TSTP Solution File: SCT170+7 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SCT170+7 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n027.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 167.82s 168.08s
% Output : Proof 167.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.35 % Problem : SCT170+7 : TPTP v8.1.2. Released v5.3.0.
% 0.09/0.36 % Command : do_cvc5 %s %d
% 0.34/0.55 % Computer : n027.cluster.edu
% 0.34/0.55 % Model : x86_64 x86_64
% 0.34/0.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.34/0.55 % Memory : 8042.1875MB
% 0.34/0.55 % OS : Linux 3.10.0-693.el7.x86_64
% 0.34/0.55 % CPULimit : 300
% 0.34/0.55 % WCLimit : 300
% 0.34/0.55 % DateTime : Thu Aug 24 17:12:03 EDT 2023
% 0.34/0.55 % CPUTime :
% 0.38/0.79 %----Proving TF0_NAR, FOF, or CNF
% 167.82/168.08 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.D9iIQJuXOq/cvc5---1.0.5_3339.p...
% 167.82/168.08 ------- get file name : TPTP file name is SCT170+7
% 167.82/168.08 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_3339.smt2...
% 167.82/168.08 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 167.82/168.08 --- Run --no-e-matching --full-saturate-quant at 5...
% 167.82/168.08 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 167.82/168.08 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 167.82/168.08 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 167.82/168.08 --- Run --trigger-sel=max --full-saturate-quant at 5...
% 167.82/168.08 --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 167.82/168.08 --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 167.82/168.08 --- Run --prenex-quant=none --full-saturate-quant at 5...
% 167.82/168.08 --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 5...
% 167.82/168.08 --- Run --relevant-triggers --full-saturate-quant at 5...
% 167.82/168.08 --- Run --finite-model-find --e-matching --sort-inference --uf-ss-fair at 5...
% 167.82/168.08 --- Run --pre-skolem-quant=on --full-saturate-quant at 10...
% 167.82/168.08 --- Run --cbqi-vo-exp --full-saturate-quant at 10...
% 167.82/168.08 --- Run --no-cbqi --full-saturate-quant at 10...
% 167.82/168.08 --- Run --macros-quant --macros-quant-mode=all --full-saturate-quant...
% 167.82/168.08 % SZS status Theorem for SCT170+7
% 167.82/168.08 % SZS output start Proof for SCT170+7
% 167.82/168.08 (
% 167.82/168.08 (let ((_let_1 (forall ((I $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.arrow_2142409994le_alt tptp.arrow_2142409994le_alt))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.arrow_1998540521e_indi _let_2 tptp.p I))) (let ((_let_4 (tptp.fun tptp.arrow_2142409994le_alt _let_2))) (let ((_let_5 (tptp.hAPP tptp.arrow_2142409994le_alt (tptp.fun tptp.arrow_2142409994le_alt _let_1) (tptp.product_Pair tptp.arrow_2142409994le_alt tptp.arrow_2142409994le_alt) tptp.a))) (let ((_let_6 (tptp.member _let_1))) (let ((_let_7 (tptp.fun _let_2 tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 _let_7 _let_6 (tptp.hAPP tptp.arrow_2142409994le_alt _let_1 _let_5 tptp.b)) _let_3)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 _let_7 _let_6 (tptp.hAPP tptp.arrow_2142409994le_alt _let_1 _let_5 tptp.c)) (tptp.hAPP tptp.arrow_2142409994le_alt _let_2 (tptp.hAPP tptp.arrow_2142409994le_alt _let_4 (tptp.hAPP _let_2 (tptp.fun tptp.arrow_2142409994le_alt _let_4) tptp.arrow_1665824030_below _let_3) tptp.c) tptp.b)))))))))))))) (let ((_let_2 (not _let_1))) (let ((_let_3 (forall ((X_b $$unsorted) (X_a $$unsorted) (P $$unsorted) (Q $$unsorted)) (= (tptp.hAPP X_b X_a (tptp.hAPP X_a (tptp.fun X_b X_a) (tptp.combk X_a X_b) P) Q) (tptp.ti X_a P))))) (let ((_let_4 (tptp.zero_zero tptp.nat))) (let ((_let_5 (tptp.size_size tptp.nat))) (let ((_let_6 (forall ((X_a $$unsorted) (As $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.list X_a))) (=> (not (= As (tptp.nil X_a))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) (tptp.hAPP _let_2 X_a (tptp.last X_a) As)) (tptp.hAPP _let_2 _let_1 (tptp.set X_a) As))))))))) (let ((_let_7 (forall ((X_a $$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_8 (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted)) (= (tptp.produc1605651328_split X_a X_b X_c) (tptp.product_prod_case X_a X_b X_c))))) (let ((_let_9 (tptp.fun tptp.arrow_2142409994le_alt tptp.bool))) (let ((_let_10 (tptp.order_215145569der_on tptp.arrow_2142409994le_alt))) (let ((_let_11 (tptp.product_prod tptp.arrow_2142409994le_alt tptp.arrow_2142409994le_alt))) (let ((_let_12 (tptp.fun _let_11 tptp.bool))) (let ((_let_13 (tptp.fun _let_12 tptp.bool))) (let ((_let_14 (tptp.hAPP _let_13 _let_13 (tptp.collect _let_12) (tptp.hAPP _let_9 _let_13 _let_10 (tptp.top_top _let_9))))) (let ((_let_15 (= tptp.arrow_1568854078le_Lin _let_14))) (let ((_let_16 (forall ((X_a $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_1) (tptp.top_top _let_1))))))) (let ((_let_17 (forall ((X_a $$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))))))))))) (let ((_let_18 (tptp.combk _let_13 tptp.arrow_1998540521e_indi))) (let ((_let_19 (tptp.fun tptp.arrow_1998540521e_indi _let_13))) (let ((_let_20 (tptp.fun tptp.arrow_1998540521e_indi tptp.bool))) (let ((_let_21 (tptp.top_top _let_20))) (let ((_let_22 (tptp.fun tptp.arrow_1998540521e_indi _let_12))) (let ((_let_23 (tptp.fun _let_22 tptp.bool))) (let ((_let_24 (tptp.hAPP _let_20 (tptp.fun _let_19 _let_23) (tptp.pi tptp.arrow_1998540521e_indi _let_12) _let_21))) (let ((_let_25 (= tptp.arrow_301600364e_Prof (tptp.hAPP _let_19 _let_23 _let_24 (tptp.hAPP _let_13 _let_19 _let_18 tptp.arrow_1568854078le_Lin))))) (let ((_let_26 (forall ((X_a $$unsorted) (X_b $$unsorted) (X_1 $$unsorted) (F $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun X_a X_b))) (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_2) B_1))) (=> (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_1 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_2))))))))))))) (let ((_let_27 (forall ((X_a $$unsorted) (Aa $$unsorted) (List $$unsorted) (A_3 $$unsorted) (List_3 $$unsorted)) (let ((_let_1 (tptp.cons X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (= (= (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_a _let_3 _let_1 Aa) List) (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_a _let_3 _let_1 A_3) List_3)) (and (= (tptp.ti X_a Aa) (tptp.ti X_a A_3)) (= List List_3))))))))) (let ((_let_28 (forall ((X_a $$unsorted) (A_6 $$unsorted) (List_4 $$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_4))))))) (let ((_let_29 (tptp.fun _let_22 _let_13))) (let ((_let_30 (tptp.fun _let_22 _let_12))) (let ((_let_31 (tptp.fun _let_30 tptp.bool))) (let ((_let_32 (tptp.member _let_22))) (let ((_let_33 (tptp.fun _let_23 tptp.bool))) (let ((_let_34 (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (L_3 $$unsorted) (Aa $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.product_Pair tptp.arrow_2142409994le_alt tptp.arrow_2142409994le_alt))) (let ((_let_2 (tptp.product_prod tptp.arrow_2142409994le_alt tptp.arrow_2142409994le_alt))) (let ((_let_3 (tptp.fun tptp.arrow_2142409994le_alt _let_2))) (let ((_let_4 (tptp.hAPP tptp.arrow_2142409994le_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_2142409994le_alt _let_2 _let_4 Y_1)))) (let ((_let_9 (tptp.ti tptp.arrow_2142409994le_alt Aa))) (let ((_let_10 (tptp.ti tptp.arrow_2142409994le_alt X_1))) (let ((_let_11 (= _let_10 _let_9))) (let ((_let_12 (tptp.ti tptp.arrow_2142409994le_alt Ba))) (let ((_let_13 (tptp.ti tptp.arrow_2142409994le_alt Y_1))) (let ((_let_14 (= _let_13 _let_9))) (let ((_let_15 (tptp.fun tptp.arrow_2142409994le_alt _let_6))) (=> (not (= _let_9 _let_12)) (=> (tptp.hBOOL (tptp.hAPP _let_7 tptp.bool (tptp.hAPP _let_6 (tptp.fun _let_7 tptp.bool) (tptp.member _let_6) L_3) tptp.arrow_1568854078le_Lin)) (= (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool _let_8 (tptp.hAPP tptp.arrow_2142409994le_alt _let_6 (tptp.hAPP tptp.arrow_2142409994le_alt _let_15 (tptp.hAPP _let_6 (tptp.fun tptp.arrow_2142409994le_alt _let_15) tptp.arrow_1665824030_below L_3) Aa) Ba))) (and (not (= _let_10 _let_13)) (=> _let_14 (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP _let_2 _let_7 _let_5 (tptp.hAPP tptp.arrow_2142409994le_alt _let_2 _let_4 Ba)) L_3))) (=> (not _let_14) (and (=> _let_11 (or (= _let_13 _let_12) (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP _let_2 _let_7 _let_5 (tptp.hAPP tptp.arrow_2142409994le_alt _let_2 (tptp.hAPP tptp.arrow_2142409994le_alt _let_3 _let_1 Ba) Y_1)) L_3)))) (=> (not _let_11) (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool _let_8 L_3))))))))))))))))))))))))))) (let ((_let_35 (tptp.fun tptp.arrow_2142409994le_alt _let_12))) (let ((_let_36 (tptp.fun tptp.arrow_2142409994le_alt _let_35))) (let ((_let_37 (tptp.fun tptp.arrow_1998540521e_indi _let_36))) (let ((_let_38 (tptp.fun _let_12 _let_36))) (let ((_let_39 (tptp.hAPP _let_38 (tptp.fun _let_22 _let_37) (tptp.combb _let_12 _let_36 tptp.arrow_1998540521e_indi) tptp.arrow_1665824030_below))) (let ((_let_40 (tptp.combc tptp.arrow_1998540521e_indi tptp.arrow_2142409994le_alt _let_35))) (let ((_let_41 (tptp.fun tptp.arrow_1998540521e_indi _let_35))) (let ((_let_42 (tptp.fun tptp.arrow_2142409994le_alt _let_41))) (let ((_let_43 (tptp.combc tptp.arrow_1998540521e_indi tptp.arrow_2142409994le_alt _let_12))) (let ((_let_44 (tptp.fun tptp.arrow_2142409994le_alt _let_22))) (let ((_let_45 (tptp.hAPP tptp.arrow_2142409994le_alt _let_22 (tptp.hAPP _let_41 _let_44 _let_43 (tptp.hAPP tptp.arrow_2142409994le_alt _let_41 (tptp.hAPP _let_37 _let_42 _let_40 (tptp.hAPP _let_22 _let_37 _let_39 tptp.p)) tptp.c)) tptp.b))) (let ((_let_46 (tptp.hAPP tptp.arrow_2142409994le_alt _let_22 (tptp.hAPP _let_41 _let_44 _let_43 (tptp.hAPP tptp.arrow_2142409994le_alt _let_41 (tptp.hAPP _let_37 _let_42 _let_40 (tptp.hAPP _let_22 _let_37 _let_39 _let_45)) tptp.b)) tptp.a))) (let ((_let_47 (tptp.nil tptp.arrow_2142409994le_alt))) (let ((_let_48 (tptp.cons tptp.arrow_2142409994le_alt))) (let ((_let_49 (tptp.list tptp.arrow_2142409994le_alt))) (let ((_let_50 (tptp.fun _let_49 _let_49))) (let ((_let_51 (tptp.hAPP _let_49 _let_49 (tptp.hAPP tptp.arrow_2142409994le_alt _let_50 _let_48 tptp.c) _let_47))) (let ((_let_52 (tptp.hAPP tptp.arrow_2142409994le_alt _let_50 _let_48 tptp.b))) (let ((_let_53 (tptp.hAPP _let_49 _let_49 _let_52 _let_51))) (let ((_let_54 (tptp.hAPP tptp.arrow_2142409994le_alt _let_50 _let_48 tptp.a))) (let ((_let_55 (tptp.distinct tptp.arrow_2142409994le_alt))) (let ((_let_56 (tptp.hBOOL (tptp.hAPP _let_49 tptp.bool _let_55 (tptp.hAPP _let_49 _let_49 _let_54 _let_53))))) (let ((_let_57 (tptp.hAPP _let_22 _let_33 _let_32 tptp.p))) (let ((_let_58 (tptp.hBOOL (tptp.hAPP _let_23 tptp.bool _let_57 tptp.arrow_301600364e_Prof)))) (let ((_let_59 (tptp.ti tptp.arrow_2142409994le_alt tptp.c))) (let ((_let_60 (= _let_59 tptp.c))) (let ((_let_61 (tptp.ti tptp.arrow_2142409994le_alt tptp.b))) (let ((_let_62 (= _let_61 tptp.b))) (let ((_let_63 (tptp.ti tptp.arrow_2142409994le_alt tptp.a))) (let ((_let_64 (= _let_63 tptp.a))) (let ((_let_65 (tptp.fun tptp.bool tptp.bool))) (let ((_let_66 (tptp.fun tptp.bool _let_65))) (let ((_let_67 (tptp.fun tptp.nat tptp.nat))) (let ((_let_68 (tptp.fun _let_12 _let_35))) (let ((_let_69 (tptp.ti _let_13 tptp.arrow_1568854078le_Lin))) (let ((_let_70 (= _let_69 tptp.arrow_1568854078le_Lin))) (let ((_let_71 (tptp.hAPP tptp.arrow_1998540521e_indi _let_12 tptp.p SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_72 (tptp.hAPP tptp.arrow_2142409994le_alt (tptp.fun tptp.arrow_2142409994le_alt _let_11) (tptp.product_Pair tptp.arrow_2142409994le_alt tptp.arrow_2142409994le_alt) tptp.a))) (let ((_let_73 (tptp.member _let_11))) (let ((_let_74 (tptp.hBOOL (tptp.hAPP _let_12 tptp.bool (tptp.hAPP _let_11 _let_13 _let_73 (tptp.hAPP tptp.arrow_2142409994le_alt _let_11 _let_72 tptp.b)) _let_71)))) (let ((_let_75 (tptp.last tptp.arrow_2142409994le_alt))) (let ((_let_76 (tptp.hAPP _let_49 tptp.arrow_2142409994le_alt _let_75 _let_51))) (let ((_let_77 (tptp.hAPP _let_49 _let_49 _let_54 _let_47))) (let ((_let_78 (tptp.hAPP _let_49 tptp.arrow_2142409994le_alt _let_75 _let_77))) (let ((_let_79 (= _let_78 _let_76))) (let ((_let_80 (not _let_79))) (let ((_let_81 (and _let_80 _let_74))) (let ((_let_82 (tptp.hBOOL (tptp.hAPP _let_12 tptp.bool (tptp.hAPP _let_11 _let_13 _let_73 (tptp.hAPP tptp.arrow_2142409994le_alt _let_11 _let_72 tptp.c)) (tptp.hAPP tptp.arrow_2142409994le_alt _let_12 (tptp.hAPP tptp.arrow_2142409994le_alt _let_35 (tptp.hAPP _let_12 _let_36 tptp.arrow_1665824030_below _let_71) tptp.c) tptp.b))))) (let ((_let_83 (= _let_82 _let_81))) (let ((_let_84 (tptp.hAPP _let_12 (tptp.fun _let_13 tptp.bool) (tptp.member _let_12) _let_71))) (let ((_let_85 (tptp.hBOOL (tptp.hAPP _let_13 tptp.bool _let_84 _let_14)))) (let ((_let_86 (not _let_85))) (let ((_let_87 (tptp.hAPP _let_49 _let_49 _let_52 _let_47))) (let ((_let_88 (tptp.hAPP _let_49 tptp.arrow_2142409994le_alt _let_75 _let_87))) (let ((_let_89 (= _let_88 _let_76))) (let ((_let_90 (or _let_89 _let_86 _let_83))) (let ((_let_91 (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (L_3 $$unsorted) (Aa $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.product_Pair tptp.arrow_2142409994le_alt tptp.arrow_2142409994le_alt))) (let ((_let_2 (tptp.product_prod tptp.arrow_2142409994le_alt tptp.arrow_2142409994le_alt))) (let ((_let_3 (tptp.fun tptp.arrow_2142409994le_alt _let_2))) (let ((_let_4 (tptp.hAPP tptp.arrow_2142409994le_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_2142409994le_alt _let_2 _let_4 Y_1)))) (let ((_let_9 (tptp.nil tptp.arrow_2142409994le_alt))) (let ((_let_10 (tptp.cons tptp.arrow_2142409994le_alt))) (let ((_let_11 (tptp.list tptp.arrow_2142409994le_alt))) (let ((_let_12 (tptp.fun _let_11 _let_11))) (let ((_let_13 (tptp.last tptp.arrow_2142409994le_alt))) (let ((_let_14 (tptp.hAPP _let_11 tptp.arrow_2142409994le_alt _let_13 (tptp.hAPP _let_11 _let_11 (tptp.hAPP tptp.arrow_2142409994le_alt _let_12 _let_10 X_1) _let_9)))) (let ((_let_15 (tptp.hAPP _let_11 tptp.arrow_2142409994le_alt _let_13 (tptp.hAPP _let_11 _let_11 (tptp.hAPP tptp.arrow_2142409994le_alt _let_12 _let_10 Aa) _let_9)))) (let ((_let_16 (= _let_15 _let_14))) (let ((_let_17 (tptp.hAPP _let_11 tptp.arrow_2142409994le_alt _let_13 (tptp.hAPP _let_11 _let_11 (tptp.hAPP tptp.arrow_2142409994le_alt _let_12 _let_10 Y_1) _let_9)))) (let ((_let_18 (tptp.hAPP _let_11 tptp.arrow_2142409994le_alt _let_13 (tptp.hAPP _let_11 _let_11 (tptp.hAPP 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(tptp.last BOUND_VARIABLE_36010) (tptp.hAPP _let_1 _let_1 (tptp.hAPP BOUND_VARIABLE_36010 (tptp.fun _let_1 _let_1) (tptp.cons BOUND_VARIABLE_36010) BOUND_VARIABLE_36011) (tptp.nil BOUND_VARIABLE_36010)))))))) (ASSUME :args (_let_25))))) (let ((_let_95 (EQ_RESOLVE (ASSUME :args (_let_34)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_34 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_94 :args ((forall ((X_1 $$unsorted) (Y_1 $$unsorted) (L_3 $$unsorted) (Aa $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.product_Pair tptp.arrow_2142409994le_alt tptp.arrow_2142409994le_alt))) (let ((_let_2 (tptp.product_prod tptp.arrow_2142409994le_alt tptp.arrow_2142409994le_alt))) (let ((_let_3 (tptp.fun tptp.arrow_2142409994le_alt _let_2))) (let ((_let_4 (tptp.hAPP tptp.arrow_2142409994le_alt _let_3 _let_1 X_1))) (let ((_let_5 (tptp.member _let_2))) (let ((_let_6 (tptp.fun _let_2 tptp.bool))) (let ((_let_7 (tptp.fun _let_6 tptp.bool))) (let ((_let_8 (tptp.hAPP _let_2 _let_7 _let_5 (tptp.hAPP tptp.arrow_2142409994le_alt _let_2 _let_4 Y_1)))) (let ((_let_9 (tptp.ti tptp.arrow_2142409994le_alt X_1))) (let ((_let_10 (tptp.ti tptp.arrow_2142409994le_alt Aa))) (let ((_let_11 (= _let_10 _let_9))) (let ((_let_12 (tptp.ti tptp.arrow_2142409994le_alt Y_1))) (let ((_let_13 (tptp.ti tptp.arrow_2142409994le_alt Ba))) (let ((_let_14 (= _let_10 _let_12))) (let ((_let_15 (tptp.fun