp.nat))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 (tptp.ord_less_eq X_a) A_2) _let_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B_1) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_2) B_1)) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_2) _let_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 (tptp.ord_less_eq X_a) B_1) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_2) B_1)) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B_1 $$unsorted) (C $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) B_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) A_2)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_2 C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_2) C)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B_1 $$unsorted) (C $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.zero_zero X_a)) A_2)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) B_1) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_2) C)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 (tptp.ord_less X_a) _let_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) _let_1) A_2)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 B_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_2) B_1))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 (tptp.ord_less X_a) _let_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 A_2)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) _let_1) B_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_2) B_1))))))))))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (=> (tptp.linordered_semidom X_a) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.zero_zero X_a)) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) _let_1) _let_1)))))) (forall ((X_a $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) (tptp.hAPP _let_1 tptp.nat (tptp.finite_card X_a) A_1))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) A_1))))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.top_top _let_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) _let_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) (tptp.hAPP _let_1 tptp.nat (tptp.finite_card X_a) _let_2))))))) (forall ((Na $$unsorted) (Pa $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa (tptp.zero_zero tptp.nat)))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa Na)) (exists ((K_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) K_2) Na)) (forall ((I_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) I_2) K_2)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa I_2))))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) K_2) (tptp.one_one tptp.nat))))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_a) A_1)) (=> (=> (exists ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) A_1)))) (= (tptp.one_one tptp.nat) _let_1)) (= (tptp.hAPP _let_2 tptp.nat (tptp.finite_card X_a) A_1) _let_1)))))) (forall ((Na $$unsorted) (Pa $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa (tptp.zero_zero tptp.nat)))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa Na)) (exists ((K_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K_2) Na)) (forall ((I_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I_2) K_2)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa I_2))))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa K_2))))))) (forall ((I $$unsorted) (J_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I) J_2)) (exists ((K_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) K_2)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) I) K_2) J_2))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((Aa $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) Aa) Aa)) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 Aa) _let_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord219039673up_add X_a) (forall ((Aa $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) Aa) Aa) _let_1) (= (tptp.ti X_a Aa) _let_1)))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun X_a X_b))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.finite_finite_1 _let_3) (tptp.top_top _let_4))) (=> (not (= (tptp.hAPP _let_2 tptp.nat (tptp.finite_card X_b) (tptp.top_top _let_2)) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat)))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) (tptp.top_top _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiri456707255roduct X_a) (forall ((Ba $$unsorted) (Aa $$unsorted)) (= (= (tptp.ti X_a Ba) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) Ba) Aa)) (= (tptp.ti X_a Aa) (tptp.zero_zero X_a)))))) (forall ((N_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N_1) (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1)))) (forall ((M_3 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M_3) N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M_3)) (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1))))))) (forall ((N_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1)))) (forall ((N_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1)) N_1)))) (forall ((M_2 $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M_2) Na))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc Na)) M_2)))))) (forall ((M_2 $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc Na))) (let ((_let_2 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M_2))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 _let_1)) (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 Na)) (= M_2 _let_1)))))) (forall ((Na $$unsorted) (M_2 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc Na)) (tptp.hAPP tptp.nat tptp.nat tptp.suc M_2))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Na) M_2)))))) (forall ((M_3 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M_3))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1)))))) (forall ((M_3 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1))) (let ((_let_2 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M_3))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 _let_1)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 N_1))) (= M_3 _let_1)))))) (forall ((M_3 