%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SCT170+6 : TPTP v8.1.2. Released v5.3.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n010.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 14:12:21 EDT 2023

% Result   : Theorem 95.50s 96.07s
% Output   : Proof 95.50s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.25  % Problem    : SCT170+6 : TPTP v8.1.2. Released v5.3.0.
% 0.25/0.26  % Command    : do_cvc5 %s %d
% 0.25/0.46  % Computer : n010.cluster.edu
% 0.25/0.46  % Model    : x86_64 x86_64
% 0.25/0.46  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.25/0.46  % Memory   : 8042.1875MB
% 0.25/0.46  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.25/0.46  % CPULimit   : 300
% 0.25/0.46  % WCLimit    : 300
% 0.25/0.46  % DateTime   : Thu Aug 24 16:08:51 EDT 2023
% 0.25/0.47  % CPUTime    : 
% 0.31/0.63  %----Proving TF0_NAR, FOF, or CNF
% 95.50/96.07  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.pUTA02dBw7/cvc5---1.0.5_9830.p...
% 95.50/96.07  ------- get file name : TPTP file name is SCT170+6
% 95.50/96.07  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_9830.smt2...
% 95.50/96.07  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 95.50/96.07  --- Run --no-e-matching --full-saturate-quant at 5...
% 95.50/96.07  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 95.50/96.07  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 95.50/96.07  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 95.50/96.07  --- Run --trigger-sel=max --full-saturate-quant at 5...
% 95.50/96.07  --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 95.50/96.07  --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 95.50/96.07  --- Run --prenex-quant=none --full-saturate-quant at 5...
% 95.50/96.07  --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 5...
% 95.50/96.07  --- Run --relevant-triggers --full-saturate-quant at 5...
% 95.50/96.07  --- Run --finite-model-find --e-matching --sort-inference --uf-ss-fair at 5...
% 95.50/96.07  --- Run --pre-skolem-quant=on --full-saturate-quant at 10...
% 95.50/96.07  --- Run --cbqi-vo-exp --full-saturate-quant at 10...
% 95.50/96.07  --- Run --no-cbqi --full-saturate-quant at 10...
% 95.50/96.07  % SZS status Theorem for SCT170+6
% 95.50/96.07  % SZS output start Proof for SCT170+6
% 95.50/96.07  (
% 95.50/96.07  (let ((_let_1 (forall ((I $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.arrow_660593299e_indi _let_2 tptp.p I))) (let ((_let_4 (tptp.fun tptp.arrow_490897120le_alt _let_2))) (let ((_let_5 (tptp.hAPP tptp.arrow_490897120le_alt (tptp.fun tptp.arrow_490897120le_alt _let_1) (tptp.product_Pair tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt) tptp.a))) (let ((_let_6 (tptp.member _let_1))) (let ((_let_7 (tptp.fun _let_2 tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 _let_7 _let_6 (tptp.hAPP tptp.arrow_490897120le_alt _let_1 _let_5 tptp.b)) _let_3)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 _let_7 _let_6 (tptp.hAPP tptp.arrow_490897120le_alt _let_1 _let_5 tptp.c)) (tptp.hAPP tptp.arrow_490897120le_alt _let_2 (tptp.hAPP tptp.arrow_490897120le_alt _let_4 (tptp.hAPP _let_2 (tptp.fun tptp.arrow_490897120le_alt _let_4) tptp.arrow_1322701812_below _let_3) tptp.c) tptp.b)))))))))))))) (let ((_let_2 (not _let_1))) (let ((_let_3 (forall ((X_a $$unsorted) (As $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.list X_a))) (=> (not (= As (tptp.nil X_a))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) (tptp.hAPP _let_2 X_a (tptp.last X_a) As)) (tptp.hAPP _let_2 _let_1 (tptp.set X_a) As))))))))) (let ((_let_4 (forall ((X_a $$unsorted) (X_1 $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.distinct X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_a (tptp.fun _let_2 _let_2) (tptp.cons X_a) X_1) Xs_1))) (and (not (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_a (tptp.fun _let_3 tptp.bool) (tptp.member X_a) X_1) (tptp.hAPP _let_2 _let_3 (tptp.set X_a) Xs_1)))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 Xs_1)))))))))) (let ((_let_5 (forall ((X_a $$unsorted) (X $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP X_a _let_2 (tptp.cons X_a) X))) (let ((_let_4 (tptp.rev X_a))) (= (tptp.hAPP _let_1 _let_1 _let_4 (tptp.hAPP _let_1 _let_1 _let_3 Xs)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.append X_a) (tptp.hAPP _let_1 _let_1 _let_4 Xs)) (tptp.hAPP _let_1 _let_1 _let_3 (tptp.nil X_a))))))))))) (let ((_let_6 (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.nil X_a))) (let ((_let_2 (tptp.list X_a))) (= (tptp.hAPP _let_2 _let_2 (tptp.rev X_a) _let_1) _let_1)))))) (let ((_let_7 (forall ((X_a $$unsorted) (X $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.list X_a))) (= (tptp.hAPP _let_1 X_a (tptp.hd X_a) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.cons X_a) X) Xs)) (tptp.ti X_a X)))))) (let ((_let_8 (forall ((X_b $$unsorted) (X_a $$unsorted) (X $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.list X_b))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP X_b _let_2 (tptp.cons X_b) X))) (let ((_let_4 (tptp.nil X_a))) (let ((_let_5 (tptp.list X_a))) (and (= (tptp.hAPP _let_5 _let_5 (tptp.rotate1 X_a) _let_4) _let_4) (= (tptp.hAPP _let_1 _let_1 (tptp.rotate1 X_b) (tptp.hAPP _let_1 _let_1 _let_3 Xs)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.append X_b) Xs) (tptp.hAPP _let_1 _let_1 _let_3 (tptp.nil X_b))))))))))))) (let ((_let_9 (forall ((X_a $$unsorted) (Ys_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.append X_a) (tptp.nil X_a)) Ys_2) Ys_2))))) (let ((_let_10 (tptp.fun tptp.arrow_490897120le_alt tptp.bool))) (let ((_let_11 (tptp.order_215145569der_on tptp.arrow_490897120le_alt))) (let ((_let_12 (tptp.product_prod tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt))) (let ((_let_13 (tptp.fun _let_12 tptp.bool))) (let ((_let_14 (tptp.fun _let_13 tptp.bool))) (let ((_let_15 (tptp.hAPP _let_14 _let_14 (tptp.collect _let_13) (tptp.hAPP _let_10 _let_14 _let_11 (tptp.top_top _let_10))))) (let ((_let_16 (= tptp.arrow_2064824852le_Lin _let_15))) (let ((_let_17 (forall ((X_a $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_1) (tptp.top_top _let_1))))))) (let ((_let_18 (forall ((X_a $$unsorted) (X $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.last X_a))) (let ((_let_2 (tptp.list X_a))) (=> (not (= Xs (tptp.nil X_a))) (= (tptp.hAPP _let_2 X_a _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_a (tptp.fun _let_2 _let_2) (tptp.cons X_a) X) Xs)) (tptp.hAPP _let_2 X_a _let_1 Xs)))))))) (let ((_let_19 (forall ((X_a $$unsorted) (X $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.list X_a))) (=> (= Xs (tptp.nil X_a)) (= (tptp.hAPP _let_1 X_a (tptp.last X_a) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.cons X_a) X) Xs)) (tptp.ti X_a X))))))) (let ((_let_20 (tptp.combk _let_14 tptp.arrow_660593299e_indi))) (let ((_let_21 (tptp.fun tptp.arrow_660593299e_indi _let_14))) (let ((_let_22 (tptp.fun tptp.arrow_660593299e_indi tptp.bool))) (let ((_let_23 (tptp.top_top _let_22))) (let ((_let_24 (tptp.fun tptp.arrow_660593299e_indi _let_13))) (let ((_let_25 (tptp.fun _let_24 tptp.bool))) (let ((_let_26 (tptp.hAPP _let_22 (tptp.fun _let_21 _let_25) (tptp.pi tptp.arrow_660593299e_indi _let_13) _let_23))) (let ((_let_27 (= tptp.arrow_1111136790e_Prof (tptp.hAPP _let_21 _let_25 _let_26 (tptp.hAPP _let_14 _let_21 _let_20 tptp.arrow_2064824852le_Lin))))) (let ((_let_28 (forall ((X_a $$unsorted) (X_b $$unsorted) (X_1 $$unsorted) (F $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.fun X_a _let_1))) (let ((_let_4 (tptp.fun X_a X_b))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP _let_4 (tptp.fun _let_5 tptp.bool) (tptp.member _let_4) F) (tptp.hAPP _let_3 _let_5 (tptp.hAPP _let_2 (tptp.fun _let_3 _let_5) (tptp.pi X_a X_b) A_1) (tptp.hAPP _let_1 _let_3 (tptp.combk _let_1 X_a) B)))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a (tptp.fun _let_2 tptp.bool) (tptp.member X_a) X_1) A_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) (tptp.hAPP X_a X_b F X_1)) B)))))))))))) (let ((_let_29 (forall ((X_a $$unsorted) (A_6 $$unsorted) (List_3 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (not (= (tptp.nil X_a) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.cons X_a) A_6) List_3))))))) (let ((_let_30 (tptp.fun _let_24 _let_14))) (let ((_let_31 (tptp.fun _let_24 _let_13))) (let ((_let_32 (tptp.fun _let_31 tptp.bool))) (let ((_let_33 (tptp.member _let_24))) (let ((_let_34 (tptp.fun _let_25 tptp.bool))) (let ((_let_35 (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (L_1 $$unsorted) (Aa $$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_1)))) (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_1))) (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_1) 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_1) 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_1))) (=> (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_1)) L_1)))) (=> (not _let_11) (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool _let_8 L_1))))))))))))))))))))))))))) (let ((_let_36 (tptp.fun tptp.arrow_490897120le_alt _let_13))) (let ((_let_37 (tptp.fun tptp.arrow_490897120le_alt _let_36))) (let ((_let_38 (tptp.fun tptp.arrow_660593299e_indi _let_37))) (let ((_let_39 (tptp.fun _let_13 _let_37))) (let ((_let_40 (tptp.hAPP _let_39 (tptp.fun _let_24 _let_38) (tptp.combb _let_13 _let_37 tptp.arrow_660593299e_indi) tptp.arrow_1322701812_below))) (let ((_let_41 (tptp.combc tptp.arrow_660593299e_indi tptp.arrow_490897120le_alt _let_36))) (let ((_let_42 (tptp.fun tptp.arrow_660593299e_indi _let_36))) (let ((_let_43 (tptp.fun tptp.arrow_490897120le_alt _let_42))) (let ((_let_44 (tptp.combc tptp.arrow_660593299e_indi tptp.arrow_490897120le_alt _let_13))) (let ((_let_45 (tptp.fun tptp.arrow_490897120le_alt _let_24))) (let ((_let_46 (tptp.hAPP tptp.arrow_490897120le_alt _let_24 (tptp.hAPP _let_42 _let_45 _let_44 (tptp.hAPP tptp.arrow_490897120le_alt _let_42 (tptp.hAPP _let_38 _let_43 _let_41 (tptp.hAPP _let_24 _let_38 _let_40 tptp.p)) tptp.c)) tptp.b))) (let ((_let_47 (tptp.hAPP tptp.arrow_490897120le_alt _let_24 (tptp.hAPP _let_42 _let_45 _let_44 (tptp.hAPP tptp.arrow_490897120le_alt _let_42 (tptp.hAPP _let_38 _let_43 _let_41 (tptp.hAPP _let_24 _let_38 _let_40 _let_46)) tptp.b)) tptp.a))) (let ((_let_48 (tptp.nil tptp.arrow_490897120le_alt))) (let ((_let_49 (tptp.cons tptp.arrow_490897120le_alt))) (let ((_let_50 (tptp.list tptp.arrow_490897120le_alt))) (let ((_let_51 (tptp.fun _let_50 _let_50))) (let ((_let_52 (tptp.hAPP _let_50 _let_50 (tptp.hAPP tptp.arrow_490897120le_alt _let_51 _let_49 tptp.c) _let_48))) (let ((_let_53 (tptp.hAPP _let_50 _let_50 (tptp.hAPP tptp.arrow_490897120le_alt _let_51 _let_49 tptp.b) _let_52))) (let ((_let_54 (tptp.distinct tptp.arrow_490897120le_alt))) (let ((_let_55 (tptp.hBOOL (tptp.hAPP _let_50 tptp.bool _let_54 (tptp.hAPP _let_50 _let_50 (tptp.hAPP tptp.arrow_490897120le_alt _let_51 _let_49 tptp.a) _let_53))))) (let ((_let_56 (tptp.hAPP _let_24 _let_34 _let_33 tptp.p))) (let ((_let_57 (tptp.hBOOL (tptp.hAPP _let_25 tptp.bool _let_56 tptp.arrow_1111136790e_Prof)))) (let ((_let_58 (tptp.ti tptp.arrow_490897120le_alt tptp.c))) (let ((_let_59 (= _let_58 tptp.c))) (let ((_let_60 (tptp.ti tptp.arrow_490897120le_alt tptp.b))) (let ((_let_61 (= _let_60 tptp.b))) (let ((_let_62 (tptp.ti tptp.arrow_490897120le_alt tptp.a))) (let ((_let_63 (= _let_62 tptp.a))) (let ((_let_64 (tptp.fun tptp.bool tptp.bool))) (let ((_let_65 (tptp.fun _let_13 _let_36))) (let ((_let_66 (tptp.hAPP tptp.arrow_660593299e_indi _let_13 tptp.p SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_67 (tptp.product_Pair tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt))) (let ((_let_68 (tptp.fun tptp.arrow_490897120le_alt _let_12))) (let ((_let_69 (tptp.hAPP tptp.arrow_490897120le_alt _let_68 _let_67 tptp.a))) (let ((_let_70 (tptp.member _let_12))) (let ((_let_71 (tptp.hBOOL (tptp.hAPP _let_13 tptp.bool (tptp.hAPP _let_12 _let_14 _let_70 (tptp.hAPP tptp.arrow_490897120le_alt _let_12 _let_69 tptp.b)) _let_66)))) (let ((_let_72 (= _let_62 _let_58))) (let ((_let_73 (not _let_72))) (let ((_let_74 (and _let_73 _let_71))) (let ((_let_75 (tptp.hBOOL (tptp.hAPP _let_13 tptp.bool (tptp.hAPP _let_12 _let_14 _let_70 (tptp.hAPP tptp.arrow_490897120le_alt _let_12 _let_69 tptp.c)) (tptp.hAPP tptp.arrow_490897120le_alt _let_13 (tptp.hAPP tptp.arrow_490897120le_alt _let_36 (tptp.hAPP _let_13 _let_37 tptp.arrow_1322701812_below _let_66) tptp.c) tptp.b))))) (let ((_let_76 (= _let_75 _let_74))) (let ((_let_77 (tptp.hBOOL (tptp.hAPP _let_14 tptp.bool (tptp.hAPP _let_13 (tptp.fun _let_14 tptp.bool) (tptp.member _let_13) _let_66) _let_15)))) (let ((_let_78 (not _let_77))) (let ((_let_79 (= _let_60 _let_58))) (let ((_let_80 (or _let_79 _let_78 _let_76))) (let ((_let_81 (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (L_1 $$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_1)))) (let ((_let_9 (tptp.ti tptp.arrow_490897120le_alt X_1))) (let ((_let_10 (tptp.ti tptp.arrow_490897120le_alt Aa))) (let ((_let_11 (= _let_10 _let_9))) (let ((_let_12 (tptp.ti tptp.arrow_490897120le_alt Y_1))) (let ((_let_13 (tptp.ti tptp.arrow_490897120le_alt Ba))) (let ((_let_14 (= _let_10 _let_12))) (let ((_let_15 (tptp.fun tptp.arrow_490897120le_alt _let_6))) (let ((_let_16 (tptp.fun tptp.arrow_490897120le_alt tptp.bool))) (or (= _let_10 _let_13) (not (tptp.hBOOL (tptp.hAPP _let_7 tptp.bool (tptp.hAPP _let_6 (tptp.fun _let_7 tptp.bool) (tptp.member _let_6) L_1) (tptp.hAPP _let_7 _let_7 (tptp.collect _let_6) (tptp.hAPP _let_16 _let_7 (tptp.order_215145569der_on tptp.arrow_490897120le_alt) (tptp.top_top _let_16)))))) (= (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_1) Aa) Ba))) (and (not (= _let_9 _let_12)) (or (not _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_1))) (or _let_14 (and (or (not _let_11) (= _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_1)) L_1))) (or _let_11 (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool _let_8 L_1))))))))))))))))))))))))))) (let ((_let_82 (AND_INTRO (ASSUME :args (_let_16)) (ASSUME :args (_let_27))))) (let ((_let_83 (EQ_RESOLVE (ASSUME :args (_let_35)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_35 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_82 :args ((forall ((X_1 $$unsorted) (Y_1 $$unsorted) (L_1 $$unsorted) (Aa $$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_1)))) (let ((_let_9 (tptp.ti tptp.arrow_490897120le_alt X_1))) (let ((_let_10 (tptp.ti tptp.arrow_490897120le_alt Aa))) (let ((_let_11 (= _let_10 _let_9))) (let ((_let_12 (tptp.ti tptp.arrow_490897120le_alt Y_1))) (let ((_let_13 (tptp.ti tptp.arrow_490897120le_alt Ba))) (let ((_let_14 (= _let_10 _let_12))) (let ((_let_15 (tptp.fun tptp.arrow_490897120le_alt _let_6))) (or (= _let_10 _let_13) (not (tptp.hBOOL (tptp.hAPP _let_7 tptp.bool (tptp.hAPP _let_6 (tptp.fun _let_7 tptp.bool) (tptp.member _let_6) L_1) 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_1) Aa) Ba))) (and (not (= _let_9 _let_12)) (or (not _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_1))) (or _let_14 (and (or (not _let_11) (= _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_1)) L_1))) (or _let_11 (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool _let_8 L_1)))))))))))))))))))))))) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_84 (tptp.set tptp.arrow_490897120le_alt))) (let ((_let_85 (tptp.hAPP _let_50 _let_10 _let_84 _let_52))) (let ((_let_86 (tptp.last tptp.arrow_490897120le_alt))) (let ((_let_87 (tptp.hAPP _let_50 tptp.arrow_490897120le_alt _let_86 _let_52))) (let ((_let_88 (tptp.member tptp.arrow_490897120le_alt))) (let ((_let_89 (tptp.fun _let_10 tptp.bool))) (let ((_let_90 (tptp.hBOOL (tptp.hAPP _let_10 tptp.bool (tptp.hAPP tptp.arrow_490897120le_alt _let_89 _let_88 _let_87) _let_85)))) (let ((_let_91 (tptp.append tptp.arrow_490897120le_alt))) (let ((_let_92 (tptp.hAPP _let_50 _let_50 (tptp.hAPP _let_50 _let_51 _let_91 _let_48) _let_52))) (let ((_let_93 (= _let_52 _let_92))) (let ((_let_94 (tptp.rev tptp.arrow_490897120le_alt))) (let ((_let_95 (tptp.hAPP _let_50 _let_50 _let_94 _let_48))) (let ((_let_96 (= (tptp.hAPP _let_50 _let_50 _let_94 _let_52) (tptp.hAPP _let_50 _let_50 (tptp.hAPP _let_50 _let_51 _let_91 _let_95) _let_52)))) (let ((_let_97 (= _let_48 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(ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_110 (_let_108))) (let ((_let_111 ((tptp.hAPP (tptp.list X_a) X_a (tptp.last X_a) As)))) (let ((_let_112 (_let_29))) (let ((_let_113 (ASSUME :args _let_112))) (let ((_let_114 (tptp.list X_a))) (let ((_let_115 ((tptp.hAPP _let_114 _let_114 (tptp.hAPP X_a (tptp.fun _let_114 _let_114) (tptp.cons X_a) A_6) List_3)))) (let ((_let_116 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_113 :args (tptp.arrow_490897120le_alt tptp.c _let_48 QUANTIFIERS_INST_E_MATCHING _let_115)) :args _let_112)) _let_113 :args ((not _let_106) false _let_29)))) (let ((_let_117 (forall ((X_a $$unsorted) (Ys_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (= Ys_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.append X_a) (tptp.nil X_a)) Ys_2)))))) (let ((_let_118 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_119 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((X_a $$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.equal_equal X_a))) (=> (tptp.cl_HOL_Oequal X_a) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a tptp.bool)) _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)) (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 $$unsorted)) (let ((_let_1 (tptp.append X_a))) (let ((_let_2 (tptp.list X_a))) (= (tptp.ti (tptp.fun _let_2 (tptp.fun _let_2 _let_2)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.butlast X_a))) (let ((_let_2 (tptp.list X_a))) (= (tptp.ti (tptp.fun _let_2 _let_2) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.distinct X_a))) (= (tptp.ti (tptp.fun (tptp.list X_a) tptp.bool) _let_1) _let_1))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.drop X_a))) (let ((_let_2 (tptp.list X_a))) (= (tptp.ti (tptp.fun tptp.nat (tptp.fun _let_2 _let_2)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.dropWhile X_a))) (let ((_let_2 (tptp.list X_a))) (= (tptp.ti (tptp.fun (tptp.fun X_a tptp.bool) (tptp.fun _let_2 _let_2)) _let_1) _let_1)))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (let ((_let_1 (tptp.foldl X_a X_b))) (= (tptp.ti (tptp.fun (tptp.fun X_a (tptp.fun X_b X_a)) (tptp.fun X_a (tptp.fun (tptp.list X_b) X_a))) _let_1) _let_1))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.hd X_a))) (= (tptp.ti (tptp.fun (tptp.list X_a) X_a) _let_1) _let_1))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.insert X_a))) (let ((_let_2 (tptp.list X_a))) (= (tptp.ti (tptp.fun X_a (tptp.fun _let_2 _let_2)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.last X_a))) (= (tptp.ti (tptp.fun (tptp.list X_a) X_a) _let_1) _let_1))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.lex X_a))) (let ((_let_2 (tptp.list X_a))) (= (tptp.ti (tptp.fun (tptp.fun (tptp.product_prod X_a X_a) tptp.bool) (tptp.fun (tptp.product_prod _let_2 _let_2) tptp.bool)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.lexn X_a))) (let ((_let_2 (tptp.list X_a))) (= (tptp.ti (tptp.fun (tptp.fun (tptp.product_prod X_a X_a) tptp.bool) (tptp.fun tptp.nat (tptp.fun (tptp.product_prod _let_2 _let_2) tptp.bool))) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.lexord X_a))) (let ((_let_2 (tptp.list X_a))) (= (tptp.ti (tptp.fun (tptp.fun (tptp.product_prod X_a X_a) tptp.bool) (tptp.fun (tptp.product_prod _let_2 _let_2) tptp.bool)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.linorder_sorted X_a))) (=> (tptp.linorder X_a) (= (tptp.ti (tptp.fun (tptp.list X_a) tptp.bool) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.cons X_a))) (let ((_let_2 (tptp.list X_a))) (= (tptp.ti (tptp.fun X_a (tptp.fun _let_2 _let_2)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.nil X_a))) (= (tptp.ti (tptp.list X_a) _let_1) _let_1))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (let ((_let_1 (tptp.list_case X_a X_b))) (let ((_let_2 (tptp.fun (tptp.list X_b) X_a))) (= (tptp.ti (tptp.fun X_a (tptp.fun (tptp.fun X_b _let_2) _let_2)) _let_1) _let_1)))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (let ((_let_1 (tptp.list_rec X_a X_b))) (let ((_let_2 (tptp.list X_b))) (= (tptp.ti (tptp.fun X_a (tptp.fun (tptp.fun X_b (tptp.fun _let_2 (tptp.fun X_a X_a))) (tptp.fun _let_2 X_a))) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.listrel X_a))) (let ((_let_2 (tptp.list X_a))) (= (tptp.ti (tptp.fun (tptp.fun (tptp.product_prod X_a X_a) tptp.bool) (tptp.fun (tptp.product_prod _let_2 _let_2) tptp.bool)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.listrel1 X_a))) (let ((_let_2 (tptp.list X_a))) (= (tptp.ti (tptp.fun (tptp.fun (tptp.product_prod X_a X_a) tptp.bool) (tptp.fun (tptp.product_prod _let_2 _let_2) tptp.bool)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.listrelp X_a))) (let ((_let_2 (tptp.list X_a))) (= (tptp.ti (tptp.fun (tptp.fun X_a (tptp.fun X_a tptp.bool)) (tptp.fun _let_2 (tptp.fun _let_2 tptp.bool))) _let_1) _let_1)))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.maps X_b X_a))) (let ((_let_2 (tptp.list X_a))) (= (tptp.ti (tptp.fun (tptp.fun X_b _let_2) (tptp.fun (tptp.list X_b) _let_2)) _let_1) _let_1)))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.null X_b))) (= (tptp.ti (tptp.fun (tptp.list X_b) tptp.bool) _let_1) _let_1))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.partition X_a))) (let ((_let_2 (tptp.list X_a))) (= (tptp.ti (tptp.fun (tptp.fun X_a tptp.bool) (tptp.fun _let_2 (tptp.product_prod _let_2 _let_2))) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.replicate X_a))) (= (tptp.ti (tptp.fun tptp.nat (tptp.fun X_a (tptp.list X_a))) _let_1) _let_1))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.rev X_a))) (let ((_let_2 (tptp.list X_a))) (= (tptp.ti (tptp.fun _let_2 _let_2) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.rotate1 X_a))) (let ((_let_2 (tptp.list X_a))) (= (tptp.ti (tptp.fun _let_2 _let_2) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.set X_a))) (= (tptp.ti (tptp.fun (tptp.list X_a) (tptp.fun X_a tptp.bool)) _let_1) _let_1))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.splice X_a))) (let ((_let_2 (tptp.list X_a))) (= (tptp.ti (tptp.fun _let_2 (tptp.fun _let_2 _let_2)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.take X_a))) (let ((_let_2 (tptp.list X_a))) (= (tptp.ti (tptp.fun tptp.nat (tptp.fun _let_2 _let_2)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.takeWhile X_a))) (let ((_let_2 (tptp.list X_a))) (= (tptp.ti (tptp.fun (tptp.fun X_a tptp.bool) (tptp.fun _let_2 _let_2)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.tl X_a))) (let ((_let_2 (tptp.list X_a))) (= (tptp.ti (tptp.fun _let_2 _let_2) _let_1) _let_1)))) (= (tptp.ti (tptp.fun tptp.nat tptp.nat) tptp.suc) tptp.suc) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.nat_case X_a))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (= (tptp.ti (tptp.fun X_a (tptp.fun _let_2 _let_2)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.size_size _let_1))) (= (tptp.ti (tptp.fun _let_1 tptp.nat) _let_2) _let_2)))) (= (tptp.ti (tptp.fun _let_10 _let_14) _let_11) _let_11) (forall ((X_a $$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_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted)) (let ((_let_1 (tptp.product_curry X_a X_b X_c))) (= (tptp.ti (tptp.fun (tptp.fun (tptp.product_prod X_a X_b) X_c) (tptp.fun X_a (tptp.fun X_b X_c))) _let_1) _let_1))) (forall ((X_b $$unsorted) (X_c $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.produc1605651328_split 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_b $$unsorted) (X_c $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.product_prod_case X_b X_c X_a))) (= (tptp.ti (tptp.fun (tptp.fun X_b (tptp.fun X_c X_a)) (tptp.fun (tptp.product_prod X_b X_c) X_a)) _let_1) _let_1))) (forall ((X_b $$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 $$unsorted)) (let ((_let_1 (tptp.collect X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (= (tptp.ti (tptp.fun _let_2 _let_2) _let_1) _let_1)))) (= (tptp.ti tptp.bool tptp.fFalse) tptp.fFalse) (= (tptp.ti _let_64 tptp.fNot) tptp.fNot) (= (tptp.ti tptp.bool tptp.fTrue) tptp.fTrue) (= (tptp.ti (tptp.fun tptp.bool _let_64) tptp.fconj) tptp.fconj) (forall ((X_a $$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 $$unsorted)) (= (tptp.hBOOL (tptp.ti tptp.bool B_1_1)) (tptp.hBOOL B_1_1))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.member X_b))) (= (tptp.ti (tptp.fun X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool)) _let_1) _let_1))) (= (tptp.ti _let_31 tptp.f) tptp.f) (= (tptp.ti _let_24 tptp.p_1) tptp.p_1) (= (tptp.ti _let_24 tptp.p) tptp.p) _let_63 _let_61 _let_59 _let_57 (tptp.hBOOL (tptp.hAPP _let_31 tptp.bool tptp.arrow_2037941124le_IIA tptp.f)) (tptp.hBOOL (tptp.hAPP _let_31 tptp.bool tptp.arrow_831799591nimity tptp.f)) (not (= tptp.a tptp.b)) _let_55 (forall ((I $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.product_Pair tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt))) (let ((_let_4 (tptp.fun tptp.arrow_490897120le_alt _let_1))) (let ((_let_5 (tptp.member _let_1))) (let ((_let_6 (tptp.fun _let_2 tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 _let_6 _let_5 (tptp.hAPP tptp.arrow_490897120le_alt _let_1 (tptp.hAPP tptp.arrow_490897120le_alt _let_4 _let_3 tptp.a) tptp.b)) (tptp.hAPP tptp.arrow_660593299e_indi _let_2 tptp.p I))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 _let_6 _let_5 (tptp.hAPP tptp.arrow_490897120le_alt _let_1 (tptp.hAPP tptp.arrow_490897120le_alt _let_4 _let_3 tptp.b) tptp.a)) (tptp.hAPP tptp.arrow_660593299e_indi _let_2 tptp.p_1 I))))))))))) (not (forall ((C_2 $$unsorted)) (let ((_let_1 (tptp.cons tptp.arrow_490897120le_alt))) (let ((_let_2 (tptp.list tptp.arrow_490897120le_alt))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (not (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.distinct tptp.arrow_490897120le_alt) (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.arrow_490897120le_alt _let_3 _let_1 tptp.a) (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.arrow_490897120le_alt _let_3 _let_1 tptp.b) (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.arrow_490897120le_alt _let_3 _let_1 C_2) (tptp.nil tptp.arrow_490897120le_alt)))))))))))) (tptp.hBOOL (tptp.hAPP _let_25 tptp.bool (tptp.hAPP _let_24 _let_34 _let_33 _let_47) tptp.arrow_1111136790e_Prof)) (tptp.hBOOL (tptp.hAPP _let_25 tptp.bool (tptp.hAPP _let_24 _let_34 _let_33 (tptp.hAPP tptp.arrow_490897120le_alt _let_24 (tptp.hAPP _let_42 _let_45 _let_44 (tptp.hAPP tptp.arrow_490897120le_alt _let_42 (tptp.hAPP _let_38 _let_43 _let_41 (tptp.hAPP _let_24 _let_38 _let_40 _let_47)) tptp.a)) tptp.c)) tptp.arrow_1111136790e_Prof)) (tptp.hBOOL (tptp.hAPP _let_25 tptp.bool (tptp.hAPP _let_24 _let_34 _let_33 _let_46) tptp.arrow_1111136790e_Prof)) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (L_1 $$unsorted) (Z_2 $$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) X_1) Y_1)))) (let ((_let_4 (tptp.ti tptp.arrow_490897120le_alt Z_2))) (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_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_1278947948_mkbot L_1) Z_2))) (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_1))))))))))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (L_1 $$unsorted) (Z_2 $$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) X_1) Y_1)))) (let ((_let_4 (tptp.ti tptp.arrow_490897120le_alt Z_2))) (let ((_let_5 (tptp.ti tptp.arrow_490897120le_alt Y_1))) (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_1) Z_2))) (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_1))))))))))))) _let_35 (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_4 $$unsorted) (B_2 $$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_4) B_2))))))) (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 ((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) (R_1 $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_a _let_3 (tptp.hAPP _let_2 (tptp.fun X_a _let_3) (tptp.in_rel X_a X_b) R_1) X_1) Y_1)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) (tptp.hAPP X_b _let_1 (tptp.hAPP X_a (tptp.fun X_b _let_1) (tptp.product_Pair X_a X_b) X_1) Y_1)) R_1))))))) (forall ((L_1 $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.product_prod tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt) tptp.bool))) (let ((_let_2 (tptp.fun 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_1))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP _let_1 _let_5 _let_3 L_1) 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_1) X_1) Y_1)) tptp.arrow_2064824852le_Lin)))))))))) (tptp.hBOOL (tptp.hAPP _let_25 tptp.bool (tptp.hAPP _let_24 _let_34 _let_33 tptp.p_1) tptp.arrow_1111136790e_Prof)) (forall ((P_a $$unsorted) (Pa $$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_a) tptp.arrow_1111136790e_Prof)) (=> (forall ((I $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.product_Pair tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt))) (let ((_let_4 (tptp.fun tptp.arrow_490897120le_alt _let_1))) (let ((_let_5 (tptp.member _let_1))) (let ((_let_6 (tptp.fun _let_2 tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 _let_6 _let_5 (tptp.hAPP tptp.arrow_490897120le_alt _let_1 (tptp.hAPP tptp.arrow_490897120le_alt _let_4 _let_3 Aa) Ba)) (tptp.hAPP tptp.arrow_660593299e_indi _let_2 Pa I))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 _let_6 _let_5 (tptp.hAPP tptp.arrow_490897120le_alt _let_1 (tptp.hAPP tptp.arrow_490897120le_alt _let_4 _let_3 A_5) B_3)) (tptp.hAPP tptp.arrow_660593299e_indi _let_2 P_a I))))))))))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 _let_7 _let_6 (tptp.hAPP tptp.arrow_490897120le_alt _let_1 (tptp.hAPP tptp.arrow_490897120le_alt _let_5 _let_4 Aa) Ba)) (tptp.hAPP _let_3 _let_2 tptp.f Pa))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 _let_7 _let_6 (tptp.hAPP tptp.arrow_490897120le_alt _let_1 (tptp.hAPP tptp.arrow_490897120le_alt _let_5 _let_4 A_5) B_3)) (tptp.hAPP _let_3 _let_2 tptp.f P_a)))))))))))))))))))))))))) (forall ((P_a $$unsorted) (Pa $$unsorted) (A_5 $$unsorted) (B_3 $$unsorted) (Aa $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun tptp.arrow_660593299e_indi _let_2))) (let ((_let_4 (tptp.product_Pair tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt))) (let ((_let_5 (tptp.fun tptp.arrow_490897120le_alt _let_1))) (let ((_let_6 (tptp.member _let_1))) (let ((_let_7 (tptp.fun _let_2 tptp.bool))) (let ((_let_8 (tptp.member _let_3))) (let ((_let_9 (tptp.fun _let_3 tptp.bool))) (let ((_let_10 (tptp.fun _let_9 tptp.bool))) (let ((_let_11 (tptp.ti tptp.arrow_490897120le_alt A_5))) (let ((_let_12 (tptp.ti tptp.arrow_490897120le_alt Ba))) (let ((_let_13 (tptp.ti tptp.arrow_490897120le_alt B_3))) (let ((_let_14 (tptp.ti tptp.arrow_490897120le_alt Aa))) (=> (not (= _let_14 _let_12)) (=> (not (= _let_11 _let_13)) (=> (not (= _let_14 _let_13)) (=> (not (= _let_12 _let_11)) (=> (tptp.hBOOL (tptp.hAPP _let_9 tptp.bool (tptp.hAPP _let_3 _let_10 _let_8 Pa) tptp.arrow_1111136790e_Prof)) (=> (tptp.hBOOL (tptp.hAPP _let_9 tptp.bool (tptp.hAPP _let_3 _let_10 _let_8 P_a) tptp.arrow_1111136790e_Prof)) (=> (forall ((I $$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))) (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_a I))))))))))) (= (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_a)))))))))))))))))))))))))) (tptp.hBOOL (tptp.hAPP _let_32 tptp.bool (tptp.hAPP _let_31 (tptp.fun _let_32 tptp.bool) (tptp.member _let_31) tptp.f) (tptp.hAPP _let_30 _let_32 (tptp.hAPP _let_25 (tptp.fun _let_30 _let_32) (tptp.pi _let_24 _let_13) tptp.arrow_1111136790e_Prof) (tptp.hAPP _let_14 _let_30 (tptp.combk _let_14 _let_24) tptp.arrow_2064824852le_Lin)))) (forall ((L_1 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.product_prod tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt) tptp.bool))) (let ((_let_2 (tptp.fun tptp.arrow_660593299e_indi _let_1))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_4 tptp.bool) (tptp.member _let_1) L_1) tptp.arrow_2064824852le_Lin)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_3 tptp.bool) (tptp.member _let_2) (tptp.hAPP _let_1 _let_2 (tptp.combk _let_1 tptp.arrow_660593299e_indi) L_1)) tptp.arrow_1111136790e_Prof)))))))) (forall ((X_1 $$unsorted) (L_1 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.product_prod tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt) tptp.bool))) (let ((_let_2 (tptp.member _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_1 _let_4 _let_2 L_1) tptp.arrow_2064824852le_Lin)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_1 _let_4 _let_2 (tptp.hAPP tptp.arrow_490897120le_alt _let_1 (tptp.hAPP _let_1 (tptp.fun tptp.arrow_490897120le_alt _let_1) tptp.arrow_1278947948_mkbot L_1) X_1)) tptp.arrow_2064824852le_Lin)))))))) (forall ((X_1 $$unsorted) (L_1 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.product_prod tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt) tptp.bool))) (let ((_let_2 (tptp.member _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_1 _let_4 _let_2 L_1) tptp.arrow_2064824852le_Lin)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_1 _let_4 _let_2 (tptp.hAPP tptp.arrow_490897120le_alt _let_1 (tptp.hAPP _let_1 (tptp.fun tptp.arrow_490897120le_alt _let_1) tptp.arrow_1427655034_mktop L_1) X_1)) tptp.arrow_2064824852le_Lin)))))))) (forall ((Aa $$unsorted) (Ba $$unsorted) (L_1 $$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_1) 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_1)) (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_1)))))))))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (L_1 $$unsorted)) (let ((_let_1 (tptp.product_Pair tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt))) (let ((_let_2 (tptp.product_prod tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt))) (let ((_let_3 (tptp.fun tptp.arrow_490897120le_alt _let_2))) (let ((_let_4 (tptp.member _let_2))) (let ((_let_5 (tptp.fun _let_2 tptp.bool))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP _let_5 (tptp.fun _let_6 tptp.bool) (tptp.member _let_5) L_1) tptp.arrow_2064824852le_Lin)) (=> (not (= (tptp.ti tptp.arrow_490897120le_alt X_1) (tptp.ti tptp.arrow_490897120le_alt Y_1))) (= (not (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP _let_2 _let_6 _let_4 (tptp.hAPP tptp.arrow_490897120le_alt _let_2 (tptp.hAPP tptp.arrow_490897120le_alt _let_3 _let_1 X_1) Y_1)) L_1))) (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP _let_2 _let_6 _let_4 (tptp.hAPP tptp.arrow_490897120le_alt _let_2 (tptp.hAPP tptp.arrow_490897120le_alt _let_3 _let_1 Y_1) X_1)) L_1)))))))))))) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (=> (not (= (tptp.ti tptp.arrow_490897120le_alt A_2) (tptp.ti tptp.arrow_490897120le_alt B_1))) (exists ((C_2 $$unsorted)) (let ((_let_1 (tptp.cons tptp.arrow_490897120le_alt))) (let ((_let_2 (tptp.list tptp.arrow_490897120le_alt))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.distinct tptp.arrow_490897120le_alt) (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.arrow_490897120le_alt _let_3 _let_1 A_2) (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.arrow_490897120le_alt _let_3 _let_1 B_1) (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.arrow_490897120le_alt _let_3 _let_1 C_2) (tptp.nil tptp.arrow_490897120le_alt)))))))))))) (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 $$unsorted)) (let ((_let_1 (tptp.fun tptp.arrow_660593299e_indi (tptp.fun (tptp.product_prod tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt) tptp.bool)))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) Xa) tptp.arrow_1111136790e_Prof)) (forall ((A_4 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun tptp.arrow_660593299e_indi _let_2))) (let ((_let_4 (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) (tptp.hAPP tptp.arrow_490897120le_alt _let_1 (tptp.hAPP tptp.arrow_490897120le_alt (tptp.fun tptp.arrow_490897120le_alt _let_1) (tptp.product_Pair tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt) A_4) B_2)))) (=> (forall ((I $$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_4) B_2)))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 (tptp.hAPP tptp.arrow_660593299e_indi _let_2 X_2 I))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 (tptp.hAPP tptp.arrow_660593299e_indi _let_2 Xa I)))))))) (= (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_4 $$unsorted) (B_2 $$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 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) (tptp.hAPP tptp.arrow_490897120le_alt _let_1 (tptp.hAPP tptp.arrow_490897120le_alt (tptp.fun tptp.arrow_490897120le_alt _let_1) (tptp.product_Pair tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt) A_4) B_2)) (tptp.hAPP tptp.arrow_660593299e_indi _let_2 X_2 I)))))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) (tptp.hAPP tptp.arrow_490897120le_alt _let_1 (tptp.hAPP tptp.arrow_490897120le_alt (tptp.fun tptp.arrow_490897120le_alt _let_1) (tptp.product_Pair tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt) A_4) B_2)) (tptp.hAPP (tptp.fun tptp.arrow_660593299e_indi _let_2) _let_2 Fa X_2)))))))))))))) (forall ((Aa $$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_1 $$unsorted) (Y_1 $$unsorted) (L_1 $$unsorted) (Aa $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.product_Pair tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt))) (let ((_let_2 (tptp.product_prod tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt))) (let ((_let_3 (tptp.fun tptp.arrow_490897120le_alt _let_2))) (let ((_let_4 (tptp.hAPP tptp.arrow_490897120le_alt _let_3 _let_1 X_1))) (let ((_let_5 (tptp.member _let_2))) (let ((_let_6 (tptp.fun _let_2 tptp.bool))) (let ((_let_7 (tptp.fun _let_6 tptp.bool))) (let ((_let_8 (tptp.hAPP _let_2 _let_7 _let_5 (tptp.hAPP tptp.arrow_490897120le_alt _let_2 _let_4 Y_1)))) (let ((_let_9 (tptp.ti tptp.arrow_490897120le_alt Ba))) (let ((_let_10 (tptp.ti tptp.arrow_490897120le_alt Y_1))) (let ((_let_11 (= _let_10 _let_9))) (let ((_let_12 (tptp.ti tptp.arrow_490897120le_alt Aa))) (let ((_let_13 (tptp.ti tptp.arrow_490897120le_alt X_1))) (let ((_let_14 (= _let_13 _let_9))) (let ((_let_15 (tptp.fun tptp.arrow_490897120le_alt _let_6))) (=> (not (= _let_12 _let_9)) (=> (tptp.hBOOL (tptp.hAPP _let_7 tptp.bool (tptp.hAPP _let_6 (tptp.fun _let_7 tptp.bool) (tptp.member _let_6) L_1) tptp.arrow_2064824852le_Lin)) (= (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool _let_8 (tptp.hAPP tptp.arrow_490897120le_alt _let_6 (tptp.hAPP tptp.arrow_490897120le_alt _let_15 (tptp.hAPP _let_6 (tptp.fun tptp.arrow_490897120le_alt _let_15) tptp.arrow_14103264_above L_1) Aa) Ba))) (and (not (= _let_13 _let_10)) (=> _let_14 (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP _let_2 _let_7 _let_5 (tptp.hAPP tptp.arrow_490897120le_alt _let_2 (tptp.hAPP tptp.arrow_490897120le_alt _let_3 _let_1 Aa) Y_1)) L_1))) (=> (not _let_14) (and (=> _let_11 (or (= _let_13 _let_12) (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP _let_2 _let_7 _let_5 (tptp.hAPP tptp.arrow_490897120le_alt _let_2 _let_4 Aa)) L_1)))) (=> (not _let_11) (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool _let_8 L_1))))))))))))))))))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (X_a $$unsorted) (F1 $$unsorted) (Aa $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.fun X_c X_a))) (let ((_let_2 (tptp.product_prod X_b X_c))) (= (tptp.hAPP _let_2 X_a (tptp.hAPP (tptp.fun X_b _let_1) (tptp.fun _let_2 X_a) (tptp.product_prod_rec X_b X_c X_a) F1) (tptp.hAPP X_c _let_2 (tptp.hAPP X_b (tptp.fun X_c _let_2) (tptp.product_Pair X_b X_c) Aa) Ba)) (tptp.hAPP X_c X_a (tptp.hAPP X_b _let_1 F1 Aa) Ba))))) (forall ((X_a $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.list X_a) tptp.bool (tptp.distinct X_a) (tptp.nil X_a)))) _let_29 (forall ((X_a $$unsorted) (A_6 $$unsorted) (List_3 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (not (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.cons X_a) A_6) List_3) (tptp.nil X_a))))) (exists ((A_4 $$unsorted) (B_2 $$unsorted) (C_2 $$unsorted)) (let ((_let_1 (tptp.cons tptp.arrow_490897120le_alt))) (let ((_let_2 (tptp.list tptp.arrow_490897120le_alt))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.distinct tptp.arrow_490897120le_alt) (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.arrow_490897120le_alt _let_3 _let_1 A_4) (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.arrow_490897120le_alt _let_3 _let_1 B_2) (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.arrow_490897120le_alt _let_3 _let_1 C_2) (tptp.nil tptp.arrow_490897120le_alt)))))))))) (exists ((L_2 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.product_prod tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt) tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) L_2) tptp.arrow_2064824852le_Lin))))) (forall ((X_a $$unsorted) (Aa $$unsorted) (List $$unsorted) (A_5 $$unsorted) (List_2 $$unsorted)) (let ((_let_1 (tptp.cons X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (= (= (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_a _let_3 _let_1 Aa) List) (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_a _let_3 _let_1 A_5) List_2)) (and (= (tptp.ti X_a Aa) (tptp.ti X_a A_5)) (= List List_2))))))) (forall ((X_a $$unsorted) (X $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.list X_a))) (not (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.cons X_a) X) Xs) Xs)))) (forall ((X_a $$unsorted) (Xs $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.list X_a))) (not (= Xs (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.cons X_a) X) Xs))))) (forall ((L_1 $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.product_prod tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt) tptp.bool))) (let ((_let_2 (tptp.fun tptp.arrow_490897120le_alt _let_1))) (let ((_let_3 (tptp.member _let_1))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (not (= (tptp.ti tptp.arrow_490897120le_alt X_1) (tptp.ti tptp.arrow_490897120le_alt Y_1))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP _let_1 _let_5 _let_3 L_1) tptp.arrow_2064824852le_Lin)) (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP _let_1 _let_5 _let_3 (tptp.hAPP tptp.arrow_490897120le_alt _let_1 (tptp.hAPP tptp.arrow_490897120le_alt _let_2 (tptp.hAPP _let_1 (tptp.fun tptp.arrow_490897120le_alt _let_2) tptp.arrow_14103264_above L_1) X_1) Y_1)) tptp.arrow_2064824852le_Lin)))))))))) (forall ((I_2 $$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_4 $$unsorted) (B_2 $$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_4) B_2)))) (=> (not (= (tptp.ti tptp.arrow_490897120le_alt A_4) (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_2))) (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_2))))))))))) (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 ((X_a $$unsorted) (Y $$unsorted)) (=> (not (= Y (tptp.nil X_a))) (not (forall ((A_4 $$unsorted) (List_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (not (= Y (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.cons X_a) A_4) List_1)))))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted)) (= (not (= Xs_1 (tptp.nil X_a))) (exists ((Y_2 $$unsorted) (Ys $$unsorted)) (let ((_let_1 (tptp.list X_a))) (= Xs_1 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.cons X_a) Y_2) Ys)))))) (forall ((Fa $$unsorted) (I_2 $$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_2)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.product_prod tptp.arrow_490897120le_alt tptp.arrow_490897120le_alt) tptp.bool))) (let ((_let_2 (tptp.fun tptp.arrow_660593299e_indi _let_1))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_3 tptp.bool) (tptp.member _let_2) X_2) tptp.arrow_1111136790e_Prof)) (= (tptp.hAPP _let_2 _let_1 Fa X_2) (tptp.hAPP tptp.arrow_660593299e_indi _let_1 X_2 I_2)))))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun X_a _let_1))) (let ((_let_3 (tptp.fun X_a X_a))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP _let_3 (tptp.fun _let_4 tptp.bool) (tptp.member _let_3) (tptp.combi X_a)) (tptp.hAPP _let_2 _let_4 (tptp.hAPP _let_1 (tptp.fun _let_2 _let_4) (tptp.pi X_a X_a) A_1) (tptp.hAPP _let_1 _let_2 (tptp.combk _let_1 X_a) A_1))))))))) _let_28 (forall ((X_a $$unsorted) (V_1 $$unsorted) (Va $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_2 (tptp.cons X_a) V_1) Va))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.splice X_a) _let_3) (tptp.nil X_a)) _let_3))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F1 $$unsorted) (F2 $$unsorted)) (let ((_let_1 (tptp.list X_b))) (let ((_let_2 (tptp.fun _let_1 X_a))) (let ((_let_3 (tptp.fun X_b _let_2))) (= (tptp.hAPP _let_1 X_a (tptp.hAPP _let_3 _let_2 (tptp.hAPP X_a (tptp.fun _let_3 _let_2) (tptp.list_case X_a X_b) F1) F2) (tptp.nil X_b)) (tptp.ti X_a F1)))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F1 $$unsorted) (F2 $$unsorted) (Aa $$unsorted) (List $$unsorted)) (let ((_let_1 (tptp.list X_b))) (let ((_let_2 (tptp.fun _let_1 X_a))) (let ((_let_3 (tptp.fun X_b _let_2))) (= (tptp.hAPP _let_1 X_a (tptp.hAPP _let_3 _let_2 (tptp.hAPP X_a (tptp.fun _let_3 _let_2) (tptp.list_case X_a X_b) F1) F2) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.cons X_b) Aa) List)) (tptp.hAPP _let_1 X_a (tptp.hAPP X_b _let_2 F2 Aa) List)))))) (forall ((X_a $$unsorted) (X $$unsorted) (Xs $$unsorted) (Y $$unsorted) (Ys_2 $$unsorted)) (let ((_let_1 (tptp.splice X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (let ((_let_4 (tptp.cons X_a))) (let ((_let_5 (tptp.hAPP X_a _let_3 _let_4 Y))) (let ((_let_6 (tptp.hAPP X_a _let_3 _let_4 X))) (= (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_3 _let_1 (tptp.hAPP _let_2 _let_2 _let_6 Xs)) (tptp.hAPP _let_2 _let_2 _let_5 Ys_2)) (tptp.hAPP _let_2 _let_2 _let_6 (tptp.hAPP _let_2 _let_2 _let_5 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_3 _let_1 Xs) Ys_2))))))))))) (forall ((X_a $$unsorted) (Ys_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.splice X_a) (tptp.nil X_a)) Ys_2) Ys_2))) (forall ((X_a $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.list X_a))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.splice X_a) Xs) (tptp.nil X_a)) Xs))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_1 $$unsorted) (F $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.fun X_a X_b))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.fun X_a _let_1))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP _let_3 (tptp.fun _let_4 tptp.bool) (tptp.member _let_3) F) (tptp.hAPP _let_5 _let_4 (tptp.hAPP _let_2 (tptp.fun _let_5 _let_4) (tptp.pi X_a X_b) A_1) B))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a (tptp.fun _let_2 tptp.bool) (tptp.member X_a) X_1) A_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) (tptp.hAPP X_a X_b F X_1)) (tptp.hAPP X_a _let_1 B X_1))))))))))) (forall ((X_b $$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 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a (tptp.fun _let_2 tptp.bool) (tptp.member X_a) X_2) A_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) (tptp.hAPP X_a X_b F X_2)) (tptp.hAPP X_a _let_1 B X_2))))))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) F) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun X_a tptp.bool) (tptp.fun _let_3 _let_2) (tptp.pi X_a X_b) A_1) B)))))))) (forall ((X_b $$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 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a (tptp.fun _let_2 tptp.bool) (tptp.member X_a) X_2) A_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) (tptp.hAPP X_a X_b F X_2)) B)))))) (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP _let_3 (tptp.fun _let_4 tptp.bool) (tptp.member _let_3) F) (tptp.hAPP _let_2 _let_4 (tptp.hAPP (tptp.fun X_a tptp.bool) (tptp.fun _let_2 _let_4) (tptp.pi X_a X_b) A_1) (tptp.hAPP _let_1 _let_2 (tptp.combk _let_1 X_a) B)))))))))) (forall ((X_b $$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 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a (tptp.fun _let_2 tptp.bool) (tptp.member X_a) X_2) A_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) (tptp.hAPP X_a X_b F X_2)) (tptp.hAPP X_a _let_1 B X_2))))))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) F) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun X_a tptp.bool) (tptp.fun _let_3 _let_2) (tptp.pi X_a X_b) A_1) B)))))))) (forall ((X_b $$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_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))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (Y $$unsorted)) (not (forall ((A_4 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_b))) (not (= (tptp.ti _let_1 Y) (tptp.hAPP X_b _let_1 (tptp.hAPP X_a (tptp.fun X_b _let_1) (tptp.product_Pair X_a X_b) A_4) B_2))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (P_2 $$unsorted)) (not (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_b))) (not (= (tptp.ti _let_1 P_2) (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) Y_2))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted) (Y $$unsorted)) (not (forall ((A_4 $$unsorted) (B_2 $$unsorted) (C_2 $$unsorted)) (let ((_let_1 (tptp.product_prod X_b X_c))) (let ((_let_2 (tptp.product_prod X_a _let_1))) (not (= (tptp.ti _let_2 Y) (tptp.hAPP _let_1 _let_2 (tptp.hAPP X_a (tptp.fun _let_1 _let_2) (tptp.product_Pair X_a _let_1) A_4) (tptp.hAPP X_c _let_1 (tptp.hAPP X_b (tptp.fun X_c _let_1) (tptp.product_Pair X_b X_c) B_2) C_2))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted) (X_1 $$unsorted) (Pa $$unsorted)) (=> (forall ((A_4 $$unsorted) (B_2 $$unsorted) (C_2 $$unsorted)) (let ((_let_1 (tptp.product_prod X_b X_c))) (let ((_let_2 (tptp.product_prod X_a _let_1))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool Pa (tptp.hAPP _let_1 _let_2 (tptp.hAPP X_a (tptp.fun _let_1 _let_2) (tptp.product_Pair X_a _let_1) A_4) (tptp.hAPP X_c _let_1 (tptp.hAPP X_b (tptp.fun X_c _let_1) (tptp.product_Pair X_b X_c) B_2) C_2))))))) (tptp.hBOOL (tptp.hAPP (tptp.product_prod X_a (tptp.product_prod X_b X_c)) tptp.bool Pa X_1)))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted) (X_d $$unsorted) (X_e $$unsorted) (X_f $$unsorted) (X_1 $$unsorted) (Pa $$unsorted)) (=> (forall ((A_4 $$unsorted) (B_2 $$unsorted) (C_2 $$unsorted) (D $$unsorted) (E $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.product_prod X_e X_f))) (let ((_let_2 (tptp.product_prod X_d _let_1))) (let ((_let_3 (tptp.product_prod X_c _let_2))) (let ((_let_4 (tptp.product_prod X_b _let_3))) (let ((_let_5 (tptp.product_prod X_a _let_4))) (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool Pa (tptp.hAPP _let_4 _let_5 (tptp.hAPP X_a (tptp.fun _let_4 _let_5) (tptp.product_Pair X_a _let_4) A_4) (tptp.hAPP _let_3 _let_4 (tptp.hAPP X_b (tptp.fun _let_3 _let_4) (tptp.product_Pair X_b _let_3) B_2) (tptp.hAPP _let_2 _let_3 (tptp.hAPP X_c (tptp.fun _let_2 _let_3) (tptp.product_Pair X_c _let_2) C_2) (tptp.hAPP _let_1 _let_2 (tptp.hAPP X_d (tptp.fun _let_1 _let_2) (tptp.product_Pair X_d _let_1) D) (tptp.hAPP X_f _let_1 (tptp.hAPP X_e (tptp.fun X_f _let_1) (tptp.product_Pair X_e X_f) E) F_1))))))))))))) (tptp.hBOOL (tptp.hAPP (tptp.product_prod X_a (tptp.product_prod X_b (tptp.product_prod X_c (tptp.product_prod X_d (tptp.product_prod X_e X_f))))) tptp.bool Pa X_1)))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted) (X_d $$unsorted) (X_e $$unsorted) (X_f $$unsorted) (Y $$unsorted)) (not (forall ((A_4 $$unsorted) (B_2 $$unsorted) (C_2 $$unsorted) (D $$unsorted) (E $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.product_prod X_e X_f))) (let ((_let_2 (tptp.product_prod X_d _let_1))) (let ((_let_3 (tptp.product_prod X_c _let_2))) (let ((_let_4 (tptp.product_prod X_b _let_3))) (let ((_let_5 (tptp.product_prod X_a _let_4))) (not (= (tptp.ti _let_5 Y) (tptp.hAPP _let_4 _let_5 (tptp.hAPP X_a (tptp.fun _let_4 _let_5) (tptp.product_Pair X_a _let_4) A_4) (tptp.hAPP _let_3 _let_4 (tptp.hAPP X_b (tptp.fun _let_3 _let_4) (tptp.product_Pair X_b _let_3) B_2) (tptp.hAPP _let_2 _let_3 (tptp.hAPP X_c (tptp.fun _let_2 _let_3) (tptp.product_Pair X_c _let_2) C_2) (tptp.hAPP _let_1 _let_2 (tptp.hAPP X_d (tptp.fun _let_1 _let_2) (tptp.product_Pair X_d _let_1) D) (tptp.hAPP X_f _let_1 (tptp.hAPP X_e (tptp.fun X_f _let_1) (tptp.product_Pair X_e X_f) E) F_1))))))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted) (X_d $$unsorted) (X_e $$unsorted) (X_1 $$unsorted) (Pa $$unsorted)) (=> (forall ((A_4 $$unsorted) (B_2 $$unsorted) (C_2 $$unsorted) (D $$unsorted) (E $$unsorted)) (let ((_let_1 (tptp.product_prod X_d X_e))) (let ((_let_2 (tptp.product_prod X_c _let_1))) (let ((_let_3 (tptp.product_prod X_b _let_2))) (let ((_let_4 (tptp.product_prod X_a _let_3))) (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool Pa (tptp.hAPP _let_3 _let_4 (tptp.hAPP X_a (tptp.fun _let_3 _let_4) (tptp.product_Pair X_a _let_3) A_4) (tptp.hAPP _let_2 _let_3 (tptp.hAPP X_b (tptp.fun _let_2 _let_3) (tptp.product_Pair X_b _let_2) B_2) (tptp.hAPP _let_1 _let_2 (tptp.hAPP X_c (tptp.fun _let_1 _let_2) (tptp.product_Pair X_c _let_1) C_2) (tptp.hAPP X_e _let_1 (tptp.hAPP X_d (tptp.fun X_e _let_1) (tptp.product_Pair X_d X_e) D) E))))))))))) (tptp.hBOOL (tptp.hAPP (tptp.product_prod X_a (tptp.product_prod X_b (tptp.product_prod X_c (tptp.product_prod X_d X_e)))) tptp.bool Pa X_1)))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted) (X_d $$unsorted) (X_e $$unsorted) (Y $$unsorted)) (not (forall ((A_4 $$unsorted) (B_2 $$unsorted) (C_2 $$unsorted) (D $$unsorted) (E $$unsorted)) (let ((_let_1 (tptp.product_prod X_d