tptp.arrow_2142409994le_alt _let_6))) (or (= _let_10 _let_13) (not (tptp.hBOOL (tptp.hAPP _let_7 tptp.bool (tptp.hAPP _let_6 (tptp.fun _let_7 tptp.bool) (tptp.member _let_6) L_3) tptp.arrow_1568854078le_Lin))) (= (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool _let_8 (tptp.hAPP tptp.arrow_2142409994le_alt _let_6 (tptp.hAPP tptp.arrow_2142409994le_alt _let_15 (tptp.hAPP _let_6 (tptp.fun tptp.arrow_2142409994le_alt _let_15) tptp.arrow_1665824030_below L_3) Aa) Ba))) (and (not (= _let_9 _let_12)) (or (not _let_14) (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP _let_2 _let_7 _let_5 (tptp.hAPP tptp.arrow_2142409994le_alt 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$$unsorted) (Q $$unsorted)) (let ((_let_1 (tptp.list X_a))) (= (tptp.hAPP X_b X_a (tptp.hAPP X_a (tptp.fun X_b X_a) (tptp.combk X_a X_b) P) Q) (tptp.hAPP _let_1 X_a (tptp.last X_a) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.cons X_a) P) (tptp.nil X_a)))))))) (let ((_let_104 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO _let_94 :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_105 (tptp.hBOOL (tptp.hAPP _let_20 tptp.bool (tptp.hAPP tptp.arrow_1998540521e_indi (tptp.fun _let_20 tptp.bool) (tptp.member tptp.arrow_1998540521e_indi) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7) _let_21)))) (let ((_let_106 (not _let_105))) (let ((_let_107 (tptp.hBOOL (tptp.hAPP _let_23 tptp.bool _let_57 (tptp.hAPP _let_19 _let_23 _let_24 _let_96))))) (let ((_let_108 (not _let_107))) (let ((_let_109 (or _let_108 _let_101 _let_106))) (let ((_let_110 (forall ((X_a $$unsorted) (X_b $$unsorted) (X_1 $$unsorted) (F $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun X_a X_b))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.fun X_a _let_2))) (or (not (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_2) B_1)))) (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_1 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_2)))))))))))) (let ((_let_111 (EQ_RESOLVE (ASSUME :args (_let_26)) (MACRO_SR_EQ_INTRO :args (_let_26 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_112 (tptp.fun (tptp.fun X_a X_b) tptp.bool))) (let ((_let_113 (tptp.fun X_a (tptp.fun X_b tptp.bool)))) (let ((_let_114 (_let_16))) (let ((_let_115 (ASSUME :args _let_114))) (let 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:args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_137 (_let_135))) (let ((_let_138 (_let_28))) (let ((_let_139 (ASSUME :args _let_138))) (let ((_let_140 (not _let_129))) (let ((_let_141 (and _let_140 (tptp.hBOOL (tptp.hAPP _let_49 tptp.bool _let_55 _let_51))))) (let ((_let_142 (tptp.hBOOL (tptp.hAPP _let_49 tptp.bool _let_55 _let_53)))) (let ((_let_143 (= _let_142 _let_141))) (let ((_let_144 (_let_7))) (let ((_let_145 (ASSUME :args _let_144))) (let ((_let_146 (tptp.arrow_2142409994le_alt tptp.b _let_51 QUANTIFIERS_INST_CBQI_CONFLICT))) (let ((_let_147 (tptp.hAPP _let_49 _let_9 _let_125 _let_53))) (let ((_let_148 (tptp.hBOOL (tptp.hAPP _let_9 tptp.bool (tptp.hAPP tptp.arrow_2142409994le_alt _let_127 _let_126 tptp.a) _let_147)))) (let ((_let_149 (not _let_148))) (let ((_let_150 (and _let_149 _let_142))) (let ((_let_151 (= _let_56 _let_150))) (let ((_let_152 (tptp.list X_a))) (let ((_let_153 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_151)) :args ((or (not 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_let_51))) (let ((_let_177 (tptp.hAPP _let_49 tptp.arrow_2142409994le_alt _let_75 _let_53))) (let ((_let_178 (= _let_76 _let_177))) (let ((_let_179 (or _let_176 _let_178))) (let ((_let_180 (= tptp.a _let_78))) (let ((_let_181 (tptp.hBOOL (tptp.hAPP _let_9 tptp.bool (tptp.hAPP tptp.arrow_2142409994le_alt _let_127 _let_126 _let_177) _let_147)))) (let ((_let_182 (forall ((X_a $$unsorted) (Aa $$unsorted) (List $$unsorted) (A_3 $$unsorted) (List_3 $$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.hAPP X_a _let_4 _let_2 A_3))) (let ((_let_6 (tptp.last X_a))) (let ((_let_7 (tptp.hAPP X_a _let_4 _let_2 Aa))) (= (= (tptp.hAPP _let_3 _let_3 _let_7 List) (tptp.hAPP _let_3 _let_3 _let_5 List_3)) (and (= (tptp.hAPP _let_3 X_a _let_6 (tptp.hAPP _let_3 _let_3 _let_7 _let_1)) (tptp.hAPP _let_3 X_a _let_6 (tptp.hAPP _let_3 _let_3 _let_5 _let_1))) (= List List_3))))))))))))) (let ((_let_183 (EQ_RESOLVE (ASSUME :args (_let_27)) (MACRO_SR_EQ_INTRO _let_94 :args (_let_27 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_184 (not _let_175))) (let ((_let_185 (tptp.list X_a))) (let ((_let_186 (not _let_173))) (let ((_let_187 (not _let_176))) (let ((_let_188 (and _let_173 _let_184))) (let ((_let_189 (ASSUME :args (_let_184)))) (let ((_let_190 (ASSUME :args (_let_173)))) (let ((_let_191 (forall ((BOUND_VARIABLE_25705 $$unsorted) (BOUND_VARIABLE_25707 $$unsorted) (BOUND_VARIABLE_25709 $$unsorted)) (let ((_let_1 (tptp.last BOUND_VARIABLE_25705))) (let ((_let_2 (tptp.list BOUND_VARIABLE_25705))) (or (= BOUND_VARIABLE_25709 (tptp.nil BOUND_VARIABLE_25705)) (= (tptp.hAPP _let_2 BOUND_VARIABLE_25705 _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP BOUND_VARIABLE_25705 (tptp.fun _let_2 _let_2) (tptp.cons BOUND_VARIABLE_25705) BOUND_VARIABLE_25707) BOUND_VARIABLE_25709)) (tptp.hAPP _let_2 BOUND_VARIABLE_25705 _let_1 BOUND_VARIABLE_25709)))))))) (let ((_let_192 (EQ_RESOLVE _let_93 (TRANS _let_92 (MACRO_SR_EQ_INTRO _let_94 :args ((and (forall ((BOUND_VARIABLE_25684 $$unsorted) (BOUND_VARIABLE_25686 $$unsorted)) (let ((_let_1 (tptp.list BOUND_VARIABLE_25684))) (= (tptp.ti BOUND_VARIABLE_25684 BOUND_VARIABLE_25686) (tptp.hAPP _let_1 BOUND_VARIABLE_25684 (tptp.last BOUND_VARIABLE_25684) (tptp.hAPP _let_1 _let_1 (tptp.hAPP BOUND_VARIABLE_25684 (tptp.fun _let_1 _let_1) (tptp.cons BOUND_VARIABLE_25684) BOUND_VARIABLE_25686) (tptp.nil BOUND_VARIABLE_25684)))))) _let_191) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_193 (EQ_RESOLVE (ASSUME :args (_let_64)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_64 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_94 :args ((= tptp.a _let_63) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_194 (= _let_47 _let_53))) (let ((_let_195 (or _let_194 _let_181))) (let ((_let_196 (ASSUME :args (_let_149)))) (let ((_let_197 (ASSUME :args (_let_79)))) (let ((_let_198 (ASSUME :args (_let_178)))) (let ((_let_199 (ASSUME :args (_let_181)))) (let ((_let_200 (_let_81))) 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(let ((_let_1 (tptp.zero_zero X_a))) (=> (tptp.zero X_a) (= (tptp.ti X_a _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.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)) (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 $$unsorted)) (let ((_let_1 (tptp.lenlex X_a))) (let ((_let_2 (tptp.list X_a))) (= (tptp.ti (tptp.fun (tptp.fun (tptp.product_prod X_a X_a) tptp.bool) (tptp.fun (tptp.product_prod _let_2 _let_2) tptp.bool)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.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.list_size X_a))) (= (tptp.ti (tptp.fun (tptp.fun X_a tptp.nat) (tptp.fun (tptp.list X_a) tptp.nat)) _let_1) _let_1))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (let ((_let_1 (tptp.list_all2 X_a X_b))) (= (tptp.ti (tptp.fun (tptp.fun X_a (tptp.fun X_b tptp.bool)) (tptp.fun (tptp.list X_a) (tptp.fun (tptp.list X_b) tptp.bool))) _let_1) _let_1))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.list_update X_a))) (let ((_let_2 (tptp.list X_a))) (= (tptp.ti (tptp.fun _let_2 (tptp.fun tptp.nat (tptp.fun X_a _let_2))) _let_1) _let_1)))) (forall ((X_a $$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_a $$unsorted)) (let ((_let_1 (tptp.listset X_a))) (= (tptp.ti (tptp.fun (tptp.list (tptp.fun X_a tptp.bool)) (tptp.fun (tptp.list X_a) tptp.bool)) _let_1) _let_1))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.maps X_b X_a))) (let ((_let_2 (tptp.list X_a))) (= (tptp.ti (tptp.fun (tptp.fun X_b _let_2) (tptp.fun (tptp.list X_b) _let_2)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.nth X_a))) (= (tptp.ti (tptp.fun (tptp.list X_a) (tptp.fun tptp.nat X_a)) _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 $$unsorted)) (let ((_let_1 (tptp.set_Cons X_a))) (let ((_let_2 (tptp.fun (tptp.list X_a) tptp.bool))) (= (tptp.ti (tptp.fun (tptp.fun X_a tptp.bool) (tptp.fun _let_2 _let_2)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.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 $$unsorted)) (let ((_let_1 (tptp.sublist X_a))) (let ((_let_2 (tptp.list X_a))) (= (tptp.ti (tptp.fun _let_2 (tptp.fun (tptp.fun tptp.nat tptp.bool) _let_2)) _let_1) _let_1)))) (forall ((X_a $$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)))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (let ((_let_1 (tptp.zip X_a X_b))) (= (tptp.ti (tptp.fun (tptp.list X_a) (tptp.fun (tptp.list X_b) (tptp.list (tptp.product_prod X_a X_b)))) _let_1) _let_1))) (= (tptp.ti _let_67 tptp.suc) tptp.suc) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.nat_case X_a))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (= (tptp.ti (tptp.fun X_a (tptp.fun _let_2 _let_2)) _let_1) _let_1)))) (= (tptp.ti _let_67 tptp.nat_size) tptp.nat_size) (= (tptp.ti _let_67 _let_5) _let_5) (forall ((X_a $$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_9 _let_13) _let_10) _let_10) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.min X_a))) (=> (tptp.ord X_a) (= (tptp.ti (tptp.fun (tptp.fun X_a (tptp.fun X_a tptp.bool)) (tptp.fun X_a (tptp.fun X_a X_a))) _let_1) _let_1)))) (forall ((X_a $$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.ord_min X_a))) (=> (tptp.ord X_a) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a X_a)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.top_top X_a))) (=> (tptp.top X_a) (= (tptp.ti X_a _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.reflp X_a))) (= (tptp.ti (tptp.fun (tptp.fun X_a (tptp.fun X_a tptp.bool)) tptp.bool) _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_a $$unsorted) (X_c $$unsorted) (X_b $$unsorted) (X_d $$unsorted)) (let ((_let_1 (tptp.product_map_pair X_a X_c X_b X_d))) (= (tptp.ti (tptp.fun (tptp.fun X_a X_c) (tptp.fun (tptp.fun X_b X_d) (tptp.fun (tptp.product_prod X_a X_b) (tptp.product_prod X_c X_d)))) _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 $$unsorted)) (let ((_let_1 (tptp.refl_on X_a))) (= (tptp.ti (tptp.fun (tptp.fun X_a tptp.bool) (tptp.fun (tptp.fun (tptp.product_prod X_a X_a) tptp.bool) tptp.bool)) _let_1) _let_1))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.collect X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (= (tptp.ti (tptp.fun _let_2 _let_2) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.transitive_rtrancl X_a))) (let ((_let_2 (tptp.fun (tptp.product_prod X_a X_a) tptp.bool))) (= (tptp.ti (tptp.fun _let_2 _let_2) _let_1) _let_1)))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (let ((_let_1 (tptp.lex_prod X_a X_b))) (let ((_let_2 (tptp.product_prod X_a X_b))) (= (tptp.ti (tptp.fun (tptp.fun (tptp.product_prod X_a X_a) tptp.bool) (tptp.fun (tptp.fun (tptp.product_prod X_b X_b) tptp.bool) (tptp.fun (tptp.product_prod _let_2 _let_2) tptp.bool))) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.measure X_a))) (= (tptp.ti (tptp.fun (tptp.fun X_a tptp.nat) (tptp.fun (tptp.product_prod X_a X_a) tptp.bool)) _let_1) _let_1))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.mlex_prod X_a))) (let ((_let_2 (tptp.fun (tptp.product_prod X_a X_a) tptp.bool))) (= (tptp.ti (tptp.fun (tptp.fun X_a tptp.nat) (tptp.fun _let_2 _let_2)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.fEx X_a))) (= (tptp.ti (tptp.fun (tptp.fun X_a tptp.bool) tptp.bool) _let_1) _let_1))) (= (tptp.ti tptp.bool tptp.fFalse) tptp.fFalse) (= (tptp.ti _let_65 tptp.fNot) tptp.fNot) (= (tptp.ti tptp.bool tptp.fTrue) tptp.fTrue) (= (tptp.ti _let_66 tptp.fconj) tptp.fconj) (= (tptp.ti _let_66 tptp.fdisj) tptp.fdisj) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.fequal X_a))) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a tptp.bool)) _let_1) _let_1))) (forall ((X_a $$unsorted) (X_c $$unsorted) (B_1_1 $$unsorted) (B_2_1 $$unsorted)) (= (tptp.hAPP X_a X_c (tptp.ti (tptp.fun X_a X_c) B_1_1) B_2_1) (tptp.hAPP X_a X_c B_1_1 B_2_1))) (forall ((X_a $$unsorted) (X_c $$unsorted) (B_1_1 $$unsorted) (B_2_1 $$unsorted)) (= (tptp.hAPP X_a X_c B_1_1 (tptp.ti X_a B_2_1)) (tptp.hAPP X_a X_c B_1_1 B_2_1))) (forall ((X_c $$unsorted) (X_a $$unsorted) (B_1_1 $$unsorted) (B_2_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a X_c B_1_1 B_2_1))) (= (tptp.ti X_c _let_1) _let_1))) (forall ((B_1_1 $$unsorted)) (= (tptp.hBOOL (tptp.ti tptp.bool B_1_1)) (tptp.hBOOL B_1_1))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.member X_b))) (= (tptp.ti (tptp.fun X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool)) _let_1) _let_1))) (= (tptp.ti _let_30 tptp.f) tptp.f) (= (tptp.ti _let_22 tptp.p_1) tptp.p_1) (= (tptp.ti _let_22 tptp.p) tptp.p) _let_64 _let_62 _let_60 _let_58 (tptp.hBOOL (tptp.hAPP _let_30 tptp.bool tptp.arrow_1541970350le_IIA tptp.f)) (tptp.hBOOL (tptp.hAPP _let_30 tptp.bool tptp.arrow_1066301521nimity tptp.f)) (not (= tptp.a tptp.b)) _let_56 (forall ((I $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.arrow_2142409994le_alt tptp.arrow_2142409994le_alt))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.product_Pair tptp.arrow_2142409994le_alt tptp.arrow_2142409994le_alt))) (let ((_let_4 (tptp.fun tptp.arrow_2142409994le_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_2142409994le_alt _let_1 (tptp.hAPP tptp.arrow_2142409994le_alt _let_4 _let_3 tptp.a) tptp.b)) (tptp.hAPP tptp.arrow_1998540521e_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_2142409994le_alt _let_1 (tptp.hAPP tptp.arrow_2142409994le_alt _let_4 _let_3 tptp.b) tptp.a)) (tptp.hAPP tptp.arrow_1998540521e_indi _let_2 tptp.p_1 I))))))))))) (not (forall ((C_2 $$unsorted)) (let ((_let_1 (tptp.cons tptp.arrow_2142409994le_alt))) (let ((_let_2 (tptp.list tptp.arrow_2142409994le_alt))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (not (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.distinct tptp.arrow_2142409994le_alt) (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.arrow_2142409994le_alt _let_3 _let_1 tptp.a) (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.arrow_2142409994le_alt _let_3 _let_1 tptp.b) (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.arrow_2142409994le_alt _let_3 _let_1 C_2) (tptp.nil tptp.arrow_2142409994le_alt)))))))))))) (tptp.hBOOL (tptp.hAPP _let_23 tptp.bool (tptp.hAPP _let_22 _let_33 _let_32 _let_46) tptp.arrow_301600364e_Prof)) (tptp.hBOOL (tptp.hAPP _let_23 tptp.bool (tptp.hAPP _let_22 _let_33 _let_32 (tptp.hAPP tptp.arrow_2142409994le_alt _let_22 (tptp.hAPP _let_41 _let_44 _let_43 (tptp.hAPP tptp.arrow_2142409994le_alt _let_41 (tptp.hAPP _let_37 _let_42 _let_40 (tptp.hAPP _let_22 _let_37 _let_39 _let_46)) tptp.a)) tptp.c)) tptp.arrow_301600364e_Prof)) (tptp.hBOOL (tptp.hAPP _let_23 tptp.bool (tptp.hAPP _let_22 _let_33 _let_32 _let_45) tptp.arrow_301600364e_Prof)) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (L_3 $$unsorted) (Z_2 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.arrow_2142409994le_alt tptp.arrow_2142409994le_alt))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) (tptp.hAPP tptp.arrow_2142409994le_alt _let_1 (tptp.hAPP tptp.arrow_2142409994le_alt (tptp.fun tptp.arrow_2142409994le_alt _let_1) (tptp.product_Pair tptp.arrow_2142409994le_alt tptp.arrow_2142409994le_alt) X_1) Y_1)))) (let ((_let_4 (tptp.ti tptp.arrow_2142409994le_alt Z_2))) (let ((_let_5 (tptp.ti tptp.arrow_2142409994le_alt X_1))) (let ((_let_6 (= _let_5 _let_4))) (let ((_let_7 (tptp.ti tptp.arrow_2142409994le_alt Y_1))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 (tptp.hAPP tptp.arrow_2142409994le_alt _let_2 (tptp.hAPP _let_2 (tptp.fun tptp.arrow_2142409994le_alt _let_2) tptp.arrow_1622070166_mkbot L_3) Z_2))) (and (not (= _let_7 _let_4)) (=> _let_6 (not (= _let_5 _let_7))) (=> (not _let_6) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 L_3))))))))))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (L_3 $$unsorted) (Z_2 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.arrow_2142409994le_alt tptp.arrow_2142409994le_alt))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) (tptp.hAPP tptp.arrow_2142409994le_alt _let_1 (tptp.hAPP tptp.arrow_2142409994le_alt (tptp.fun tptp.arrow_2142409994le_alt _let_1) (tptp.product_Pair tptp.arrow_2142409994le_alt tptp.arrow_2142409994le_alt) X_1) Y_1)))) (let ((_let_4 (tptp.ti tptp.arrow_2142409994le_alt Z_2))) (let ((_let_5 (tptp.ti tptp.arrow_2142409994le_alt Y_1))) (let ((_let_6 (= _let_5 _let_4))) (let ((_let_7 (tptp.ti tptp.arrow_2142409994le_alt X_1))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 (tptp.hAPP tptp.arrow_2142409994le_alt _let_2 (tptp.hAPP _let_2 (tptp.fun tptp.arrow_2142409994le_alt _let_2) tptp.arrow_1770777252_mktop L_3) Z_2))) (and (not (= _let_7 _let_4)) (=> _let_6 (not (= _let_7 _let_5))) (=> (not _let_6) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 L_3))))))))))))) _let_34 (forall ((X_a $$unsorted) (X_b $$unsorted) (Pa $$unsorted)) (= (forall ((X1 $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.product_prod X_a X_b) tptp.bool Pa X1))) (forall ((A_5 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_b))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa (tptp.hAPP X_b _let_1 (tptp.hAPP X_a (tptp.fun X_b _let_1) (tptp.product_Pair X_a X_b) A_5) B_2))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (Aa $$unsorted) (Ba $$unsorted) (A_3 $$unsorted) (B_3 $$unsorted)) (let ((_let_1 (tptp.product_Pair X_a X_b))) (let ((_let_2 (tptp.product_prod X_a X_b))) (let ((_let_3 (tptp.fun X_b _let_2))) (= (= (tptp.hAPP X_b _let_2 (tptp.hAPP X_a _let_3 _let_1 Aa) Ba) (tptp.hAPP X_b _let_2 (tptp.hAPP X_a _let_3 _let_1 A_3) B_3)) (and (= (tptp.ti X_a Aa) (tptp.ti X_a A_3)) (= (tptp.ti X_b Ba) (tptp.ti X_b B_3)))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted) (A_6 $$unsorted) (B_4 $$unsorted)) (let ((_let_1 (tptp.product_Pair X_a X_b))) (let ((_let_2 (tptp.product_prod X_a X_b))) (let ((_let_3 (tptp.fun X_b _let_2))) (=> (= (tptp.hAPP X_b _let_2 (tptp.hAPP X_a _let_3 _let_1 A_1) B) (tptp.hAPP X_b _let_2 (tptp.hAPP X_a _let_3 _let_1 A_6) B_4)) (not (=> (= (tptp.ti X_a A_1) (tptp.ti X_a A_6)) (not (= (tptp.ti X_b B) (tptp.ti X_b B_4)))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (R_2 $$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_2) 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_2))))))) (forall ((L_3 $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.product_prod tptp.arrow_2142409994le_alt tptp.arrow_2142409994le_alt) tptp.bool))) (let ((_let_2 (tptp.fun tptp.arrow_2142409994le_alt _let_1))) (let ((_let_3 (tptp.member _let_1))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (not (= (tptp.ti tptp.arrow_2142409994le_alt X_1) (tptp.ti tptp.arrow_2142409994le_alt Y_1))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP _let_1 _let_5 _let_3 L_3) tptp.arrow_1568854078le_Lin)) (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP _let_1 _let_5 _let_3 (tptp.hAPP tptp.arrow_2142409994le_alt _let_1 (tptp.hAPP tptp.arrow_2142409994le_alt _let_2 (tptp.hAPP _let_1 (tptp.fun tptp.arrow_2142409994le_alt _let_2) tptp.arrow_1665824030_below L_3) X_1) Y_1)) tptp.arrow_1568854078le_Lin)))))))))) (tptp.hBOOL (tptp.hAPP _let_23 tptp.bool (tptp.hAPP _let_22 _let_33 _let_32 tptp.p_1) tptp.arrow_301600364e_Prof)) (forall ((P_a $$unsorted) (Pa $$unsorted) (A_3 $$unsorted) (B_3 $$unsorted) (Aa $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.arrow_2142409994le_alt tptp.arrow_2142409994le_alt))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun tptp.arrow_1998540521e_indi _let_2))) (let ((_let_4 (tptp.product_Pair tptp.arrow_2142409994le_alt tptp.arrow_2142409994le_alt))) (let ((_let_5 (tptp.fun tptp.arrow_2142409994le_alt _let_1))) (let ((_let_6 (tptp.member _let_1))) (let ((_let_7 (tptp.fun _let_2 tptp.bool))) (let ((_let_8 (tptp.member _let_3))) (let ((_let_9 (tptp.fun _let_3 tptp.bool))) (let ((_let_10 (tptp.fun _let_9 tptp.bool))) (let ((_let_11 (tptp.ti tptp.arrow_2142409994le_alt A_3))) (let ((_let_12 (tptp.ti tptp.arrow_2142409994le_alt Ba))) (let ((_let_13 (tptp.ti tptp.arrow_2142409994le_alt B_3))) (let ((_let_14 (tptp.ti tptp.arrow_2142409994le_alt Aa))) (=> (not (= _let_14 _let_12)) (=> (not (= _let_11 _let_13)) (=> (not (= _let_14 _let_13)) (=> (not (= _let_12 _let_11)) (=> (tptp.hBOOL (tptp.hAPP _let_9 tptp.bool (tptp.hAPP _let_3 _let_10 _let_8 Pa) tptp.arrow_301600364e_Prof)) (=> (tptp.hBOOL (tptp.hAPP _let_9 tptp.bool (tptp.hAPP _let_3 _let_10 _let_8 P_a) tptp.arrow_301600364e_Prof)) (=> (forall ((I $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.arrow_2142409994le_alt tptp.arrow_2142409994le_alt))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.product_Pair tptp.arrow_2142409994le_alt tptp.arrow_2142409994le_alt))) (let ((_let_4 (tptp.fun tptp.arrow_2142409994le_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_2142409994le_alt _let_1 (tptp.hAPP tptp.arrow_2142409994le_alt _let_4 _let_3 Aa) Ba)) (tptp.hAPP tptp.arrow_1998540521e_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_2142409994le_alt _let_1 (tptp.hAPP tptp.arrow_2142409994le_alt _let_4 _let_3 A_3) B_3)) (tptp.hAPP tptp.arrow_1998540521e_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_2142409994le_alt _let_1 (tptp.hAPP tptp.arrow_2142409994le_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_2142409994le_alt _let_1 (tptp.hAPP tptp.arrow_2142409994le_alt _let_5 _let_4 A_3) B_3)) (tptp.hAPP _let_3 _let_2 tptp.f P_a)))))))))))))))))))))))))) (forall ((P_a $$unsorted) (Pa $$unsorted) (A_3 $$unsorted) (B_3 $$unsorted) (Aa $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.arrow_2142409994le_alt tptp.arrow_2142409994le_alt))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun tptp.arrow_1998540521e_indi _let_2))) (let ((_let_4 (tptp.product_Pair tptp.arrow_2142409994le_alt tptp.arrow_2142409994le_alt))) (let ((_let_5 (tptp.fun tptp.arrow_2142409994le_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_2142409994le_alt A_3))) (let ((_let_12 (tptp.ti tptp.arrow_2142409994le_alt Ba))) (let ((_let_13 (tptp.ti tptp.arrow_2142409994le_alt B_3))) (let ((_let_14 (tptp.ti tptp.arrow_2142409994le_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_301600364e_Prof)) (=> (tptp.hBOOL (tptp.hAPP _let_9 tptp.bool (tptp.hAPP _let_3 _let_10 _let_8 P_a) tptp.arrow_301600364e_Prof)) (=> (forall ((I $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.arrow_2142409994le_alt tptp.arrow_2142409994le_alt))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.product_Pair tptp.arrow_2142409994le_alt tptp.arrow_2142409994le_alt))) (let ((_let_4 (tptp.fun tptp.arrow_2142409994le_alt _let_1))) (let ((_let_5 (tptp.member _let_1))) (let ((_let_6 (tptp.fun _let_2 tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 _let_6 _let_5 (tptp.hAPP tptp.arrow_2142409994le_alt _let_1 (tptp.hAPP tptp.arrow_2142409994le_alt _let_4 _let_3 Aa) Ba)) (tptp.hAPP tptp.arrow_1998540521e_indi _let_2 Pa I))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 _let_6 _let_5 (tptp.hAPP tptp.arrow_2142409994le_alt _let_1 (tptp.hAPP tptp.arrow_2142409994le_alt _let_4 _let_3 A_3) B_3)) (tptp.hAPP tptp.arrow_1998540521e_indi _let_2 P_a I))))))))))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 _let_7 _let_6 (tptp.hAPP tptp.arrow_2142409994le_alt _let_1 (tptp.hAPP tptp.arrow_2142409994le_alt _let_5 _let_4 Aa) Ba)) (tptp.hAPP _let_3 _let_2 tptp.f Pa))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 _let_7 _let_6 (tptp.hAPP tptp.arrow_2142409994le_alt _let_1 (tptp.hAPP tptp.arrow_2142409994le_alt _let_5 _let_4 A_3) B_3)) (tptp.hAPP _let_3 _let_2 tptp.f P_a)))))))))))))))))))))))))) (tptp.hBOOL (tptp.hAPP _let_31 tptp.bool (tptp.hAPP _let_30 (tptp.fun _let_31 tptp.bool) (tptp.member _let_30) tptp.f) (tptp.hAPP _let_29 _let_31 (tptp.hAPP _let_23 (tptp.fun _let_29 _let_31) (tptp.pi _let_22 _let_12) tptp.arrow_301600364e_Prof) (tptp.hAPP _let_13 _let_29 (tptp.combk _let_13 _let_22) tptp.arrow_1568854078le_Lin)))) (forall ((L_3 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.product_prod tptp.arrow_2142409994le_alt tptp.arrow_2142409994le_alt) tptp.bool))) (let ((_let_2 (tptp.fun tptp.arrow_1998540521e_indi _let_1))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_4 tptp.bool) (tptp.member _let_1) L_3) tptp.arrow_1568854078le_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_1998540521e_indi) L_3)) tptp.arrow_301600364e_Prof)))))))) (forall ((X_1 $$unsorted) (L_3 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.product_prod tptp.arrow_2142409994le_alt tptp.arrow_2142409994le_alt) tptp.bool))) (let ((_let_2 (tptp.member _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_1 _let_4 _let_2 L_3) tptp.arrow_1568854078le_Lin)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_1 _let_4 _let_2 (tptp.hAPP tptp.arrow_2142409994le_alt _let_1 (tptp.hAPP _let_1 (tptp.fun tptp.arrow_2142409994le_alt _let_1) tptp.arrow_1622070166_mkbot L_3) X_1)) tptp.arrow_1568854078le_Lin)))))))) (forall ((X_1 $$unsorted) (L_3 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.product_prod tptp.arrow_2142409994le_alt tptp.arrow_2142409994le_alt) tptp.bool))) (let ((_let_2 (tptp.member _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_1 _let_4 _let_2 L_3) tptp.arrow_1568854078le_Lin)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_1 _let_4 _let_2 (tptp.hAPP tptp.arrow_2142409994le_alt _let_1 (tptp.hAPP _let_1 (tptp.fun tptp.arrow_2142409994le_alt _let_1) tptp.arrow_1770777252_mktop L_3) X_1)) tptp.arrow_1568854078le_Lin)))))))) (forall ((Aa $$unsorted) (Ba $$unsorted) (L_3 $$unsorted)) (let ((_let_1 (tptp.product_Pair tptp.arrow_2142409994le_alt tptp.arrow_2142409994le_alt))) (let ((_let_2 (tptp.product_prod tptp.arrow_2142409994le_alt tptp.arrow_2142409994le_alt))) (let ((_let_3 (tptp.fun tptp.arrow_2142409994le_alt _let_2))) (let ((_let_4 (tptp.member _let_2))) (let ((_let_5 (tptp.fun _let_2 tptp.bool))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP _let_5 (tptp.fun _let_6 tptp.bool) (tptp.member _let_5) L_3) tptp.arrow_1568854078le_Lin)) (=> (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP _let_2 _let_6 _let_4 (tptp.hAPP tptp.arrow_2142409994le_alt _let_2 (tptp.hAPP tptp.arrow_2142409994le_alt _let_3 _let_1 Aa) Ba)) L_3)) (not (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP _let_2 _let_6 _let_4 (tptp.hAPP tptp.arrow_2142409994le_alt _let_2 (tptp.hAPP tptp.arrow_2142409994le_alt _let_3 _let_1 Ba) Aa)) L_3)))))))))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (L_3 $$unsorted)) (let ((_let_1 (tptp.product_Pair tptp.arrow_2142409994le_alt tptp.arrow_2142409994le_alt))) (let ((_let_2 (tptp.product_prod tptp.arrow_2142409994le_alt tptp.arrow_2142409994le_alt))) (let ((_let_3 (tptp.fun tptp.arrow_2142409994le_alt _let_2))) (let ((_let_4 (tptp.member _let_2))) (let ((_let_5 (tptp.fun _let_2 tptp.bool))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP _let_5 (tptp.fun _let_6 tptp.bool) (tptp.member _let_5) L_3) tptp.arrow_1568854078le_Lin)) (=> (not (= (tptp.ti tptp.arrow_2142409994le_alt X_1) (tptp.ti tptp.arrow_2142409994le_alt Y_1))) (= (not (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP _let_2 _let_6 _let_4 (tptp.hAPP tptp.arrow_2142409994le_alt _let_2 (tptp.hAPP tptp.arrow_2142409994le_alt _let_3 _let_1 X_1) Y_1)) L_3))) (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP _let_2 _let_6 _let_4 (tptp.hAPP tptp.arrow_2142409994le_alt _let_2 (tptp.hAPP tptp.arrow_2142409994le_alt _let_3 _let_1 Y_1) X_1)) L_3)))))))))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (=> (not (= (tptp.ti tptp.arrow_2142409994le_alt A_1) (tptp.ti tptp.arrow_2142409994le_alt B))) (exists ((C_2 $$unsorted)) (let ((_let_1 (tptp.cons tptp.arrow_2142409994le_alt))) (let ((_let_2 (tptp.list tptp.arrow_2142409994le_alt))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.distinct tptp.arrow_2142409994le_alt) (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.arrow_2142409994le_alt _let_3 _let_1 A_1) (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.arrow_2142409994le_alt _let_3 _let_1 B) (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.arrow_2142409994le_alt _let_3 _let_1 C_2) (tptp.nil tptp.arrow_2142409994le_alt)))))))))))) (forall ((Fa_1 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.product_prod tptp.arrow_2142409994le_alt tptp.arrow_2142409994le_alt) tptp.bool))) (= (tptp.hBOOL (tptp.hAPP (tptp.fun (tptp.fun tptp.arrow_1998540521e_indi _let_1) _let_1) tptp.bool tptp.arrow_1541970350le_IIA Fa_1)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.arrow_1998540521e_indi (tptp.fun (tptp.product_prod tptp.arrow_2142409994le_alt tptp.arrow_2142409994le_alt) tptp.bool)))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) X_2) tptp.arrow_301600364e_Prof)) (forall ((Xa $$unsorted)) (let ((_let_1 (tptp.fun tptp.arrow_1998540521e_indi (tptp.fun (tptp.product_prod tptp.arrow_2142409994le_alt tptp.arrow_2142409994le_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_301600364e_Prof)) (forall ((A_5 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.arrow_2142409994le_alt tptp.arrow_2142409994le_alt))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun tptp.arrow_1998540521e_indi _let_2))) (let ((_let_4 (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) (tptp.hAPP tptp.arrow_2142409994le_alt _let_1 (tptp.hAPP tptp.arrow_2142409994le_alt (tptp.fun tptp.arrow_2142409994le_alt _let_1) (tptp.product_Pair tptp.arrow_2142409994le_alt tptp.arrow_2142409994le_alt) A_5) B_2)))) (=> (forall ((I $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.arrow_2142409994le_alt tptp.arrow_2142409994le_alt))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) (tptp.hAPP tptp.arrow_2142409994le_alt _let_1 (tptp.hAPP tptp.arrow_2142409994le_alt (tptp.fun tptp.arrow_2142409994le_alt _let_1) (tptp.product_Pair tptp.arrow_2142409994le_alt tptp.arrow_2142409994le_alt) A_5) B_2)))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 (tptp.hAPP tptp.arrow_1998540521e_indi _let_2 X_2 I))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 (tptp.hAPP tptp.arrow_1998540521e_indi _let_2 Xa I)))))))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_4 (tptp.hAPP _let_3 _let_2 Fa_1 X_2))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_4 (tptp.hAPP _let_3 _let_2 Fa_1 Xa))))))))))))))))))))) (forall ((Fa_1 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.product_prod tptp.arrow_2142409994le_alt tptp.arrow_2142409994le_alt) tptp.bool))) (= (tptp.hBOOL (tptp.hAPP (tptp.fun (tptp.fun tptp.arrow_1998540521e_indi _let_1) _let_1) tptp.bool tptp.arrow_1066301521nimity Fa_1)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.arrow_1998540521e_indi (tptp.fun (tptp.product_prod tptp.arrow_2142409994le_alt tptp.arrow_2142409994le_alt) tptp.bool)))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) X_2) tptp.arrow_301600364e_Prof)) (forall ((A_5 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.arrow_2142409994le_alt tptp.arrow_2142409994le_alt))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (forall ((I $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.arrow_2142409994le_alt tptp.arrow_2142409994le_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_2142409994le_alt _let_1 (tptp.hAPP tptp.arrow_2142409994le_alt (tptp.fun tptp.arrow_2142409994le_alt _let_1) (tptp.product_Pair tptp.arrow_2142409994le_alt tptp.arrow_2142409994le_alt) A_5) B_2)) (tptp.hAPP tptp.arrow_1998540521e_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_2142409994le_alt _let_1 (tptp.hAPP tptp.arrow_2142409994le_alt (tptp.fun tptp.arrow_2142409994le_alt _let_1) (tptp.product_Pair