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M_3)) N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M_3) N_1)))))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (= (tptp.hAPP tptp.nat tptp.nat tptp.suc X) (tptp.hAPP tptp.nat tptp.nat tptp.suc Y)) (= X Y))) (forall ((Nat_4 $$unsorted) (Nat_3 $$unsorted)) (= (= (tptp.hAPP tptp.nat tptp.nat tptp.suc Nat_4) (tptp.hAPP tptp.nat tptp.nat tptp.suc Nat_3)) (= Nat_4 Nat_3))) (forall ((N_1 $$unsorted)) (not (= (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1) N_1))) (forall ((N_1 $$unsorted)) (not (= N_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1)))) (forall ((M_3 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M_3)) N_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M_3) (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1)))))) (forall ((M_3 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M_3)) N_1) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M_3) N_1)))))) (forall ((M_3 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M_3))) (= (tptp.hAPP tptp.nat tptp.nat _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1)) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat _let_1 N_1))))) (forall ((M_2 $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M_2) Na))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Na) (tptp.hAPP tptp.nat tptp.nat tptp.suc M_2))))))) (forall ((M_2 $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M_2))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc Na))) (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 Na)) (= M_2 Na))))) (forall ((M_2 $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M_2)) (tptp.hAPP tptp.nat tptp.nat tptp.suc Na))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M_2) Na)))))) (forall ((Na $$unsorted) (M_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) Na))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 M_2))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M_2))) (= Na M_2))))) (forall ((N_1 $$unsorted) (M_3 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N_1))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 M_3))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M_3))) (= M_3 N_1))))) (forall ((M_3 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M_3))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1)))))) (forall ((M_3 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M_3))) (let ((_let_2 (tptp.ord_less tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 M_3) N_1)) (=> (not (= _let_1 N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 _let_1) N_1)))))))) (forall ((K_1 $$unsorted) (I $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 I) J_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 J_2) K_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc I)) K_1))))))) (forall ((M_3 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M_3))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 N_1))) (= M_3 N_1))))) (forall ((M_3 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M_3)) N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M_3) N_1)))))) (forall ((M_3 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M_3)) (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M_3) N_1)))))) (= _let_19 (tptp.hAPP tptp.nat tptp.nat tptp.suc _let_15)) (forall ((M_3 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc M_3)) N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) M_3) N_1))))) (forall ((M_2 $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) M_2) Na)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) Na) (tptp.hAPP tptp.nat tptp.nat tptp.suc M_2))) (= Na M_2))))) (forall ((M_3 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) M_3) N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc M_3)) N_1))))) (forall ((M_3 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) M_3) N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) M_3) (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1)))))) (forall ((M_2 $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc M_2)) Na)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) M_2) Na))))) (forall ((M_2 $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) M_2) (tptp.hAPP tptp.nat tptp.nat tptp.suc Na))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) M_2) Na))))) (forall ((Na $$unsorted) (M_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) Na) M_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc Na)) M_2))))) (forall ((M_2 $$unsorted) (Na $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M_2) Na)) (exists ((K_2 $$unsorted)) (= Na (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M_2) K_2)))))) (forall ((I $$unsorted) (M_3 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M_3) I))))) (forall ((I $$unsorted) (M_3 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) I) M_3))))) (forall ((M_2 $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.nat tptp.nat tptp.suc _let_1))) (= (= _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M_2) Na)) (or (and (= M_2 _let_2) (= Na _let_1)) (and (= M_2 _let_1) (= Na _let_2))))))) (forall ((M_2 $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.nat tptp.nat tptp.suc _let_1))) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M_2) Na) _let_2) (or (and (= M_2 _let_2) (= Na _let_1)) (and (= M_2 _let_1) (= Na _let_2))))))) (forall ((Na $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) Na)) (exists ((M $$unsorted)) (= Na (tptp.hAPP tptp.nat tptp.nat tptp.suc M))))) (forall ((Na $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) Na) (tptp.hAPP tptp.nat tptp.nat tptp.suc _let_1))) (= Na _let_1)))) (forall ((M_2 $$unsorted) (Na $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M_2) (tptp.hAPP tptp.nat tptp.nat tptp.suc Na))) (or (= M_2 (tptp.zero_zero tptp.nat)) (exists ((J $$unsorted)) (and (= M_2 (tptp.hAPP tptp.nat tptp.nat tptp.suc J)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) J) Na))))))) (forall ((N_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP (tptp.fun tptp.nat tptp.nat) (tptp.fun _let_1 tptp.bool) (tptp.inj_on tptp.nat