X_e))) (let ((_let_2 (tptp.product_prod X_c _let_1))) (let ((_let_3 (tptp.product_prod X_b _let_2))) (let ((_let_4 (tptp.product_prod X_a _let_3))) (not (= (tptp.ti _let_4 Y) (tptp.hAPP _let_3 _let_4 (tptp.hAPP X_a (tptp.fun _let_3 _let_4) (tptp.product_Pair X_a _let_3) A_4) (tptp.hAPP _let_2 _let_3 (tptp.hAPP X_b (tptp.fun _let_2 _let_3) (tptp.product_Pair X_b _let_2) B_2) (tptp.hAPP _let_1 _let_2 (tptp.hAPP X_c (tptp.fun _let_1 _let_2) (tptp.product_Pair X_c _let_1) C_2) (tptp.hAPP X_e _let_1 (tptp.hAPP X_d (tptp.fun X_e _let_1) (tptp.product_Pair X_d X_e) D) E))))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted) (X_d $$unsorted) (X_1 $$unsorted) (Pa $$unsorted)) (=> (forall ((A_4 $$unsorted) (B_2 $$unsorted) (C_2 $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.product_prod X_c X_d))) (let ((_let_2 (tptp.product_prod X_b _let_1))) (let ((_let_3 (tptp.product_prod X_a _let_2))) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool Pa (tptp.hAPP _let_2 _let_3 (tptp.hAPP X_a (tptp.fun _let_2 _let_3) (tptp.product_Pair X_a _let_2) A_4) (tptp.hAPP _let_1 _let_2 (tptp.hAPP X_b (tptp.fun _let_1 _let_2) (tptp.product_Pair X_b _let_1) B_2) (tptp.hAPP X_d _let_1 (tptp.hAPP X_c (tptp.fun X_d _let_1) (tptp.product_Pair X_c X_d) C_2) D))))))))) (tptp.hBOOL (tptp.hAPP (tptp.product_prod X_a (tptp.product_prod X_b (tptp.product_prod X_c X_d))) tptp.bool Pa X_1)))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted) (X_d $$unsorted) (Y $$unsorted)) (not (forall ((A_4 $$unsorted) (B_2 $$unsorted) (C_2 $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.product_prod X_c X_d))) (let ((_let_2 (tptp.product_prod X_b _let_1))) (let ((_let_3 (tptp.product_prod X_a _let_2))) (not (= (tptp.ti _let_3 Y) (tptp.hAPP _let_2 _let_3 (tptp.hAPP X_a (tptp.fun _let_2 _let_3) (tptp.product_Pair X_a _let_2) A_4) (tptp.hAPP _let_1 _let_2 (tptp.hAPP X_b (tptp.fun _let_1 _let_2) (tptp.product_Pair X_b _let_1) B_2) (tptp.hAPP X_d _let_1 (tptp.hAPP X_c (tptp.fun X_d _let_1) (tptp.product_Pair X_c X_d) C_2) D))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (Pa $$unsorted)) (= (exists ((X1 $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.product_prod X_a X_b) tptp.bool Pa X1))) (exists ((A_4 $$unsorted) (B_2 $$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_4) B_2))))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (X_a $$unsorted) (Ca $$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.produc1605651328_split X_b X_c X_a) Ca) (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 Ca Aa) Ba))))) (forall ((X_a $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.nil X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (= (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_a _let_3 (tptp.insert X_a) X) _let_1) (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_a _let_3 (tptp.cons X_a) X) _let_1)))))) (forall ((X_a $$unsorted) (X $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.distinct X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 Xs)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.insert X_a) X) Xs))))))) (forall ((X_a $$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 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (= (tptp.hAPP _let_1 _let_1 (tptp.collect X_a) Pa) (tptp.ti _let_1 Pa)))) (forall ((X_a $$unsorted) (Pa $$unsorted) (Xs_1 $$unsorted)) (=> (not (= Xs_1 (tptp.nil X_a))) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.cons X_a) X_2) (tptp.nil X_a)))))) (=> (forall ((X_2 $$unsorted) (Xs_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (=> (not (= Xs_2 (tptp.nil X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa Xs_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.cons X_a) X_2) Xs_2))))))) (tptp.hBOOL (tptp.hAPP (tptp.list X_a) tptp.bool Pa Xs_1)))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F1 $$unsorted) (F2 $$unsorted)) (let ((_let_1 (tptp.list X_b))) (let ((_let_2 (tptp.fun _let_1 X_a))) (let ((_let_3 (tptp.fun X_b (tptp.fun _let_1 (tptp.fun X_a X_a))))) (= (tptp.hAPP _let_1 X_a (tptp.hAPP _let_3 _let_2 (tptp.hAPP X_a (tptp.fun _let_3 _let_2) (tptp.list_rec X_a X_b) F1) F2) (tptp.nil X_b)) (tptp.ti X_a F1)))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F1 $$unsorted) (F2 $$unsorted) (Aa $$unsorted) (List $$unsorted)) (let ((_let_1 (tptp.list X_b))) (let ((_let_2 (tptp.fun _let_1 X_a))) (let ((_let_3 (tptp.fun X_a X_a))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.fun X_b _let_4))) (let ((_let_6 (tptp.hAPP _let_5 _let_2 (tptp.hAPP X_a (tptp.fun _let_5 _let_2) (tptp.list_rec X_a X_b) F1) F2))) (= (tptp.hAPP _let_1 X_a _let_6 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.cons X_b) Aa) List)) (tptp.hAPP X_a X_a (tptp.hAPP _let_1 _let_3 (tptp.hAPP X_b _let_4 F2 Aa) List) (tptp.hAPP _let_1 X_a _let_6 List)))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (X_a $$unsorted) (X_2 $$unsorted) (Xa $$unsorted) (Xb $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_b))) (let ((_let_2 (tptp.fun X_b X_c))) (= (tptp.hAPP X_b X_c (tptp.hAPP X_a _let_2 (tptp.hAPP (tptp.fun _let_1 X_c) (tptp.fun X_a _let_2) (tptp.product_curry X_a X_b X_c) X_2) Xa) Xb) (tptp.hAPP _let_1 X_c X_2 (tptp.hAPP X_b _let_1 (tptp.hAPP X_a (tptp.fun X_b _let_1) (tptp.product_Pair X_a X_b) Xa) Xb)))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (F $$unsorted) (Aa $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.product_prod X_a X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool F (tptp.hAPP X_b _let_2 (tptp.hAPP X_a (tptp.fun X_b _let_2) (tptp.product_Pair X_a X_b) Aa) Ba))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_a _let_1 (tptp.hAPP (tptp.fun _let_2 tptp.bool) (tptp.fun X_a _let_1) (tptp.product_curry X_a X_b tptp.bool) F) Aa) Ba)))))) (forall ((X_b $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.list X_b) tptp.bool (tptp.null X_b) (tptp.nil X_b)))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.list X_a) tptp.bool (tptp.null X_a) Xs_1)) (= Xs_1 (tptp.nil X_a)))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted)) (= (= Xs_1 (tptp.nil X_a)) (tptp.hBOOL (tptp.hAPP (tptp.list X_a) tptp.bool (tptp.null X_a) Xs_1)))) (forall ((X_a $$unsorted) (X $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.list X_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.null X_a) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.cons X_a) X) Xs)))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F $$unsorted) (Aa $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_a _let_2 (tptp.hAPP (tptp.fun _let_1 tptp.bool) (tptp.fun X_a _let_2) (tptp.product_curry X_a X_b tptp.bool) F) Aa) Ba)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool F (tptp.hAPP X_b _let_1 (tptp.hAPP X_a (tptp.fun X_b _let_1) (tptp.product_Pair X_a X_b) Aa) Ba))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F $$unsorted) (Aa $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_a _let_2 (tptp.hAPP (tptp.fun _let_1 tptp.bool) (tptp.fun X_a _let_2) (tptp.product_curry X_a X_b tptp.bool) F) Aa) Ba)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool F (tptp.hAPP X_b _let_1 (tptp.hAPP X_a (tptp.fun X_b _let_1) (tptp.product_Pair X_a X_b) Aa) Ba))))))) (forall ((X_c $$unsorted) (X_a $$unsorted) (X_b $$unsorted) (F $$unsorted) (Aa $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.product_prod X_b X_c))) (let ((_let_2 (tptp.fun X_c X_a))) (= (tptp.hAPP X_c X_a (tptp.hAPP X_b _let_2 (tptp.hAPP (tptp.fun _let_1 X_a) (tptp.fun X_b _let_2) (tptp.product_curry X_b X_c X_a) F) Aa) Ba) (tptp.hAPP _let_1 X_a F (tptp.hAPP X_c _let_1 (tptp.hAPP X_b (tptp.fun X_c _let_1) (tptp.product_Pair X_b X_c) Aa) Ba)))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.equal_equal _let_1) Xs_1) (tptp.nil X_a))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.null X_a) Xs_1))))) _let_27 (forall ((X_a $$unsorted) (Aa $$unsorted) (X_1 $$unsorted) (Ba $$unsorted) (Y_1 $$unsorted) (R_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.product_prod _let_1 _let_1))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.product_prod X_a X_a))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (let ((_let_6 (tptp.hAPP _let_5 _let_3 (tptp.lexord X_a) R_2))) (let ((_let_7 (tptp.product_Pair _let_1 _let_1))) (let ((_let_8 (tptp.fun _let_1 _let_2))) (let ((_let_9 (tptp.member _let_2))) (let ((_let_10 (tptp.fun _let_3 tptp.bool))) (let ((_let_11 (tptp.cons X_a))) (let ((_let_12 (tptp.fun _let_1 _let_1))) (= (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 _let_10 _let_9 (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_1 _let_8 _let_7 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_12 _let_11 Aa) X_1)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_12 _let_11 Ba) Y_1))) _let_6)) (or (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP _let_4 (tptp.fun _let_5 tptp.bool) (tptp.member _let_4) (tptp.hAPP X_a _let_4 (tptp.hAPP X_a (tptp.fun X_a _let_4) (tptp.product_Pair X_a X_a) Aa) Ba)) R_2)) (and (= (tptp.ti X_a Aa) (tptp.ti X_a Ba)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 _let_10 _let_9 (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_1 _let_8 _let_7 X_1) Y_1)) _let_6)))))))))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.list X_b))) (= (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_b _let_1) (tptp.fun _let_2 _let_1) (tptp.maps X_b X_a) F) (tptp.nil X_b)) (tptp.nil X_a))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted)) (let ((_let_1 (tptp.list X_a))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.linorder_sorted X_a) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.cons X_a) X) (tptp.nil X_a)))))))) (forall ((X_a $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.distinct X_a))) (=> (not (= Xs (tptp.nil X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 Xs)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.butlast X_a) Xs)))))))) _let_19 _let_18 (forall ((X_a $$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)) (=> (tptp.linorder X_a) (tptp.hBOOL (tptp.hAPP (tptp.list X_a) tptp.bool (tptp.linorder_sorted X_a) (tptp.nil X_a))))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.equal_equal _let_1) X_1) Y_1)) (= X_1 Y_1)))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((Xs $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.linorder_sorted X_a))) (=> (not (= Xs (tptp.nil X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 Xs)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.butlast X_a) Xs)))))))))) (forall ((X_a $$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_a $$unsorted)) (let ((_let_1 (tptp.nil X_a))) (let ((_let_2 (tptp.list X_a))) (= (tptp.hAPP _let_2 _let_2 (tptp.butlast X_a) _let_1) _let_1)))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (R_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.product_prod _let_1 _let_1))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (not (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.hAPP _let_1 (tptp.fun _let_1 _let_2) (tptp.product_Pair _let_1 _let_1) X_1) (tptp.nil X_a))) (tptp.hAPP (tptp.fun (tptp.product_prod X_a X_a) tptp.bool) _let_3 (tptp.lexord X_a) R_2)))))))) (forall ((X_a $$unsorted) (X $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.butlast X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.hAPP X_a (tptp.fun _let_2 _let_2) (tptp.cons X_a) X))) (let ((_let_4 (tptp.hAPP _let_2 _let_2 _let_1 (tptp.hAPP _let_2 _let_2 _let_3 Xs)))) (let ((_let_5 (tptp.nil X_a))) (let ((_let_6 (= Xs _let_5))) (and (=> _let_6 (= _let_4 _let_5)) (=> (not _let_6) (= _let_4 (tptp.hAPP _let_2 _let_2 _let_3 (tptp.hAPP _let_2 _let_2 _let_1 Xs)))))))))))) (forall ((X_a $$unsorted) (X $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.last X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.hAPP _let_2 X_a _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_a (tptp.fun _let_2 _let_2) (tptp.cons X_a) X) Xs)))) (let ((_let_4 (= Xs (tptp.nil X_a)))) (and (=> _let_4 (= _let_3 (tptp.ti X_a X))) (=> (not _let_4) (= _let_3 (tptp.hAPP _let_2 X_a _let_1 Xs))))))))) (forall ((X_a $$unsorted) (Y_1 $$unsorted) (R_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.product_prod _let_1 _let_1))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_3 tptp.bool) (tptp.member _let_2) (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_2) (tptp.product_Pair _let_1 _let_1) (tptp.nil X_a)) Y_1)) (tptp.hAPP (tptp.fun (tptp.product_prod X_a X_a) tptp.bool) _let_3 (tptp.lexord X_a) R_2))) (exists ((A_4 $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (= Y_1 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.cons X_a) A_4) X_2))))))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (R_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.product_prod _let_1 _let_1))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_a))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (not (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) (tptp.hAPP X_a _let_1 (tptp.hAPP X_a (tptp.fun X_a _let_1) (tptp.product_Pair X_a X_a) X_2) X_2)) R_2)))))) (not (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_3 tptp.bool) (tptp.member _let_2) (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_2) (tptp.product_Pair _let_1 _let_1) Xs_1) Xs_1)) (tptp.hAPP (tptp.fun (tptp.product_prod X_a X_a) tptp.bool) _let_3 (tptp.lexord X_a) R_2))))))))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted) (R_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.product_prod _let_1 _let_1))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.hAPP (tptp.fun (tptp.product_prod X_a X_a) tptp.bool) _let_3 (tptp.lexord X_a) R_2))) (let ((_let_5 (tptp.product_Pair _let_1 _let_1))) (let ((_let_6 (tptp.fun _let_1 _let_2))) (let ((_let_7 (tptp.member _let_2))) (let ((_let_8 (tptp.fun _let_3 tptp.bool))) (=> (forall ((A_4 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.product_Pair X_a X_a))) (let ((_let_2 (tptp.product_prod X_a X_a))) (let ((_let_3 (tptp.fun X_a _let_2))) (let ((_let_4 (tptp.member _let_2))) (let ((_let_5 (tptp.fun _let_2 tptp.bool))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (or (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP _let_2 _let_6 _let_4 (tptp.hAPP X_a _let_2 (tptp.hAPP X_a _let_3 _let_1 A_4) B_2)) R_2)) (= (tptp.ti X_a A_4) (tptp.ti X_a B_2)) (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP _let_2 _let_6 _let_4 (tptp.hAPP X_a _let_2 (tptp.hAPP X_a _let_3 _let_1 B_2) A_4)) R_2)))))))))) (or (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 _let_8 _let_7 (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_1 _let_6 _let_5 X_1) Y_1)) _let_4)) (= X_1 Y_1) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 _let_8 _let_7 (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_1 _let_6 _let_5 Y_1) X_1)) _let_4))))))))))))) _let_17 (forall ((X_a $$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_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 $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.fun X_a _let_2))) (=> (not (= Xs_1 (tptp.nil X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.distinct X_a) Xs_1)) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_2 (tptp.fun _let_1 _let_1) (tptp.takeWhile X_a) (tptp.hAPP _let_2 _let_2 (tptp.hAPP (tptp.fun tptp.bool tptp.bool) (tptp.fun _let_2 _let_2) (tptp.combb tptp.bool tptp.bool X_a) tptp.fNot) (tptp.hAPP X_a _let_2 (tptp.hAPP _let_3 _let_3 (tptp.combc X_a X_a tptp.bool) (tptp.fequal X_a)) (tptp.hAPP _let_1 X_a (tptp.last X_a) Xs_1)))) Xs_1) (tptp.hAPP _let_1 _let_1 (tptp.butlast X_a) Xs_1)))))))) (forall ((X_a $$unsorted) (Pa $$unsorted)) (let ((_let_1 (tptp.nil X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.product_prod _let_2 _let_2))) (let ((_let_4 (tptp.fun _let_2 _let_3))) (= (tptp.hAPP _let_2 _let_3 (tptp.hAPP (tptp.fun X_a tptp.bool) _let_4 (tptp.partition X_a) Pa) _let_1) (tptp.hAPP _let_2 _let_3 (tptp.hAPP _let_2 _let_4 (tptp.product_Pair _let_2 _let_2) _let_1) _let_1))))))) (forall ((X_a $$unsorted) (Pa $$unsorted)) (let ((_let_1 (tptp.nil X_a))) (let ((_let_2 (tptp.list X_a))) (= (tptp.hAPP _let_2 _let_2 (tptp.hAPP (tptp.fun X_a tptp.bool) (tptp.fun _let_2 _let_2) (tptp.takeWhile X_a) Pa) _let_1) _let_1)))) (forall ((X_a $$unsorted) (Pa $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.distinct X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 Xs_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_a tptp.bool) (tptp.fun _let_1 _let_1) (tptp.takeWhile X_a) Pa) Xs_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((Pa $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.linorder_sorted X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 Xs_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_a tptp.bool) (tptp.fun _let_1 _let_1) (tptp.takeWhile X_a) Pa) Xs_1))))))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (Pa $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP X_a _let_2 (tptp.cons X_a) X_1))) (let ((_let_4 (tptp.hAPP (tptp.fun X_a tptp.bool) _let_2 (tptp.takeWhile X_a) Pa))) (let ((_let_5 (tptp.hAPP _let_1 _let_1 _let_4 (tptp.hAPP _let_1 _let_1 _let_3 Xs_1)))) (let ((_let_6 (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa X_1)))) (and (=> _let_6 (= _let_5 (tptp.hAPP _let_1 _let_1 _let_3 (tptp.hAPP _let_1 _let_1 _let_4 Xs_1)))) (=> (not _let_6) (= _let_5 (tptp.nil X_a))))))))))) (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) (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))) (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.top_top _let_1) (tptp.ti _let_1 A_1))))) (forall ((X_a $$unsorted)) (exists ((X_2 $$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) (tptp.top_top _let_1)))))) _let_16 (forall ((X_a $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.nil X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (=> (not (= Xs _let_1)) (= (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_3 (tptp.append X_a) (tptp.hAPP _let_2 _let_2 (tptp.butlast X_a) Xs)) (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_a _let_3 (tptp.cons X_a) (tptp.hAPP _let_2 X_a (tptp.last X_a) Xs)) _let_1)) Xs)))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (X_1 $$unsorted) (Ys_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.nil X_a))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (= (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 (tptp.append X_a) Xs_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_3 (tptp.cons X_a) X_1) _let_2)) Ys_1) (and (not (= Ys_1 _let_2)) (= (tptp.hAPP _let_1 _let_1 (tptp.butlast X_a) Ys_1) Xs_1) (= (tptp.hAPP _let_1 X_a (tptp.last X_a) Ys_1) (tptp.ti X_a X_1)))))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (R_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.product_prod _let_1 _let_1))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (not (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_3 tptp.bool) (tptp.member _let_2) (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_2) (tptp.product_Pair _let_1 _let_1) Xs_1) (tptp.nil X_a))) (tptp.hAPP (tptp.fun (tptp.product_prod X_a X_a) tptp.bool) _let_3 (tptp.lex X_a) R_2)))))))) (forall ((X_a $$unsorted) (Ys_1 $$unsorted) (R_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.product_prod _let_1 _let_1))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (not (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.hAPP _let_1 (tptp.fun _let_1 _let_2) (tptp.product_Pair _let_1 _let_1) (tptp.nil X_a)) Ys_1)) (tptp.hAPP (tptp.fun (tptp.product_prod X_a X_a) tptp.bool) _let_3 (tptp.lex X_a) R_2)))))))) (forall ((X_a $$unsorted) (Ys_2 $$unsorted) (Us_2 $$unsorted) (Xs $$unsorted) (Xs1 $$unsorted) (Zs_1 $$unsorted)) (let ((_let_1 (tptp.append X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (let ((_let_4 (tptp.hAPP _let_2 _let_3 _let_1 Xs))) (=> (= (tptp.hAPP _let_2 _let_2 _let_4 Xs1) Zs_1) (=> (= Ys_2 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_3 _let_1 Xs1) Us_2)) (= (tptp.hAPP _let_2 _let_2 _let_4 Ys_2) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_3 _let_1 Zs_1) Us_2))))))))) (forall ((X_a $$unsorted) (Ys_1 $$unsorted) (Xs_1 $$unsorted) (Zs $$unsorted)) (let ((_let_1 (tptp.append X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (= (= (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_3 _let_1 Ys_1) Xs_1) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_3 _let_1 Zs) Xs_1)) (= Ys_1 Zs)))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (Ys_1 $$unsorted) (Zs $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.append X_a) Xs_1))) (= (= (tptp.hAPP _let_1 _let_1 _let_2 Ys_1) (tptp.hAPP _let_1 _let_1 _let_2 Zs)) (= Ys_1 Zs))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (Ys_1 $$unsorted) (Zs $$unsorted) (Ts $$unsorted)) (let ((_let_1 (tptp.append X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (= (= (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_3 _let_1 Xs_1) Ys_1) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_3 _let_1 Zs) Ts)) (exists ((Us $$unsorted)) (let ((_let_1 (tptp.append X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (let ((_let_4 (tptp.hAPP _let_2 _let_3 _let_1 Us))) (or (and (= Xs_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_3 _let_1 Zs) Us)) (= (tptp.hAPP _let_2 _let_2 _let_4 Ys_1) Ts)) (and (= (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_3 _let_1 Xs_1) Us) Zs) (= Ys_1 (tptp.hAPP _let_2 _let_2 _let_4 Ts)))))))))))))) (forall ((X_a $$unsorted) (Xs $$unsorted) (Ys_2 $$unsorted) (Zs_1 $$unsorted)) (let ((_let_1 (tptp.append X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (let ((_let_4 (tptp.hAPP _let_2 _let_3 _let_1 Xs))) (= (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_3 _let_1 (tptp.hAPP _let_2 _let_2 _let_4 Ys_2)) Zs_1) (tptp.hAPP _let_2 _let_2 _let_4 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_3 _let_1 Ys_2) Zs_1)))))))) (forall ((X_a $$unsorted) (X $$unsorted) (Xs $$unsorted) (Ys_2 $$unsorted)) (let ((_let_1 (tptp.append X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (let ((_let_4 (tptp.hAPP X_a _let_3 (tptp.cons X_a) X))) (= (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_3 _let_1 (tptp.hAPP _let_2 _let_2 _let_4 Xs)) Ys_2) (tptp.hAPP _let_2 _let_2 _let_4 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_3 _let_1 Xs) Ys_2)))))))) (forall ((X_a $$unsorted) (Xs $$unsorted) (Zs_1 $$unsorted) (X $$unsorted) (Xs1 $$unsorted) (Ys_2 $$unsorted)) (let ((_let_1 (tptp.append X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (let ((_let_4 (tptp.hAPP X_a _let_3 (tptp.cons X_a) X))) (=> (= (tptp.hAPP _let_2 _let_2 _let_4 Xs1) Ys_2) (=> (= Xs (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_3 _let_1 Xs1) Zs_1)) (= (tptp.hAPP _let_2 _let_2 _let_4 Xs) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_3 _let_1 Ys_2) Zs_1))))))))) _let_9 (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (Ys_1 $$unsorted)) (let ((_let_1 (tptp.nil X_a))) (let ((_let_2 (tptp.list X_a))) (= (= _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 (tptp.fun _let_2 _let_2) (tptp.append X_a) Xs_1) Ys_1)) (and (= Xs_1 _let_1) (= Ys_1 _let_1)))))) (forall ((X_a $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.list X_a))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.append X_a) Xs) (tptp.nil X_a)) Xs))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (Ys_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (= (= Xs_1 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.append X_a) Xs_1) Ys_1)) (= Ys_1 (tptp.nil X_a))))) (forall ((X_a $$unsorted) (Ys_1 $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (= (= Ys_1 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.append X_a) Xs_1) Ys_1)) (= Xs_1 (tptp.nil X_a))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (Ys_1 $$unsorted)) (let ((_let_1 (tptp.nil X_a))) (let ((_let_2 (tptp.list X_a))) (= (= (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 (tptp.fun _let_2 _let_2) (tptp.append X_a) Xs_1) Ys_1) _let_1) (and (= Xs_1 _let_1) (= Ys_1 _let_1)))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (Ys_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (= (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.append X_a) Xs_1) Ys_1) Xs_1) (= Ys_1 (tptp.nil X_a))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (Ys_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (= (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.append X_a) Xs_1) Ys_1) Ys_1) (= Xs_1 (tptp.nil X_a))))) (forall ((X_a $$unsorted) (Xs $$unsorted) (Ys_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (=> (= Xs Ys_2) (= Xs (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.append X_a) (tptp.nil X_a)) Ys_2))))) (forall ((X_a $$unsorted) (Ys_1 $$unsorted) (Zs $$unsorted) (X_1 $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_2 (tptp.cons X_a) X_1) Xs_1))) (= (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.append X_a) Ys_1) Zs) _let_3) (or (and (= Ys_1 (tptp.nil X_a)) (= Zs _let_3)) (exists ((Ys_3 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (and (= Ys_1 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_2 (tptp.cons X_a) X_1) Ys_3)) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.append X_a) Ys_3) Zs) Xs_1))))))))))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (Xs_1 $$unsorted) (Ys_1 $$unsorted) (Zs $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_2 (tptp.cons X_a) X_1) Xs_1))) (= (= _let_3 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.append X_a) Ys_1) Zs)) (or (and (= Ys_1 (tptp.nil X_a)) (= _let_3 Zs)) (exists ((Ys_3 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (and (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_2 (tptp.cons X_a) X_1) Ys_3) Ys_1) (= Xs_1 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.append X_a) Ys_3) Zs)))))))))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (X_1 $$unsorted) (Ys_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.nil X_a))) (let ((_let_2 (tptp.cons X_a))) (let ((_let_3 (tptp.list X_a))) (let ((_let_4 (tptp.fun _let_3 _let_3))) (let ((_let_5 (tptp.append X_a))) (= (= (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_3 _let_4 _let_5 Xs_1) (tptp.hAPP _let_3 _let_3 (tptp.hAPP X_a _let_4 _let_2 X_1) _let_1)) (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_3 _let_4 _let_5 Ys_1) (tptp.hAPP _let_3 _let_3 (tptp.hAPP X_a _let_4 _let_2 Y_1) _let_1))) (and (= Xs_1 Ys_1) (= (tptp.ti X_a X_1) (tptp.ti X_a Y_1)))))))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (L $$unsorted) (Pa $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP (tptp.fun X_a tptp.bool) _let_2 (tptp.takeWhile X_a) Pa))) (=> (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa X_1))) (= (tptp.hAPP _let_1 _let_1 _let_3 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.append X_a) Xs_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_2 (tptp.cons X_a) X_1) L))) (tptp.hAPP _let_1 _let_1 _let_3 Xs_1))))))) (forall ((X_a $$unsorted) (Xs $$unsorted) (Ys_2 $$unsorted)) (let ((_let_1 (tptp.butlast X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.hAPP _let_2 (tptp.fun _let_2 _let_2) (tptp.append X_a) Xs))) (let ((_let_4 (tptp.hAPP _let_2 _let_2 _let_1 (tptp.hAPP _let_2 _let_2 _let_3 Ys_2)))) (let ((_let_5 (= Ys_2 (tptp.nil X_a)))) (and (=> _let_5 (= _let_4 (tptp.hAPP _let_2 _let_2 _let_1 Xs))) (=> (not _let_5) (= _let_4 (tptp.hAPP _let_2 _let_2 _let_3 (tptp.hAPP _let_2 _let_2 _let_1 Ys_2))))))))))) (forall ((X_a $$unsorted) (Xs $$unsorted) (Ys_2 $$unsorted)) (let ((_let_1 (tptp.last X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.hAPP _let_2 X_a _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 (tptp.fun _let_2 _let_2) (tptp.append X_a) Xs) Ys_2)))) (let ((_let_4 (= Ys_2 (tptp.nil X_a)))) (and (=> _let_4 (= _let_3 (tptp.hAPP _let_2 X_a _let_1 Xs))) (=> (not _let_4) (= _let_3 (tptp.hAPP _let_2 X_a _let_1 Ys_2))))))))) (forall ((X_a $$unsorted) (Xs $$unsorted) (Ys_2 $$unsorted)) (let ((_let_1 (tptp.last X_a))) (let ((_let_2 (tptp.list X_a))) (=> (not (= Ys_2 (tptp.nil X_a))) (= (tptp.hAPP _let_2 X_a _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 (tptp.fun _let_2 _let_2) (tptp.append X_a) Xs) Ys_2)) (tptp.hAPP _let_2 X_a _let_1 Ys_2)))))) (forall ((X_a $$unsorted) (Xs $$unsorted) (Ys_2 $$unsorted)) (let ((_let_1 (tptp.last X_a))) (let ((_let_2 (tptp.list X_a))) (=> (= Ys_2 (tptp.nil X_a)) (= (tptp.hAPP _let_2 X_a _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 (tptp.fun _let_2 _let_2) (tptp.append X_a) Xs) Ys_2)) (tptp.hAPP _let_2 X_a _let_1 Xs)))))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (U $$unsorted) (V $$unsorted) (R_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.product_prod _let_1 _let_1))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.hAPP (tptp.fun (tptp.product_prod X_a X_a) tptp.bool) _let_3 (tptp.lexord X_a) R_2))) (let ((_let_5 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.append X_a) X_1))) (let ((_let_6 (tptp.product_Pair _let_1 _let_1))) (let ((_let_7 (tptp.fun _let_1 _let_2))) (let ((_let_8 (tptp.member _let_2))) (let ((_let_9 (tptp.fun _let_3 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 _let_9 _let_8 (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_1 _let_7 _let_6 U) V)) _let_4)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 _let_9 _let_8 (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_1 _let_7 _let_6 (tptp.hAPP _let_1 _let_1 _let_5 U)) (tptp.hAPP _let_1 _let_1 _let_5 V))) _let_4))))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F $$unsorted) (X_1 $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.list X_b))) (let ((_let_3 (tptp.hAPP (tptp.fun X_b _let_1) (tptp.fun _let_2 _let_1) (tptp.maps X_b X_a) F))) (= (tptp.hAPP _let_2 _let_1 _let_3 (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_b (tptp.fun _let_2 _let_2) (tptp.cons X_b) X_1) Xs_1)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.append X_a) (tptp.hAPP X_b _let_1 F X_1)) (tptp.hAPP _let_2 _let_1 _let_3 Xs_1))))))) (forall ((X_a $$unsorted) (Xs $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (= (tptp.hAPP _let_1 _let_1 (tptp.butlast X_a) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.append X_a) Xs) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_2 (tptp.cons X_a) X) (tptp.nil X_a)))) Xs)))) (forall ((X_a $$unsorted) (Xs $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (= (tptp.hAPP _let_1 X_a (tptp.last X_a) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.append X_a) Xs) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_2 (tptp.cons X_a) X) (tptp.nil X_a)))) (tptp.ti X_a X))))) (forall ((X_a $$unsorted) (U $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted) (Aa $$unsorted) (Ba $$unsorted) (R_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.product_prod _let_1 _let_1))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.product_prod X_a X_a))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (let ((_let_6 (tptp.cons X_a))) (let ((_let_7 (tptp.fun _let_1 _let_1))) (let ((_let_8 (tptp.hAPP _let_1 _let_7 (tptp.append X_a) U))) (=> (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP _let_4 (tptp.fun _let_5 tptp.bool) (tptp.member _let_4) (tptp.hAPP X_a _let_4 (tptp.hAPP X_a (tptp.fun X_a _let_4) (tptp.product_Pair X_a X_a) Aa) Ba)) R_2)) (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.hAPP _let_1 (tptp.fun _let_1 _let_2) (tptp.product_Pair _let_1 _let_1) (tptp.hAPP _let_1 _let_1 _let_8 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_7 _let_6 Aa) X_1))) (tptp.hAPP _let_1 _let_1 _let_8 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_7 _let_6 Ba) Y_1)))) (tptp.hAPP _let_5 _let_3 (tptp.lexord X_a) R_2))))))))))))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (R_2 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.product_prod _let_1 _let_1))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (exists ((B_2 $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (= Y_1 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.cons X_a) B_2) Z_1)))) (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.hAPP _let_1 (tptp.fun _let_1 _let_2) (tptp.product_Pair _let_1 _let_1) X_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.append X_a) X_1) Y_1))) (tptp.hAPP (tptp.fun (tptp.product_prod X_a X_a) tptp.bool) _let_3 (tptp.lexord X_a) R_2)))))))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (U $$unsorted) (V $$unsorted) (R_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.product_prod _let_1 _let_1))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.hAPP (tptp.fun (tptp.product_prod X_a X_a) tptp.bool) _let_3 (tptp.lexord X_a) R_2))) (let ((_let_5 (tptp.product_Pair _let_1 _let_1))) (let ((_let_6 (tptp.fun _let_1 _let_2))) (let ((_let_7 (tptp.member _let_2))) (let ((_let_8 (tptp.fun _let_3 tptp.bool))) (let ((_let_9 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.append X_a) X_1))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 _let_8 _let_7 (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_1 _let_6 _let_5 (tptp.hAPP _let_1 _let_1 _let_9 U)) (tptp.hAPP _let_1 _let_1 _let_9 V))) _let_4)) (=> (forall ((A_4 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_a))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (not (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_a _let_1 (tptp.hAPP X_a (tptp.fun X_a _let_1) (tptp.product_Pair X_a X_a) A_4) A_4)) R_2)))))) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 _let_8 _let_7 (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_1 _let_6 _let_5 U) V)) _let_4)))))))))))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (Pa $$unsorted)) (let ((_let_1 (tptp.list X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa (tptp.nil X_a))) (=> (forall ((X_2 $$unsorted) (Xs_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa Xs_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.append X_a) Xs_2) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_2 (tptp.cons X_a) X_2) (tptp.nil X_a))))))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa Xs_1)))))) (forall ((X_a $$unsorted) (Xs $$unsorted)) (=> (not (= Xs (tptp.nil X_a))) (not (forall ((Ys $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (not (= Xs (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.append X_a) Ys) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_2 (tptp.cons X_a) Y_2) (tptp.nil X_a))))))))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (X_1 $$unsorted) (Ys_1 $$unsorted) (Y_1 $$unsorted) (R_2 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_a))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.list X_a))) (let ((_let_4 (tptp.product_prod _let_3 _let_3))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (let ((_let_6 (tptp.hAPP _let_2 _let_5 (tptp.listrel1 X_a) R_2))) (let ((_let_7 (tptp.product_Pair _let_3 _let_3))) (let ((_let_8 (tptp.fun _let_3 _let_4))) (let ((_let_9 (tptp.member _let_4))) (let ((_let_10 (tptp.fun _let_5 tptp.bool))) (let ((_let_11 (tptp.nil X_a))) (let ((_let_12 (tptp.cons X_a))) (let ((_let_13 (tptp.fun _let_3 _let_3))) (let ((_let_14 (tptp.append X_a))) (= (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP _let_4 _let_10 _let_9 (tptp.hAPP _let_3 _let_4 (tptp.hAPP _let_3 _let_8 _let_7 (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_3 _let_13 _let_14 Xs_1) (tptp.hAPP _let_3 _let_3 (tptp.hAPP X_a _let_13 _let_12 X_1) _let_11))) (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_3 _let_13 _let_14 Ys_1) (tptp.hAPP _let_3 _let_3 (tptp.hAPP X_a _let_13 _let_12 Y_1) _let_11)))) _let_6)) (or (and (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP _let_4 _let_10 _let_9 (tptp.hAPP _let_3 _let_4 (tptp.hAPP _let_3 _let_8 _let_7 Xs_1) Ys_1)) _let_6)) (= (tptp.ti X_a X_1) (tptp.ti X_a Y_1))) (and (= Xs_1 Ys_1) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) (tptp.hAPP X_a _let_1 (tptp.hAPP X_a (tptp.fun X_a _let_1) (tptp.product_Pair X_a X_a) X_1) Y_1)) R_2)))))))))))))))))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.nil X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun X_a _let_2))) (let ((_let_4 (tptp.fun _let_2 _let_2))) (let ((_let_5 (tptp.fun X_a _let_4))) (let ((_let_6 (tptp.fun _let_2 _let_4))) (= (tptp.hAPP _let_2 _let_2 (tptp.rotate1 X_a) Xs_1) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_5 _let_4 (tptp.hAPP _let_2 (tptp.fun _let_5 _let_4) (tptp.list_case _let_2 X_a) _let_1) (tptp.hAPP _let_3 _let_5 (tptp.hAPP _let_6 (tptp.fun _let_3 _let_5) (tptp.combb _let_2 _let_4 X_a) (tptp.hAPP _let_6 _let_6 (tptp.combc _let_2 _let_2 _let_2) (tptp.append X_a))) (tptp.hAPP _let_2 _let_3 (tptp.hAPP _let_5 (tptp.fun _let_2 _let_3) (tptp.combc X_a _let_2 _let_2) (tptp.cons X_a)) _let_1))) Xs_1))))))))) _let_8 (forall ((X_a $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.nil X_a))) (let ((_let_2 (tptp.list X_a))) (= (= (tptp.hAPP _let_2 _let_2 (tptp.rotate1 X_a) Xs_1) _let_1) (= Xs_1 _let_1))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.distinct X_a))) (let ((_let_2 (tptp.list X_a))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 (tptp.hAPP _let_2 _let_2 (tptp.rotate1 X_a) Xs_1))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 Xs_1)))))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (Xs_1 $$unsorted) (Ys_1 $$unsorted) (R_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.product_prod _let_1 _let_1))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.hAPP (tptp.fun (tptp.product_prod X_a X_a) tptp.bool) _let_3 (tptp.listrel1 X_a) R_2))) (let ((_let_5 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.cons X_a) X_1))) (let ((_let_6 (tptp.product_Pair _let_1 _let_1))) (let ((_let_7 (tptp.fun _let_1 _let_2))) (let ((_let_8 (tptp.member _let_2))) (let ((_let_9 (tptp.fun _let_3 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 _let_9 _let_8 (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_1 _let_7 _let_6 Xs_1) Ys_1)) _let_4)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 _let_9 _let_8 (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_1 _let_7 _let_6 (tptp.hAPP _let_1 _let_1 _let_5 Xs_1)) (tptp.hAPP _let_1 _let_1 _let_5 Ys_1))) _let_4))))))))))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (R_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.product_prod _let_1 _let_1))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (not (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_3 tptp.bool) (tptp.member _let_2) (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_2) (tptp.product_Pair _let_1 _let_1) Xs_1) (tptp.nil X_a))) (tptp.hAPP (tptp.fun (tptp.product_prod X_a X_a) tptp.bool) _let_3 (tptp.listrel1 X_a) R_2)))))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (R_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.product_prod _let_1 _let_1))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (not (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.hAPP _let_1 (tptp.fun _let_1 _let_2) (tptp.product_Pair _let_1 _let_1) (tptp.nil X_a)) Xs_1)) (tptp.hAPP (tptp.fun (tptp.product_prod X_a X_a) tptp.bool) _let_3 (tptp.listrel1 X_a) R_2)))))))) (forall ((X_a $$unsorted) (Us_1 $$unsorted) (Vs_1 $$unsorted) (Xs_1 $$unsorted) (Ys_1 $$unsorted) (R_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.product_prod _let_1 _let_1))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.hAPP (tptp.fun (tptp.product_prod X_a X_a) tptp.bool) _let_3 (tptp.listrel1 X_a) R_2))) (let ((_let_5 (tptp.append X_a))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (let ((_let_7 (tptp.product_Pair _let_1 _let_1))) (let ((_let_8 (tptp.fun _let_1 _let_2))) (let ((_let_9 (tptp.member _let_2))) (let ((_let_10 (tptp.fun _let_3 tptp.bool))) (=> (or (and (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 _let_10 _let_9 (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_1 _let_8 _let_7 Xs_1) Ys_1)) _let_4)) (= Us_1 Vs_1)) (and (= Xs_1 Ys_1) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 _let_10 _let_9 (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_1 _let_8 _let_7 Us_1) Vs_1)) _let_4)))) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 _let_10 _let_9 (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_1 _let_8 _let_7 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_6 _let_5 Xs_1) Us_1)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_6 _let_5 Ys_1) Vs_1))) _let_4)))))))))))))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (Xs_1 $$unsorted) (Y_1 $$unsorted) (Ys_1 $$unsorted) (R_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.product_prod _let_1 _let_1))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.product_prod X_a X_a))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (let ((_let_6 (tptp.hAPP _let_5 _let_3 (tptp.listrel1 X_a) R_2))) (let ((_let_7 (tptp.product_Pair _let_1 _let_1))) (let ((_let_8 (tptp.fun _let_1 _let_2))) (let ((_let_9 (tptp.member _let_2))) (let ((_let_10 (tptp.fun _let_3 tptp.bool))) (let ((_let_11 (tptp.cons X_a))) (let ((_let_12 (tptp.fun _let_1 _let_1))) (= (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 _let_10 _let_9 (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_1 _let_8 _let_7 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_12 _let_11 X_1) Xs_1)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_12 _let_11 Y_1) Ys_1))) _let_6)) (or (and (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP _let_4 (tptp.fun _let_5 tptp.bool) (tptp.member _let_4) (tptp.hAPP X_a _let_4 (tptp.hAPP X_a (tptp.fun X_a _let_4) (tptp.product_Pair X_a X_a) X_1) Y_1)) R_2)) (= Xs_1 Ys_1)) (and (= (tptp.ti X_a X_1) (tptp.ti X_a Y_1)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 _let_10 _let_9 (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_1 _let_8 _let_7 Xs_1) Ys_1)) _let_6)))))))))))))))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted) (R_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.product_prod _let_1 _let_1))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.product_prod X_a X_a))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (let ((_let_6 (tptp.cons X_a))) (let ((_let_7 (tptp.fun _let_1 _let_1))) (=> (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP _let_4 (tptp.fun _let_5 tptp.bool) (tptp.member _let_4) (tptp.hAPP X_a _let_4 (tptp.hAPP X_a (tptp.fun X_a _let_4) (tptp.product_Pair X_a X_a) X_1) Y_1)) R_2)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_3 tptp.bool) (tptp.member _let_2) (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_2) (tptp.product_Pair _let_1 _let_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_7 _let_6 X_1) Xs_1)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_7 _let_6 Y_1) Xs_1))) (tptp.hAPP _let_5 _let_3 (tptp.listrel1 X_a) R_2)))))))))))) (forall ((X_a $$unsorted) (Ys_1 $$unsorted) (Xs_1 $$unsorted) (Us_1 $$unsorted) (Vs_1 $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted) (R_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.product_prod _let_1 _let_1))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.product_prod X_a X_a))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (let ((_let_6 (tptp.cons X_a))) (let ((_let_7 (tptp.fun _let_1 _let_1))) (let ((_let_8 (tptp.hAPP _let_1 _let_7 (tptp.append X_a) Us_1))) (=> (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP _let_4 (tptp.fun _let_5 tptp.bool) (tptp.member _let_4) (tptp.hAPP X_a _let_4 (tptp.hAPP X_a (tptp.fun X_a _let_4) (tptp.product_Pair X_a X_a) X_1) Y_1)) R_2)) (=> (= Xs_1 (tptp.hAPP _let_1 _let_1 _let_8 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_7 _let_6 X_1) Vs_1))) (=> (= Ys_1 (tptp.hAPP _let_1 _let_1 _let_8 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_7 _let_6 Y_1) Vs_1))) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_3 tptp.bool) (tptp.member _let_2) (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_2) (tptp.product_Pair _let_1 _let_1) Xs_1) Ys_1)) (tptp.hAPP _let_5 _let_3 (tptp.listrel1 X_a) R_2))))))))))))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (Ys_1 $$unsorted) (R_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.product_prod _let_1 _let_1))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_3 tptp.bool) (tptp.member _let_2) (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_2) (tptp.product_Pair _let_1 _let_1) Xs_1) Ys_1)) (tptp.hAPP (tptp.fun (tptp.product_prod X_a X_a) tptp.bool) _let_3 (tptp.listrel1 X_a) R_2))) (not (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_a))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) (tptp.hAPP X_a _let_1 (tptp.hAPP X_a (tptp.fun X_a _let_1) (tptp.product_Pair X_a X_a) X_2) Y_2)) R_2)) (forall ((Us $$unsorted) (Vs $$unsorted)) (let ((_let_1 (tptp.cons X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (let ((_let_4 (tptp.hAPP _let_2 _let_3 (tptp.append X_a) Us))) (=> (= Xs_1 (tptp.hAPP _let_2 _let_2 _let_4 (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_a _let_3 _let_1 X_2) Vs))) (not (= Ys_1 (tptp.hAPP _let_2 _let_2 _let_4 (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_a _let_3 _let_1 Y_2) Vs)))))))))))))))))))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (Xs_1 $$unsorted) (Ys_1 $$unsorted) (R_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.product_prod _let_1 _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) (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_2) (tptp.product_Pair _let_1 _let_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.cons X_a) X_1) Xs_1)) Ys_1)) (tptp.hAPP (tptp.fun (tptp.product_prod X_a X_a) tptp.bool) _let_3 (tptp.listrel1 X_a) R_2))) (=> (forall ((Y_2 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_a))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.list X_a))) (=> (= Ys_1 (tptp.hAPP _let_3 _let_3 (tptp.hAPP X_a (tptp.fun _let_3 _let_3) (tptp.cons X_a) Y_2) Xs_1)) (not (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) (tptp.hAPP X_a _let_1 (tptp.hAPP X_a (tptp.fun X_a _let_1) (tptp.product_Pair X_a X_a) X_1) Y_2)) R_2)))))))) (not (forall ((Zs_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.product_prod _let_1 _let_1))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (= Ys_1 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.cons X_a) X_1) Zs_2)) (not (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.hAPP _let_1 (tptp.fun _let_1 _let_2) (tptp.product_Pair _let_1 _let_1) Xs_1) Zs_2)) (tptp.hAPP (tptp.fun (tptp.product_prod X_a X_a) tptp.bool) _let_3 (tptp.listrel1 X_a) R_2)))))))))))))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (Y_1 $$unsorted) (Ys_1 $$unsorted) (R_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.product_prod _let_1 _let_1))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_3 tptp.bool) (tptp.member _let_2) (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_2) (tptp.product_Pair _let_1 _let_1) Xs_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.cons X_a) Y_1) Ys_1))) (tptp.hAPP (tptp.fun (tptp.product_prod X_a X_a) tptp.bool) _let_3 (tptp.listrel1 X_a) R_2))) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_a))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.list X_a))) (=> (= Xs_1 (tptp.hAPP _let_3 _let_3 (tptp.hAPP X_a (tptp.fun _let_3 _let_3) (tptp.cons X_a) X_2) Ys_1)) (not (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_a _let_1 (tptp.hAPP X_a (tptp.fun X_a _let_1) (tptp.product_Pair X_a X_a) X_2) Y_1)) R_2)))))))) (not (forall ((Zs_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.product_prod _let_1 _let_1))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (= Xs_1 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.cons X_a) Y_1) Zs_2)) (not (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_3 tptp.bool) (tptp.member _let_2) (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_2) (tptp.product_Pair _let_1 _let_1) Zs_2) Ys_1)) (tptp.hAPP (tptp.fun (tptp.product_prod X_a X_a) tptp.bool) _let_3 (tptp.listrel1 X_a) R_2)))))))))))))))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (Xs_1 $$unsorted) (Y_1 $$unsorted) (Ys_1 $$unsorted) (R_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.product_prod _let_1 _let_1))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.product_prod X_a X_a))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (let ((_let_6 (tptp.hAPP _let_5 _let_3 (tptp.lex X_a) R_2))) (let ((_let_7 (tptp.product_Pair _let_1 _let_1))) (let ((_let_8 (tptp.fun _let_1 _let_2))) (let ((_let_9 (tptp.member _let_2))) (let ((_let_10 (tptp.fun _let_3 tptp.bool))) (let ((_let_11 (tptp.size_size _let_1))) (let ((_let_12 (tptp.cons X_a))) (let ((_let_13 (tptp.fun _let_1 _let_1))) (= (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 _let_10 _let_9 (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_1 _let_8 _let_7 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_13 _let_12 X_1) Xs_1)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_13 _let_12 Y_1) Ys_1))) _let_6)) (or (and (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP _let_4 (tptp.fun _let_5 tptp.bool) (tptp.member _let_4) (tptp.hAPP X_a _let_4 (tptp.hAPP X_a (tptp.fun X_a _let_4) (tptp.product_Pair X_a X_a) X_1) Y_1)) R_2)) (= (tptp.hAPP _let_1 tptp.nat _let_11 Xs_1) (tptp.hAPP _let_1 tptp.nat _let_11 Ys_1))) (and (= (tptp.ti X_a X_1) (tptp.ti X_a Y_1)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 _let_10 _let_9 (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_1 _let_8 _let_7 Xs_1) Ys_1)) _let_6))))))))))))))))))) (forall ((X_a $$unsorted) (Pa $$unsorted) (Xs_1 $$unsorted) (Y_1 $$unsorted) (Ys_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_2 (tptp.cons X_a) Y_1) Ys_1))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (= (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_4 _let_2 (tptp.dropWhile X_a) Pa) Xs_1) _let_3) (and (= Xs_1 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.append X_a) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_4 _let_2 (tptp.takeWhile X_a) Pa) Xs_1)) _let_3)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa Y_1)))))))))) (forall ((X_a $$unsorted) (Pa $$unsorted) (X_1 $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.product_prod _let_1 _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_2))) (let ((_let_4 (tptp.hAPP (tptp.fun X_a tptp.bool) _let_3 (tptp.partition X_a) Pa))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (let ((_let_6 (tptp.hAPP X_a _let_5 (tptp.cons X_a) X_1))) (let ((_let_7 (tptp.product_Pair _let_1 _let_1))) (let ((_let_8 (tptp.fun _let_5 _let_3))) (let ((_let_9 (tptp.fun _let_1 _let_8))) (let ((_let_10 (tptp.fun _let_1 _let_3))) (let ((_let_11 (tptp.fun _let_5 _let_10))) (let ((_let_12 (tptp.fun _let_2 _let_2))) (let ((_let_13 (tptp.fun _let_2 _let_12))) (let ((_let_14 (tptp.fun _let_1 _let_12))) (let ((_let_15 (tptp.fun _let_3 _let_14))) (let ((_let_16 (tptp.fun _let_1 _let_14))) (let ((_let_17 (tptp.fun _let_3 _let_3))) (let ((_let_18 (tptp.fun _let_1 _let_17))) (= (tptp.hAPP _let_1 _let_2 _let_4 (tptp.hAPP _let_1 _let_1 _let_6 Xs_1)) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_10 _let_12 (tptp.product_prod_case _let_1 _let_1 _let_2) (tptp.hAPP _let_10 _let_10 (tptp.hAPP _let_18 (tptp.fun _let_10 _let_10) (tptp.combs _let_1 _let_3 _let_3) (tptp.hAPP _let_16 _let_18 (tptp.hAPP (tptp.fun _let_14 _let_17) (tptp.fun _let_16 _let_18) (tptp.combb _let_14 _let_17 _let_1) (tptp.combs _let_1 _let_2 _let_2)) (tptp.hAPP _let_10 _let_16 (tptp.hAPP _let_15 (tptp.fun _let_10 _let_16) (tptp.combb _let_3 _let_14 _let_1) (tptp.hAPP _let_13 _let_15 (tptp.combb _let_2 _let_12 _let_1) (tptp.hAPP tptp.bool _let_13 (tptp.if _let_2) (tptp.hAPP X_a tptp.bool Pa X_1)))) (tptp.hAPP _let_5 _let_10 (tptp.hAPP _let_10 _let_11 (tptp.combb _let_1 _let_3 _let_1) _let_7) _let_6)))) (tptp.hAPP _let_5 _let_10 (tptp.hAPP _let_9 _let_11 (tptp.combc _let_1 _let_5 _let_3) (tptp.hAPP _let_10 _let_9 (tptp.hAPP (tptp.fun _let_3 _let_8) (tptp.fun _let_10 _let_9) (tptp.combb _let_3 _let_8 _let_1) (tptp.combb _let_1 _let_2 _let_1)) _let_7)) _let_6))) (tptp.hAPP _let_1 _let_2 _let_4 Xs_1)))))))))))))))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (X_a $$unsorted) (X_d $$unsorted) (X_e $$unsorted) (F $$unsorted) (G $$unsorted) (P_1 $$unsorted)) (let ((_let_1 (tptp.product_prod X_b X_c))) (let ((_let_2 (tptp.fun _let_1 X_a))) (let ((_let_3 (tptp.hAPP (tptp.fun X_b (tptp.fun X_c X_a)) _let_2 (tptp.product_prod_case X_b X_c X_a) F))) (let ((_let_4 (tptp.fun X_e X_a))) (let ((_let_5 (tptp.fun X_e _let_1))) (let ((_let_6 (tptp.fun _let_5 _let_4))) (let ((_let_7 (tptp.fun X_d _let_4))) (let ((_let_8 (tptp.fun X_d _let_5))) (let ((_let_9 (tptp.product_prod X_d X_e))) (= (tptp.hAPP _let_1 X_a _let_3 (tptp.hAPP _let_9 _let_1 (tptp.hAPP _let_8 (tptp.fun _let_9 _let_1) (tptp.product_prod_case X_d X_e _let_1) G) P_1)) (tptp.hAPP _let_9 X_a (tptp.hAPP _let_7 (tptp.fun _let_9 X_a) (tptp.product_prod_case X_d X_e X_a) (tptp.hAPP _let_8 _let_7 (tptp.hAPP _let_6 (tptp.fun _let_8 _let_7) (tptp.combb _let_5 _let_4 X_d) (tptp.hAPP _let_2 _let_6 (tptp.combb _let_1 X_a X_e) _let_3)) G)) P_1)))))))))))) (forall ((X_a $$unsorted) (Xs $$unsorted) (Ys_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.size_size _let_1))) (=> (not (= (tptp.hAPP _let_1 tptp.nat _let_2 Xs) (tptp.hAPP _let_1 tptp.nat _let_2 Ys_2))) (not (= Xs Ys_2)))))) (forall ((X_c $$unsorted) (X_a $$unsorted) (X_b $$unsorted) (Ca $$unsorted) (P_1 $$unsorted) (Q_2 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_b))) (let ((_let_2 (tptp.hAPP (tptp.fun X_a (tptp.fun X_b X_c)) (tptp.fun _let_1 X_c) (tptp.product_prod_case X_a X_b X_c) Ca))) (=> (= (tptp.ti _let_1 P_1) (tptp.ti _let_1 Q_2)) (= (tptp.hAPP _let_1 X_c _let_2 P_1) (tptp.hAPP _let_1 X_c _let_2 Q_2)))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (X_a $$unsorted) (F1 $$unsorted) (Aa $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.fun X_c X_a))) (let ((_let_2 (tptp.product_prod X_b X_c))) (= (tptp.hAPP _let_2 X_a (tptp.hAPP (tptp.fun X_b _let_1) (tptp.fun _let_2 X_a) (tptp.product_prod_case X_b X_c X_a) F1) (tptp.hAPP X_c _let_2 (tptp.hAPP X_b (tptp.fun X_c _let_2) (tptp.product_Pair X_b X_c) Aa) Ba)) (tptp.hAPP X_c X_a (tptp.hAPP X_b _let_1 F1 Aa) Ba))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (X_a $$unsorted) (F $$unsorted) (Aa $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.fun X_c X_a))) (let ((_let_2 (tptp.product_prod X_b X_c))) (= (tptp.hAPP _let_2 X_a (tptp.hAPP (tptp.fun X_b _let_1) (tptp.fun _let_2 X_a) (tptp.product_prod_case X_b X_c X_a) F) (tptp.hAPP X_c _let_2 (tptp.hAPP X_b (tptp.fun X_c _let_2) (tptp.product_Pair X_b X_c) Aa) Ba)) (tptp.hAPP X_c X_a (tptp.hAPP X_b _let_1 F Aa) Ba))))) (forall ((X_a $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.size_size _let_1))) (= (tptp.hAPP _let_1 tptp.nat _let_2 (tptp.hAPP _let_1 _let_1 (tptp.rotate1 X_a) Xs)) (tptp.hAPP _let_1 tptp.nat _let_2 Xs))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (Pa $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_2 (tptp.cons X_a) X_1) Xs_1))) (let ((_let_4 (tptp.hAPP (tptp.fun X_a tptp.bool) _let_2 (tptp.dropWhile X_a) Pa))) (let ((_let_5 (tptp.hAPP _let_1 _let_1 _let_4 _let_3))) (let ((_let_6 (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa X_1)))) (and (=> _let_6 (= _let_5 (tptp.hAPP _let_1 _let_1 _let_4 Xs_1))) (=> (not _let_6) (= _let_5 _let_3)))))))))) (forall ((X_a $$unsorted) (Pa $$unsorted)) (let ((_let_1 (tptp.nil X_a))) (let ((_let_2 (tptp.list X_a))) (= (tptp.hAPP _let_2 _let_2 (tptp.hAPP (tptp.fun X_a tptp.bool) (tptp.fun _let_2 _let_2) (tptp.dropWhile X_a) Pa) _let_1) _let_1)))) (forall ((X_a $$unsorted) (Pa $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.distinct X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 Xs_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_a tptp.bool) (tptp.fun _let_1 _let_1) (tptp.dropWhile X_a) Pa) Xs_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((Pa $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.linorder_sorted X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 Xs_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_a tptp.bool) (tptp.fun _let_1 _let_1) (tptp.dropWhile X_a) Pa) Xs_1))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_b))) (let ((_let_2 (tptp.fun _let_1 X_c))) (let ((_let_3 (tptp.fun X_b X_c))) (let ((_let_4 (tptp.fun X_b _let_1))) (let ((_let_5 (tptp.fun _let_4 _let_3))) (let ((_let_6 (tptp.fun X_a _let_3))) (let ((_let_7 (tptp.fun X_a _let_4))) (= (tptp.hAPP _let_6 _let_2 (tptp.product_prod_case X_a X_b X_c) (tptp.hAPP _let_7 _let_6 (tptp.hAPP _let_5 (tptp.fun _let_7 _let_6) (tptp.combb _let_4 _let_3 X_a) (tptp.hAPP _let_2 _let_5 (tptp.combb _let_1 X_c X_b) F)) (tptp.product_Pair X_a X_b))) (tptp.ti _let_2 F)))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun (tptp.product_prod X_a X_b) X_c))) (let ((_let_2 (tptp.fun X_a (tptp.fun X_b X_c)))) (= (tptp.hAPP _let_2 _let_1 (tptp.product_prod_case X_a X_b X_c) (tptp.hAPP _let_1 _let_2 (tptp.product_curry X_a X_b X_c) F)) (tptp.ti _let_1 F))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun X_a (tptp.fun X_b X_c)))) (let ((_let_2 (tptp.fun (tptp.product_prod X_a X_b) X_c))) (= (tptp.hAPP _let_2 _let_1 (tptp.product_curry X_a X_b X_c) (tptp.hAPP _let_1 _let_2 (tptp.product_prod_case X_a X_b X_c) F)) (tptp.ti _let_1 F))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (Ys_1 $$unsorted) (R_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.size_size _let_1))) (let ((_let_3 (tptp.product_prod _let_1 _let_1))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP _let_3 (tptp.fun _let_4 tptp.bool) (tptp.member _let_3) (tptp.hAPP _let_1 _let_3 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_3) (tptp.product_Pair _let_1 _let_1) Xs_1) Ys_1)) (tptp.hAPP (tptp.fun (tptp.product_prod X_a X_a) tptp.bool) _let_4 (tptp.listrel1 X_a) R_2))) (= (tptp.hAPP _let_1 tptp.nat _let_2 Xs_1) (tptp.hAPP _let_1 tptp.nat _let_2 Ys_1)))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted)) (= (tptp.produc1605651328_split X_a X_b X_c) (tptp.product_prod_case X_a X_b X_c))) (forall ((X_a $$unsorted) (Pa $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.append X_a) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_3 _let_2 (tptp.takeWhile X_a) Pa) Xs_1)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_3 _let_2 (tptp.dropWhile X_a) Pa) Xs_1)) Xs_1))))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted) (R_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.size_size _let_1))) (let ((_let_3 (tptp.product_prod _let_1 _let_1))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.fun (tptp.product_prod X_a X_a) tptp.bool))) (let ((_let_6 (tptp.hAPP _let_3 (tptp.fun _let_4 tptp.bool) (tptp.member _let_3) (tptp.hAPP _let_1 _let_3 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_3) (tptp.product_Pair _let_1 _let_1) X_1) Y_1)))) (= (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool _let_6 (tptp.hAPP _let_5 _let_4 (tptp.lex X_a) R_2))) (and (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool _let_6 (tptp.hAPP _let_5 _let_4 (tptp.lexord X_a) R_2))) (= (tptp.hAPP _let_1 tptp.nat _let_2 X_1) (tptp.hAPP _let_1 tptp.nat _let_2 Y_1))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (Pa $$unsorted) (Xs_1 $$unsorted) (Ys_1 $$unsorted)) (let ((_let_1 (tptp.list X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.list X_a))) (=> (= (tptp.hAPP _let_3 tptp.nat (tptp.size_size _let_3) Xs_1) (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) Ys_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_3 _let_2 Pa (tptp.nil X_a)) (tptp.nil X_b))) (=> (forall ((X_2 $$unsorted) (Xs_2 $$unsorted) (Y_2 $$unsorted) (Ys $$unsorted)) (let ((_let_1 (tptp.list X_b))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (=> (= (tptp.hAPP _let_2 tptp.nat (tptp.size_size _let_2) Xs_2) (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) Ys)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_2 _let_3 Pa Xs_2) Ys)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_2 _let_3 Pa (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_a (tptp.fun _let_2 _let_2) (tptp.cons X_a) X_2) Xs_2)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.cons X_b) Y_2) Ys))))))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_3 _let_2 Pa Xs_1) Ys_1))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (X_a $$unsorted) (F $$unsorted) (G $$unsorted)) (let ((_let_1 (tptp.fun (tptp.product_prod X_a X_b) X_c))) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_b))) (= (tptp.hAPP X_b X_c (tptp.hAPP X_a (tptp.fun X_b X_c) F X_2) Y_2) (tptp.hAPP _let_1 X_c G (tptp.hAPP X_b _let_1 (tptp.hAPP X_a (tptp.fun X_b _let_1) (tptp.product_Pair X_a X_b) X_2) Y_2))))) (= (tptp.hAPP (tptp.fun X_a (tptp.fun X_b X_c)) _let_1 (tptp.product_prod_case X_a X_b X_c) F) (tptp.ti _let_1 G))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (X_a $$unsorted) (P_1 $$unsorted) (F $$unsorted) (G $$unsorted) (Q_2 $$unsorted)) (let ((_let_1 (tptp.product_prod_case X_a X_b X_c))) (let ((_let_2 (tptp.product_prod X_a X_b))) (let ((_let_3 (tptp.fun _let_2 X_c))) (let ((_let_4 (tptp.fun X_a (tptp.fun X_b X_c)))) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b X_c))) (let ((_let_2 (tptp.product_prod X_a X_b))) (=> (= (tptp.hAPP X_b _let_2 (tptp.hAPP X_a (tptp.fun X_b _let_2) (tptp.product_Pair X_a X_b) X_2) Y_2) (tptp.ti _let_2 Q_2)) (= (tptp.hAPP X_b X_c (tptp.hAPP X_a _let_1 F X_2) Y_2) (tptp.hAPP X_b X_c (tptp.hAPP X_a _let_1 G X_2) Y_2)))))) (=> (= (tptp.ti _let_2 P_1) (tptp.ti _let_2 Q_2)) (= (tptp.hAPP _let_2 X_c (tptp.hAPP _let_4 _let_3 _let_1 F) P_1) (tptp.hAPP _let_2 X_c (tptp.hAPP _let_4 _let_3 _let_1 G) Q_2))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted) (Q_1 $$unsorted) (Pa $$unsorted) (Z_2 $$unsorted)) (let ((_let_1 (tptp.product_prod X_b X_c))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool Q_1 (tptp.hAPP _let_1 X_a (tptp.hAPP (tptp.fun X_b (tptp.fun X_c X_a)) (tptp.fun _let_1 X_a) (tptp.product_prod_case X_b X_c X_a) Pa) Z_2))) (not (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.product_prod X_b X_c))) (=> (= (tptp.ti _let_1 Z_2) (tptp.hAPP X_c _let_1 (tptp.hAPP X_b (tptp.fun X_c _let_1) (tptp.product_Pair X_b X_c) X_2) Y_2)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool Q_1 (tptp.hAPP X_c X_a (tptp.hAPP X_b (tptp.fun X_c X_a) Pa X_2) Y_2))))))))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (Ys_1 $$unsorted) (R_2 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.size_size _let_1))) (let ((_let_3 (tptp.product_prod _let_1 _let_1))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP _let_3 (tptp.fun _let_4 tptp.bool) (tptp.member _let_3) (tptp.hAPP _let_1 _let_3 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_3) (tptp.product_Pair _let_1 _let_1) Xs_1) Ys_1)) (tptp.hAPP tptp.nat _let_4 (tptp.hAPP (tptp.fun (tptp.product_prod X_a X_a) tptp.bool) (tptp.fun tptp.nat _let_4) (tptp.lexn X_a) R_2) N))) (and (= (tptp.hAPP _let_1 tptp.nat _let_2 Xs_1) N) (= (tptp.hAPP _let_1 tptp.nat _let_2 Ys_1) N)))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F $$unsorted) (Aa $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_a _let_2 F Aa) Ba)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP (tptp.fun X_a _let_2) (tptp.fun _let_1 tptp.bool) (tptp.product_prod_case X_a X_b tptp.bool) F) (tptp.hAPP X_b _let_1 (tptp.hAPP X_a (tptp.fun X_b _let_1) (tptp.product_Pair X_a X_b) Aa) Ba))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F1 $$unsorted) (Aa $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_a _let_2 F1 Aa) Ba)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP (tptp.fun X_a _let_2) (tptp.fun _let_1 tptp.bool) (tptp.product_prod_case X_a X_b tptp.bool) F1) (tptp.hAPP X_b _let_1 (tptp.hAPP X_a (tptp.fun X_b _let_1) (tptp.product_Pair X_a X_b) Aa) Ba))))))) (forall ((X_a $$unsorted) (X_c $$unsorted) (X_b $$unsorted) (Z_2 $$unsorted) (Ca $$unsorted) (Aa $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.product_prod X_b X_c))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.fun X_c _let_2))) (let ((_let_4 (tptp.hAPP X_a (tptp.fun _let_2 tptp.bool) (tptp.member X_a) Z_2))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_4 (tptp.hAPP X_c _let_2 (tptp.hAPP X_b _let_3 Ca Aa) Ba))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_4 (tptp.hAPP _let_1 _let_2 (tptp.hAPP (tptp.fun X_b _let_3) (tptp.fun _let_1 _let_2) (tptp.product_prod_case X_b X_c _let_2) Ca) (tptp.hAPP X_c _let_1 (tptp.hAPP X_b (tptp.fun X_c _let_1) (tptp.product_Pair X_b X_c) Aa) Ba)))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (F $$unsorted) (Aa $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.product_prod X_a X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP (tptp.fun X_a _let_1) (tptp.fun _let_2 tptp.bool) (tptp.product_prod_case X_a X_b tptp.bool) F) (tptp.hAPP X_b _let_2 (tptp.hAPP X_a (tptp.fun X_b _let_2) (tptp.product_Pair X_a X_b) Aa) Ba))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_a _let_1 F Aa) Ba)))))) (forall ((X_c $$unsorted) (X_a $$unsorted) (X_b $$unsorted) (R_1 $$unsorted) (Aa $$unsorted) (Ba $$unsorted) (Ca $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b _let_1))) (let ((_let_3 (tptp.product_prod X_a X_b))) (=> (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP _let_3 _let_1 (tptp.hAPP (tptp.fun X_a _let_2) (tptp.fun _let_3 _let_1) (tptp.product_prod_case X_a X_b _let_1) R_1) (tptp.hAPP X_b _let_3 (tptp.hAPP X_a (tptp.fun X_b _let_3) (tptp.product_Pair X_a X_b) Aa) Ba)) Ca)) (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_b _let_1 (tptp.hAPP X_a _let_2 R_1 Aa) Ba) Ca))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (Ca $$unsorted) (P_1 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_b))) (=> (forall ((A_4 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_b))) (=> (= (tptp.ti _let_1 P_1) (tptp.hAPP X_b _let_1 (tptp.hAPP X_a (tptp.fun X_b _let_1) (tptp.product_Pair X_a X_b) A_4) B_2)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_a (tptp.fun X_b tptp.bool) Ca A_4) B_2))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP (tptp.fun X_a (tptp.fun X_b tptp.bool)) (tptp.fun _let_1 tptp.bool) (tptp.product_prod_case X_a X_b tptp.bool) Ca) P_1))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (Ca $$unsorted) (P_1 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP (tptp.fun X_a (tptp.fun X_b tptp.bool)) (tptp.fun _let_1 tptp.bool) (tptp.product_prod_case X_a X_b tptp.bool) Ca) P_1)) (not (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_b))) (=> (= (tptp.ti _let_1 P_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) Y_2)) (not (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_a (tptp.fun X_b tptp.bool) Ca X_2) Y_2)))))))))) (forall ((X_c $$unsorted) (X_a $$unsorted) (X_b $$unsorted) (Z_2 $$unsorted) (Ca $$unsorted) (P_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.product_prod X_a X_b))) (=> (forall ((A_4 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.product_prod X_a X_b))) (=> (= (tptp.ti _let_2 P_1) (tptp.hAPP X_b _let_2 (tptp.hAPP X_a (tptp.fun X_b _let_2) (tptp.product_Pair X_a X_b) A_4) B_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_c (tptp.fun _let_1 tptp.bool) (tptp.member X_c) Z_2) (tptp.hAPP X_b _let_1 (tptp.hAPP X_a (tptp.fun X_b _let_1) Ca A_4) B_2))))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_c (tptp.fun _let_1 tptp.bool) (tptp.member X_c) Z_2) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_a (tptp.fun X_b _let_1)) (tptp.fun _let_2 _let_1) (tptp.product_prod_case X_a X_b _let_1) Ca) P_1))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (X_a $$unsorted) (Ca $$unsorted) (X_1 $$unsorted) (P_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.product_prod X_a X_b))) (=> (forall ((A_4 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.product_prod X_a X_b))) (=> (= (tptp.hAPP X_b _let_2 (tptp.hAPP X_a (tptp.fun X_b _let_2) (tptp.product_Pair X_a X_b) A_4) B_2) (tptp.ti _let_2 P_1)) (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_b _let_1 (tptp.hAPP X_a (tptp.fun X_b _let_1) Ca A_4) B_2) X_1)))))) (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_a (tptp.fun X_b _let_1)) (tptp.fun _let_2 _let_1) (tptp.product_prod_case X_a X_b _let_1) Ca) P_1) X_1)))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted) (Z_2 $$unsorted) (Ca $$unsorted) (P_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.product_prod X_b X_c))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) Z_2) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_b (tptp.fun X_c _let_1)) (tptp.fun _let_2 _let_1) (tptp.product_prod_case X_b X_c _let_1) Ca) P_1))) (not (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.product_prod X_b X_c))) (=> (= (tptp.ti _let_2 P_1) (tptp.hAPP X_c _let_2 (tptp.hAPP X_b (tptp.fun X_c _let_2) (tptp.product_Pair X_b X_c) X_2) Y_2)) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) Z_2) (tptp.hAPP X_c _let_1 (tptp.hAPP X_b (tptp.fun X_c _let_1) Ca X_2) Y_2))))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (Pa $$unsorted) (Q_1 $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.product_prod_case X_a X_b tptp.bool))) (let ((_let_2 (tptp.product_prod X_a X_b))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.fun X_b tptp.bool))) (let ((_let_5 (tptp.fun X_a _let_4))) (let ((_let_6 (tptp.fun tptp.bool tptp.bool))) (let ((_let_7 (tptp.fun _let_4 _let_4))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_5 _let_3 _let_1 (tptp.hAPP _let_5 _let_5 (tptp.hAPP _let_7 (tptp.fun _let_5 _let_5) (tptp.combb _let_4 _let_4 X_a) (tptp.hAPP _let_6 _let_7 (tptp.combb tptp.bool tptp.bool X_b) (tptp.hAPP tptp.bool _let_6 tptp.fconj Pa))) Q_1)) X_2)) (and (tptp.hBOOL Pa) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_5 _let_3 _let_1 Q_1) X_2)))))))))))) (forall ((X_c $$unsorted) (X_a $$unsorted) (X_b $$unsorted) (Ca $$unsorted) (P_1 $$unsorted) (Z_2 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.product_prod X_a X_b))) (=> (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_a (tptp.fun X_b _let_1)) (tptp.fun _let_2 _let_1) (tptp.product_prod_case X_a X_b _let_1) Ca) P_1) Z_2)) (not (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.product_prod X_a X_b))) (=> (= (tptp.ti _let_2 P_1) (tptp.hAPP X_b _let_2 (tptp.hAPP X_a (tptp.fun X_b _let_2) (tptp.product_Pair X_a X_b) X_2) Y_2)) (not (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_b _let_1 (tptp.hAPP X_a (tptp.fun X_b _let_1) Ca X_2) Y_2) Z_2)))))))))))) (forall ((X_a $$unsorted) (N_1 $$unsorted)) (exists ((Xs_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (= (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) Xs_2) N_1)))) (forall ((X_a $$unsorted) (Ws $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.list X_a) tptp.bool (tptp.distinct X_a) Ws))) (exists ((Xs_2 $$unsorted) (Ys $$unsorted) (Zs_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.append X_a))) (let ((_let_4 (tptp.hAPP _let_1 _let_2 _let_3 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_2 (tptp.cons X_a) Y_2) (tptp.nil X_a))))) (= Ws (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 _let_3 Xs_2) (tptp.hAPP _let_1 _let_1 _let_4 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 _let_3 Ys) (tptp.hAPP _let_1 _let_1 _let_4 Zs_2)))))))))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (Ys_1 $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted) (R_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.product_prod _let_1 _let_1))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.product_prod X_a X_a))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (let ((_let_6 (tptp.hAPP _let_5 _let_3 (tptp.listrel X_a) R_2))) (let ((_let_7 (tptp.cons X_a))) (let ((_let_8 (tptp.fun _let_1 _let_1))) (let ((_let_9 (tptp.product_Pair _let_1 _let_1))) (let ((_let_10 (tptp.fun _let_1 _let_2))) (let ((_let_11 (tptp.member _let_2))) (let ((_let_12 (tptp.fun _let_3 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP _let_4 (tptp.fun _let_5 tptp.bool) (tptp.member _let_4) (tptp.hAPP X_a _let_4 (tptp.hAPP X_a (tptp.fun X_a _let_4) (tptp.product_Pair X_a X_a) X_1) Y_1)) R_2)) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 _let_12 _let_11 (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_1 _let_10 _let_9 Xs_1) Ys_1)) _let_6)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 _let_12 _let_11 (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_1 _let_10 _let_9 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_8 _let_7 X_1) Xs_1)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_8 _let_7 Y_1) Ys_1))) _let_6))))))))))))))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (Ys_1 $$unsorted)) (let ((_let_1 (tptp.append X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (let ((_let_4 (tptp.fun _let_2 _let_3))) (let ((_let_5 (tptp.fun X_a _let_3))) (let ((_let_6 (tptp.tl X_a))) (= (tptp.hAPP _let_2 _let_2 _let_6 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_3 _let_1 Xs_1) Ys_1)) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_5 _let_3 (tptp.hAPP _let_2 (tptp.fun _let_5 _let_3) (tptp.list_case _let_2 X_a) (tptp.hAPP _let_2 _let_2 _let_6 Ys_1)) (tptp.hAPP _let_3 _let_5 (tptp.combk _let_3 X_a) (tptp.hAPP _let_2 _let_3 (tptp.hAPP _let_4 _let_4 (tptp.combc _let_2 _let_2 _let_2) _let_1) Ys_1))) Xs_1))))))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (R_2 $$unsorted)) (let ((_let_1 (tptp.nil X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.product_prod _let_2 _let_2))) (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.hAPP _let_2 _let_3 (tptp.hAPP _let_2 (tptp.fun _let_2 _let_3) (tptp.product_Pair _let_2 _let_2) Xs_1) _let_1)) (tptp.hAPP (tptp.fun (tptp.product_prod X_a X_a) tptp.bool) _let_4 (tptp.listrel X_a) R_2))) (= Xs_1 _let_1))))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (R_2 $$unsorted)) (let ((_let_1 (tptp.nil X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.product_prod _let_2 _let_2))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP _let_3 (tptp.fun _let_4 tptp.bool) (tptp.member _let_3) (tptp.hAPP _let_2 _let_3 (tptp.hAPP _let_2 (tptp.fun _let_2 _let_3) (tptp.product_Pair _let_2 _let_2) _let_1) Xs_1)) (tptp.hAPP (tptp.fun (tptp.product_prod X_a X_a) tptp.bool) _let_4 (tptp.listrel X_a) R_2))) (= Xs_1 _let_1))))))) (forall ((X_a $$unsorted) (X $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.list X_a))) (= (tptp.hAPP _let_1 _let_1 (tptp.tl X_a) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.cons X_a) X) Xs)) Xs))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.nil X_a))) (let ((_let_2 (tptp.list X_a))) (= (tptp.hAPP _let_2 _let_2 (tptp.tl X_a) _let_1) _let_1)))) (forall ((X_a $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.distinct X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 Xs)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.tl X_a) Xs))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((Xs $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.linorder_sorted X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 Xs)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.tl X_a) Xs))))))))) (forall ((X_a $$unsorted) (R_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.product_prod _let_1 _let_1))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.nil X_a))) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_3 tptp.bool) (tptp.member _let_2) (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_2) (tptp.product_Pair _let_1 _let_1) _let_4) _let_4)) (tptp.hAPP (tptp.fun (tptp.product_prod X_a X_a) tptp.bool) _let_3 (tptp.listrel X_a) R_2)))))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (Ys_1 $$unsorted) (R_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.size_size _let_1))) (let ((_let_3 (tptp.product_prod _let_1 _let_1))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP _let_3 (tptp.fun _let_4 tptp.bool) (tptp.member _let_3) (tptp.hAPP _let_1 _let_3 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_3) (tptp.product_Pair _let_1 _let_1) Xs_1) Ys_1)) (tptp.hAPP (tptp.fun (tptp.product_prod X_a X_a) tptp.bool) _let_4 (tptp.listrel X_a) R_2))) (= (tptp.hAPP _let_1 tptp.nat _let_2 Xs_1) (tptp.hAPP _let_1 tptp.nat _let_2 Ys_1)))))))) (forall ((X_a $$unsorted) (Ys_2 $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.tl X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.append X_a))) (let ((_let_4 (tptp.fun _let_2 _let_2))) (=> (not (= Xs (tptp.nil X_a))) (= (tptp.hAPP _let_2 _let_2 _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_4 _let_3 Xs) Ys_2)) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_4 _let_3 (tptp.hAPP _let_2 _let_2 _let_1 Xs)) Ys_2)))))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (Y_1 $$unsorted) (Ys_1 $$unsorted) (R_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.product_prod _let_1 _let_1))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_3 tptp.bool) (tptp.member _let_2) (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_2) (tptp.product_Pair _let_1 _let_1) Xs_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.cons X_a) Y_1) Ys_1))) (tptp.hAPP (tptp.fun (tptp.product_prod X_a X_a) tptp.bool) _let_3 (tptp.listrel X_a) R_2))) (not (forall ((X_2 $$unsorted) (Xs_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.product_prod _let_1 _let_1))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.product_prod X_a X_a))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (= Xs_1 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.cons X_a) X_2) Xs_2)) (=> (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP _let_4 (tptp.fun _let_5 tptp.bool) (tptp.member _let_4) (tptp.hAPP X_a _let_4 (tptp.hAPP X_a (tptp.fun X_a _let_4) (tptp.product_Pair X_a X_a) X_2) Y_1)) R_2)) (not (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_3 tptp.bool) (tptp.member _let_2) (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_2) (tptp.product_Pair _let_1 _let_1) Xs_2) Ys_1)) (tptp.hAPP _let_5 _let_3 (tptp.listrel X_a) R_2)))))))))))))))))) (forall ((X_a $$unsorted) (Y_1 $$unsorted) (Ys_1 $$unsorted) (Xs_1 $$unsorted) (R_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.product_prod _let_1 _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) (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_2) (tptp.product_Pair _let_1 _let_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.cons X_a) Y_1) Ys_1)) Xs_1)) (tptp.hAPP (tptp.fun (tptp.product_prod X_a X_a) tptp.bool) _let_3 (tptp.listrel X_a) R_2))) (not (forall ((Y_2 $$unsorted) (Ys $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.product_prod _let_1 _let_1))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.product_prod X_a X_a))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (= Xs_1 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.cons X_a) Y_2) Ys)) (=> (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP _let_4 (tptp.fun _let_5 tptp.bool) (tptp.member _let_4) (tptp.hAPP X_a _let_4 (tptp.hAPP X_a (tptp.fun X_a _let_4) (tptp.product_Pair X_a X_a) Y_1) Y_2)) R_2)) (not (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.hAPP _let_1 (tptp.fun _let_1 _let_2) (tptp.product_Pair _let_1 _let_1) Ys_1) Ys)) (tptp.hAPP _let_5 _let_3 (tptp.listrel X_a) R_2)))))))))))))))))) (forall ((X_a $$unsorted) (R_2 $$unsorted) (X_2 $$unsorted) (Xa $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.product_prod _let_1 _let_1))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.product_prod X_a X_a))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (let ((_let_7 (tptp.fun X_a _let_6))) (let ((_let_8 (tptp.fun X_a _let_4))) (let ((_let_9 (tptp.fun _let_8 _let_7))) (let ((_let_10 (tptp.fun X_a _let_7))) (let ((_let_11 (tptp.fun X_a _let_8))) (let ((_let_12 (tptp.fun X_a tptp.bool))) (let ((_let_13 (tptp.fun _let_5 _let_12))) (let ((_let_14 (tptp.fun X_a _let_13))) (let ((_let_15 (tptp.fun X_a _let_12))) (let ((_let_16 (tptp.fun _let_1 tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_16 (tptp.hAPP _let_15 (tptp.fun _let_1 _let_16) (tptp.listrelp X_a) (tptp.hAPP _let_5 _let_15 (tptp.hAPP _let_14 (tptp.fun _let_5 _let_15) (tptp.combc X_a _let_5 _let_12) (tptp.hAPP _let_10 _let_14 (tptp.hAPP (tptp.fun _let_7 _let_13) (tptp.fun _let_10 _let_14) (tptp.combb _let_7 _let_13 X_a) (tptp.combc X_a _let_5 tptp.bool)) (tptp.hAPP _let_11 _let_10 (tptp.hAPP _let_9 (tptp.fun _let_11 _let_10) (tptp.combb _let_8 _let_7 X_a) (tptp.hAPP (tptp.fun _let_4 _let_6) _let_9 (tptp.combb _let_4 _let_6 X_a) (tptp.member _let_4))) (tptp.product_Pair X_a X_a)))) R_2)) X_2) Xa)) (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.hAPP _let_1 (tptp.fun _let_1 _let_2) (tptp.product_Pair _let_1 _let_1) X_2) Xa)) (tptp.hAPP _let_5 _let_3 (tptp.listrel X_a) R_2))))))))))))))))))))) (forall ((X_a $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.nil