tptp.arrow_2142409994le_alt tptp.arrow_2142409994le_alt) A_5) B_2)) (tptp.hAPP (tptp.fun tptp.arrow_1998540521e_indi _let_2) _let_2 Fa_1 X_2)))))))))))))) (forall ((Aa $$unsorted) (Ba $$unsorted)) (=> (not (= (tptp.ti tptp.arrow_2142409994le_alt Aa) (tptp.ti tptp.arrow_2142409994le_alt Ba))) (exists ((X_2 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.arrow_2142409994le_alt tptp.arrow_2142409994le_alt))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (and (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_3 tptp.bool) (tptp.member _let_2) X_2) tptp.arrow_1568854078le_Lin)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 _let_3 (tptp.member _let_1) (tptp.hAPP tptp.arrow_2142409994le_alt _let_1 (tptp.hAPP tptp.arrow_2142409994le_alt (tptp.fun tptp.arrow_2142409994le_alt _let_1) (tptp.product_Pair tptp.arrow_2142409994le_alt tptp.arrow_2142409994le_alt) Aa) Ba)) X_2))))))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (L_3 $$unsorted) (Aa $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.product_Pair tptp.arrow_2142409994le_alt tptp.arrow_2142409994le_alt))) (let ((_let_2 (tptp.product_prod tptp.arrow_2142409994le_alt tptp.arrow_2142409994le_alt))) (let ((_let_3 (tptp.fun tptp.arrow_2142409994le_alt _let_2))) (let ((_let_4 (tptp.hAPP tptp.arrow_2142409994le_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_2142409994le_alt _let_2 _let_4 Y_1)))) (let ((_let_9 (tptp.ti tptp.arrow_2142409994le_alt Ba))) (let ((_let_10 (tptp.ti tptp.arrow_2142409994le_alt Y_1))) (let ((_let_11 (= _let_10 _let_9))) (let ((_let_12 (tptp.ti tptp.arrow_2142409994le_alt Aa))) (let ((_let_13 (tptp.ti tptp.arrow_2142409994le_alt X_1))) (let ((_let_14 (= _let_13 _let_9))) (let ((_let_15 (tptp.fun tptp.arrow_2142409994le_alt _let_6))) (=> (not (= _let_12 _let_9)) (=> (tptp.hBOOL (tptp.hAPP _let_7 tptp.bool (tptp.hAPP _let_6 (tptp.fun _let_7 tptp.bool) (tptp.member _let_6) L_3) tptp.arrow_1568854078le_Lin)) (= (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool _let_8 (tptp.hAPP tptp.arrow_2142409994le_alt _let_6 (tptp.hAPP tptp.arrow_2142409994le_alt _let_15 (tptp.hAPP _let_6 (tptp.fun tptp.arrow_2142409994le_alt _let_15) tptp.arrow_357225482_above L_3) Aa) Ba))) (and (not (= _let_13 _let_10)) (=> _let_14 (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP _let_2 _let_7 _let_5 (tptp.hAPP tptp.arrow_2142409994le_alt _let_2 (tptp.hAPP tptp.arrow_2142409994le_alt _let_3 _let_1 Aa) Y_1)) L_3))) (=> (not _let_14) (and (=> _let_11 (or (= _let_13 _let_12) (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP _let_2 _let_7 _let_5 (tptp.hAPP tptp.arrow_2142409994le_alt _let_2 _let_4 Aa)) L_3)))) (=> (not _let_11) (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool _let_8 L_3))))))))))))))))))))))))) (forall ((X_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 $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.list X_a) tptp.bool (tptp.distinct X_a) (tptp.nil X_a)))) _let_28 (forall ((X_a $$unsorted) (A_6 $$unsorted) (List_4 $$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_4) (tptp.nil X_a))))) (exists ((A_5 $$unsorted) (B_2 $$unsorted) (C_2 $$unsorted)) (let ((_let_1 (tptp.cons tptp.arrow_2142409994le_alt))) (let ((_let_2 (tptp.list tptp.arrow_2142409994le_alt))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.distinct tptp.arrow_2142409994le_alt) (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.arrow_2142409994le_alt _let_3 _let_1 A_5) (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.arrow_2142409994le_alt _let_3 _let_1 B_2) (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.arrow_2142409994le_alt _let_3 _let_1 C_2) (tptp.nil tptp.arrow_2142409994le_alt)))))))))) (exists ((L_4 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.product_prod tptp.arrow_2142409994le_alt tptp.arrow_2142409994le_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_4) tptp.arrow_1568854078le_Lin))))) (forall ((Fa_1 $$unsorted) (I_1 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.product_prod tptp.arrow_2142409994le_alt tptp.arrow_2142409994le_alt) tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.arrow_1998540521e_indi tptp.bool (tptp.hAPP (tptp.fun (tptp.fun tptp.arrow_1998540521e_indi _let_1) _let_1) (tptp.fun tptp.arrow_1998540521e_indi tptp.bool) tptp.arrow_708804735ctator Fa_1) I_1)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.product_prod tptp.arrow_2142409994le_alt tptp.arrow_2142409994le_alt) tptp.bool))) (let ((_let_2 (tptp.fun tptp.arrow_1998540521e_indi _let_1))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_3 tptp.bool) (tptp.member _let_2) X_2) tptp.arrow_301600364e_Prof)) (= (tptp.hAPP _let_2 _let_1 Fa_1 X_2) (tptp.hAPP tptp.arrow_1998540521e_indi _let_1 X_2 I_1)))))))))) _let_27 (forall ((X_a $$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 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (not (= Xs (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.cons X_a) X) Xs))))) (forall ((L_3 $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.product_prod tptp.arrow_2142409994le_alt tptp.arrow_2142409994le_alt) tptp.bool))) (let ((_let_2 (tptp.fun tptp.arrow_2142409994le_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_2142409994le_alt X_1) (tptp.ti tptp.arrow_2142409994le_alt Y_1))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP _let_1 _let_5 _let_3 L_3) tptp.arrow_1568854078le_Lin)) (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP _let_1 _let_5 _let_3 (tptp.hAPP tptp.arrow_2142409994le_alt _let_1 (tptp.hAPP tptp.arrow_2142409994le_alt _let_2 (tptp.hAPP _let_1 (tptp.fun tptp.arrow_2142409994le_alt _let_2) tptp.arrow_357225482_above L_3) X_1) Y_1)) tptp.arrow_1568854078le_Lin)))))))))) (forall ((I_1 $$unsorted) (Fa_1 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.product_prod tptp.arrow_2142409994le_alt tptp.arrow_2142409994le_alt) tptp.bool))) (let ((_let_2 (tptp.fun tptp.arrow_1998540521e_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_1) (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_301600364e_Prof) (tptp.hAPP _let_4 _let_5 (tptp.combk _let_4 _let_2) tptp.arrow_1568854078le_Lin)))) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.arrow_1998540521e_indi (tptp.fun (tptp.product_prod tptp.arrow_2142409994le_alt tptp.arrow_2142409994le_alt) tptp.bool)))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) X_2) tptp.arrow_301600364e_Prof)) (forall ((A_5 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.arrow_2142409994le_alt tptp.arrow_2142409994le_alt))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) (tptp.hAPP tptp.arrow_2142409994le_alt _let_1 (tptp.hAPP tptp.arrow_2142409994le_alt (tptp.fun tptp.arrow_2142409994le_alt _let_1) (tptp.product_Pair tptp.arrow_2142409994le_alt tptp.arrow_2142409994le_alt) A_5) B_2)))) (=> (not (= (tptp.ti tptp.arrow_2142409994le_alt A_5) (tptp.ti tptp.arrow_2142409994le_alt B_2))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 (tptp.hAPP tptp.arrow_1998540521e_indi _let_2 X_2 I_1))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 (tptp.hAPP (tptp.fun tptp.arrow_1998540521e_indi _let_2) _let_2 Fa_1 X_2))))))))))))) (tptp.hBOOL (tptp.hAPP tptp.arrow_1998540521e_indi tptp.bool (tptp.hAPP _let_3 (tptp.fun tptp.arrow_1998540521e_indi tptp.bool) tptp.arrow_708804735ctator Fa_1) I_1))))))))))) _let_26 (forall ((X_a $$unsorted) (Y $$unsorted)) (=> (not (= Y (tptp.nil X_a))) (not (forall ((A_5 $$unsorted) (List_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (not (= Y (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.cons X_a) A_5) List_2)))))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted)) (= (not (= Xs_1 (tptp.nil X_a))) (exists ((Y_2 $$unsorted) (Ys_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (= Xs_1 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.cons X_a) Y_2) Ys_2)))))) (forall ((X_a $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun X_a _let_1))) (let ((_let_3 (tptp.fun X_a X_a))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP _let_3 (tptp.fun _let_4 tptp.bool) (tptp.member _let_3) (tptp.combi X_a)) (tptp.hAPP _let_2 _let_4 (tptp.hAPP _let_1 (tptp.fun _let_2 _let_4) (tptp.pi X_a X_a) A_2) (tptp.hAPP _let_1 _let_2 (tptp.combk _let_1 X_a) A_2))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_1 $$unsorted) (F $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.fun X_a _let_1))) (let ((_let_4 (tptp.fun X_a X_b))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP _let_4 (tptp.fun _let_5 tptp.bool) (tptp.member _let_4) F) (tptp.hAPP _let_3 _let_5 (tptp.hAPP _let_2 (tptp.fun _let_3 _let_5) (tptp.pi X_a X_b) A_2) (tptp.hAPP _let_1 _let_3 (tptp.combk _let_1 X_a) B_1)))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a (tptp.fun _let_2 tptp.bool) (tptp.member X_a) X_1) A_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) (tptp.hAPP X_a X_b F X_1)) B_1)))))))))) (forall ((X_a $$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 $$unsorted) (X_b $$unsorted) (Pa $$unsorted)) (= (exists ((X1 $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.product_prod X_a X_b) tptp.bool Pa X1))) (exists ((A_5 $$unsorted) (B_2 $$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_5) B_2))))))) (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_5 $$unsorted) (B_2 $$unsorted) (C_2 $$unsorted) (D_3 $$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_5) (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_3) (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 $$unsorted) (X $$unsorted) (Xs $$unsorted) (Y $$unsorted) (Ys_1 $$unsorted)) (let ((_let_1 (tptp.splice X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (let ((_let_4 (tptp.cons X_a))) (let ((_let_5 (tptp.hAPP X_a _let_3 _let_4 Y))) (let ((_let_6 (tptp.hAPP X_a _let_3 _let_4 X))) (= (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_3 _let_1 (tptp.hAPP _let_2 _let_2 _let_6 Xs)) (tptp.hAPP _let_2 _let_2 _let_5 Ys_1)) (tptp.hAPP _let_2 _let_2 _let_6 (tptp.hAPP _let_2 _let_2 _let_5 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_3 _let_1 Xs) Ys_1))))))))))) (forall ((X_a $$unsorted) (Ys_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.splice X_a) (tptp.nil X_a)) Ys_1) Ys_1))) (forall ((X_a $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.list X_a))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.splice X_a) Xs) (tptp.nil X_a)) Xs))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_1 $$unsorted) (F $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.fun X_a X_b))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.fun X_a _let_1))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP _let_3 (tptp.fun _let_4 tptp.bool) (tptp.member _let_3) F) (tptp.hAPP _let_5 _let_4 (tptp.hAPP _let_2 (tptp.fun _let_5 _let_4) (tptp.pi X_a X_b) A_2) B_1))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a (tptp.fun _let_2 tptp.bool) (tptp.member X_a) X_1) A_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) (tptp.hAPP X_a X_b F X_1)) (tptp.hAPP X_a _let_1 B_1 X_1))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted) (X_d $$unsorted) (X_e $$unsorted) (X_f $$unsorted) (Y $$unsorted)) (not (forall ((A_5 $$unsorted) (B_2 $$unsorted) (C_2 $$unsorted) (D_3 $$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_5) (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_3) (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 $$unsorted) (Y $$unsorted)) (not (forall ((A_5 $$unsorted) (B_2 $$unsorted) (C_2 $$unsorted) (D_3 $$unsorted) (E $$unsorted)) (let ((_let_1 (tptp.product_prod X_d X_e))) (let ((_let_2 (tptp.product_prod X_c _let_1))) (let ((_let_3 (tptp.product_prod X_b _let_2))) (let ((_let_4 (tptp.product_prod X_a _let_3))) (not (= (tptp.ti _let_4 Y) (tptp.hAPP _let_3 _let_4 (tptp.hAPP X_a (tptp.fun _let_3 _let_4) (tptp.product_Pair X_a _let_3) A_5) (tptp.hAPP _let_2 _let_3 (tptp.hAPP X_b (tptp.fun _let_2 _let_3) (tptp.product_Pair X_b _let_2) B_2) (tptp.hAPP _let_1 _let_2 (tptp.hAPP X_c (tptp.fun _let_1 _let_2) (tptp.product_Pair X_c _let_1) C_2) (tptp.hAPP X_e _let_1 (tptp.hAPP X_d (tptp.fun X_e _let_1) (tptp.product_Pair X_d X_e) D_3) E))))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted) (X_d $$unsorted) (X_e $$unsorted) (X_1 $$unsorted) (Pa $$unsorted)) (=> (forall ((A_5 $$unsorted) (B_2 $$unsorted) (C_2 $$unsorted) (D_3 $$unsorted) (E $$unsorted)) (let ((_let_1 (tptp.product_prod X_d X_e))) (let ((_let_2 (tptp.product_prod X_c _let_1))) (let ((_let_3 (tptp.product_prod X_b _let_2))) (let ((_let_4 (tptp.product_prod X_a _let_3))) (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool Pa (tptp.hAPP _let_3 _let_4 (tptp.hAPP X_a (tptp.fun _let_3 _let_4) (tptp.product_Pair X_a _let_3) A_5) (tptp.hAPP _let_2 _let_3 (tptp.hAPP X_b (tptp.fun _let_2 _let_3) (tptp.product_Pair X_b _let_2) B_2) (tptp.hAPP _let_1 _let_2 (tptp.hAPP X_c (tptp.fun _let_1 _let_2) (tptp.product_Pair X_c _let_1) C_2) (tptp.hAPP X_e _let_1 (tptp.hAPP X_d (tptp.fun X_e _let_1) (tptp.product_Pair X_d X_e) D_3) E))))))))))) (tptp.hBOOL (tptp.hAPP (tptp.product_prod X_a (tptp.product_prod X_b (tptp.product_prod X_c (tptp.product_prod X_d X_e)))) tptp.bool Pa X_1)))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F $$unsorted) (B_1 $$unsorted) (A_2 $$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 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a (tptp.fun _let_2 tptp.bool) (tptp.member X_a) X_2) A_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) (tptp.hAPP X_a X_b F X_2)) (tptp.hAPP X_a _let_1 B_1 X_2))))))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) F) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun X_a tptp.bool) (tptp.fun _let_3 _let_2) (tptp.pi X_a X_b) A_2) B_1)))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted) (X_d $$unsorted) (Y $$unsorted)) (not (forall ((A_5 $$unsorted) (B_2 $$unsorted) (C_2 $$unsorted) (D_3 $$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_5) (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_3))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted) (X_d $$unsorted) (X_1 $$unsorted) (Pa $$unsorted)) (=> (forall ((A_5 $$unsorted) (B_2 $$unsorted) (C_2 $$unsorted) (D_3 $$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_5) (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_3))))))))) (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 $$unsorted) (Y $$unsorted)) (not (forall ((A_5 $$unsorted) (B_2 $$unsorted) (C_2 $$unsorted)) (let ((_let_1 (tptp.product_prod X_b X_c))) (let ((_let_2 (tptp.product_prod X_a _let_1))) (not (= (tptp.ti _let_2 Y) (tptp.hAPP _let_1 _let_2 (tptp.hAPP X_a (tptp.fun _let_1 _let_2) (tptp.product_Pair X_a _let_1) A_5) (tptp.hAPP X_c _let_1 (tptp.hAPP X_b (tptp.fun X_c _let_1) (tptp.product_Pair X_b X_c) B_2) C_2))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted) (X_1 $$unsorted) (Pa $$unsorted)) (=> (forall ((A_5 $$unsorted) (B_2 $$unsorted) (C_2 $$unsorted)) (let ((_let_1 (tptp.product_prod X_b X_c))) (let ((_let_2 (tptp.product_prod X_a _let_1))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool Pa (tptp.hAPP _let_1 _let_2 (tptp.hAPP X_a (tptp.fun _let_1 _let_2) (tptp.product_Pair X_a _let_1) A_5) (tptp.hAPP X_c _let_1 (tptp.hAPP X_b (tptp.fun X_c _let_1) (tptp.product_Pair X_b X_c) B_2) C_2))))))) (tptp.hBOOL (tptp.hAPP (tptp.product_prod X_a (tptp.product_prod X_b X_c)) tptp.bool Pa X_1)))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F $$unsorted) (B_1 $$unsorted) (A_2 $$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 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a (tptp.fun _let_2 tptp.bool) (tptp.member X_a) X_2) A_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) (tptp.hAPP X_a X_b F X_2)) B_1)))))) (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP _let_3 (tptp.fun _let_4 tptp.bool) (tptp.member _let_3) F) (tptp.hAPP _let_2 _let_4 (tptp.hAPP (tptp.fun X_a tptp.bool) (tptp.fun _let_2 _let_4) (tptp.pi X_a X_b) A_2) (tptp.hAPP _let_1 _let_2 (tptp.combk _let_1 X_a) B_1)))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F $$unsorted) (B_1 $$unsorted) (A_2 $$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 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a (tptp.fun _let_2 tptp.bool) (tptp.member X_a) X_2) A_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) (tptp.hAPP X_a X_b F X_2)) (tptp.hAPP X_a _let_1 B_1 X_2))))))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) F) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun X_a tptp.bool) (tptp.fun _let_3 _let_2) (tptp.pi X_a X_b) A_2) B_1)))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (B_1 $$unsorted) (F $$unsorted) (G $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun X_a (tptp.fun X_b tptp.bool)))) (let ((_let_4 (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun X_a tptp.bool) (tptp.fun _let_3 _let_2) (tptp.pi X_a X_b) A_2) B_1))) (let ((_let_5 (tptp.member _let_1))) (let ((_let_6 (tptp.fun _let_2 tptp.bool))) (=> (forall ((W $$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_2)) (= (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) (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 $$unsorted) (Y $$unsorted)) (not (forall ((A_5 $$unsorted) (B_2 $$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_5) B_2))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (S_2 $$unsorted) (R_2 $$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_2)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 S_2))))))) (= (tptp.ti _let_1 R_2) (tptp.ti _let_1 S_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 $$unsorted) (Pa $$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_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 $$unsorted) (A_2 $$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_1) A_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool A_2 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_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 $$unsorted) (Xb_1 $$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_1) (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_1)))))) (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) (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 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_a _let_2 (tptp.hAPP (tptp.fun _let_1 tptp.bool) (tptp.fun X_a _let_2) (tptp.product_curry X_a X_b tptp.bool) F) Aa) Ba)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool F (tptp.hAPP X_b _let_1 (tptp.hAPP X_a (tptp.fun X_b _let_1) (tptp.product_Pair X_a X_b) Aa) Ba))))))) (forall ((X_a $$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_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_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)))))) _let_25 (forall ((X_a $$unsorted) (Aa $$unsorted) (X_1 $$unsorted) (Ba $$unsorted) (Y_1 $$unsorted) (R_1 $$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.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_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))) (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_1)) (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 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.distinct X_a))) (=> (not (= Xs (tptp.nil X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 Xs)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.butlast X_a) Xs)))))))) _let_17 (forall ((X_a $$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 $$unsorted)) (=> (tptp.linorder X_a) (forall ((Xs $$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_2 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.fun X_a X_b) tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun X_a _let_2))) (= (tptp.hAPP _let_3 _let_1 (tptp.hAPP (tptp.fun X_a tptp.bool) (tptp.fun _let_3 _let_1) (tptp.pi X_a X_b) A_2) (tptp.hAPP _let_2 _let_3 (tptp.combk _let_2 X_a) (tptp.top_top _let_2))) (tptp.top_top _let_1)))))) (forall ((X_a $$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_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.product_prod _let_1 _let_1))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (not (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_3 tptp.bool) (tptp.member _let_2) (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_2) (tptp.product_Pair _let_1 _let_1) X_1) (tptp.nil X_a))) (tptp.hAPP (tptp.fun (tptp.product_prod X_a X_a) tptp.bool) _let_3 (tptp.lexord X_a) R_1)))))))) (forall ((X_a $$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 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (=> (= Xs (tptp.nil X_a)) (= (tptp.hAPP _let_1 X_a (tptp.last X_a) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.cons X_a) X) Xs)) (tptp.ti X_a X))))) (forall ((X_a $$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)))))) (forall ((X_a $$unsorted) (Y_1 $$unsorted) (R_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.product_prod _let_1 _let_1))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_3 tptp.bool) (tptp.member _let_2) (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_2) (tptp.product_Pair _let_1 _let_1) (tptp.nil X_a)) Y_1)) (tptp.hAPP (tptp.fun (tptp.product_prod X_a X_a) tptp.bool) _let_3 (tptp.lexord X_a) R_1))) (exists ((A_5 $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (= Y_1 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.cons X_a) A_5) X_2))))))))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted) (R_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.product_prod _let_1 _let_1))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.hAPP (tptp.fun (tptp.product_prod X_a X_a) tptp.bool) _let_3 (tptp.lexord X_a) R_1))) (let ((_let_5 (tptp.product_Pair _let_1 _let_1))) (let ((_let_6 (tptp.fun _let_1 _let_2))) (let ((_let_7 (tptp.member _let_2))) (let ((_let_8 (tptp.fun _let_3 tptp.bool))) (=> (forall ((A_5 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.product_Pair X_a X_a))) (let ((_let_2 (tptp.product_prod X_a X_a))) (let ((_let_3 (tptp.fun X_a _let_2))) (let ((_let_4 (tptp.member _let_2))) (let ((_let_5 (tptp.fun _let_2 tptp.bool))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (or (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP _let_2 _let_6 _let_4 (tptp.hAPP X_a _let_2 (tptp.hAPP X_a _let_3 _let_1 A_5) B_2)) R_1)) (= (tptp.ti X_a A_5) (tptp.ti X_a B_2)) (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP _let_2 _let_6 _let_4 (tptp.hAPP X_a _let_2 (tptp.hAPP X_a _let_3 _let_1 B_2) A_5)) R_1)))))))))) (or (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 _let_8 _let_7 (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_1 _let_6 _let_5 X_1) Y_1)) _let_4)) (= X_1 Y_1) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 _let_8 _let_7 (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_1 _let_6 _let_5 Y_1) X_1)) _let_4))))))))))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (R_1 $$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))) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_a))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (not (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) (tptp.hAPP X_a _let_1 (tptp.hAPP X_a (tptp.fun X_a _let_1) (tptp.product_Pair X_a X_a) X_2) X_2)) R_1)))))) (not (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_3 tptp.bool) (tptp.member _let_2) (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_2) (tptp.product_Pair _let_1 _let_1) Xs_1) Xs_1)) (tptp.hAPP (tptp.fun (tptp.product_prod X_a X_a) tptp.bool) _let_3 (tptp.lexord X_a) R_1))))))))) _let_16 (forall ((X_a $$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 $$unsorted) (Xs_1 $$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))))) (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 $$unsorted) (Xs $$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) (L_1 $$unsorted) (Pa $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP (tptp.fun X_a tptp.bool) _let_2 (tptp.takeWhile X_a) Pa))) (=> (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa X_1))) (= (tptp.hAPP _let_1 _let_1 _let_3 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.append X_a) Xs_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_2 (tptp.cons X_a) X_1) L_1))) (tptp.hAPP _let_1 _let_1 _let_3 Xs_1))))))) (forall ((X_a $$unsorted) (Ys_1 $$unsorted) (Us_2 $$unsorted) (Xs $$unsorted) (Xs1 $$unsorted) (Zs_2 $$unsorted)) (let ((_let_1 (tptp.append X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (let ((_let_4 (tptp.hAPP _let_2 _let_3 _let_1 Xs))) (=> (= (tptp.hAPP _let_2 _let_2 _let_4 Xs1) Zs_2) (=> (= Ys_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_3 _let_1 Xs1) Us_2)) (= (tptp.hAPP _let_2 _let_2 _let_4 Ys_1) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_3 _let_1 Zs_2) Us_2))))))))) (forall ((X_a $$unsorted) (Ys $$unsorted) (Xs_1 $$unsorted) (Zs_1 $$unsorted)) (let ((_let_1 (tptp.append X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (= (= (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_3 _let_1 Ys) Xs_1) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_3 _let_1 Zs_1) Xs_1)) (= Ys Zs_1)))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (Ys $$unsorted) (Zs_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.append X_a) Xs_1))) (= (= (tptp.hAPP _let_1 _let_1 _let_2 Ys) (tptp.hAPP _let_1 _let_1 _let_2 Zs_1)) (= Ys Zs_1))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (Ys $$unsorted) (Zs_1 $$unsorted) (Ts $$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) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_3 _let_1 Zs_1) Ts)) (exists ((Us $$unsorted)) (let ((_let_1 (tptp.append X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (let ((_let_4 (tptp.hAPP _let_2 _let_3 _let_1 Us))) (or (and (= Xs_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_3 _let_1 Zs_1) Us)) (= (tptp.hAPP _let_2 _let_2 _let_4 Ys) Ts)) (and (= (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_3 _let_1 Xs_1) Us) Zs_1) (= Ys (tptp.hAPP _let_2 _let_2 _let_4 Ts)))))))))))))) (forall ((X_a $$unsorted) (Xs $$unsorted) (Ys_1 $$unsorted) (Zs_2 $$unsorted)) (let ((_let_1 (tptp.append X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (let ((_let_4 (tptp.hAPP _let_2 _let_3 _let_1 Xs))) (= (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_3 _let_1 (tptp.hAPP _let_2 _let_2 _let_4 Ys_1)) Zs_2) (tptp.hAPP _let_2 _let_2 _let_4 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_3 _let_1 Ys_1) Zs_2)))))))) (forall ((X_a $$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 $$unsorted) (X $$unsorted) (Xs $$unsorted) (Ys_1 $$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.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_1) (tptp.hAPP _let_2 _let_2 _let_4 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_3 _let_1 Xs) Ys_1)))))))) (forall ((X_a $$unsorted) (Xs $$unsorted) (Zs_2 $$unsorted) (X $$unsorted) (Xs1 $$unsorted) (Ys_1 $$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.hAPP X_a _let_3 (tptp.cons X_a) X))) (=> (= (tptp.hAPP _let_2 _let_2 _let_4 Xs1) Ys_1) (=> (= Xs (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_3 _let_1 Xs1) Zs_2)) (= (tptp.hAPP _let_2 _let_2 _let_4 Xs) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_3 _let_1 Ys_1) Zs_2))))))))) (forall ((X_a $$unsorted) (Ys_1 $$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) (tptp.nil X_a)) Ys_1) Ys_1))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (Ys $$unsorted)) (let ((_let_1 (tptp.nil X_a))) (let ((_let_2 (tptp.list X_a))) (= (= _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 (tptp.fun _let_2 _let_2) (tptp.append X_a) Xs_1) Ys)) (and (= Xs_1 _let_1) (= Ys _let_1)))))) (forall ((X_a $$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 $$unsorted) (Ys $$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)) (= Ys (tptp.nil X_a))))) (forall ((X_a $$unsorted) (Ys $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (= (= Ys (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.append X_a) Xs_1) Ys)) (= Xs_1 (tptp.nil X_a))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (Ys $$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) _let_1) (and (= Xs_1 _let_1) (= Ys _let_1)))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (Ys $$unsorted)) (let ((_let_1 (tptp.list X_a))) (= (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.append X_a) Xs_1) Ys) Xs_1) (= Ys (tptp.nil X_a))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (Ys $$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) Ys) (= Xs_1 (tptp.nil X_a))))) (forall ((X_a $$unsorted) (Xs $$unsorted) (Ys_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (=> (= Xs Ys_1) (= Xs (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.append X_a) (tptp.nil X_a)) Ys_1))))) (forall ((X_a $$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) (Ys $$unsorted) (Zs_1 $$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) Zs_1) _let_3) (or (and (= Ys (tptp.nil X_a)) (= Zs_1 _let_3)) (exists ((Ys_3 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (and (= Ys (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_2 (tptp.cons X_a) X_1) Ys_3)) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.append X_a) Ys_3) Zs_1) Xs_1))))))))))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (Xs_1 $$unsorted) (Ys $$unsorted) (Zs_1 $$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_3 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.append X_a) Ys) Zs_1)) (or (and (= Ys (tptp.nil X_a)) (= _let_3 Zs_1)) (exists ((Ys_3 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (and (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_2 (tptp.cons X_a) X_1) Ys_3) Ys) (= Xs_1 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.append X_a) Ys_3) Zs_1)))))))))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (X_1 $$unsorted) (Ys $$unsorted) (Y_1 $$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) (tptp.hAPP _let_3 _let_3 (tptp.hAPP X_a _let_4 _let_2 Y_1) _let_1))) (and (= Xs_1 Ys) (= (tptp.ti X_a X_1) (tptp.ti X_a Y_1)))))))))) (forall ((X_a $$unsorted) (Xs $$unsorted) (Ys_1 $$unsorted)) (let ((_let_1 (tptp.butlast X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.hAPP _let_2 (tptp.fun _let_2 _let_2) (tptp.append X_a) Xs))) (let ((_let_4 (tptp.hAPP _let_2 _let_2 _let_1 (tptp.hAPP _let_2 _let_2 _let_3 Ys_1)))) (let ((_let_5 (= Ys_1 (tptp.nil X_a)))) (and (=> _let_5 (= _let_4 (tptp.hAPP _let_2 _let_2 _let_1 Xs))) (=> (not _let_5) (= _let_4 (tptp.hAPP _let_2 _let_2 _let_3 (tptp.hAPP _let_2 _let_2 _let_1 Ys_1))))))))))) (forall ((X_a $$unsorted) (Xs $$unsorted) (Ys_1 $$unsorted)) (let ((_let_1 (tptp.last X_a))) (let ((_let_2 (tptp.list X_a))) (=> (= Ys_1 (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_1)) (tptp.hAPP _let_2 X_a _let_1 Xs)))))) (forall ((X_a $$unsorted) (Xs $$unsorted) (Ys_1 $$unsorted)) (let ((_let_1 (tptp.last X_a))) (let ((_let_2 (tptp.list X_a))) (=> (not (= Ys_1 (tptp.nil X_a))) (= (tptp.hAPP _let_2 X_a _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 (tptp.fun _let_2 _let_2) (tptp.append X_a) Xs) Ys_1)) (tptp.hAPP _let_2 X_a _let_1 Ys_1)))))) (forall ((X_a $$unsorted) (Xs $$unsorted) (Ys_1 $$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_1)))) (let ((_let_4 (= Ys_1 (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_1))))))))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (U $$unsorted) (V $$unsorted) (R_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.product_prod _let_1 _let_1))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.hAPP (tptp.fun (tptp.product_prod X_a X_a) tptp.bool) _let_3 (tptp.lexord X_a) R_1))) (let ((_let_5 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.append X_a) X_1))) (let ((_let_6 (tptp.product_Pair _let_1 _let_1))) (let ((_let_7 (tptp.fun _let_1 _let_2))) (let ((_let_8 (tptp.member _let_2))) (let ((_let_9 (tptp.fun _let_3 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 _let_9 _let_8 (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_1 _let_7 _let_6 U) V)) _let_4)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 _let_9 _let_8 (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_1 _let_7 _let_6 (tptp.hAPP _let_1 _let_1 _let_5 U)) (tptp.hAPP _let_1 _let_1 _let_5 V))) _let_4))))))))))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (Pa $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP X_a _let_2 (tptp.cons X_a) X_1))) (let ((_let_4 (tptp.hAPP (tptp.fun X_a tptp.bool) _let_2 (tptp.takeWhile X_a) Pa))) (let ((_let_5 (tptp.hAPP _let_1 _let_1 _let_4 (tptp.hAPP _let_1 _let_1 _let_3 Xs_1)))) (let ((_let_6 (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa X_1)))) (and (=> _let_6 (= _let_5 (tptp.hAPP _let_1 _let_1 _let_3 (tptp.hAPP _let_1 _let_1 _let_4 Xs_1)))) (=> (not _let_6) (= _let_5 (tptp.nil X_a))))))))))) (forall ((X_b $$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 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (= (tptp.top_top _let_1) (tptp.hAPP _let_1 _let_1 (tptp.collect X_a) (tptp.hAPP tptp.bool _let_1 (tptp.combk tptp.bool X_a) tptp.fTrue))))) (forall ((X_a $$unsorted) (U $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted) (Aa $$unsorted) (Ba $$unsorted) (R_1 $$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.