tptp.nat) tptp.suc) N_3)))) (forall ((M_3 $$unsorted)) (not (= (tptp.hAPP tptp.nat tptp.nat tptp.suc M_3) (tptp.zero_zero tptp.nat)))) (forall ((M_3 $$unsorted)) (not (= (tptp.zero_zero tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc M_3)))) (forall ((Nat_2 $$unsorted)) (not (= (tptp.hAPP tptp.nat tptp.nat tptp.suc Nat_2) (tptp.zero_zero tptp.nat)))) (forall ((M_3 $$unsorted)) (not (= (tptp.hAPP tptp.nat tptp.nat tptp.suc M_3) (tptp.zero_zero tptp.nat)))) (forall ((Nat_1 $$unsorted)) (not (= (tptp.zero_zero tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc Nat_1)))) (forall ((M_3 $$unsorted)) (not (= (tptp.zero_zero tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc M_3)))) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) X_2) (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc X_2))))) (forall ((Na $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (= (tptp.hAPP _let_1 tptp.nat (tptp.finite_card tptp.nat) (tptp.hAPP _let_1 _let_1 (tptp.collect tptp.nat) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc tptp.nat tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat)) Na))) (tptp.hAPP tptp.nat tptp.nat tptp.suc Na))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_2 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_2) C) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 C) A_2))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_2 $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 A_2))) (let ((_let_4 (tptp.hAPP X_a _let_2 _let_1 C))) (= (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a _let_4 D)) (tptp.hAPP X_a X_a _let_4 (tptp.hAPP X_a X_a _let_3 D)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_2 $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 A_2))) (= (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 C) D)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 C)) D)))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 A_2))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 B_1)) C) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B_1) C))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 A_2))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 B_1)) C) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 C)) B_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 A_2))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 B_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 C) D)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B_1) D))))))))) (forall ((I_1 $$unsorted) (M_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (let ((_let_3 (tptp.hAPP _let_2 _let_2 (tptp.combc tptp.nat tptp.nat tptp.bool) (tptp.ord_less tptp.nat)))) (let ((_let_4 (tptp.member tptp.nat))) (let ((_let_5 (tptp.combc tptp.nat _let_1 tptp.bool))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (let ((_let_7 (tptp.fun _let_1 tptp.bool))) (let ((_let_8 (tptp.fun tptp.nat _let_7))) (let ((_let_9 (tptp.fun tptp.bool tptp.bool))) (let ((_let_10 (tptp.fun tptp.nat _let_9))) (let ((_let_11 (tptp.hAPP (tptp.fun tptp.bool _let_9) (tptp.fun _let_1 _let_10) (tptp.combb tptp.bool _let_9 tptp.nat) tptp.fconj))) (let ((_let_12 (tptp.combs tptp.nat tptp.bool tptp.bool))) (let ((_let_13 (tptp.collect tptp.nat))) (let ((_let_14 (tptp.finite_card tptp.nat))) (let ((_let_15 (tptp.fun tptp.nat tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.nat _let_7 _let_4 (tptp.zero_zero tptp.nat)) M_4)) (= (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP _let_1 tptp.nat _let_14 (tptp.hAPP _let_1 _let_1 _let_13 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_10 _let_6 _let_12 (tptp.hAPP _let_1 _let_10 _let_11 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_8 _let_6 _let_5 (tptp.hAPP _let_15 _let_8 (tptp.hAPP _let_8 (tptp.fun _let_15 _let_8) (tptp.combb tptp.nat _let_7 tptp.nat) _let_4) tptp.suc)) M_4))) (tptp.hAPP tptp.nat _let_1 _let_3 I_1))))) (tptp.hAPP _let_1 tptp.nat _let_14 (tptp.hAPP _let_1 _let_1 _let_13 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_10 _let_6 _let_12 (tptp.hAPP _let_1 _let_10 _let_11 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_8 _let_6 _let_5 _let_4) M_4))) (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat tptp.suc I_1))))))))))))))))))))))) (forall ((I_1 $$unsorted) (M_4 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (let ((_let_4 (tptp.member tptp.nat))) (let ((_let_5 (tptp.fun _let_2 _let_2))) (let ((_let_6 (tptp.fun _let_2 tptp.bool))) (let ((_let_7 (tptp.fun tptp.bool tptp.bool))) (let ((_let_8 (tptp.fun tptp.nat _let_7))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.nat _let_6 _let_4 _let_1) M_4)) (not (= (tptp.hAPP _let_2 tptp.nat (tptp.finite_card tptp.nat) (tptp.hAPP _let_2 _let_2 (tptp.collect tptp.nat) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_8 _let_5 (tptp.combs tptp.nat tptp.bool tptp.bool) (tptp.hAPP _let_2 _let_8 (tptp.hAPP (tptp.fun tptp.bool _let_7) (tptp.fun _let_2 _let_8) (tptp.combb tptp.bool _let_7 tptp.nat) tptp.fconj) (tptp.hAPP _let_2 _let_2 (tptp.hAPP (tptp.fun tptp.nat _let_6) _let_5 (tptp.combc tptp.nat _let_2 tptp.bool) _let_4) M_4))) (tptp.hAPP tptp.nat _let_2 (tptp.hAPP _let_3 _let_3 (tptp.combc tptp.nat tptp.nat tptp.bool) (tptp.ord_less tptp.nat)) (tptp.hAPP tptp.nat tptp.nat tptp.suc I_1))))) _let_1)))))))))))) (forall ((I_1 $$unsorted) (M_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (let ((_let_3 (tptp.hAPP _let_2 _let_2 (tptp.combc tptp.nat tptp.nat tptp.bool) (tptp.ord_less tptp.nat)))) (let ((_let_4 (tptp.member tptp.nat))) (let ((_let_5 (tptp.combc tptp.nat _let_1 tptp.bool))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (let ((_let_7 (tptp.fun _let_1 tptp.bool))) (let ((_let_8 (tptp.fun tptp.nat _let_7))) (let ((_let_9 (tptp.fun tptp.bool tptp.bool))) (let ((_let_10 (tptp.fun tptp.nat _let_9))) (let ((_let_11 (tptp.hAPP (tptp.fun tptp.bool _let_9) (tptp.fun _let_1 _let_10) (tptp.combb tptp.bool _let_9 tptp.nat) tptp.fconj))) (let ((_let_12 (tptp.combs tptp.nat tptp.bool tptp.bool))) (let ((_let_13 (tptp.collect tptp.nat))) (let ((_let_14 (tptp.finite_card tptp.nat))) (let ((_let_15 (tptp.fun tptp.nat tptp.nat))) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.nat _let_7 _let_4 (tptp.zero_zero tptp.nat)) M_4))) (= (tptp.hAPP _let_1 tptp.nat _let_14 (tptp.hAPP _let_1 _let_1 _let_13 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_10 _let_6 _let_12 (tptp.hAPP _let_1 _let_10 _let_11 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_8 _let_6 _let_5 (tptp.hAPP _let_15 _let_8 (tptp.hAPP _let_8 (tptp.fun _let_15 _let_8) (tptp.combb tptp.nat _let_7 tptp.nat) _let_4) tptp.suc)) M_4))) (tptp.hAPP tptp.nat _let_1 _let_3 I_1)))) (tptp.hAPP _let_1 tptp.nat _let_14 (tptp.hAPP _let_1 _let_1 _let_13 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_10 _let_6 _let_12 (tptp.hAPP _let_1 _let_10 _let_11 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_8 _let_6 _let_5 _let_4) M_4))) (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat tptp.suc I_1))))))))))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_2 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) (tptp.zero_zero X_a)) A_2) (tptp.ti X_a A_2))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_2 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_2) (tptp.zero_zero X_a)) (tptp.ti X_a A_2))))) (forall ((Pa $$unsorted) (I_1 $$unsorted) (J_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) I_1) J_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa J_1)) (=> (forall ((I_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I_2) J_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa (tptp.hAPP tptp.nat tptp.nat tptp.suc I_2))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa I_2))))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa I_1)))))) (forall ((M_3 $$unsorted) (N_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M_3) N_1)) (exists ((K_2 $$unsorted)) (= N_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M_3) K_2)))))) (forall ((N_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N_1)) (exists ((M $$unsorted)) (= N_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((Na $$unsorted) (N_2 $$unsorted) (F $$unsorted)) (=> (forall ((N $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP tptp.nat X_a F N)) (tptp.hAPP tptp.nat X_a F (tptp.hAPP tptp.nat tptp.nat tptp.suc N))))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) Na) N_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP tptp.nat X_a F Na)) (tptp.hAPP tptp.nat X_a F N_2)))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((Na $$unsorted) (N_2 $$unsorted) (F $$unsorted)) (=> (forall ((N $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.hAPP tptp.nat X_a F N)) (tptp.hAPP tptp.nat X_a F (tptp.hAPP tptp.nat tptp.nat tptp.suc N))))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) Na) N_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.hAPP tptp.nat X_a F Na)) (tptp.hAPP tptp.nat X_a F N_2)))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((Na $$unsorted) (M_2 $$unsorted) (F $$unsorted)) (=> (forall ((N $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.hAPP tptp.nat X_a F N)) (tptp.hAPP tptp.nat X_a F (tptp.hAPP tptp.nat tptp.nat tptp.suc N))))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.hAPP tptp.nat X_a F Na)) (tptp.hAPP tptp.nat X_a F M_2))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) Na) M_2))))))) (forall ((N_1 $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) (tptp.one_one tptp.nat)) N_1))) (forall ((N_1 $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) N_1) (tptp.one_one tptp.nat)))) (forall ((N_1 $$unsorted) (M_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1)) M_1)) (exists ((M $$unsorted)) (= M_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M))))) (forall ((I $$unsorted) (K_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I) K_1)) (=> (not (= K_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc I))) (not (forall ((J $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I) J)) (not (= K_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc J))))))))) (forall ((I $$unsorted) (K_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc I)) K_1)) (not (forall ((J $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I) J)) (not (= K_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc J)))))))) (forall ((N_1 $$unsorted)) (=> (not (= N_1 (tptp.zero_zero tptp.nat))) (exists ((M $$unsorted)) (= N_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M))))) (forall ((Y $$unsorted)) (=> (not (= Y (tptp.zero_zero tptp.nat))) (not (forall ((Nat $$unsorted)) (not (= Y (tptp.hAPP tptp.nat tptp.nat tptp.suc Nat))))))) (forall ((Pa $$unsorted) (K $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa K)) (=> (forall ((N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa (tptp.hAPP tptp.nat tptp.nat tptp.suc N))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa N)))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa (tptp.zero_zero tptp.nat)))))) (forall ((Na $$unsorted) (Pa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa (tptp.zero_zero tptp.nat))) (=> (forall ((N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa (tptp.hAPP tptp.nat tptp.nat tptp.suc N))))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa Na))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_field X_a) (forall ((X $$unsorted) (Y $$unsorted)) (=> (forall ((E $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) (tptp.zero_zero X_a)) E)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) X) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) Y) E)))))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X) Y)))))) (forall ((X_a $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.nat))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat _let_3))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_a) A_1)) (= (tptp.hAPP _let_2 tptp.nat (tptp.finite_card X_a) A_1) (tptp.hAPP _let_2 tptp.nat (tptp.hAPP tptp.nat _let_3 (tptp.hAPP _let_1 _let_4 (tptp.hAPP (tptp.fun tptp.nat (tptp.fun tptp.nat tptp.nat)) (tptp.fun _let_1 _let_4) (tptp.finite_fold_image tptp.nat X_a) (tptp.plus_plus tptp.nat)) (tptp.hAPP tptp.nat _let_1 (tptp.combk tptp.nat X_a) (tptp.one_one tptp.nat))) (tptp.zero_zero tptp.nat)) A_1)))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP _let_2 tptp.nat (tptp.finite_card X_a) A_1))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_a) A_1)))) (let ((_let_5 (tptp.fun X_a tptp.nat))) (let ((_let_6 (tptp.fun _let_2 tptp.nat))) (let ((_let_7 (tptp.fun tptp.nat _let_6))) (and (=> _let_4 (= _let_3 (tptp.hAPP _let_2 tptp.nat (tptp.hAPP tptp.nat _let_6 (tptp.hAPP _let_5 _let_7 (tptp.hAPP (tptp.fun tptp.nat (tptp.fun tptp.nat tptp.nat)) (tptp.fun _let_5 _let_7) (tptp.finite_fold_image tptp.nat X_a) (tptp.plus_plus tptp.nat)) (tptp.hAPP tptp.nat _let_5 (tptp.combk tptp.nat X_a) (tptp.one_one tptp.nat))) _let_1) A_1))) (=> (not _let_4) (= _let_3 _let_1))))))))))) (= (tptp.hAPP _let_12 _let_16 (tptp.hAPP _let_18 (tptp.fun _let_12 _let_16) (tptp.image tptp.arrow_660593299e_indi tptp.nat) tptp.h) _let_13) (tptp.hAPP tptp.nat _let_16 (tptp.hAPP tptp.nat _let_17 (tptp.ord_atLeastLessThan tptp.nat) _let_15) _let_14)) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((Aa $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.plus_plus X_a))) (let ((_let_5 (tptp.fun X_a X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_a (tptp.fun _let_3 tptp.bool) (tptp.member X_a) Aa) (tptp.ring_1_Ints X_a))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_5 _let_4 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_5 _let_4 (tptp.one_one X_a)) Aa)) Aa)) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 Aa) _let_1)))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (A_1 $$unsorted) (Ba $$unsorted) (F $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (= (tptp.ti X_a Ba) (tptp.hAPP X_b X_a F X_1)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_b (tptp.fun _let_2 tptp.bool) (tptp.member X_b) X_1) A_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) Ba) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_b X_a) (tptp.fun _let_2 _let_1) (tptp.image X_b X_a) F) A_1)))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (Ha $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_a) Fa)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun _let_2 _let_1) (tptp.image X_a X_b) Ha) Fa))))))) (forall ((L $$unsorted) (U $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 tptp.nat) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_1) (tptp.ord_atLeastLessThan tptp.nat) L) U))))) (not (forall ((H $$unsorted)) (let ((_let_1 (tptp.fun tptp.arrow_660593299e_indi tptp.bool))) (let ((_let_2 (tptp.top_top _let_1))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (let ((_let_4 (tptp.fun tptp.arrow_660593299e_indi tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_4 (tptp.fun _let_1 tptp.bool) (tptp.inj_on tptp.arrow_660593299e_indi tptp.nat) H) _let_2)) (not (= (tptp.hAPP _let_1 _let_3 (tptp.hAPP _let_4 (tptp.fun _let_1 _let_3) (tptp.image tptp.arrow_660593299e_indi tptp.nat) H) _let_2) (tptp.hAPP tptp.nat _let_3 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_3) (tptp.ord_atLeastLessThan tptp.nat) (tptp.zero_zero tptp.nat)) (tptp.hAPP _let_1 tptp.nat (tptp.finite_card tptp.arrow_660593299e_indi) _let_2))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((Aa $$unsorted) (Ba $$unsorted) (Ca $$unsorted) (Da $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 Ba))) (let ((_let_4 (tptp.ord_atLeastLessThan X_a))) (let ((_let_5 (tptp.fun X_a _let_2))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) (tptp.hAPP X_a _let_2 (tptp.hAPP X_a _let_5 _let_4 Aa) Ba)) (tptp.hAPP X_a _let_2 (tptp.hAPP X_a _let_5 _let_4 Ca) Da))) (or (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 Aa)) (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Ca) Aa)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 Da))))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (F $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.fun X_a X_b))) (let ((_let_4 (tptp.fun X_a _let_1))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP _let_3 (tptp.fun _let_5 tptp.bool) (tptp.member _let_3) F) (tptp.hAPP _let_4 _let_5 (tptp.hAPP _let_2 (tptp.fun _let_4 _let_5) (tptp.pi X_a X_b) A_1) (tptp.hAPP _let_1 _let_4 (tptp.combk _let_1 X_a) B)))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) (tptp.hAPP _let_2 _let_1 (tptp.hAPP _let_3 (tptp.fun _let_2 _let_1) (tptp.image X_a X_b) F) A_1)) B))))))))) (forall ((X_a $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun X_a X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) A_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_3 (tptp.fun _let_1 _let_1) (tptp.image X_a X_a) F) A_1))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_3 _let_2 (tptp.inj_on X_a X_a) F) A_1)))))))) (forall ((X_a $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_2 (tptp.fun _let_1 _let_1) (tptp.image X_a X_a) F) A_1))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) A_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_4 (tptp.ord_less_eq _let_1) _let_3) A_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_2 _let_4 (tptp.inj_on X_a X_a) F) A_1)) (= _let_3 (tptp.ti _let_1 A_1)))))))))) (forall ((X_a $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.top_top _let_1))) (let ((_let_3 (tptp.fun X_a X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) _let_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_3 (tptp.fun _let_1 tptp.bool) (tptp.inj_on X_a X_a) F) _let_2)) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_3 (tptp.fun _let_1 _let_1) (tptp.image X_a X_a) F) _let_2) _let_2))))))) (forall ((X_a $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.top_top _let_1))) (let ((_let_3 (tptp.fun X_a X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) _let_2)) (=> (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_3 (tptp.fun _let_1 _let_1) (tptp.image X_a X_a) F) _let_2) _let_2) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_3 (tptp.fun _let_1 tptp.bool) (tptp.inj_on X_a X_a) F) _let_2)))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (A_1 $$unsorted) (B $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun X_b tptp.bool))) (let ((_let_4 (tptp.fun X_a X_b))) (let ((_let_5 (tptp.hAPP _let_4 (tptp.fun _let_1 _let_3) (tptp.image X_a X_b) F))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_4 _let_2 (tptp.inj_on X_a X_b) F) (tptp.top_top _let_1))) (= (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_3 (tptp.fun _let_3 tptp.bool) (tptp.ord_less_eq _let_3) (tptp.hAPP _let_1 _let_3 _let_5 A_1)) (tptp.hAPP _let_1 _let_3 _let_5 B))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_1) B)))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) A_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP _let_2 tptp.nat (tptp.finite_card X_b) (tptp.hAPP _let_1 _let_2 (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun _let_1 _let_2) (tptp.image X_a X_b) F) A_1))) (tptp.hAPP _let_1 tptp.nat (tptp.finite_card X_a) A_1))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun X_a X_b))) (let ((_let_3 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) A_1)) (=> (= (tptp.hAPP _let_3 tptp.nat (tptp.finite_card X_b) (tptp.hAPP _let_1 _let_3 (tptp.hAPP _let_2 (tptp.fun _let_1 _let_3) (tptp.image X_a X_b) F) A_1)) (tptp.hAPP _let_1 tptp.nat (tptp.finite_card X_a) A_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_1 tptp.bool) (tptp.inj_on X_a X_b) F) A_1)))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun X_a X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) A_1)) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_3 (tptp.fun _let_1 tptp.bool) (tptp.inj_on X_a X_b) F) A_1)) (= (tptp.hAPP _let_2 tptp.nat (tptp.finite_card X_b) (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_3 (tptp.fun _let_1 _let_2) (tptp.image X_a X_b) F) A_1)) (tptp.hAPP _let_1 tptp.nat (tptp.finite_card X_a) A_1)))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_b X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP _let_3 tptp.nat (tptp.finite_card X_a) (tptp.hAPP _let_1 _let_3 (tptp.hAPP _let_2 (tptp.fun _let_1 _let_3) (tptp.image X_b X_a) F) A_1))) (tptp.hAPP _let_1 tptp.nat (tptp.finite_card X_b) A_1))) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_1 tptp.bool) (tptp.inj_on X_b X_a) F) A_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.ring_char_0 X_a) (forall ((Aa $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a (tptp.fun _let_2 tptp.bool) (tptp.member X_a) Aa) (tptp.ring_1_Ints X_a))) (= (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) Aa) Aa) _let_1) (= (tptp.ti X_a Aa) _let_1)))))))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.ring_1 X_a) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) (tptp.zero_zero X_a)) (tptp.ring_1_Ints X_a)))))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.ring_1 X_a) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) (tptp.one_one X_a)) (tptp.ring_1_Ints X_a)))))) (forall ((X_a $$unsorted)) (=> (tptp.ring_1 X_a) (forall ((Ba $$unsorted) (Aa $$unsorted)) (let ((_let_1 (tptp.ring_1_Ints X_a))) (let ((_let_2 (tptp.member X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_a _let_4 _let_2 Aa) _let_1)) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_a _let_4 _let_2 Ba) _let_1)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_a _let_4 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) Aa) Ba)) _let_1))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (A_1 $$unsorted) (F $$unsorted) (X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.fun X_a X_b))) (let ((_let_4 (tptp.hAPP _let_2 _let_1 (tptp.hAPP _let_3 (tptp.fun _let_2 _let_1) (tptp.image X_a X_b) F) A_1))) (let ((_let_5 (tptp.member X_b))) (let ((_let_6 (tptp.fun _let_1 tptp.bool))) (let ((_let_7 (tptp.fun X_b X_a))) (let ((_let_8 (tptp.hAPP _let_3 _let_7 (tptp.hAPP _let_2 (tptp.fun _let_3 _let_7) (tptp.hilbert_inv_into X_a X_b) A_1) F))) (=> (= (tptp.hAPP X_b X_a _let_8 X_1) (tptp.hAPP X_b X_a _let_8 Y_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_6 _let_5 X_1) _let_4)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_6 _let_5 Y_2) _let_4)) (= (tptp.ti X_b X_1) (tptp.ti X_b Y_2)))))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_1 $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_b))) (let ((_let_2 (tptp.fun X_b X_a))) (let ((_let_3 (tptp.fun X_b tptp.bool))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP X_a (tptp.fun _let_4 tptp.bool) (tptp.member X_a) X_1) (tptp.hAPP _let_3 _let_4 (tptp.hAPP _let_2 (tptp.fun _let_3 _let_4) (tptp.image X_b X_a) F) A_1))) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_b (tptp.fun _let_3 tptp.bool) (tptp.member X_b) (tptp.hAPP X_a X_b (tptp.hAPP _let_2 _let_1 (tptp.hAPP _let_3 (tptp.fun _let_2 _let_1) (tptp.hilbert_inv_into X_b X_a) A_1) F) X_1)) A_1)))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (Y_2 $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_b))) (let ((_let_2 (tptp.fun X_b X_a))) (let ((_let_3 (tptp.fun X_b tptp.bool))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP X_a (tptp.fun _let_4 tptp.bool) (tptp.member X_a) Y_2) (tptp.hAPP _let_3 _let_4 (tptp.hAPP _let_2 (tptp.fun _let_3 _let_4) (tptp.image X_b X_a) F) A_1))) (= (tptp.hAPP X_b X_a F (tptp.hAPP X_a X_b (tptp.hAPP _let_2 _let_1 (tptp.hAPP _let_3 (tptp.fun _let_2 _let_1) (tptp.hilbert_inv_into X_b X_a) A_1) F) Y_2)) (tptp.ti X_a Y_2)))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (Ba $$unsorted) (F $$unsorted) (X_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a (tptp.fun _let_2 tptp.bool) (tptp.member X_a) X_1) A_1)) (=> (= (tptp.ti X_b Ba) (tptp.hAPP X_a X_b F X_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) Ba) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun _let_2 _let_1) (tptp.image X_a X_b) F) A_1)))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F $$unsorted) (X_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a (tptp.fun _let_2 tptp.bool) (tptp.member X_a) X_1) A_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) (tptp.hAPP X_a X_b F X_1)) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun _let_2 _let_1) (tptp.image X_a X_b) F) A_1))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (Z $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) Z) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_b X_a) (tptp.fun _let_2 _let_1) (tptp.image X_b X_a) F) A_1))) (exists ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_2) A_1)) (= (tptp.ti X_a Z) (tptp.hAPP X_b X_a