X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (=> (not (= Xs _let_1)) (= (tptp.hAPP _let_2 _let_2 (tptp.rotate1 X_a) Xs) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_3 (tptp.append X_a) (tptp.hAPP _let_2 _let_2 (tptp.tl X_a) Xs)) (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_a _let_3 (tptp.cons X_a) (tptp.hAPP _let_2 X_a (tptp.hd X_a) Xs)) _let_1)))))))) (forall ((X_a $$unsorted) (A1 $$unsorted) (A2 $$unsorted) (R_2 $$unsorted)) (let ((_let_1 (tptp.nil X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.product_prod _let_2 _let_2))) (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.hAPP _let_2 _let_3 (tptp.hAPP _let_2 (tptp.fun _let_2 _let_3) (tptp.product_Pair _let_2 _let_2) A1) A2)) (tptp.hAPP (tptp.fun (tptp.product_prod X_a X_a) tptp.bool) _let_4 (tptp.listrel X_a) R_2))) (or (and (= A1 _let_1) (= A2 _let_1)) (exists ((X_2 $$unsorted) (Y_2 $$unsorted) (Xs_2 $$unsorted) (Ys $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.product_prod _let_1 _let_1))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.product_prod X_a X_a))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (let ((_let_6 (tptp.cons X_a))) (let ((_let_7 (tptp.fun _let_1 _let_1))) (and (= A1 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_7 _let_6 X_2) Xs_2)) (= A2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_7 _let_6 Y_2) Ys)) (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP _let_4 (tptp.fun _let_5 tptp.bool) (tptp.member _let_4) (tptp.hAPP X_a _let_4 (tptp.hAPP X_a (tptp.fun X_a _let_4) (tptp.product_Pair X_a X_a) X_2) Y_2)) R_2)) (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.hAPP _let_1 (tptp.fun _let_1 _let_2) (tptp.product_Pair _let_1 _let_1) Xs_2) Ys)) (tptp.hAPP _let_5 _let_3 (tptp.listrel X_a) R_2))))))))))))))))))) _let_7 (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (Ys_1 $$unsorted) (R_2 $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.cons X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (let ((_let_5 (tptp.fun X_a tptp.bool))) (let ((_let_6 (tptp.hAPP (tptp.fun X_a _let_5) (tptp.fun _let_2 _let_4) (tptp.listrelp X_a) R_2))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_5 R_2 X_1) Y_1)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 _let_4 _let_6 Xs_1) Ys_1)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 _let_4 _let_6 (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_a _let_3 _let_1 X_1) Xs_1)) (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_a _let_3 _let_1 Y_1) Ys_1)))))))))))) (forall ((X_a $$unsorted) (R_2 $$unsorted)) (let ((_let_1 (tptp.nil X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 _let_3 (tptp.hAPP (tptp.fun X_a (tptp.fun X_a tptp.bool)) (tptp.fun _let_2 _let_3) (tptp.listrelp X_a) R_2) _let_1) _let_1)))))) (forall ((X_a $$unsorted) (Ys_2 $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.hd X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.hAPP _let_2 X_a _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 (tptp.fun _let_2 _let_2) (tptp.append X_a) Xs) Ys_2)))) (let ((_let_4 (= Xs (tptp.nil X_a)))) (and (=> _let_4 (= _let_3 (tptp.hAPP _let_2 X_a _let_1 Ys_2))) (=> (not _let_4) (= _let_3 (tptp.hAPP _let_2 X_a _let_1 Xs))))))))) (forall ((X_a $$unsorted) (Ys_2 $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.hd X_a))) (let ((_let_2 (tptp.list X_a))) (=> (not (= Xs (tptp.nil X_a))) (= (tptp.hAPP _let_2 X_a _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 (tptp.fun _let_2 _let_2) (tptp.append X_a) Xs) Ys_2)) (tptp.hAPP _let_2 X_a _let_1 Xs)))))) (forall ((X_a $$unsorted) (Pa $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_a tptp.bool) (tptp.fun _let_1 _let_1) (tptp.dropWhile X_a) Pa) Xs_1))) (=> (not (= _let_2 (tptp.nil X_a))) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa (tptp.hAPP _let_1 X_a (tptp.hd X_a) _let_2)))))))) (forall ((X_a $$unsorted) (R_2 $$unsorted) (A1 $$unsorted) (A2 $$unsorted)) (let ((_let_1 (tptp.nil X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 _let_3 (tptp.hAPP (tptp.fun X_a (tptp.fun X_a tptp.bool)) (tptp.fun _let_2 _let_3) (tptp.listrelp X_a) R_2) A1) A2)) (or (and (= A1 _let_1) (= A2 _let_1)) (exists ((X_2 $$unsorted) (Y_2 $$unsorted) (Xs_2 $$unsorted) (Ys $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.cons X_a))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (and (= A1 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_5 _let_4 X_2) Xs_2)) (= A2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_5 _let_4 Y_2) Ys)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 R_2 X_2) Y_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.hAPP (tptp.fun X_a _let_3) (tptp.fun _let_1 _let_2) (tptp.listrelp X_a) R_2) Xs_2) Ys))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.cl_HOL_Oequal X_a) (= (tptp.equal_equal X_a) (tptp.fequal X_a)))) (forall ((X_a $$unsorted)) (=> (tptp.cl_HOL_Oequal X_a) (forall ((X $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.equal_equal X_a) X) X))))) (forall ((X_a $$unsorted)) (=> (tptp.cl_HOL_Oequal X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.equal_equal X_a) X_1) Y_1)) (= (tptp.ti X_a X_1) (tptp.ti X_a Y_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.cl_HOL_Oequal X_a) (= (tptp.fequal X_a) (tptp.equal_equal X_a)))) (forall ((X_a $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.list X_a))) (=> (not (= Xs (tptp.nil X_a))) (= (tptp.hAPP _let_1 X_a (tptp.last X_a) (tptp.hAPP _let_1 _let_1 (tptp.rev X_a) Xs)) (tptp.hAPP _let_1 X_a (tptp.hd X_a) Xs))))) (forall ((X_a $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.list X_a))) (=> (not (= Xs (tptp.nil X_a))) (= (tptp.hAPP _let_1 X_a (tptp.hd X_a) (tptp.hAPP _let_1 _let_1 (tptp.rev X_a) Xs)) (tptp.hAPP _let_1 X_a (tptp.last X_a) Xs))))) (forall ((X_a $$unsorted) (I_1 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.hAPP tptp.nat (tptp.fun X_a _let_1) (tptp.replicate X_a) I_1) X))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.hAPP X_a _let_3 (tptp.cons X_a) X))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 (tptp.append X_a) _let_2) (tptp.hAPP _let_1 _let_1 _let_4 (tptp.nil X_a))) (tptp.hAPP _let_1 _let_1 _let_4 _let_2))))))) (forall ((X_a $$unsorted) (Pa $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_3 _let_2 (tptp.dropWhile X_a) Pa) Xs_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.nat _let_2 (tptp.drop X_a) (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_3 _let_2 (tptp.takeWhile X_a) Pa) Xs_1))) Xs_1)))))) (forall ((X_a $$unsorted) (N_1 $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.butlast X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.hAPP tptp.nat (tptp.fun _let_2 _let_2) (tptp.drop X_a) N_1))) (= (tptp.hAPP _let_2 _let_2 _let_1 (tptp.hAPP _let_2 _let_2 _let_3 Xs)) (tptp.hAPP _let_2 _let_2 _let_3 (tptp.hAPP _let_2 _let_2 _let_1 Xs))))))) (forall ((X_a $$unsorted) (N_1 $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.hAPP tptp.nat (tptp.fun _let_1 _let_1) (tptp.drop X_a) N_1))) (let ((_let_3 (tptp.butlast X_a))) (= (tptp.hAPP _let_1 _let_1 _let_2 (tptp.hAPP _let_1 _let_1 _let_3 Xs)) (tptp.hAPP _let_1 _let_1 _let_3 (tptp.hAPP _let_1 _let_1 _let_2 Xs))))))) (forall ((X_a $$unsorted) (N_1 $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.tl X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.hAPP tptp.nat (tptp.fun _let_2 _let_2) (tptp.drop X_a) N_1))) (= (tptp.hAPP _let_2 _let_2 _let_1 (tptp.hAPP _let_2 _let_2 _let_3 Xs)) (tptp.hAPP _let_2 _let_2 _let_3 (tptp.hAPP _let_2 _let_2 _let_1 Xs))))))) (forall ((X_a $$unsorted) (N_1 $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.hAPP tptp.nat (tptp.fun _let_1 _let_1) (tptp.drop X_a) N_1))) (let ((_let_3 (tptp.tl X_a))) (= (tptp.hAPP _let_1 _let_1 _let_2 (tptp.hAPP _let_1 _let_1 _let_3 Xs)) (tptp.hAPP _let_1 _let_1 _let_3 (tptp.hAPP _let_1 _let_1 _let_2 Xs))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((N_1 $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.linorder_sorted X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 Xs)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.nat (tptp.fun _let_1 _let_1) (tptp.drop X_a) N_1) Xs))))))))) (forall ((X_a $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.nil X_a))) (let ((_let_2 (tptp.list X_a))) (= (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.nat (tptp.fun _let_2 _let_2) (tptp.drop X_a) N_1) _let_1) _let_1)))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (Ys_1 $$unsorted)) (let ((_let_1 (tptp.rev X_a))) (let ((_let_2 (tptp.list X_a))) (= (= (tptp.hAPP _let_2 _let_2 _let_1 Xs_1) (tptp.hAPP _let_2 _let_2 _let_1 Ys_1)) (= Xs_1 Ys_1))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (Ys_1 $$unsorted)) (let ((_let_1 (tptp.rev X_a))) (let ((_let_2 (tptp.list X_a))) (= (= (tptp.hAPP _let_2 _let_2 _let_1 Xs_1) Ys_1) (= Xs_1 (tptp.hAPP _let_2 _let_2 _let_1 Ys_1)))))) (forall ((X_a $$unsorted) (N_1 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.hAPP tptp.nat (tptp.fun X_a _let_1) (tptp.replicate X_a) N_1) X))) (= (tptp.hAPP _let_1 _let_1 (tptp.rev X_a) _let_2) _let_2)))) (forall ((X_a $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.rev X_a))) (let ((_let_2 (tptp.list X_a))) (= (tptp.hAPP _let_2 _let_2 _let_1 (tptp.hAPP _let_2 _let_2 _let_1 Xs)) Xs)))) (forall ((X_a $$unsorted) (I_1 $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.distinct X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 Xs)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.nat (tptp.fun _let_1 _let_1) (tptp.drop X_a) I_1) Xs))))))) (forall ((X_a $$unsorted) (Xs $$unsorted) (Ys_2 $$unsorted)) (let ((_let_1 (tptp.rev X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.append X_a))) (let ((_let_4 (tptp.fun _let_2 _let_2))) (= (tptp.hAPP _let_2 _let_2 _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_4 _let_3 Xs) Ys_2)) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_4 _let_3 (tptp.hAPP _let_2 _let_2 _let_1 Ys_2)) (tptp.hAPP _let_2 _let_2 _let_1 Xs)))))))) (forall ((X_a $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.size_size _let_1))) (= (tptp.hAPP _let_1 tptp.nat _let_2 (tptp.hAPP _let_1 _let_1 (tptp.rev X_a) Xs)) (tptp.hAPP _let_1 tptp.nat _let_2 Xs))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.nil X_a))) (let ((_let_2 (tptp.list X_a))) (= (= (tptp.hAPP _let_2 _let_2 (tptp.rev X_a) Xs_1) _let_1) (= Xs_1 _let_1))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.nil X_a))) (let ((_let_2 (tptp.list X_a))) (= (= _let_1 (tptp.hAPP _let_2 _let_2 (tptp.rev X_a) Xs_1)) (= Xs_1 _let_1))))) _let_6 (forall ((X_a $$unsorted) (N_1 $$unsorted) (X $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.replicate X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun X_a _let_2))) (let ((_let_4 (tptp.hAPP X_a _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 N_1) X))) (let ((_let_5 (tptp.hAPP X_a _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 K) X))) (let ((_let_6 (tptp.append X_a))) (let ((_let_7 (tptp.fun _let_2 _let_2))) (= (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_7 _let_6 _let_4) _let_5) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_7 _let_6 _let_5) _let_4)))))))))) (forall ((X_a $$unsorted) (N_1 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.list X_a))) (= (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) (tptp.hAPP X_a _let_1 (tptp.hAPP tptp.nat (tptp.fun X_a _let_1) (tptp.replicate X_a) N_1) X)) N_1))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.distinct X_a))) (let ((_let_2 (tptp.list X_a))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 (tptp.hAPP _let_2 _let_2 (tptp.rev X_a) Xs_1))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 Xs_1)))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.cons X_a) X_1) (tptp.nil X_a)))) (= (= (tptp.hAPP _let_1 _let_1 (tptp.rev X_a) Xs_1) _let_2) (= Xs_1 _let_2))))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.cons X_a) X_1) (tptp.nil X_a)))) (= (= _let_2 (tptp.hAPP _let_1 _let_1 (tptp.rev X_a) Xs_1)) (= Xs_1 _let_2))))) (forall ((X_a $$unsorted) (N_1 $$unsorted) (X $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP _let_1 _let_2 (tptp.append X_a) (tptp.hAPP X_a _let_1 (tptp.hAPP tptp.nat (tptp.fun X_a _let_1) (tptp.replicate X_a) N_1) X)))) (let ((_let_4 (tptp.hAPP X_a _let_2 (tptp.cons X_a) X))) (= (tptp.hAPP _let_1 _let_1 _let_3 (tptp.hAPP _let_1 _let_1 _let_4 Xs)) (tptp.hAPP _let_1 _let_1 _let_4 (tptp.hAPP _let_1 _let_1 _let_3 Xs)))))))) _let_5 (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (Y_1 $$unsorted) (Ys_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP X_a _let_2 (tptp.cons X_a) Y_1))) (let ((_let_4 (tptp.rev X_a))) (= (= (tptp.hAPP _let_1 _let_1 _let_4 Xs_1) (tptp.hAPP _let_1 _let_1 _let_3 Ys_1)) (= Xs_1 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.append X_a) (tptp.hAPP _let_1 _let_1 _let_4 Ys_1)) (tptp.hAPP _let_1 _let_1 _let_3 (tptp.nil X_a)))))))))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun X_a _let_1))) (let ((_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) (tptp.hAPP X_a _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc X_a X_a tptp.bool) (tptp.fequal X_a)) X_1)))) (let ((_let_4 (tptp.list X_a))) (let ((_let_5 (tptp.fun _let_4 _let_4))) (let ((_let_6 (tptp.rev X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.distinct X_a) Xs_1)) (=> (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.hAPP _let_4 _let_1 (tptp.set X_a) Xs_1))) (= (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_1 _let_5 (tptp.takeWhile X_a) _let_3) (tptp.hAPP _let_4 _let_4 _let_6 Xs_1)) (tptp.hAPP _let_4 _let_4 _let_6 (tptp.hAPP _let_4 _let_4 (tptp.tl X_a) (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_1 _let_5 (tptp.dropWhile X_a) _let_3) Xs_1))))))))))))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun X_a _let_1))) (let ((_let_3 (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun tptp.bool tptp.bool) (tptp.fun _let_1 _let_1) (tptp.combb tptp.bool tptp.bool X_a) tptp.fNot) (tptp.hAPP X_a _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc X_a X_a tptp.bool) (tptp.fequal X_a)) X_1)))) (let ((_let_4 (tptp.list X_a))) (let ((_let_5 (tptp.fun _let_4 _let_4))) (let ((_let_6 (tptp.rev X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.distinct X_a) Xs_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_1) (tptp.hAPP _let_4 _let_1 (tptp.set X_a) Xs_1))) (= (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_1 _let_5 (tptp.dropWhile X_a) _let_3) (tptp.hAPP _let_4 _let_4 _let_6 Xs_1)) (tptp.hAPP _let_4 _let_4 (tptp.hAPP X_a _let_5 (tptp.cons X_a) X_1) (tptp.hAPP _let_4 _let_4 _let_6 (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_1 _let_5 (tptp.takeWhile X_a) _let_3) Xs_1))))))))))))) (forall ((X_a $$unsorted) (N $$unsorted) (X_1 $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.drop X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (let ((_let_4 (tptp.fun _let_2 _let_2))) (let ((_let_5 (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_a _let_4 (tptp.cons X_a) X_1) Xs_1))) (= (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.nat _let_4 _let_1 N) _let_5) (tptp.hAPP tptp.nat _let_2 (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_2 (tptp.fun _let_3 _let_3) (tptp.nat_case _let_2) _let_5) (tptp.hAPP _let_2 _let_3 (tptp.hAPP (tptp.fun tptp.nat _let_4) (tptp.fun _let_2 _let_3) (tptp.combc tptp.nat _let_2 _let_2) _let_1) Xs_1)) N)))))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun _let_1 (tptp.fun X_a _let_1)))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (= (tptp.hAPP _let_1 _let_1 (tptp.rev X_a) Xs_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 (tptp.hAPP _let_2 (tptp.fun _let_1 _let_3) (tptp.foldl _let_1 X_a) (tptp.hAPP (tptp.fun X_a _let_3) _let_2 (tptp.combc X_a _let_1 _let_1) (tptp.cons X_a))) (tptp.nil X_a)) Xs_1)))))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (N $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.set X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.list X_a))) (let ((_let_4 (tptp.hAPP X_a (tptp.fun _let_2 tptp.bool) (tptp.member X_a) X_1))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_4 (tptp.hAPP _let_3 _let_2 _let_1 (tptp.hAPP _let_3 _let_3 (tptp.hAPP tptp.nat (tptp.fun _let_3 _let_3) (tptp.drop X_a) N) Xs_1)))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_4 (tptp.hAPP _let_3 _let_2 _let_1 Xs_1))))))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.set X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.list X_a))) (= (tptp.hAPP _let_3 _let_2 _let_1 (tptp.hAPP _let_3 _let_3 (tptp.rev X_a) Xs_1)) (tptp.hAPP _let_3 _let_2 _let_1 Xs_1)))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.set X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.list X_a))) (= (tptp.hAPP _let_3 _let_2 _let_1 (tptp.hAPP _let_3 _let_3 (tptp.rotate1 X_a) Xs_1)) (tptp.hAPP _let_3 _let_2 _let_1 Xs_1)))))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (Pa $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.set X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.list X_a))) (let ((_let_4 (tptp.hAPP X_a (tptp.fun _let_2 tptp.bool) (tptp.member X_a) X_1))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_4 (tptp.hAPP _let_3 _let_2 _let_1 (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_2 (tptp.fun _let_3 _let_3) (tptp.takeWhile X_a) Pa) Xs_1)))) (and (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_4 (tptp.hAPP _let_3 _let_2 _let_1 Xs_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa X_1))))))))) (forall ((X_a $$unsorted) (Pa $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (= (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_a tptp.bool) (tptp.fun _let_1 _let_1) (tptp.takeWhile X_a) Pa) Xs_1) Xs_1) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) (tptp.hAPP (tptp.list X_a) _let_1 (tptp.set X_a) Xs_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa X_2)))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F $$unsorted) (Aa $$unsorted) (Xs_1 $$unsorted) (Ys_1 $$unsorted)) (let ((_let_1 (tptp.list X_b))) (let ((_let_2 (tptp.fun _let_1 X_a))) (let ((_let_3 (tptp.hAPP (tptp.fun X_a (tptp.fun X_b X_a)) (tptp.fun X_a _let_2) (tptp.foldl X_a X_b) F))) (let ((_let_4 (tptp.hAPP X_a _let_2 _let_3 Aa))) (= (tptp.hAPP _let_1 X_a _let_4 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.append X_b) Xs_1) Ys_1)) (tptp.hAPP _let_1 X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP _let_1 X_a _let_4 Xs_1)) Ys_1))))))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.set X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.list X_a))) (let ((_let_4 (tptp.hAPP X_a (tptp.fun _let_2 tptp.bool) (tptp.member X_a) X_1))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_4 (tptp.hAPP _let_3 _let_2 _let_1 (tptp.hAPP _let_3 _let_3 (tptp.butlast X_a) Xs_1)))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_4 (tptp.hAPP _let_3 _let_2 _let_1 Xs_1))))))))) (forall ((X_a $$unsorted) (Y_1 $$unsorted) (X_1 $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.set X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.list X_a))) (let ((_let_4 (tptp.hAPP X_a (tptp.fun _let_2 tptp.bool) (tptp.member X_a) Y_1))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_4 (tptp.hAPP _let_3 _let_2 _let_1 (tptp.hAPP _let_3 _let_3 (tptp.hAPP X_a (tptp.fun _let_3 _let_3) (tptp.cons X_a) X_1) Xs_1)))) (or (= (tptp.ti X_a Y_1) (tptp.ti X_a X_1)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_4 (tptp.hAPP _let_3 _let_2 _let_1 Xs_1)))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F $$unsorted) (Aa $$unsorted)) (let ((_let_1 (tptp.list X_b))) (let ((_let_2 (tptp.fun _let_1 X_a))) (= (tptp.hAPP _let_1 X_a (tptp.hAPP X_a _let_2 (tptp.hAPP (tptp.fun X_a (tptp.fun X_b X_a)) (tptp.fun X_a _let_2) (tptp.foldl X_a X_b) F) Aa) (tptp.nil X_b)) (tptp.ti X_a Aa))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F $$unsorted) (Aa $$unsorted) (X_1 $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b X_a))) (let ((_let_2 (tptp.list X_b))) (let ((_let_3 (tptp.fun _let_2 X_a))) (let ((_let_4 (tptp.hAPP (tptp.fun X_a _let_1) (tptp.fun X_a _let_3) (tptp.foldl X_a X_b) F))) (= (tptp.hAPP _let_2 X_a (tptp.hAPP X_a _let_3 _let_4 Aa) (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_b (tptp.fun _let_2 _let_2) (tptp.cons X_b) X_1) Xs_1)) (tptp.hAPP _let_2 X_a (tptp.hAPP X_a _let_3 _let_4 (tptp.hAPP X_b X_a (tptp.hAPP X_a _let_1 F Aa) X_1)) Xs_1))))))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a (tptp.fun _let_2 tptp.bool) (tptp.member X_a) X_1) (tptp.hAPP _let_1 _let_2 (tptp.set X_a) Xs_1))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.insert X_a) X_1) Xs_1) Xs_1))))) _let_4 (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((Ys_1 $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.set X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.list X_a))) (let ((_let_4 (tptp.distinct X_a))) (let ((_let_5 (tptp.linorder_sorted X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool _let_5 Xs_1)) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool _let_4 Xs_1)) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool _let_5 Ys_1)) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool _let_4 Ys_1)) (=> (= (tptp.hAPP _let_3 _let_2 _let_1 Xs_1) (tptp.hAPP _let_3 _let_2 _let_1 Ys_1)) (= Xs_1 Ys_1)))))))))))))) (forall ((X_a $$unsorted) (Ys_1 $$unsorted) (Pa $$unsorted) (X_1 $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.hAPP _let_3 _let_2 (tptp.takeWhile X_a) Pa))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_a (tptp.fun _let_3 tptp.bool) (tptp.member X_a) X_1) (tptp.hAPP _let_1 _let_3 (tptp.set X_a) Xs_1))) (=> (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa X_1))) (= (tptp.hAPP _let_1 _let_1 _let_4 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.append X_a) Xs_1) Ys_1)) (tptp.hAPP _let_1 _let_1 _let_4 Xs_1))))))))) _let_3 (forall ((X_a $$unsorted) (Pa $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (= (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_a tptp.bool) (tptp.fun _let_1 _let_1) (tptp.dropWhile X_a) Pa) Xs_1) (tptp.nil X_a)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) (tptp.hAPP (tptp.list X_a) _let_1 (tptp.set X_a) Xs_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa X_2)))))))) (forall ((X_a $$unsorted) (Ys_1 $$unsorted) (X_1 $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.butlast X_a))) (let ((_let_3 (tptp.set X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (let ((_let_5 (tptp.hAPP X_a (tptp.fun _let_4 tptp.bool) (tptp.member X_a) X_1))) (=> (or (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool _let_5 (tptp.hAPP _let_1 _let_4 _let_3 (tptp.hAPP _let_1 _let_1 _let_2 Xs_1)))) (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool _let_5 (tptp.hAPP _let_1 _let_4 _let_3 (tptp.hAPP _let_1 _let_1 _let_2 Ys_1))))) (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool _let_5 (tptp.hAPP _let_1 _let_4 _let_3 (tptp.hAPP _let_1 _let_1 _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.append X_a) Xs_1) Ys_1)))))))))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.list X_a))) (=> (not (= Xs_1 (tptp.nil X_a))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) (tptp.hAPP _let_2 X_a (tptp.hd X_a) Xs_1)) (tptp.hAPP _let_2 _let_1 (tptp.set X_a) Xs_1))))))) (forall ((X_a $$unsorted) (Ys_1 $$unsorted) (Pa $$unsorted) (X_1 $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.hAPP _let_3 _let_2 (tptp.dropWhile X_a) Pa))) (let ((_let_5 (tptp.append X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_a (tptp.fun _let_3 tptp.bool) (tptp.member X_a) X_1) (tptp.hAPP _let_1 _let_3 (tptp.set X_a) Xs_1))) (=> (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa X_1))) (= (tptp.hAPP _let_1 _let_1 _let_4 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 _let_5 Xs_1) Ys_1)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 _let_5 (tptp.hAPP _let_1 _let_1 _let_4 Xs_1)) Ys_1)))))))))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_2 (tptp.insert X_a) X_1) Xs_1))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (let ((_let_5 (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP X_a (tptp.fun _let_4 tptp.bool) (tptp.member X_a) X_1) (tptp.hAPP _let_1 _let_4 (tptp.set X_a) Xs_1))))) (and (=> _let_5 (= _let_3 Xs_1)) (=> (not _let_5) (= _let_3 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_2 (tptp.cons X_a) X_1) Xs_1)))))))))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (not (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_a (tptp.fun _let_3 tptp.bool) (tptp.member X_a) X_1) (tptp.hAPP _let_1 _let_3 (tptp.set X_a) Xs_1)))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_2 (tptp.insert X_a) X_1) Xs_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_2 (tptp.cons X_a) X_1) Xs_1))))))) (forall ((X_a $$unsorted) (Pa $$unsorted) (Xs_1 $$unsorted) (Yes $$unsorted) (No $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.product_prod _let_1 _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_2))) (=> (= (tptp.hAPP _let_1 _let_2 (tptp.hAPP (tptp.fun X_a tptp.bool) _let_3 (tptp.partition X_a) Pa) Xs_1) (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_1 _let_3 (tptp.product_Pair _let_1 _let_1) Yes) No)) (and (forall ((X_2 $$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) (tptp.hAPP (tptp.list X_a) _let_1 (tptp.set X_a) Yes))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa X_2))))) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) (tptp.hAPP (tptp.list X_a) _let_1 (tptp.set X_a) No))) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa X_2)))))))))))) (forall ((X_a $$unsorted) (Zs $$unsorted) (Ys_1 $$unsorted) (R_2 $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.product_prod _let_1 _let_1))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.hAPP (tptp.fun (tptp.product_prod X_a X_a) tptp.bool) _let_3 (tptp.lexord X_a) R_2))) (let ((_let_5 (tptp.product_Pair _let_1 _let_1))) (let ((_let_6 (tptp.fun _let_1 _let_2))) (let ((_let_7 (tptp.hAPP _let_1 _let_6 _let_5 Xs_1))) (let ((_let_8 (tptp.member _let_2))) (let ((_let_9 (tptp.fun _let_3 tptp.bool))) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.product_Pair X_a X_a))) (let ((_let_2 (tptp.product_prod X_a X_a))) (let ((_let_3 (tptp.fun X_a _let_2))) (let ((_let_4 (tptp.hAPP X_a _let_3 _let_1 X_2))) (let ((_let_5 (tptp.member _let_2))) (let ((_let_6 (tptp.fun _let_2 tptp.bool))) (let ((_let_7 (tptp.fun _let_6 tptp.bool))) (let ((_let_8 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_8 tptp.bool (tptp.hAPP X_a (tptp.fun _let_8 tptp.bool) (tptp.member X_a) X_2) (tptp.hAPP (tptp.list X_a) _let_8 (tptp.set X_a) Xs_1))) (=> (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP _let_2 _let_7 _let_5 (tptp.hAPP X_a _let_2 _let_4 Y_2)) R_2)) (=> (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP _let_2 _let_7 _let_5 (tptp.hAPP X_a _let_2 (tptp.hAPP