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_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) (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_1))))))))))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (X_1 $$unsorted) (Ys $$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) (and (not (= Ys _let_2)) (= (tptp.hAPP _let_1 _let_1 (tptp.butlast X_a) Ys) Xs_1) (= (tptp.hAPP _let_1 X_a (tptp.last X_a) Ys) (tptp.ti X_a X_1)))))))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (R_1 $$unsorted) (Y_1 $$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 $$unsorted) (Z $$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)))) (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_1)))))))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (U $$unsorted) (V $$unsorted) (R_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.product_prod _let_1 _let_1))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.hAPP (tptp.fun (tptp.product_prod X_a X_a) tptp.bool) _let_3 (tptp.lexord X_a) R_1))) (let ((_let_5 (tptp.product_Pair _let_1 _let_1))) (let ((_let_6 (tptp.fun _let_1 _let_2))) (let ((_let_7 (tptp.member _let_2))) (let ((_let_8 (tptp.fun _let_3 tptp.bool))) (let ((_let_9 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.append X_a) X_1))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 _let_8 _let_7 (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_1 _let_6 _let_5 (tptp.hAPP _let_1 _let_1 _let_9 U)) (tptp.hAPP _let_1 _let_1 _let_9 V))) _let_4)) (=> (forall ((A_5 $$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_5) A_5)) R_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 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 $$unsorted)) (=> (not (= Xs (tptp.nil X_a))) (not (forall ((Ys_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (not (= Xs (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.append X_a) Ys_2) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_2 (tptp.cons X_a) Y_2) (tptp.nil X_a))))))))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (X_1 $$unsorted) (Ys $$unsorted) (Y_1 $$unsorted) (R_1 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_a))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.list X_a))) (let ((_let_4 (tptp.product_prod _let_3 _let_3))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (let ((_let_6 (tptp.hAPP _let_2 _let_5 (tptp.listrel1 X_a) R_1))) (let ((_let_7 (tptp.product_Pair _let_3 _let_3))) (let ((_let_8 (tptp.fun _let_3 _let_4))) (let ((_let_9 (tptp.member _let_4))) (let ((_let_10 (tptp.fun _let_5 tptp.bool))) (let ((_let_11 (tptp.nil X_a))) (let ((_let_12 (tptp.cons X_a))) (let ((_let_13 (tptp.fun _let_3 _let_3))) (let ((_let_14 (tptp.append X_a))) (= (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP _let_4 _let_10 _let_9 (tptp.hAPP _let_3 _let_4 (tptp.hAPP _let_3 _let_8 _let_7 (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_3 _let_13 _let_14 Xs_1) (tptp.hAPP _let_3 _let_3 (tptp.hAPP X_a _let_13 _let_12 X_1) _let_11))) (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_3 _let_13 _let_14 Ys) (tptp.hAPP _let_3 _let_3 (tptp.hAPP X_a _let_13 _let_12 Y_1) _let_11)))) _let_6)) (or (and (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP _let_4 _let_10 _let_9 (tptp.hAPP _let_3 _let_4 (tptp.hAPP _let_3 _let_8 _let_7 Xs_1) Ys)) _let_6)) (= (tptp.ti X_a X_1) (tptp.ti X_a Y_1))) (and (= Xs_1 Ys) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) (tptp.hAPP X_a _let_1 (tptp.hAPP X_a (tptp.fun X_a _let_1) (tptp.product_Pair X_a X_a) X_1) Y_1)) R_1)))))))))))))))))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.nil X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun X_a _let_2))) (let ((_let_4 (tptp.fun _let_2 _let_2))) (let ((_let_5 (tptp.fun X_a _let_4))) (let ((_let_6 (tptp.fun _let_2 _let_4))) (= (tptp.hAPP _let_2 _let_2 (tptp.rotate1 X_a) Xs_1) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_5 _let_4 (tptp.hAPP _let_2 (tptp.fun _let_5 _let_4) (tptp.list_case _let_2 X_a) _let_1) (tptp.hAPP _let_3 _let_5 (tptp.hAPP _let_6 (tptp.fun _let_3 _let_5) (tptp.combb _let_2 _let_4 X_a) (tptp.hAPP _let_6 _let_6 (tptp.combc _let_2 _let_2 _let_2) (tptp.append X_a))) (tptp.hAPP _let_2 _let_3 (tptp.hAPP _let_5 (tptp.fun _let_2 _let_3) (tptp.combc X_a _let_2 _let_2) (tptp.cons X_a)) _let_1))) Xs_1))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (X $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.list X_b))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP X_b _let_2 (tptp.cons X_b) X))) (let ((_let_4 (tptp.nil X_a))) (let ((_let_5 (tptp.list X_a))) (and (= (tptp.hAPP _let_5 _let_5 (tptp.rotate1 X_a) _let_4) _let_4) (= (tptp.hAPP _let_1 _let_1 (tptp.rotate1 X_b) (tptp.hAPP _let_1 _let_1 _let_3 Xs)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.append X_b) Xs) (tptp.hAPP _let_1 _let_1 _let_3 (tptp.nil X_b))))))))))) (forall ((X_a $$unsorted)) (exists ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) (tptp.top_top _let_1)))))) (forall ((X_a $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (forall ((X_2 $$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_2)))) (= (tptp.top_top _let_1) (tptp.ti _let_1 A_2))))) (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 $$unsorted) (Ys $$unsorted) (R_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.product_prod _let_1 _let_1))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.hAPP (tptp.fun (tptp.product_prod X_a X_a) tptp.bool) _let_3 (tptp.listrel1 X_a) R_1))) (let ((_let_5 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.cons X_a) X_1))) (let ((_let_6 (tptp.product_Pair _let_1 _let_1))) (let ((_let_7 (tptp.fun _let_1 _let_2))) (let ((_let_8 (tptp.member _let_2))) (let ((_let_9 (tptp.fun _let_3 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 _let_9 _let_8 (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_1 _let_7 _let_6 Xs_1) Ys)) _let_4)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 _let_9 _let_8 (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_1 _let_7 _let_6 (tptp.hAPP _let_1 _let_1 _let_5 Xs_1)) (tptp.hAPP _let_1 _let_1 _let_5 Ys))) _let_4))))))))))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (R_1 $$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))) (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_1)))))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (R_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.product_prod _let_1 _let_1))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (not (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_3 tptp.bool) (tptp.member _let_2) (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_2) (tptp.product_Pair _let_1 _let_1) (tptp.nil X_a)) Xs_1)) (tptp.hAPP (tptp.fun (tptp.product_prod X_a X_a) tptp.bool) _let_3 (tptp.listrel1 X_a) R_1)))))))) (forall ((X_a $$unsorted) (Us_1 $$unsorted) (Vs_1 $$unsorted) (Xs_1 $$unsorted) (Ys $$unsorted) (R_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.product_prod _let_1 _let_1))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.hAPP (tptp.fun (tptp.product_prod X_a X_a) tptp.bool) _let_3 (tptp.listrel1 X_a) R_1))) (let ((_let_5 (tptp.append X_a))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (let ((_let_7 (tptp.product_Pair _let_1 _let_1))) (let ((_let_8 (tptp.fun _let_1 _let_2))) (let ((_let_9 (tptp.member _let_2))) (let ((_let_10 (tptp.fun _let_3 tptp.bool))) (=> (or (and (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 _let_10 _let_9 (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_1 _let_8 _let_7 Xs_1) Ys)) _let_4)) (= Us_1 Vs_1)) (and (= Xs_1 Ys) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 _let_10 _let_9 (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_1 _let_8 _let_7 Us_1) Vs_1)) _let_4)))) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 _let_10 _let_9 (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_1 _let_8 _let_7 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_6 _let_5 Xs_1) Us_1)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_6 _let_5 Ys) Vs_1))) _let_4)))))))))))))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (Xs_1 $$unsorted) (Y_1 $$unsorted) (Ys $$unsorted) (R_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.product_prod _let_1 _let_1))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.product_prod X_a X_a))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (let ((_let_6 (tptp.hAPP _let_5 _let_3 (tptp.listrel1 X_a) R_1))) (let ((_let_7 (tptp.product_Pair _let_1 _let_1))) (let ((_let_8 (tptp.fun _let_1 _let_2))) (let ((_let_9 (tptp.member _let_2))) (let ((_let_10 (tptp.fun _let_3 tptp.bool))) (let ((_let_11 (tptp.cons X_a))) (let ((_let_12 (tptp.fun _let_1 _let_1))) (= (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 _let_10 _let_9 (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_1 _let_8 _let_7 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_12 _let_11 X_1) Xs_1)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_12 _let_11 Y_1) Ys))) _let_6)) (or (and (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP _let_4 (tptp.fun _let_5 tptp.bool) (tptp.member _let_4) (tptp.hAPP X_a _let_4 (tptp.hAPP X_a (tptp.fun X_a _let_4) (tptp.product_Pair X_a X_a) X_1) Y_1)) R_1)) (= Xs_1 Ys)) (and (= (tptp.ti X_a X_1) (tptp.ti X_a Y_1)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 _let_10 _let_9 (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_1 _let_8 _let_7 Xs_1) Ys)) _let_6)))))))))))))))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted) (R_1 $$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.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_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) (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_1)))))))))))) (forall ((X_a $$unsorted) (Ys $$unsorted) (Xs_1 $$unsorted) (Us_1 $$unsorted) (Vs_1 $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted) (R_1 $$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.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_1)) (=> (= 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 (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)) (tptp.hAPP _let_5 _let_3 (tptp.listrel1 X_a) R_1))))))))))))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (Ys $$unsorted) (R_1 $$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))) (=> (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)) (tptp.hAPP (tptp.fun (tptp.product_prod X_a X_a) tptp.bool) _let_3 (tptp.listrel1 X_a) R_1))) (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_1)) (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 (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 $$unsorted) (Ys $$unsorted) (R_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.product_prod _let_1 _let_1))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_3 tptp.bool) (tptp.member _let_2) (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_2) (tptp.product_Pair _let_1 _let_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.cons X_a) X_1) Xs_1)) Ys)) (tptp.hAPP (tptp.fun (tptp.product_prod X_a X_a) tptp.bool) _let_3 (tptp.listrel1 X_a) R_1))) (=> (forall ((Y_2 $$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 (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_1)))))))) (not (forall ((Zs $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.product_prod _let_1 _let_1))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (= Ys (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.cons X_a) X_1) Zs)) (not (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_3 tptp.bool) (tptp.member _let_2) (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_2) (tptp.product_Pair _let_1 _let_1) Xs_1) Zs)) (tptp.hAPP (tptp.fun (tptp.product_prod X_a X_a) tptp.bool) _let_3 (tptp.listrel1 X_a) R_1)))))))))))))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (Y_1 $$unsorted) (Ys $$unsorted) (R_1 $$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))) (=> (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))) (tptp.hAPP (tptp.fun (tptp.product_prod X_a X_a) tptp.bool) _let_3 (tptp.listrel1 X_a) R_1))) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_a))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.list X_a))) (=> (= Xs_1 (tptp.hAPP _let_3 _let_3 (tptp.hAPP X_a (tptp.fun _let_3 _let_3) (tptp.cons X_a) X_2) Ys)) (not (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) (tptp.hAPP X_a _let_1 (tptp.hAPP X_a (tptp.fun X_a _let_1) (tptp.product_Pair X_a X_a) X_2) Y_1)) R_1)))))))) (not (forall ((Zs $$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)) (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) Ys)) (tptp.hAPP (tptp.fun (tptp.product_prod X_a X_a) tptp.bool) _let_3 (tptp.listrel1 X_a) R_1)))))))))))))))) _let_15 (forall ((X_a $$unsorted) (Pa $$unsorted) (Xs_1 $$unsorted) (Y_1 $$unsorted) (Ys $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_2 (tptp.cons X_a) Y_1) Ys))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (= (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_4 _let_2 (tptp.dropWhile X_a) Pa) Xs_1) _let_3) (and (= Xs_1 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.append X_a) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_4 _let_2 (tptp.takeWhile X_a) Pa) Xs_1)) _let_3)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa Y_1)))))))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (R_1 $$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))) (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_1)))))))) (forall ((X_a $$unsorted) (Ys $$unsorted) (R_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.product_prod _let_1 _let_1))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (not (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_3 tptp.bool) (tptp.member _let_2) (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_2) (tptp.product_Pair _let_1 _let_1) (tptp.nil X_a)) Ys)) (tptp.hAPP (tptp.fun (tptp.product_prod X_a X_a) tptp.bool) _let_3 (tptp.lex X_a) R_1)))))))) (forall ((X_a $$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 $$unsorted)) (let ((_let_1 (tptp.product_prod X_b X_c))) (let ((_let_2 (tptp.fun _let_1 X_a))) (let ((_let_3 (tptp.hAPP (tptp.fun X_b (tptp.fun X_c X_a)) _let_2 (tptp.product_prod_case X_b X_c X_a) F))) (let ((_let_4 (tptp.fun X_e X_a))) (let ((_let_5 (tptp.fun X_e _let_1))) (let ((_let_6 (tptp.fun _let_5 _let_4))) (let ((_let_7 (tptp.fun X_d _let_4))) (let ((_let_8 (tptp.fun X_d _let_5))) (let ((_let_9 (tptp.product_prod X_d X_e))) (= (tptp.hAPP _let_1 X_a _let_3 (tptp.hAPP _let_9 _let_1 (tptp.hAPP _let_8 (tptp.fun _let_9 _let_1) (tptp.product_prod_case X_d X_e _let_1) G) P_1)) (tptp.hAPP _let_9 X_a (tptp.hAPP _let_7 (tptp.fun _let_9 X_a) (tptp.product_prod_case X_d X_e X_a) (tptp.hAPP _let_8 _let_7 (tptp.hAPP _let_6 (tptp.fun _let_8 _let_7) (tptp.combb _let_5 _let_4 X_d) (tptp.hAPP _let_2 _let_6 (tptp.combb _let_1 X_a X_e) _let_3)) G)) P_1)))))))))))) (forall ((X_c $$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_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 $$unsorted)) (let ((_let_1 (tptp.fun X_a (tptp.fun X_b X_c)))) (let ((_let_2 (tptp.fun (tptp.product_prod X_a X_b) X_c))) (= (tptp.hAPP _let_2 _let_1 (tptp.product_curry X_a X_b X_c) (tptp.hAPP _let_1 _let_2 (tptp.product_prod_case X_a X_b X_c) F)) (tptp.ti _let_1 F))))) _let_8 (forall ((X_a $$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_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 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_b))) (= (tptp.hAPP X_b X_c (tptp.hAPP X_a (tptp.fun X_b X_c) F X_2) Y_2) (tptp.hAPP _let_1 X_c G (tptp.hAPP X_b _let_1 (tptp.hAPP X_a (tptp.fun X_b _let_1) (tptp.product_Pair X_a X_b) X_2) Y_2))))) (= (tptp.hAPP (tptp.fun X_a (tptp.fun X_b X_c)) _let_1 (tptp.product_prod_case X_a X_b X_c) F) (tptp.ti _let_1 G))))) (forall ((X_a $$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 $$unsorted)) (let ((_let_1 (tptp.product_prod X_b X_c))) (=> (= (tptp.ti _let_1 Z_2) (tptp.hAPP X_c _let_1 (tptp.hAPP X_b (tptp.fun X_c _let_1) (tptp.product_Pair X_b X_c) X_2) Y_2)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool Q_1 (tptp.hAPP X_c X_a (tptp.hAPP X_b (tptp.fun X_c X_a) Pa X_2) Y_2))))))))))) (forall ((X_c $$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 $$unsorted) (X_1 $$unsorted) (Xs_1 $$unsorted) (Y_1 $$unsorted) (Ys $$unsorted) (R_1 $$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.