F X_2))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (X_c $$unsorted) (F $$unsorted) (G $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c X_a))) (let ((_let_2 (tptp.fun X_c X_b))) (let ((_let_3 (tptp.fun X_b X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (let ((_let_5 (tptp.fun X_c tptp.bool))) (let ((_let_6 (tptp.fun X_b tptp.bool))) (= (tptp.hAPP _let_6 _let_4 (tptp.hAPP _let_3 (tptp.fun _let_6 _let_4) (tptp.image X_b X_a) F) (tptp.hAPP _let_5 _let_6 (tptp.hAPP _let_2 (tptp.fun _let_5 _let_6) (tptp.image X_c X_b) G) A_1)) (tptp.hAPP _let_5 _let_4 (tptp.hAPP _let_1 (tptp.fun _let_5 _let_4) (tptp.image X_c X_a) (tptp.hAPP _let_2 _let_1 (tptp.hAPP _let_3 (tptp.fun _let_2 _let_1) (tptp.combb X_b X_a X_c) F) G)) A_1))))))))) (forall ((X_a $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_a X_a) (tptp.fun _let_1 _let_1) (tptp.image X_a X_a) (tptp.combi X_a)) Y_1) (tptp.ti _let_1 Y_1)))) (forall ((X_a $$unsorted) (X_b $$unsorted) (B $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) B) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_b X_a) (tptp.fun _let_2 _let_1) (tptp.image X_b X_a) F) A_1))) (exists ((AA $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (and (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) AA) A_1)) (= (tptp.ti _let_1 B) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_b X_a) (tptp.fun _let_2 _let_1) (tptp.image X_b X_a) F) AA)))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun _let_2 _let_1) (tptp.image X_a X_b) F))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) A_1) B)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) (tptp.hAPP _let_2 _let_1 _let_3 A_1)) (tptp.hAPP _let_2 _let_1 _let_3 B)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((Ca $$unsorted) (Da $$unsorted) (Aa $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.ord_atLeastLessThan X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.fun X_a _let_2))) (let ((_let_4 (tptp.ord_less X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_4 Aa) Ba)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_4 Ca) Da)) (= (= (tptp.hAPP X_a _let_2 (tptp.hAPP X_a _let_3 _let_1 Aa) Ba) (tptp.hAPP X_a _let_2 (tptp.hAPP X_a _let_3 _let_1 Ca) Da)) (and (= (tptp.ti X_a Aa) (tptp.ti X_a Ca)) (= (tptp.ti X_a Ba) (tptp.ti X_a Da))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((Aa $$unsorted) (Ba $$unsorted) (Ca $$unsorted) (Da $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.ord_atLeastLessThan X_a))) (let ((_let_4 (tptp.fun X_a _let_2))) (=> (= (tptp.hAPP X_a _let_2 (tptp.hAPP X_a _let_4 _let_3 Aa) Ba) (tptp.hAPP X_a _let_2 (tptp.hAPP X_a _let_4 _let_3 Ca) Da)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Aa) Ba)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Ca) Da)) (= (tptp.ti X_a Aa) (tptp.ti X_a Ca)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((Aa $$unsorted) (Ba $$unsorted) (Ca $$unsorted) (Da $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.ord_atLeastLessThan X_a))) (let ((_let_4 (tptp.fun X_a _let_2))) (=> (= (tptp.hAPP X_a _let_2 (tptp.hAPP X_a _let_4 _let_3 Aa) Ba) (tptp.hAPP X_a _let_2 (tptp.hAPP X_a _let_4 _let_3 Ca) Da)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Aa) Ba)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Ca) Da)) (= (tptp.ti X_a Ba) (tptp.ti X_a Da)))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (X_c $$unsorted) (F $$unsorted) (G $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.top_top _let_1))) (let ((_let_3 (tptp.fun X_c tptp.bool))) (let ((_let_4 (tptp.fun X_b X_c))) (let ((_let_5 (tptp.fun X_a tptp.bool))) (let ((_let_6 (tptp.fun X_c X_a))) (let ((_let_7 (tptp.fun X_b X_a))) (= (tptp.hAPP _let_1 _let_5 (tptp.hAPP _let_7 (tptp.fun _let_1 _let_5) (tptp.image X_b X_a) (tptp.hAPP _let_4 _let_7 (tptp.hAPP _let_6 (tptp.fun _let_4 _let_7) (tptp.combb X_c X_a X_b) F) G)) _let_2) (tptp.hAPP _let_3 _let_5 (tptp.hAPP _let_6 (tptp.fun _let_3 _let_5) (tptp.image X_c X_a) F) (tptp.hAPP _let_1 _let_3 (tptp.hAPP _let_4 (tptp.fun _let_1 _let_3) (tptp.image X_b X_c) G) _let_2))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (Ba $$unsorted) (F $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (= (tptp.ti X_a Ba) (tptp.hAPP X_b X_a F X_1)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a (tptp.fun _let_2 tptp.bool) (tptp.member X_a) Ba) (tptp.hAPP _let_1 _let_2 (tptp.hAPP (tptp.fun X_b X_a) (tptp.fun _let_1 _let_2) (tptp.image X_b X_a) F) (tptp.top_top _let_1)))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (F $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a (tptp.fun _let_2 tptp.bool) (tptp.member X_a) (tptp.hAPP X_b X_a F X_1)) (tptp.hAPP _let_1 _let_2 (tptp.hAPP (tptp.fun X_b X_a) (tptp.fun _let_1 _let_2) (tptp.image X_b X_a) F) (tptp.top_top _let_1))))))) (forall ((X_c $$unsorted) (X_a $$unsorted) (X_b $$unsorted) (F $$unsorted) (G $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.top_top _let_1))) (let ((_let_3 (tptp.fun X_b X_c))) (let ((_let_4 (tptp.fun X_b X_a))) (let ((_let_5 (tptp.fun X_c tptp.bool))) (let ((_let_6 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.finite_finite_1 X_a) (tptp.hAPP _let_1 _let_6 (tptp.hAPP _let_4 (tptp.fun _let_1 _let_6) (tptp.image X_b X_a) G) _let_2))) (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.finite_finite_1 X_c) (tptp.hAPP _let_1 _let_5 (tptp.hAPP _let_3 (tptp.fun _let_1 _let_5) (tptp.image X_b X_c) (tptp.hAPP _let_4 _let_3 (tptp.hAPP (tptp.fun X_a X_c) (tptp.fun _let_4 _let_3) (tptp.combb X_a X_c X_b) F) G)) _let_2))))))))))) (forall ((A_1 $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_1) (tptp.ord_atLeastLessThan tptp.nat) K) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) K) (tptp.hAPP _let_1 tptp.nat (tptp.finite_card tptp.nat) A_1))))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) A_1) _let_2)) (= A_1 _let_2))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (A_1 $$unsorted) (F $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.fun X_a X_b))) (let ((_let_4 (tptp.hAPP _let_3 (tptp.fun _let_2 _let_1) (tptp.image X_a X_b) F))) (let ((_let_5 (tptp.fun _let_2 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_3 _let_5 (tptp.inj_on X_a X_b) F) B)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 _let_5 (tptp.ord_less _let_2) A_1) B)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less _let_1) (tptp.hAPP _let_2 _let_1 _let_4 A_1)) (tptp.hAPP _let_2 _let_1 _let_4 B))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (A_1 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.top_top _let_2))) (let ((_let_4 (tptp.fun X_a X_b))) (let ((_let_5 (tptp.fun X_b X_a))) (let ((_let_6 (tptp.hAPP _let_5 (tptp.fun _let_2 _let_1) (tptp.image X_b X_a) F))) (=> (= (tptp.hAPP _let_2 _let_1 _let_6 _let_3) (tptp.top_top _let_1)) (= (tptp.hAPP _let_2 _let_1 _let_6 (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_4 (tptp.fun _let_1 _let_2) (tptp.image X_a X_b) (tptp.hAPP _let_5 _let_4 (tptp.hAPP _let_2 (tptp.fun _let_5 _let_4) (tptp.hilbert_inv_into X_b X_a) _let_3) F)) A_1)) (tptp.ti _let_1 A_1)))))))))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.preorder T_1) (tptp.preorder (tptp.fun T_2 T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (and (tptp.finite_finite T_1) (tptp.finite_finite T_2)) (tptp.finite_finite (tptp.fun T_2 T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.order T_1) (tptp.order (tptp.fun T_2 T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.top T_1) (tptp.top (tptp.fun T_2 T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.ord T_1) (tptp.ord (tptp.fun T_2 T_1)))) (tptp.semiri456707255roduct tptp.nat) (tptp.ordere223160158up_add tptp.nat) (tptp.ordere236663937imp_le tptp.nat) (tptp.ordere779506340up_add tptp.nat) (tptp.ordere216010020id_add tptp.nat) (tptp.cancel146912293up_add tptp.nat) (tptp.cancel_semigroup_add tptp.nat) (tptp.linordered_semidom tptp.nat) (tptp.ab_semigroup_add tptp.nat) (tptp.comm_monoid_add tptp.nat) (tptp.comm_semiring_1 tptp.nat) (tptp.zero_neq_one tptp.nat) (tptp.preorder tptp.nat) (tptp.linorder tptp.nat) (tptp.monoid_add tptp.nat) (tptp.order tptp.nat) (tptp.ord tptp.nat) (tptp.zero tptp.nat) (tptp.one tptp.nat) (tptp.preorder tptp.bool) (tptp.finite_finite tptp.bool) (tptp.order tptp.bool) (tptp.top tptp.bool) (tptp.ord tptp.bool) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (and (tptp.finite_finite T_1) (tptp.finite_finite T_2)) (tptp.finite_finite (tptp.sum_sum T_2 T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.finite_finite T_1) (tptp.finite_finite (tptp.option T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (and (tptp.finite_finite T_1) (tptp.finite_finite T_2)) (tptp.finite_finite (tptp.product_prod T_2 T_1)))) (tptp.finite_finite tptp.product_unit) (forall ((T $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.ti T A))) (= (tptp.ti T _let_1) _let_1))) (forall ((X_a $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.hAPP tptp.bool (tptp.fun X_a _let_1) (tptp.if X_a) tptp.fTrue) X) Y) (tptp.ti X_a X)))) (forall ((X_a $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.hAPP tptp.bool (tptp.fun X_a _let_1) (tptp.if X_a) tptp.fFalse) X) Y) (tptp.ti X_a Y)))) (forall ((P $$unsorted)) (let ((_let_1 (tptp.ti tptp.bool P))) (or (= _let_1 tptp.fTrue) (= _let_1 tptp.fFalse)))) (forall ((P $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool tptp.fNot P))) (not (tptp.hBOOL P)))) (forall ((P $$unsorted)) (or (tptp.hBOOL P) (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool tptp.fNot P)))) (forall ((X_a $$unsorted) (X_c $$unsorted) (X_b $$unsorted) (P $$unsorted) (Q $$unsorted) (R $$unsorted)) (let ((_let_1 (tptp.fun X_a X_c))) (let ((_let_2 (tptp.fun X_a X_b))) (= (tptp.hAPP X_a X_c (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun _let_2 _let_1) (tptp.combb X_b X_c X_a) P) Q) R) (tptp.hAPP X_b X_c P (tptp.hAPP X_a X_b Q R)))))) (forall ((X_a $$unsorted) (X_c $$unsorted) (X_b $$unsorted) (P $$unsorted) (Q $$unsorted) (R $$unsorted)) (let ((_let_1 (tptp.fun X_b X_c))) (let ((_let_2 (tptp.fun X_a X_c))) (= (tptp.hAPP X_a X_c (tptp.hAPP X_b _let_2 (tptp.hAPP (tptp.fun X_a _let_1) (tptp.fun X_b _let_2) (tptp.combc X_a X_b X_c) P) Q) R) (tptp.hAPP X_b X_c (tptp.hAPP X_a _let_1 P R) Q))))) (forall ((X_a $$unsorted) (P $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.combi X_a) P) (tptp.ti X_a P))) (forall ((X_b $$unsorted) (X_a $$unsorted) (P $$unsorted) (Q $$unsorted)) (= (tptp.hAPP X_b X_a (tptp.hAPP X_a (tptp.fun X_b X_a) (tptp.combk X_a X_b) P) Q) (tptp.ti X_a P))) (forall ((X_a $$unsorted) (X_c $$unsorted) (X_b $$unsorted) (P $$unsorted) (Q $$unsorted) (R $$unsorted)) (let ((_let_1 (tptp.fun X_b X_c))) (let ((_let_2 (tptp.fun X_a X_c))) (let ((_let_3 (tptp.fun X_a X_b))) (= (tptp.hAPP X_a X_c (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun X_a _let_1) (tptp.fun _let_3 _let_2) (tptp.combs X_a X_b X_c) P) Q) R) (tptp.hAPP X_b X_c (tptp.hAPP X_a _let_1 P R) (tptp.hAPP X_a X_b Q R))))))) (tptp.hBOOL tptp.fTrue) (forall ((P $$unsorted)) (let ((_let_1 (tptp.ti tptp.bool P))) (or (= _let_1 tptp.fTrue) (= _let_1 tptp.fFalse)))) (forall ((Q $$unsorted) (P $$unsorted)) (or (not (tptp.hBOOL P)) (not (tptp.hBOOL Q)) (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fconj P) Q)))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fconj P) Q))) (tptp.hBOOL P))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fconj P) Q))) (tptp.hBOOL Q))) (forall ((Q $$unsorted) (P $$unsorted)) (or (not (tptp.hBOOL P)) (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fdisj P) Q)))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL Q)) (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fdisj P) Q)))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fdisj P) Q))) (tptp.hBOOL P) (tptp.hBOOL Q))) (forall ((X_a $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.fequal X_a) X) Y))) (= (tptp.ti X_a X) (tptp.ti X_a Y)))) (forall ((X_a $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (= (tptp.ti X_a X) (tptp.ti X_a Y))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.fequal X_a) X) Y)))) _let_11 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.82/1.26  )
% 0.82/1.26  % SZS output end Proof for SCT171+6
% 0.82/1.26  % cvc5---1.0.5 exiting
% 0.82/1.26  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------