X_a _let_3 _let_1 Y_2) Z_1)) R_2)) (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP _let_2 _let_7 _let_5 (tptp.hAPP X_a _let_2 _let_4 Z_1)) R_2)))))))))))))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 _let_9 _let_8 (tptp.hAPP _let_1 _let_2 _let_7 Ys_1)) _let_4)) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 _let_9 _let_8 (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_1 _let_6 _let_5 Ys_1) Zs)) _let_4)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 _let_9 _let_8 (tptp.hAPP _let_1 _let_2 _let_7 Zs)) _let_4))))))))))))))) (forall ((X_a $$unsorted) (Ys_1 $$unsorted) (Pa $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP (tptp.fun X_a tptp.bool) _let_2 (tptp.dropWhile X_a) Pa))) (=> (forall ((X_2 $$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) (tptp.hAPP (tptp.list X_a) _let_1 (tptp.set X_a) Xs_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa X_2))))) (= (tptp.hAPP _let_1 _let_1 _let_3 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.append X_a) Xs_1) Ys_1)) (tptp.hAPP _let_1 _let_1 _let_3 Ys_1))))))) (forall ((X_a $$unsorted) (Ys_1 $$unsorted) (Pa $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP (tptp.fun X_a tptp.bool) _let_2 (tptp.takeWhile X_a) Pa))) (let ((_let_4 (tptp.hAPP _let_1 _let_2 (tptp.append X_a) Xs_1))) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) (tptp.hAPP (tptp.list X_a) _let_1 (tptp.set X_a) Xs_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa X_2))))) (= (tptp.hAPP _let_1 _let_1 _let_3 (tptp.hAPP _let_1 _let_1 _let_4 Ys_1)) (tptp.hAPP _let_1 _let_1 _let_4 (tptp.hAPP _let_1 _let_1 _let_3 Ys_1))))))))) (forall ((X_a $$unsorted) (Pa $$unsorted) (Xs_1 $$unsorted)) (=> (exists ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) (tptp.hAPP (tptp.list X_a) _let_1 (tptp.set X_a) Xs_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa X_2))))) (not (forall ((Ys $$unsorted) (X_2 $$unsorted)) (=> (exists ((Zs_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (= Xs_1 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.append X_a) Ys) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_2 (tptp.cons X_a) X_2) Zs_2)))))) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa X_2)))))))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_1) (tptp.hAPP (tptp.list X_a) _let_1 (tptp.set X_a) Xs_1))) (exists ((Ys $$unsorted) (Zs_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (= Xs_1 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.append X_a) Ys) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_2 (tptp.cons X_a) X_1) Zs_2))))))))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (Xs_1 $$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.hAPP (tptp.list X_a) _let_1 (tptp.set X_a) Xs_1))) (exists ((Ys $$unsorted) (Zs_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (and (= Xs_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_3 (tptp.append X_a) Ys) (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_a _let_3 (tptp.cons X_a) X_1) Zs_2))) (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) (tptp.hAPP _let_2 _let_1 (tptp.set X_a) Zs_2)))))))))))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_1) (tptp.hAPP (tptp.list X_a) _let_1 (tptp.set X_a) Xs_1))) (exists ((Ys $$unsorted) (Zs_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (and (= Xs_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_3 (tptp.append X_a) Ys) (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_a _let_3 (tptp.cons X_a) X_1) Zs_2))) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_1) (tptp.hAPP _let_2 _let_1 (tptp.set X_a) Ys)))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (S_2 $$unsorted) (Xs_1 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun _let_1 X_b))) (let ((_let_3 (tptp.hAPP X_b _let_2 (tptp.hAPP (tptp.fun X_b (tptp.fun X_a X_b)) (tptp.fun X_b _let_2) (tptp.foldl X_b X_a) F) S_2))) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted) (S_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_b))) (let ((_let_2 (tptp.hAPP X_b _let_1 F S_3))) (= (tptp.hAPP X_a X_b (tptp.hAPP X_b _let_1 F (tptp.hAPP X_a X_b _let_2 X_2)) Y_2) (tptp.hAPP X_a X_b (tptp.hAPP X_b _let_1 F (tptp.hAPP X_a X_b _let_2 Y_2)) X_2))))) (= (tptp.hAPP _let_1 X_b _let_3 (tptp.hAPP _let_1 _let_1 (tptp.rev X_a) Xs_1)) (tptp.hAPP _let_1 X_b _let_3 Xs_1))))))) (forall ((X_a $$unsorted) (Q_1 $$unsorted) (Pa $$unsorted) (L $$unsorted) (K_1 $$unsorted)) (let ((_let_1 (tptp.dropWhile X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (= L K_1) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) (tptp.hAPP (tptp.list X_a) _let_1 (tptp.set X_a) L))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa X_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool Q_1 X_2)))))) (= (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_4 _let_3 _let_1 Pa) L) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_4 _let_3 _let_1 Q_1) K_1))))))))) (forall ((X_a $$unsorted) (Q_1 $$unsorted) (Pa $$unsorted) (L $$unsorted) (K_1 $$unsorted)) (let ((_let_1 (tptp.takeWhile X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (= L K_1) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) (tptp.hAPP (tptp.list X_a) _let_1 (tptp.set X_a) L))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa X_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool Q_1 X_2)))))) (= (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_4 _let_3 _let_1 Pa) L) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_4 _let_3 _let_1 Q_1) K_1))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F $$unsorted) (G $$unsorted) (L $$unsorted) (K_1 $$unsorted) (Aa $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.foldl X_a X_b))) (let ((_let_2 (tptp.list X_b))) (let ((_let_3 (tptp.fun _let_2 X_a))) (let ((_let_4 (tptp.fun X_a _let_3))) (let ((_let_5 (tptp.fun X_a (tptp.fun X_b X_a)))) (=> (= (tptp.ti X_a Aa) (tptp.ti X_a Ba)) (=> (= L K_1) (=> (forall ((A_4 $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b X_a))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_b (tptp.fun _let_2 tptp.bool) (tptp.member X_b) X_2) (tptp.hAPP (tptp.list X_b) _let_2 (tptp.set X_b) L))) (= (tptp.hAPP X_b X_a (tptp.hAPP X_a _let_1 F A_4) X_2) (tptp.hAPP X_b X_a (tptp.hAPP X_a _let_1 G A_4) X_2)))))) (= (tptp.hAPP _let_2 X_a (tptp.hAPP X_a _let_3 (tptp.hAPP _let_5 _let_4 _let_1 F) Aa) L) (tptp.hAPP _let_2 X_a (tptp.hAPP X_a _let_3 (tptp.hAPP _let_5 _let_4 _let_1 G) Ba) K_1))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F $$unsorted) (Xs_1 $$unsorted) (Pa $$unsorted) (S_2 $$unsorted)) (let ((_let_1 (tptp.list X_b))) (let ((_let_2 (tptp.fun _let_1 X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa S_2)) (=> (forall ((S_3 $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_2) (tptp.hAPP (tptp.list X_b) _let_1 (tptp.set X_b) Xs_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa S_3)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa (tptp.hAPP X_b X_a (tptp.hAPP X_a (tptp.fun X_b X_a) F S_3) X_2))))))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa (tptp.hAPP _let_1 X_a (tptp.hAPP X_a _let_2 (tptp.hAPP (tptp.fun X_a (tptp.fun X_b X_a)) (tptp.fun X_a _let_2) (tptp.foldl X_a X_b) F) S_2) Xs_1)))))))) (forall ((X_a $$unsorted) (Pa $$unsorted) (Xs_1 $$unsorted)) (=> (exists ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) (tptp.hAPP (tptp.list X_a) _let_1 (tptp.set X_a) Xs_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa X_2))))) (not (forall ((Ys $$unsorted) (X_2 $$unsorted)) (=> (exists ((Zs_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (= Xs_1 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.append X_a) Ys) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_2 (tptp.cons X_a) X_2) Zs_2)))))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa X_2)) (not (forall ((Xa $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) Xa) (tptp.hAPP (tptp.list X_a) _let_1 (tptp.set X_a) Ys))) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa Xa))))))))))))) (forall ((X_a $$unsorted) (Pa $$unsorted) (Xs_1 $$unsorted)) (= (exists ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) (tptp.hAPP (tptp.list X_a) _let_1 (tptp.set X_a) Xs_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa X_2))))) (exists ((Ys $$unsorted) (X_2 $$unsorted) (Zs_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (and (= Xs_1 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.append X_a) Ys) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_2 (tptp.cons X_a) X_2) Zs_2))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa X_2)) (forall ((Xa $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) Xa) (tptp.hAPP (tptp.list X_a) _let_1 (tptp.set X_a) Zs_2))) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa Xa)))))))))))) (forall ((X_a $$unsorted) (Pa $$unsorted) (Xs_1 $$unsorted)) (= (exists ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) (tptp.hAPP (tptp.list X_a) _let_1 (tptp.set X_a) Xs_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa X_2))))) (exists ((Ys $$unsorted) (X_2 $$unsorted)) (and (exists ((Zs_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (= Xs_1 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.append X_a) Ys) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_2 (tptp.cons X_a) X_2) Zs_2)))))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa X_2)) (forall ((Xa $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) Xa) (tptp.hAPP (tptp.list X_a) _let_1 (tptp.set X_a) Ys))) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa Xa)))))))))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (Xs_1 $$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.hAPP (tptp.list X_a) _let_1 (tptp.set X_a) Xs_1))) (exists ((Ys $$unsorted) (Zs_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (= Xs_1 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.append X_a) Ys) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_2 (tptp.cons X_a) X_1) Zs_2))))))))) (forall ((X_a $$unsorted) (Pa $$unsorted) (Xs_1 $$unsorted)) (=> (exists ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) (tptp.hAPP (tptp.list X_a) _let_1 (tptp.set X_a) Xs_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa X_2))))) (not (forall ((Ys $$unsorted) (X_2 $$unsorted) (Zs_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (=> (= Xs_1 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.append X_a) Ys) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_2 (tptp.cons X_a) X_2) Zs_2))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa X_2)) (not (forall ((Xa $$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) (tptp.hAPP (tptp.list X_a) _let_1 (tptp.set X_a) Zs_2))) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa Xa))))))))))))))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_1) (tptp.hAPP (tptp.list X_a) _let_1 (tptp.set X_a) Xs_1))) (exists ((Ys $$unsorted) (Zs_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (and (= Xs_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_3 (tptp.append X_a) Ys) (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_a _let_3 (tptp.cons X_a) X_1) Zs_2))) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_1) (tptp.hAPP _let_2 _let_1 (tptp.set X_a) Ys)))))))))))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (Xs_1 $$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.hAPP (tptp.list X_a) _let_1 (tptp.set X_a) Xs_1))) (exists ((Ys $$unsorted) (Zs_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (and (= Xs_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_3 (tptp.append X_a) Ys) (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_a _let_3 (tptp.cons X_a) X_1) Zs_2))) (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) (tptp.hAPP _let_2 _let_1 (tptp.set X_a) Zs_2)))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (S_2 $$unsorted) (Xs_1 $$unsorted) (X_1 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun X_a X_b))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun _let_2 X_b))) (let ((_let_4 (tptp.hAPP (tptp.fun X_b _let_1) (tptp.fun X_b _let_3) (tptp.foldl X_b X_a) F))) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted) (S_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_b))) (let ((_let_2 (tptp.hAPP X_b _let_1 F S_3))) (= (tptp.hAPP X_a X_b (tptp.hAPP X_b _let_1 F (tptp.hAPP X_a X_b _let_2 X_2)) Y_2) (tptp.hAPP X_a X_b (tptp.hAPP X_b _let_1 F (tptp.hAPP X_a X_b _let_2 Y_2)) X_2))))) (= (tptp.hAPP X_a X_b (tptp.hAPP X_b _let_1 F (tptp.hAPP _let_2 X_b (tptp.hAPP X_b _let_3 _let_4 S_2) Xs_1)) X_1) (tptp.hAPP _let_2 X_b (tptp.hAPP X_b _let_3 _let_4 (tptp.hAPP X_a X_b (tptp.hAPP X_b _let_1 F S_2) X_1)) Xs_1)))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F $$unsorted) (Pa $$unsorted) (Xs_1 $$unsorted) (Q_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.list X_b))) (let ((_let_2 (tptp.fun _let_1 X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool Q_1 X_1)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_2) (tptp.hAPP (tptp.list X_b) _let_1 (tptp.set X_b) Xs_1))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa X_2))))) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (=> (and (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa X_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool Q_1 Y_2))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool Q_1 (tptp.hAPP X_b X_a (tptp.hAPP X_a (tptp.fun X_b X_a) F Y_2) X_2))))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool Q_1 (tptp.hAPP _let_1 X_a (tptp.hAPP X_a _let_2 (tptp.hAPP (tptp.fun X_a (tptp.fun X_b X_a)) (tptp.fun X_a _let_2) (tptp.foldl X_a X_b) F) X_1) Xs_1))))))))) (forall ((X_a $$unsorted) (N $$unsorted) (X_1 $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.take X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (let ((_let_4 (tptp.fun _let_2 _let_2))) (let ((_let_5 (tptp.hAPP X_a _let_4 (tptp.cons X_a) X_1))) (let ((_let_6 (tptp.fun _let_3 _let_3))) (= (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.nat _let_4 _let_1 N) (tptp.hAPP _let_2 _let_2 _let_5 Xs_1)) (tptp.hAPP tptp.nat _let_2 (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_2 _let_6 (tptp.nat_case _let_2) (tptp.nil X_a)) (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_4 _let_6 (tptp.combb _let_2 _let_2 tptp.nat) _let_5) (tptp.hAPP _let_2 _let_3 (tptp.hAPP (tptp.fun tptp.nat _let_4) (tptp.fun _let_2 _let_3) (tptp.combc tptp.nat _let_2 _let_2) _let_1) Xs_1))) N))))))))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (N $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.set X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.list X_a))) (let ((_let_4 (tptp.hAPP X_a (tptp.fun _let_2 tptp.bool) (tptp.member X_a) X_1))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_4 (tptp.hAPP _let_3 _let_2 _let_1 (tptp.hAPP _let_3 _let_3 (tptp.hAPP tptp.nat (tptp.fun _let_3 _let_3) (tptp.take X_a) N) Xs_1)))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_4 (tptp.hAPP _let_3 _let_2 _let_1 Xs_1))))))))) (forall ((X_a $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.nil X_a))) (let ((_let_2 (tptp.list X_a))) (= (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.nat (tptp.fun _let_2 _let_2) (tptp.take X_a) N_1) _let_1) _let_1)))) (forall ((X_a $$unsorted) (I_1 $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.distinct X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 Xs)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.nat (tptp.fun _let_1 _let_1) (tptp.take X_a) I_1) Xs))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((N_1 $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.linorder_sorted X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 Xs)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.nat (tptp.fun _let_1 _let_1) (tptp.take X_a) N_1) Xs))))))))) (forall ((X_a $$unsorted) (N_1 $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.append X_a) (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.nat _let_2 (tptp.take X_a) N_1) Xs)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.nat _let_2 (tptp.drop X_a) N_1) Xs)) Xs)))) (forall ((X_a $$unsorted) (Pa $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_a tptp.bool) _let_2 (tptp.takeWhile X_a) Pa) Xs_1))) (= _let_3 (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.nat _let_2 (tptp.take X_a) (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) _let_3)) Xs_1)))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (Ys_1 $$unsorted) (Zs $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) Xs_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (= (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 (tptp.append X_a) Xs_1) Ys_1) Zs) (and (= Xs_1 (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.nat _let_3 (tptp.take X_a) _let_2) Zs)) (= Ys_1 (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.nat _let_3 (tptp.drop X_a) _let_2) Zs)))))))) (forall ((X_a $$unsorted) (N_1 $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.take X_a))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (=> (not (= Xs (tptp.nil X_a))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1)) Xs) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_3 (tptp.cons X_a) (tptp.hAPP _let_1 X_a (tptp.hd X_a) Xs)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.nat _let_3 _let_2 N_1) (tptp.hAPP _let_1 _let_1 (tptp.tl X_a) Xs))))))))) (forall ((X_a $$unsorted) (Xs $$unsorted) (Ys_2 $$unsorted)) (=> (forall ((I $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.hAPP tptp.nat (tptp.fun _let_1 _let_1) (tptp.take X_a) I))) (= (tptp.hAPP _let_1 _let_1 _let_2 Xs) (tptp.hAPP _let_1 _let_1 _let_2 Ys_2))))) (= Xs Ys_2))) (forall ((X_a $$unsorted) (Xs_1_1 $$unsorted) (Xs_2_1 $$unsorted) (Ys_1_1 $$unsorted) (Ys_2_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.size_size _let_1))) (let ((_let_3 (tptp.hAPP _let_1 tptp.nat _let_2 Ys_1_1))) (let ((_let_4 (tptp.drop X_a))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (let ((_let_6 (tptp.append X_a))) (let ((_let_7 (tptp.take X_a))) (let ((_let_8 (tptp.hAPP _let_1 tptp.nat _let_2 Xs_1_1))) (let ((_let_9 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) _let_8) _let_3)))) (= (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_5 _let_6 Xs_1_1) Xs_2_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_5 _let_6 Ys_1_1) Ys_2_1)) (and (=> _let_9 (and (= Xs_1_1 (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.nat _let_5 _let_7 _let_8) Ys_1_1)) (= Xs_2_1 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_5 _let_6 (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.nat _let_5 _let_4 _let_8) Ys_1_1)) Ys_2_1)))) (=> (not _let_9) (and (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.nat _let_5 _let_7 _let_3) Xs_1_1) Ys_1_1) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_5 _let_6 (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.nat _let_5 _let_4 _let_3) Xs_1_1)) Xs_2_1) Ys_2_1))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((X $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X) X))))) (forall ((X_a $$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 $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$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)) (=> (tptp.order X_a) (forall ((X_1 $$unsorted) (Y_1 $$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_1)) (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X_1) Y_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y_1) 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) (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 $$unsorted)) (=> (tptp.order X_a) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y_1) X_1)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X_1) Y_1)) (= (tptp.ti X_a X_1) (tptp.ti X_a Y_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ord X_a) (forall ((C_1 $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (= A_2 B_1) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B_1) C_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_2) C_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((C_1 $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) C_1))) (=> (= (tptp.ti X_a A_2) (tptp.ti X_a B_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_2)))))))) (forall ((X_a $$unsorted)) (=> (tptp.ord X_a) (forall ((C_1 $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) A_2))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B_1)) (=> (= B_1 C_1) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 C_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((C_1 $$unsorted) (B_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B_1) A_2)) (=> (= (tptp.ti X_a B_1) (tptp.ti X_a C_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 C_1) A_2))))))))) (forall ((X_a $$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 $$unsorted)) (=> (tptp.preorder X_a) (forall ((Z $$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)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 Z)))))))))) (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.order X_a) (forall ((Z $$unsorted) (Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 Z))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 X)))))))))) (forall ((X_a $$unsorted) (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 $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$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)) (=> (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)) (=> (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 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) A_2) (tptp.top_top X_a)))))) (forall ((X_a $$unsorted) (X $$unsorted) (Xs $$unsorted) (Ys_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.size_size _let_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP _let_1 tptp.nat _let_2 Xs)) (tptp.hAPP _let_1 tptp.nat _let_2 Ys_2))) (not (= Xs (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.cons X_a) X) Ys_2))))))) (forall ((X_a $$unsorted) (N_1 $$unsorted) (X $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.take X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (let ((_let_4 (tptp.hAPP X_a _let_3 (tptp.cons X_a) X))) (= (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1)) (tptp.hAPP _let_2 _let_2 _let_4 Xs)) (tptp.hAPP _let_2 _let_2 _let_4 (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 N_1) Xs)))))))) (forall ((X_a $$unsorted) (N_1 $$unsorted) (X $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.drop X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (= (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1)) (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_a _let_3 (tptp.cons X_a) X) Xs)) (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 N_1) Xs)))))) (forall ((X_a $$unsorted) (N_1 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.replicate X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun X_a _let_2))) (= (tptp.hAPP X_a _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1)) X) (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_a (tptp.fun _let_2 _let_2) (tptp.cons X_a) X) (tptp.hAPP X_a _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 N_1) X))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((Zs_1 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cons X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (let ((_let_4 (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_a _let_3 _let_1 Y) Zs_1))) (let ((_let_5 (tptp.linorder_sorted 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) X) Y)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_5 _let_4)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_5 (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_a _let_3 _let_1 X) _let_4))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (Zs $$unsorted)) (let ((_let_1 (tptp.cons X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (let ((_let_4 (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_a _let_3 _let_1 Y_1) Zs))) (let ((_let_5 (tptp.linorder_sorted X_a))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_5 (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_a _let_3 _let_1 X_1) _let_4))) (and (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_1) Y_1)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_5 _let_4)))))))))))) (forall ((X_a $$unsorted) (Xs $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) Xs)) N_1)) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.nat (tptp.fun _let_1 _let_1) (tptp.take X_a) N_1) Xs) Xs)))) (forall ((X_a $$unsorted) (Pa $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.size_size _let_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_1 tptp.nat _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_a tptp.bool) (tptp.fun _let_1 _let_1) (tptp.takeWhile X_a) Pa) Xs_1))) (tptp.hAPP _let_1 tptp.nat _let_2 Xs_1)))))) (forall ((X_a $$unsorted) (N_1 $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.take X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (let ((_let_4 (tptp.tl X_a))) (= (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 N_1) (tptp.hAPP _let_2 _let_2 _let_4 Xs)) (tptp.hAPP _let_2 _let_2 _let_4 (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1)) Xs)))))))) (forall ((X_a $$unsorted) (Pa $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.size_size _let_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_1 tptp.nat _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_a tptp.bool) (tptp.fun _let_1 _let_1) (tptp.dropWhile X_a) Pa) Xs_1))) (tptp.hAPP _let_1 tptp.nat _let_2 Xs_1)))))) (forall ((X_a $$unsorted) (N_1 $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.drop X_a))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1)) Xs) (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.nat _let_3 _let_2 N_1) (tptp.hAPP _let_1 _let_1 (tptp.tl X_a) Xs))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X_1 $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.linorder_sorted X_a))) (let ((_let_2 (tptp.list X_a))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_a (tptp.fun _let_2 _let_2) (tptp.cons X_a) X_1) Xs_1))) (and (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 Xs_1)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) (tptp.hAPP (tptp.list X_a) _let_1 (tptp.set X_a) Xs_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) X_1) X_2)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((Xs_1 $$unsorted) (Ys_1 $$unsorted)) (let ((_let_1 (tptp.linorder_sorted X_a))) (let ((_let_2 (tptp.list X_a))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 (tptp.fun _let_2 _let_2) (tptp.append X_a) Xs_1) Ys_1))) (and (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 Xs_1)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 Ys_1)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) (tptp.hAPP (tptp.list X_a) _let_1 (tptp.set X_a) Xs_1))) (forall ((Xa $$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) (tptp.hAPP (tptp.list X_a) _let_1 (tptp.set X_a) Ys_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) X_2) Xa))))))))))))))) (forall ((X_a $$unsorted) (N $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (= (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.nat (tptp.fun _let_1 _let_1) (tptp.drop X_a) N) Xs_1) (tptp.nil X_a)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) Xs_1)) N))))) (forall ((X_a $$unsorted) (Xs $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (=> (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 (tptp.size_size _let_1) Xs)) N_1)) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.nat (tptp.fun _let_1 _let_1) (tptp.drop X_a) N_1) Xs) (tptp.nil X_a))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((Aa $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.list X_a) tptp.bool (tptp.linorder_sorted X_a) Aa)) (or (= Aa (tptp.nil X_a)) (exists ((Xs_2 $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (and (= Aa (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.cons X_a) X_2) Xs_2)) (forall ((Xa $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) Xa) (tptp.hAPP (tptp.list X_a) _let_1 (tptp.set X_a) Xs_2))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) X_2) Xa))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.linorder_sorted X_a) Xs_2)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X_1 $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.linorder_sorted X_a))) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) (tptp.hAPP (tptp.list X_a) _let_1 (tptp.set X_a) Xs_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) X_1) X_2))))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 Xs_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.cons X_a) X_1) Xs_1)))))))))) (forall ((X_a $$unsorted) (N $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (= (= (tptp.hAPP tptp.nat tptp.nat tptp.suc N) (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) Xs_1)) (exists ((Y_2 $$unsorted) (Ys $$unsorted)) (let ((_let_1 (tptp.list X_a))) (and (= Xs_1 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.cons X_a) Y_2) Ys)) (= (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) Ys) N))))))) (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) (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_b $$unsorted) (X_a $$unsorted) (B $$unsorted) (A_3 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.pi X_a X_b))) (let ((_let_2 (tptp.fun (tptp.fun X_a X_b) tptp.bool))) (let ((_let_3 (tptp.fun X_a (tptp.fun X_b tptp.bool)))) (let ((_let_4 (tptp.fun _let_3 _let_2))) (let ((_let_5 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP _let_5 (tptp.fun _let_5 tptp.bool) (tptp.ord_less_eq _let_5) A_3) A_1)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) (tptp.hAPP _let_3 _let_2 (tptp.hAPP _let_5 _let_4 _let_1 A_1) B)) (tptp.hAPP _let_3 _let_2 (tptp.hAPP _let_5 _let_4 _let_1 A_3) B)))))))))) (forall ((X_a $$unsorted) (R_2 $$unsorted) (S_2 $$unsorted)) (let ((_let_1 (tptp.listrel1 X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun (tptp.product_prod _let_2 _let_2) tptp.bool))) (let ((_let_4 (tptp.fun (tptp.product_prod X_a X_a) tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP _let_4 (tptp.fun _let_4 tptp.bool) (tptp.ord_less_eq _let_4) R_2) S_2)) (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_4 _let_3 _let_1 R_2)) (tptp.hAPP _let_4 _let_3 _let_1 S_2))))))))) (forall ((X_a $$unsorted) (R_2 $$unsorted) (S_2 $$unsorted)) (let ((_let_1 (tptp.listrel X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun (tptp.product_prod _let_2 _let_2) tptp.bool))) (let ((_let_4 (tptp.fun (tptp.product_prod X_a X_a) tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP _let_4 (tptp.fun _let_4 tptp.bool) (tptp.ord_less_eq _let_4) R_2) S_2)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_3 (tptp.fun _let_3 tptp.bool) (tptp.ord_less_eq _let_3) (tptp.hAPP _let_4 _let_3 _let_1 R_2)) (tptp.hAPP _let_4 _let_3 _let_1 S_2))))))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.set X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (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_2 Xs_1)) (tptp.hAPP _let_1 _let_3 _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.cons X_a) X_1) Xs_1)))))))) (forall ((X_a $$unsorted) (N $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.set X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.list X_a))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) (tptp.hAPP _let_3 _let_2 _let_1 (tptp.hAPP _let_3 _let_3 (tptp.hAPP tptp.nat (tptp.fun _let_3 _let_3) (tptp.take X_a) N) Xs_1))) (tptp.hAPP _let_3 _let_2 _let_1 Xs_1))))))) (forall ((X_a $$unsorted) (N $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.set X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.list X_a))) (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 _let_1 (tptp.hAPP _let_3 _let_3 (tptp.hAPP tptp.nat (tptp.fun _let_3 _let_3) (tptp.drop X_a) N) Xs_1))) (tptp.hAPP _let_3 _let_2 _let_1 Xs_1))))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.take X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (let ((_let_4 (tptp.set X_a))) (let ((_let_5 (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_eq tptp.nat) M) N)) (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP _let_5 (tptp.fun _let_5 tptp.bool) (tptp.ord_less_eq _let_5) (tptp.hAPP _let_2 _let_5 _let_4 (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 M) Xs_1))) (tptp.hAPP _let_2 _let_5 _let_4 (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 N) Xs_1))))))))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.drop X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (let ((_let_4 (tptp.set X_a))) (let ((_let_5 (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_eq tptp.nat) N) M)) (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP _let_5 (tptp.fun _let_5 tptp.bool) (tptp.ord_less_eq _let_5) (tptp.hAPP _let_2 _let_5 _let_4 (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 M) Xs_1))) (tptp.hAPP _let_2 _let_5 _let_4 (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 N) Xs_1))))))))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.list X_a))) (= (= (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) Xs_1) (tptp.hAPP tptp.nat tptp.nat tptp.suc N)) (exists ((Y_2 $$unsorted) (Ys $$unsorted)) (let ((_let_1 (tptp.list X_a))) (and (= Xs_1 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.cons X_a) Y_2) Ys)) (= (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) Ys) N))))))) (forall ((X_a $$unsorted) (Ca $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 (tptp.member X_a) Ca))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_1) B)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 A_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 B)))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (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 _let_2 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 B) A_1)) (= (tptp.ti _let_1 A_1) (tptp.ti _let_1 B)))))))) (forall ((X_a $$unsorted) (R_1 $$unsorted) (S_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.ord_less_eq _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.hAPP (tptp.fun X_a _let_3) (tptp.fun _let_1 _let_1) (tptp.combc X_a _let_1 tptp.bool) (tptp.member X_a)))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 (tptp.hAPP _let_1 _let_1 _let_4 R_1)) (tptp.hAPP _let_1 _let_1 _let_4 S_1))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 R_1) S_1)))))))) (forall ((X_a $$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) (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_b $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted) (Pa $$unsorted) (Q_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a _let_1))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) Pa) Q_1)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_a _let_1 Pa X_1) Y_1)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_a _let_1 Q_1 X_1) Y_1))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (Q_1 $$unsorted) (Pa $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a _let_1))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_a _let_1 Pa X_1) Y_1)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) Pa) Q_1)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_a _let_1 Q_1 X_1) Y_1))))))) (forall ((X_a $$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) (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) (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) (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 $$unsorted) (X_1 $$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) (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 $$unsorted) (C $$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)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_4 C))))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.ord_less_eq _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (=> (= (tptp.ti _let_1 A_1) (tptp.ti _let_1 B)) (not (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 A_1) B)) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 B) A_1)))))))))) (forall ((X_b $$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_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_a _let_1 Pa X_2) Y_2)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_a _let_1 Q_1 X_2) Y_2))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) Pa) Q_1))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (B $$unsorted) (C $$unsorted) (A_1 $$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 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a (tptp.fun _let_2 tptp.bool) (tptp.member X_a) X_2) A_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) (tptp.hAPP X_a _let_1 B X_2)) (tptp.hAPP X_a _let_1 C X_2))))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) (tptp.hAPP _let_2 _let_1 _let_3 B)) (tptp.hAPP _let_2 _let_1 _let_3 C)))))))) (forall ((X_a $$unsorted) (B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B)))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) A_1) B))))) (forall ((X_a $$unsorted) (N_1 $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.take X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun _let_2 _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) N_1) (tptp.hAPP _let_2 tptp.nat (tptp.size_size _let_2) Xs))) (= (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_3 (tptp.append X_a) (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 N_1) Xs)) (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_a _let_3 (tptp.cons X_a) (tptp.hAPP _let_2 X_a (tptp.hd X_a) (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.nat _let_3 (tptp.drop X_a) N_1) Xs))) (tptp.nil X_a))) (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1)) Xs))))))) (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 $$unsorted)) (=> (tptp.linorder X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (= (not (= (tptp.ti X_a X_1) (tptp.ti X_a Y_1))) (or (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X_1) Y_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y_1) X_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X_1 $$unsorted) (Y_1 $$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 X_1) Y_1))) (or (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y_1) X_1)) (= (tptp.ti X_a X_1) (tptp.ti X_a Y_1))))))))) (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 ((Y_1 $$unsorted) (X_1 $$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_1) X_1))) (= (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X_1) Y_1))) (= (tptp.ti X_a X_1) (tptp.ti X_a Y_1))))))))) (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.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.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 $$unsorted)) (=> (tptp.preorder X_a) (forall ((Pa $$unsorted) (X_1 $$unsorted) (Y_1 $$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 X_1) Y_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y_1) X_1)) (tptp.hBOOL Pa)))))))) (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.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 $$unsorted)) (=> (tptp.ord X_a) (forall ((C_1 $$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_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_2) C_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((C_1 $$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_1))) (=> (= (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 $$unsorted)) (=> (tptp.ord X_a) (forall ((C_1 $$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_1) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 C_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((C_1 $$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_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 C_1) A_2))))))))) (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((Z $$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)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 Z)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((Z $$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))) (=> (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 $$unsorted)) (=> (tptp.preorder X_a) (forall ((X $$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.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 $$unsorted)) (=> (tptp.top X_a) (forall ((Aa $$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))))))) (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 $$unsorted)) (=> (tptp.order X_a) (forall ((Z $$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))) (=> (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 $$unsorted)) (=> (tptp.preorder X_a) (forall ((Z $$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)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X) Z))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((Z $$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) Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Z) X))))))))) (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((Z $$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)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_2 Z))))))))) (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.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 $$unsorted)) (=> (tptp.order X_a) (forall ((X $$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.linorder X_a) (forall ((X_1 $$unsorted) (Y_1 $$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) X_1) Y_1)) (= (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) X_1) Y_1))) (= (tptp.ti X_a X_1) (tptp.ti X_a Y_1)))))))) (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 ((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 $$unsorted)) (=> (tptp.order X_a) (forall ((A_2 $$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.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 $$unsorted)) (=> (tptp.linorder X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) X_1) Y_1))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) X_1) Y_1)) (= (tptp.ti X_a X_1) (tptp.ti X_a Y_1)))))))) (forall ((X_a $$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 $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$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.order X_a) (forall ((X_1 $$unsorted) (Y_1 $$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) X_1) Y_1)) (or (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) X_1) Y_1)) (= (tptp.ti X_a X_1) (tptp.ti X_a Y_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less X_a) X_1) Y_1)) (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X_1) Y_1)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y_1) X_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((X_1 $$unsorted) (Y_1 $$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 X_a) X_1) Y_1)) (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) X_1) Y_1)) (not (= (tptp.ti X_a X_1) (tptp.ti X_a Y_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.linorder X_a) (forall ((X_1 $$unsorted) (Y_1 $$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_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) Y_1) X_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (= (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) X_1) Y_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) Y_1) X_1))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) X) Y)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) X) Y))))) (forall ((X_a $$unsorted) (N_1 $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.hAPP tptp.nat (tptp.fun _let_1 _let_1) (tptp.take X_a) N_1))) (=> (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 _let_1 tptp.nat (tptp.size_size _let_1) Xs))) (= (tptp.hAPP _let_1 _let_1 _let_2 (tptp.hAPP _let_1 _let_1 (tptp.butlast X_a) Xs)) (tptp.hAPP _let_1 _let_1 _let_2 Xs)))))) (forall ((X_a $$unsorted) (N_1 $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.last X_a))) (let ((_let_2 (tptp.list X_a))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N_1) (tptp.hAPP _let_2 tptp.nat (tptp.size_size _let_2) Xs))) (= (tptp.hAPP _let_2 X_a _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.nat (tptp.fun _let_2 _let_2) (tptp.drop X_a) N_1) Xs)) (tptp.hAPP _let_2 X_a _let_1 Xs)))))) (forall ((N_1 $$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_1 $$unsorted) (N_1 $$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_1) 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_1)) (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1))))))) (forall ((X_a $$unsorted) (C $$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)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 A_1) C)))))))) (forall ((X_a $$unsorted) (C $$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)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 C)))))))) (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) (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 $$unsorted) (X_b $$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_a $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less _let_1) A_1) B)) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_1) B)) (not (= (tptp.ti _let_1 A_1) (tptp.ti _let_1 B)))))))) (forall ((N_1 $$unsorted)) (not (= N_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1)))) (forall ((N_1 $$unsorted)) (not (= (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1) N_1))) (forall ((Nat $$unsorted) (Nat_1 $$unsorted)) (= (= (tptp.hAPP tptp.nat tptp.nat tptp.suc Nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc Nat_1)) (= Nat Nat_1))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (= (tptp.hAPP tptp.nat tptp.nat tptp.suc X) (tptp.hAPP tptp.nat tptp.nat tptp.suc Y)) (= X Y))) (forall ((N_1 $$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 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (not (= M N)) (or (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 N) M))))))) (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_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N_1) M_1)) (not (= M_1 N_1)))) (forall ((S $$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 $$unsorted) (N $$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 N) M)))) (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) N)) _let_2) (=> (=> (= M N) _let_2) (=> (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 _let_3 N) M)) _let_2) _let_2))))))) (forall ((N_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N_1) N_1))) (forall ((M_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M_1) N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 N_1) M_1)))))) (forall ((M_1 $$unsorted) (N_1 $$unsorted)) (=> (= M_1 N_1) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M_1) N_1)))) (forall ((K $$unsorted) (I_1 $$unsorted) (J $$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_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 J)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 J) K)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 K)))))))) (forall ((M_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 M_1) N_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 N_1) M_1)) (= M_1 N_1)))))) (forall ((M_1 $$unsorted) (N_1 $$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_1)) (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_1) N_1)))))) (forall ((M_1 $$unsorted) (N_1 $$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_1)) N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M_1) N_1)))))) (forall ((M_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M_1))) (=> (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_1 N_1))))) (forall ((K $$unsorted) (I_1 $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 I_1) J)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 J) K)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc I_1)) K))))))) (forall ((M_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M_1))) (let ((_let_2 (tptp.ord_less tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 M_1) N_1)) (=> (not (= _let_1 N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 _let_1) N_1)))))))) (forall ((M_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1)))))) (forall ((N_1 $$unsorted) (M_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N_1))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 M_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M_1))) (= M_1 N_1))))) (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 M))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M))) (= N M))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M)) (tptp.hAPP tptp.nat tptp.nat tptp.suc N))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) N)))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N))) (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 N)) (= M N))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) N))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 N) (tptp.hAPP tptp.nat tptp.nat tptp.suc M))))))) (forall ((N_1 $$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 $$unsorted) (N $$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) N))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N)) M)))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N))) (let ((_let_2 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 _let_1)) (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 N)) (= M _let_1)))))) (forall ((N $$unsorted) (M $$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 N)) (tptp.hAPP tptp.nat tptp.nat tptp.suc M))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 N) M)))))) (forall ((M_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M_1))) (=> (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_1 $$unsorted) (N_1 $$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_1))) (=> (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_1 _let_1)))))) (forall ((M_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.suc M_1)) N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M_1) N_1)))))) (forall ((M_1 $$unsorted) (N_1 $$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_1) N_1)) (= M_1 N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) M_1) N_1))))) (forall ((M_1 $$unsorted) (N_1 $$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_1) N_1)) (=> (not (= M_1 N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) M_1) N_1)))))) (forall ((M_1 $$unsorted) (N_1 $$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_1) N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) M_1) N_1))))) (forall ((M $$unsorted) (N $$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) N)) (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) M) N)) (= M N))))) (forall ((M $$unsorted) (N $$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) N)) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) M) N)) (not (= M N)))))) (forall ((X_a $$unsorted) (F1 $$unsorted) (F2 $$unsorted) (Nat $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat X_a))) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.nat_case X_a) F1) F2) (tptp.hAPP tptp.nat tptp.nat tptp.suc Nat)) (tptp.hAPP tptp.nat X_a F2 Nat)))) (forall ((M_1 $$unsorted) (N_1 $$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_1)) N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) M_1) N_1))))) (forall ((M $$unsorted) (N $$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) N)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) N) (tptp.hAPP tptp.nat tptp.nat tptp.suc M))) (= N M))))) (forall ((M_1 $$unsorted) (N_1 $$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_1) 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_1)) N_1))))) (forall ((M_1 $$unsorted) (N_1 $$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_1) N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) M_1) (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1)))))) (forall ((M $$unsorted) (N $$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)) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) M) N))))) (forall ((M $$unsorted) (N $$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) (tptp.hAPP tptp.nat tptp.nat tptp.suc N))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) M) N))))) (forall ((N $$unsorted) (M $$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) N) M)) (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 N)) M))))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (and (tptp.enum T_1) (tptp.enum T_2)) (tptp.enum (tptp.product_prod T_2 T_1)))) (tptp.enum tptp.bool) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (and (tptp.enum T_1) (tptp.enum T_2)) (tptp.enum (tptp.fun T_2 T_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)) (=> (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)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (and (tptp.cl_HOL_Oequal T_1) (tptp.enum T_2)) (tptp.cl_HOL_Oequal (tptp.fun T_2 T_1)))) (tptp.preorder tptp.nat) (tptp.linorder tptp.nat) (tptp.order tptp.nat) (tptp.ord tptp.nat) (tptp.cl_HOL_Oequal tptp.nat) (tptp.preorder tptp.bool) (tptp.order tptp.bool) (tptp.top tptp.bool) (tptp.ord tptp.bool) (tptp.cl_HOL_Oequal tptp.bool) (forall ((T_1 $$unsorted)) (tptp.cl_HOL_Oequal (tptp.list T_1))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (tptp.cl_HOL_Oequal (tptp.product_prod T_2 T_1))) (forall ((T $$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 $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fconj P) Q))) (tptp.hBOOL Q))) (forall ((X_a $$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_2 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 95.50/96.08  )
% 95.50/96.08  % SZS output end Proof for SCT170+6
% 95.50/96.08  % cvc5---1.0.5 exiting
% 95.50/96.08  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------