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_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))) (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))) _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_1)) (= (tptp.hAPP _let_1 tptp.nat _let_11 Xs_1) (tptp.hAPP _let_1 tptp.nat _let_11 Ys))) (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)) _let_6))))))))))))))))))) (forall ((X_a $$unsorted) (Ws_1 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.list X_a) tptp.bool (tptp.distinct X_a) Ws_1))) (exists ((Xs_2 $$unsorted) (Ys_2 $$unsorted) (Zs $$unsorted) (Y_2 $$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_1 (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_2) (tptp.hAPP _let_1 _let_1 _let_4 Zs)))))))))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (Ys $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted) (R_1 $$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.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_1))) (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_1)) (=> (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)) _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))) _let_6))))))))))))))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (Ys $$unsorted)) (let ((_let_1 (tptp.append X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (let ((_let_4 (tptp.fun _let_2 _let_3))) (let ((_let_5 (tptp.fun X_a _let_3))) (let ((_let_6 (tptp.tl X_a))) (= (tptp.hAPP _let_2 _let_2 _let_6 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_3 _let_1 Xs_1) Ys)) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_5 _let_3 (tptp.hAPP _let_2 (tptp.fun _let_5 _let_3) (tptp.list_case _let_2 X_a) (tptp.hAPP _let_2 _let_2 _let_6 Ys)) (tptp.hAPP _let_3 _let_5 (tptp.combk _let_3 X_a) (tptp.hAPP _let_2 _let_3 (tptp.hAPP _let_4 _let_4 (tptp.combc _let_2 _let_2 _let_2) _let_1) Ys))) Xs_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.cl_HOL_Oequal X_a) (= (tptp.equal_equal X_a) (tptp.fequal X_a)))) (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) (Xs_1 $$unsorted) (R_1 $$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_1))) (= Xs_1 _let_1))))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (R_1 $$unsorted)) (let ((_let_1 (tptp.nil X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.product_prod _let_2 _let_2))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP _let_3 (tptp.fun _let_4 tptp.bool) (tptp.member _let_3) (tptp.hAPP _let_2 _let_3 (tptp.hAPP _let_2 (tptp.fun _let_2 _let_3) (tptp.product_Pair _let_2 _let_2) _let_1) Xs_1)) (tptp.hAPP (tptp.fun (tptp.product_prod X_a X_a) tptp.bool) _let_4 (tptp.listrel X_a) R_1))) (= Xs_1 _let_1))))))) (forall ((X_a $$unsorted) (Xs $$unsorted) (Ys_1 $$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_1))) (not (= Xs Ys_1)))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (Ys $$unsorted) (R_1 $$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)) (tptp.hAPP (tptp.fun (tptp.product_prod X_a X_a) tptp.bool) _let_4 (tptp.listrel X_a) R_1))) (= (tptp.hAPP _let_1 tptp.nat _let_2 Xs_1) (tptp.hAPP _let_1 tptp.nat _let_2 Ys)))))))) (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_2 $$unsorted) (Aa $$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_2) (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_2 Aa) Ba) Ca))))))) (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 $$unsorted) (X $$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 $$unsorted) (Xs_1 $$unsorted) (Ys $$unsorted) (R_1 $$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)) (tptp.hAPP (tptp.fun (tptp.product_prod X_a X_a) tptp.bool) _let_4 (tptp.listrel1 X_a) R_1))) (= (tptp.hAPP _let_1 tptp.nat _let_2 Xs_1) (tptp.hAPP _let_1 tptp.nat _let_2 Ys)))))))) (forall ((X_a $$unsorted) (R_1 $$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.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_1)))))))) (forall ((X_a $$unsorted) (Ys_1 $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.tl X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.append X_a))) (let ((_let_4 (tptp.fun _let_2 _let_2))) (=> (not (= Xs (tptp.nil X_a))) (= (tptp.hAPP _let_2 _let_2 _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_4 _let_3 Xs) Ys_1)) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_4 _let_3 (tptp.hAPP _let_2 _let_2 _let_1 Xs)) Ys_1)))))))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted) (R_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.size_size _let_1))) (let ((_let_3 (tptp.product_prod _let_1 _let_1))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.fun (tptp.product_prod X_a X_a) tptp.bool))) (let ((_let_6 (tptp.hAPP _let_3 (tptp.fun _let_4 tptp.bool) (tptp.member _let_3) (tptp.hAPP _let_1 _let_3 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_3) (tptp.product_Pair _let_1 _let_1) X_1) Y_1)))) (= (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool _let_6 (tptp.hAPP _let_5 _let_4 (tptp.lex X_a) R_1))) (and (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool _let_6 (tptp.hAPP _let_5 _let_4 (tptp.lexord X_a) R_1))) (= (tptp.hAPP _let_1 tptp.nat _let_2 X_1) (tptp.hAPP _let_1 tptp.nat _let_2 Y_1))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.cl_HOL_Oequal X_a) (= (tptp.fequal X_a) (tptp.equal_equal X_a)))) (forall ((X_a $$unsorted)) (=> (tptp.cl_HOL_Oequal X_a) (forall ((X_1 $$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) (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) (Xs_1 $$unsorted) (Y_1 $$unsorted) (Ys $$unsorted) (R_1 $$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))) (=> (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))) (tptp.hAPP (tptp.fun (tptp.product_prod X_a X_a) tptp.bool) _let_3 (tptp.listrel X_a) R_1))) (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_1)) (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)) (tptp.hAPP _let_5 _let_3 (tptp.listrel X_a) R_1)))))))))))))))))) (forall ((X_a $$unsorted) (Y_1 $$unsorted) (Ys $$unsorted) (Xs_1 $$unsorted) (R_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.product_prod _let_1 _let_1))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_3 tptp.bool) (tptp.member _let_2) (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_2) (tptp.product_Pair _let_1 _let_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.cons X_a) Y_1) Ys)) Xs_1)) (tptp.hAPP (tptp.fun (tptp.product_prod X_a X_a) tptp.bool) _let_3 (tptp.listrel X_a) R_1))) (not (forall ((Y_2 $$unsorted) (Ys_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.product_prod _let_1 _let_1))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.product_prod X_a X_a))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (= Xs_1 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.cons X_a) Y_2) Ys_2)) (=> (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP _let_4 (tptp.fun _let_5 tptp.bool) (tptp.member _let_4) (tptp.hAPP X_a _let_4 (tptp.hAPP X_a (tptp.fun X_a _let_4) (tptp.product_Pair X_a X_a) Y_1) Y_2)) R_1)) (not (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_3 tptp.bool) (tptp.member _let_2) (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_2) (tptp.product_Pair _let_1 _let_1) Ys) Ys_2)) (tptp.hAPP _let_5 _let_3 (tptp.listrel X_a) R_1)))))))))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (Pa $$unsorted) (Xs_1 $$unsorted) (Ys $$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)) (=> (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 $$unsorted) (Ys_2 $$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_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_2 _let_3 Pa Xs_2) Ys_2)) (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_2))))))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_3 _let_2 Pa Xs_1) Ys))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (Ca $$unsorted) (P_1 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_b))) (=> (forall ((A_5 $$unsorted) (B_2 $$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_5) B_2)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_a (tptp.fun X_b tptp.bool) Ca A_5) 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_5 $$unsorted) (B_2 $$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_5) 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_5) 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_5 $$unsorted) (B_2 $$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_5) 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_5) 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) (R_1 $$unsorted) (X_2 $$unsorted) (Xa $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.product_prod _let_1 _let_1))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.product_prod X_a X_a))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (let ((_let_7 (tptp.fun X_a _let_6))) (let ((_let_8 (tptp.fun X_a _let_4))) (let ((_let_9 (tptp.fun _let_8 _let_7))) (let ((_let_10 (tptp.fun X_a _let_7))) (let ((_let_11 (tptp.fun X_a _let_8))) (let ((_let_12 (tptp.fun X_a tptp.bool))) (let ((_let_13 (tptp.fun _let_5 _let_12))) (let ((_let_14 (tptp.fun X_a _let_13))) (let ((_let_15 (tptp.fun X_a _let_12))) (let ((_let_16 (tptp.fun _let_1 tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_16 (tptp.hAPP _let_15 (tptp.fun _let_1 _let_16) (tptp.listrelp X_a) (tptp.hAPP _let_5 _let_15 (tptp.hAPP _let_14 (tptp.fun _let_5 _let_15) (tptp.combc X_a _let_5 _let_12) (tptp.hAPP _let_10 _let_14 (tptp.hAPP (tptp.fun _let_7 _let_13) (tptp.fun _let_10 _let_14) (tptp.combb _let_7 _let_13 X_a) (tptp.combc X_a _let_5 tptp.bool)) (tptp.hAPP _let_11 _let_10 (tptp.hAPP _let_9 (tptp.fun _let_11 _let_10) (tptp.combb _let_8 _let_7 X_a) (tptp.hAPP (tptp.fun _let_4 _let_6) _let_9 (tptp.combb _let_4 _let_6 X_a) (tptp.member _let_4))) (tptp.product_Pair X_a X_a)))) R_1)) X_2) Xa)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_3 tptp.bool) (tptp.member _let_2) (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_2) (tptp.product_Pair _let_1 _let_1) X_2) Xa)) (tptp.hAPP _let_5 _let_3 (tptp.listrel X_a) R_1))))))))))))))))))))) (forall ((X_a $$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_1 $$unsorted)) (let ((_let_1 (tptp.nil X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.product_prod _let_2 _let_2))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP _let_3 (tptp.fun _let_4 tptp.bool) (tptp.member _let_3) (tptp.hAPP _let_2 _let_3 (tptp.hAPP _let_2 (tptp.fun _let_2 _let_3) (tptp.product_Pair _let_2 _let_2) A1) A2)) (tptp.hAPP (tptp.fun (tptp.product_prod X_a X_a) tptp.bool) _let_4 (tptp.listrel X_a) R_1))) (or (and (= A1 _let_1) (= A2 _let_1)) (exists ((X_2 $$unsorted) (Y_2 $$unsorted) (Xs_2 $$unsorted) (Ys_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.product_prod _let_1 _let_1))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.product_prod X_a X_a))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (let ((_let_6 (tptp.cons X_a))) (let ((_let_7 (tptp.fun _let_1 _let_1))) (and (= A1 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_7 _let_6 X_2) Xs_2)) (= A2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_7 _let_6 Y_2) Ys_2)) (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP _let_4 (tptp.fun _let_5 tptp.bool) (tptp.member _let_4) (tptp.hAPP X_a _let_4 (tptp.hAPP X_a (tptp.fun X_a _let_4) (tptp.product_Pair X_a X_a) X_2) Y_2)) R_1)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_3 tptp.bool) (tptp.member _let_2) (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_2) (tptp.product_Pair _let_1 _let_1) Xs_2) Ys_2)) (tptp.hAPP _let_5 _let_3 (tptp.listrel X_a) R_1))))))))))))))))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (Ys $$unsorted) (R_1 $$unsorted) (N_2 $$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)) (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_1) N_2))) (and (= (tptp.hAPP _let_1 tptp.nat _let_2 Xs_1) N_2) (= (tptp.hAPP _let_1 tptp.nat _let_2 Ys) N_2)))))))) (forall ((X_a $$unsorted) (N $$unsorted)) (exists ((Xs_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (= (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) Xs_2) N)))) (forall ((X_a $$unsorted) (I_2 $$unsorted) (X $$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_2) 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 $$unsorted) (N $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.list X_a))) (= (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) (tptp.hAPP X_a _let_1 (tptp.hAPP tptp.nat (tptp.fun X_a _let_1) (tptp.replicate X_a) N) X)) N))) (forall ((X_a $$unsorted) (N $$unsorted) (X $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.replicate X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun X_a _let_2))) (let ((_let_4 (tptp.hAPP X_a _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 N) X))) (let ((_let_5 (tptp.hAPP X_a _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 K) X))) (let ((_let_6 (tptp.append X_a))) (let ((_let_7 (tptp.fun _let_2 _let_2))) (= (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_7 _let_6 _let_4) _let_5) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_7 _let_6 _let_5) _let_4)))))))))) (forall ((X_a $$unsorted) (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)))) (forall ((X_a $$unsorted) (N $$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) 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)))))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (Ys $$unsorted) (R_1 $$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_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_5 R_1 X_1) Y_1)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 _let_4 _let_6 Xs_1) Ys)) (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)))))))))))) (forall ((X_a $$unsorted) (R_1 $$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_1) _let_1) _let_1)))))) (forall ((X_a $$unsorted) (Ys_1 $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.hd X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.hAPP _let_2 X_a _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 (tptp.fun _let_2 _let_2) (tptp.append X_a) Xs) Ys_1)))) (let ((_let_4 (= Xs (tptp.nil X_a)))) (and (=> _let_4 (= _let_3 (tptp.hAPP _let_2 X_a _let_1 Ys_1))) (=> (not _let_4) (= _let_3 (tptp.hAPP _let_2 X_a _let_1 Xs))))))))) (forall ((X_a $$unsorted) (Ys_1 $$unsorted) (Xs $$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_1)) (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_1 $$unsorted) (A1 $$unsorted) (A2 $$unsorted)) (let ((_let_1 (tptp.nil X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 _let_3 (tptp.hAPP (tptp.fun X_a (tptp.fun X_a tptp.bool)) (tptp.fun _let_2 _let_3) (tptp.listrelp X_a) R_1) A1) A2)) (or (and (= A1 _let_1) (= A2 _let_1)) (exists ((X_2 $$unsorted) (Y_2 $$unsorted) (Xs_2 $$unsorted) (Ys_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.cons X_a))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (and (= A1 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_5 _let_4 X_2) Xs_2)) (= A2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_5 _let_4 Y_2) Ys_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 R_1 X_2) Y_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.hAPP (tptp.fun X_a _let_3) (tptp.fun _let_1 _let_2) (tptp.listrelp X_a) R_1) Xs_2) Ys_2))))))))))))))) (forall ((X_a $$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) (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 $$unsorted) (Xs $$unsorted) (X $$unsorted) (Ys_1 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cons X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (let ((_let_4 (tptp.hAPP _let_2 _let_3 (tptp.append X_a) Xs))) (let ((_let_5 (tptp.fun X_a _let_2))) (= (tptp.hAPP X_a _let_2 (tptp.hAPP tptp.nat _let_5 (tptp.hAPP _let_2 (tptp.fun tptp.nat _let_5) (tptp.list_update X_a) (tptp.hAPP _let_2 _let_2 _let_4 (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_a _let_3 _let_1 X) Ys_1))) (tptp.hAPP _let_2 tptp.nat (tptp.size_size _let_2) Xs)) Y) (tptp.hAPP _let_2 _let_2 _let_4 (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_a _let_3 _let_1 Y) Ys_1))))))))) (forall ((X_b $$unsorted) (X_d $$unsorted) (X_a $$unsorted) (X_c $$unsorted) (F $$unsorted) (G $$unsorted)) (let ((_let_1 (tptp.product_prod X_c X_d))) (let ((_let_2 (tptp.fun X_d _let_1))) (let ((_let_3 (tptp.fun X_a _let_2))) (let ((_let_4 (tptp.fun X_a X_c))) (let ((_let_5 (tptp.fun X_b _let_1))) (let ((_let_6 (tptp.fun X_b X_d))) (let ((_let_7 (tptp.fun _let_6 _let_5))) (let ((_let_8 (tptp.fun X_a _let_7))) (let ((_let_9 (tptp.fun X_a _let_5))) (let ((_let_10 (tptp.fun (tptp.product_prod X_a X_b) _let_1))) (= (tptp.hAPP _let_6 _let_10 (tptp.hAPP _let_4 (tptp.fun _let_6 _let_10) (tptp.product_map_pair X_a X_c X_b X_d) F) G) (tptp.hAPP _let_9 _let_10 (tptp.product_prod_case X_a X_b _let_1) (tptp.hAPP _let_6 _let_9 (tptp.hAPP _let_8 (tptp.fun _let_6 _let_9) (tptp.combc X_a _let_6 _let_5) (tptp.hAPP _let_3 _let_8 (tptp.hAPP (tptp.fun _let_2 _let_7) (tptp.fun _let_3 _let_8) (tptp.combb _let_2 _let_7 X_a) (tptp.combb X_d _let_1 X_b)) (tptp.hAPP _let_4 _let_3 (tptp.hAPP (tptp.fun X_c _let_2) (tptp.fun _let_4 _let_3) (tptp.combb X_c _let_2 X_a) (tptp.product_Pair X_c X_d)) F))) G)))))))))))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (Ys $$unsorted) (R_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.product_prod _let_1 _let_1))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.fun (tptp.product_prod X_a X_a) tptp.bool))) (let ((_let_5 (tptp.hAPP _let_2 (tptp.fun _let_3 tptp.bool) (tptp.member _let_2) (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_2) (tptp.product_Pair _let_1 _let_1) Xs_1) Ys)))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool _let_5 (tptp.hAPP _let_4 _let_3 (tptp.listrel X_a) R_1))) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool _let_5 (tptp.hAPP _let_3 _let_3 (tptp.transitive_rtrancl _let_1) (tptp.hAPP _let_4 _let_3 (tptp.listrel1 X_a) R_1))))))))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (R_1 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.product_prod X_a X_a) tptp.bool))) (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) Xs_1)) (tptp.hAPP _let_1 _let_4 (tptp.listrel X_a) (tptp.hAPP _let_1 _let_1 (tptp.transitive_rtrancl X_a) R_1))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_b))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.fun X_b X_b))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun X_a X_a) (tptp.fun _let_3 _let_2) (tptp.product_map_pair X_a X_a X_b X_b) (tptp.combi X_a)) (tptp.combi X_b)) X_2) (tptp.ti _let_1 X_2)))))) (forall ((X_a $$unsorted) (Xs $$unsorted) (X $$unsorted) (X_3 $$unsorted) (I_2 $$unsorted) (I_4 $$unsorted)) (let ((_let_1 (tptp.list_update X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun X_a _let_2))) (let ((_let_4 (tptp.fun tptp.nat _let_3))) (let ((_let_5 (tptp.hAPP _let_2 _let_4 _let_1 Xs))) (=> (not (= I_2 I_4)) (= (tptp.hAPP X_a _let_2 (tptp.hAPP tptp.nat _let_3 (tptp.hAPP _let_2 _let_4 _let_1 (tptp.hAPP X_a _let_2 (tptp.hAPP tptp.nat _let_3 _let_5 I_2) X)) I_4) X_3) (tptp.hAPP X_a _let_2 (tptp.hAPP tptp.nat _let_3 (tptp.hAPP _let_2 _let_4 _let_1 (tptp.hAPP X_a _let_2 (tptp.hAPP tptp.nat _let_3 _let_5 I_4) X_3)) I_2) X))))))))) (forall ((X_a $$unsorted) (Xs $$unsorted) (I_2 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.list_update X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun X_a _let_2))) (let ((_let_4 (tptp.fun tptp.nat _let_3))) (let ((_let_5 (tptp.hAPP tptp.nat _let_3 (tptp.hAPP _let_2 _let_4 _let_1 Xs) I_2))) (= (tptp.hAPP X_a _let_2 (tptp.hAPP tptp.nat _let_3 (tptp.hAPP _let_2 _let_4 _let_1 (tptp.hAPP X_a _let_2 _let_5 X)) I_2) Y) (tptp.hAPP X_a _let_2 _let_5 Y)))))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (Ys $$unsorted)) (let ((_let_1 (tptp.rev X_a))) (let ((_let_2 (tptp.list X_a))) (= (= (tptp.hAPP _let_2 _let_2 _let_1 Xs_1) (tptp.hAPP _let_2 _let_2 _let_1 Ys)) (= Xs_1 Ys))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (Ys $$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) (= Xs_1 (tptp.hAPP _let_2 _let_2 _let_1 Ys)))))) (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 $$unsorted) (R_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun (tptp.product_prod _let_1 _let_1) tptp.bool))) (let ((_let_3 (tptp.fun (tptp.product_prod X_a X_a) tptp.bool))) (= (tptp.hAPP _let_3 _let_2 (tptp.listrel X_a) (tptp.hAPP _let_3 _let_3 (tptp.transitive_rtrancl X_a) R_1)) (tptp.hAPP _let_2 _let_2 (tptp.transitive_rtrancl _let_1) (tptp.hAPP _let_3 _let_2 (tptp.listrel1 X_a) R_1))))))) (forall ((X_a $$unsorted) (N $$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) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.nil X_a))) (let ((_let_2 (tptp.list X_a))) (= (tptp.hAPP _let_2 _let_2 (tptp.rev X_a) _let_1) _let_1)))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.nil X_a))) (let ((_let_2 (tptp.list X_a))) (= (= _let_1 (tptp.hAPP _let_2 _let_2 (tptp.rev X_a) Xs_1)) (= Xs_1 _let_1))))) (forall ((X_a $$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 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.size_size _let_1))) (= (tptp.hAPP _let_1 tptp.nat _let_2 (tptp.hAPP _let_1 _let_1 (tptp.rev X_a) Xs)) (tptp.hAPP _let_1 tptp.nat _let_2 Xs))))) (forall ((X_a $$unsorted) (Xs $$unsorted) (Ys_1 $$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_1)) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_4 _let_3 (tptp.hAPP _let_2 _let_2 _let_1 Ys_1)) (tptp.hAPP _let_2 _let_2 _let_1 Xs)))))))) (forall ((X_a $$unsorted) (I_2 $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.distinct X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 Xs)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.nat (tptp.fun _let_1 _let_1) (tptp.drop X_a) I_2) Xs))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((N $$unsorted) (Xs $$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) Xs))))))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (K_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.nil X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun X_a _let_2))) (= (= (tptp.hAPP X_a _let_2 (tptp.hAPP tptp.nat _let_3 (tptp.hAPP _let_2 (tptp.fun tptp.nat _let_3) (tptp.list_update X_a) Xs_1) K_1) X_1) _let_1) (= Xs_1 _let_1)))))) (forall ((X_a $$unsorted) (I_2 $$unsorted) (V_1 $$unsorted)) (let ((_let_1 (tptp.nil X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun X_a _let_2))) (= (tptp.hAPP X_a _let_2 (tptp.hAPP tptp.nat _let_3 (tptp.hAPP _let_2 (tptp.fun tptp.nat _let_3) (tptp.list_update X_a) _let_1) I_2) V_1) _let_1))))) (forall ((X_a $$unsorted) (I_2 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.nil 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 (tptp.hAPP _let_2 (tptp.fun tptp.nat _let_3) (tptp.list_update X_a) _let_1) I_2) Y) _let_1))))) (forall ((X_a $$unsorted) (Xs $$unsorted) (I_2 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.size_size _let_1))) (let ((_let_3 (tptp.fun X_a _let_1))) (= (tptp.hAPP _let_1 tptp.nat _let_2 (tptp.hAPP X_a _let_1 (tptp.hAPP tptp.nat _let_3 (tptp.hAPP _let_1 (tptp.fun tptp.nat _let_3) (tptp.list_update X_a) Xs) I_2) X)) (tptp.hAPP _let_1 tptp.nat _let_2 Xs)))))) (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 $$unsorted) (N $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.hAPP tptp.nat (tptp.fun X_a _let_1) (tptp.replicate X_a) N) X))) (= (tptp.hAPP _let_1 _let_1 (tptp.rev X_a) _let_2) _let_2)))) (forall ((X_a $$unsorted) (N $$unsorted) (Xs $$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))) (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 $$unsorted) (N $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.butlast X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.hAPP tptp.nat (tptp.fun _let_2 _let_2) (tptp.drop X_a) N))) (= (tptp.hAPP _let_2 _let_2 _let_1 (tptp.hAPP _let_2 _let_2 _let_3 Xs)) (tptp.hAPP _let_2 _let_2 _let_3 (tptp.hAPP _let_2 _let_2 _let_1 Xs))))))) (forall ((X_a $$unsorted) (N $$unsorted) (Xs $$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))) (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 $$unsorted) (N $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.tl X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.hAPP tptp.nat (tptp.fun _let_2 _let_2) (tptp.drop X_a) N))) (= (tptp.hAPP _let_2 _let_2 _let_1 (tptp.hAPP _let_2 _let_2 _let_3 Xs)) (tptp.hAPP _let_2 _let_2 _let_3 (tptp.hAPP _let_2 _let_2 _let_1 Xs))))))) (forall ((X_c $$unsorted) (X_d $$unsorted) (X_a $$unsorted) (X_b $$unsorted) (F $$unsorted) (G $$unsorted) (Aa $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_b))) (let ((_let_2 (tptp.product_prod X_c X_d))) (let ((_let_3 (tptp.fun _let_2 _let_1))) (let ((_let_4 (tptp.fun X_d X_b))) (= (tptp.hAPP _let_2 _let_1 (tptp.hAPP _let_4 _let_3 (tptp.hAPP (tptp.fun X_c X_a) (tptp.fun _let_4 _let_3) (tptp.product_map_pair X_c X_a X_d X_b) F) G) (tptp.hAPP X_d _let_2 (tptp.hAPP X_c (tptp.fun X_d _let_2) (tptp.product_Pair X_c X_d) Aa) Ba)) (tptp.hAPP X_b _let_1 (tptp.hAPP X_a (tptp.fun X_b _let_1) (tptp.product_Pair X_a X_b) (tptp.hAPP X_c X_a F Aa)) (tptp.hAPP X_d X_b G Ba)))))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (Ys $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted) (R_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.product_prod _let_1 _let_1))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.product_prod X_a X_a))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (let ((_let_6 (tptp.hAPP _let_3 _let_3 (tptp.transitive_rtrancl _let_1) (tptp.hAPP _let_5 _let_3 (tptp.listrel1 X_a) R_1)))) (let ((_let_7 (tptp.cons X_a))) (let ((_let_8 (tptp.fun _let_1 _let_1))) (let ((_let_9 (tptp.product_Pair _let_1 _let_1))) (let ((_let_10 (tptp.fun _let_1 _let_2))) (let ((_let_11 (tptp.member _let_2))) (let ((_let_12 (tptp.fun _let_3 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP _let_4 (tptp.fun _let_5 tptp.bool) (tptp.member _let_4) (tptp.hAPP X_a _let_4 (tptp.hAPP X_a (tptp.fun X_a _let_4) (tptp.product_Pair X_a X_a) X_1) Y_1)) (tptp.hAPP _let_5 _let_5 (tptp.transitive_rtrancl X_a) R_1))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 _let_12 _let_11 (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_1 _let_10 _let_9 Xs_1) Ys)) _let_6)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 _let_12 _let_11 (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_1 _let_10 _let_9 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_8 _let_7 X_1) Xs_1)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_8 _let_7 Y_1) Ys))) _let_6))))))))))))))))) (forall ((X_a $$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) (Zs_1 $$unsorted) (Xs_1 $$unsorted) (Ys $$unsorted) (R_1 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.product_prod X_a X_a) tptp.bool))) (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))) (let ((_let_5 (tptp.hAPP _let_1 _let_4 (tptp.listrel X_a) (tptp.hAPP _let_1 _let_1 (tptp.transitive_rtrancl X_a) R_1)))) (let ((_let_6 (tptp.product_Pair _let_2 _let_2))) (let ((_let_7 (tptp.fun _let_2 _let_3))) (let ((_let_8 (tptp.hAPP _let_2 _let_7 _let_6 Xs_1))) (let ((_let_9 (tptp.member _let_3))) (let ((_let_10 (tptp.fun _let_4 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP _let_3 _let_10 _let_9 (tptp.hAPP _let_2 _let_3 _let_8 Ys)) _let_5)) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP _let_3 _let_10 _let_9 (tptp.hAPP _let_2 _let_3 (tptp.hAPP _let_2 _let_7 _let_6 Ys) Zs_1)) _let_5)) (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP _let_3 _let_10 _let_9 (tptp.hAPP _let_2 _let_3 _let_8 Zs_1)) _let_5))))))))))))))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (Xs_1 $$unsorted) (Ys $$unsorted) (R_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.product_prod _let_1 _let_1))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.hAPP _let_3 _let_3 (tptp.transitive_rtrancl _let_1) (tptp.hAPP (tptp.fun (tptp.product_prod X_a X_a) tptp.bool) _let_3 (tptp.listrel1 X_a) R_1)))) (let ((_let_5 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.cons X_a) X_1))) (let ((_let_6 (tptp.product_Pair _let_1 _let_1))) (let ((_let_7 (tptp.fun _let_1 _let_2))) (let ((_let_8 (tptp.member _let_2))) (let ((_let_9 (tptp.fun _let_3 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 _let_9 _let_8 (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_1 _let_7 _let_6 Xs_1) Ys)) _let_4)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 _let_9 _let_8 (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_1 _let_7 _let_6 (tptp.hAPP _let_1 _let_1 _let_5 Xs_1)) (tptp.hAPP _let_1 _let_1 _let_5 Ys))) _let_4))))))))))))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted) (R_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.size_size _let_1))) (let ((_let_3 (tptp.product_prod _let_1 _let_1))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP _let_3 (tptp.fun _let_4 tptp.bool) (tptp.member _let_3) (tptp.hAPP _let_1 _let_3 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_3) (tptp.product_Pair _let_1 _let_1) X_1) Y_1)) (tptp.hAPP _let_4 _let_4 (tptp.transitive_rtrancl _let_1) (tptp.hAPP (tptp.fun (tptp.product_prod X_a X_a) tptp.bool) _let_4 (tptp.listrel1 X_a) R_1)))) (= (tptp.hAPP _let_1 tptp.nat _let_2 X_1) (tptp.hAPP _let_1 tptp.nat _let_2 Y_1)))))))) (forall ((X_a $$unsorted) (X $$unsorted) (Xs $$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))))))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (Y_1 $$unsorted) (Ys $$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)) (= 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)) (tptp.hAPP _let_1 _let_1 _let_3 (tptp.nil X_a)))))))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (Ys $$unsorted) (R_1 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.product_prod X_a X_a) tptp.bool))) (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))) (let ((_let_5 (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) Ys)))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool _let_5 (tptp.hAPP _let_1 _let_4 (tptp.listrel1 X_a) R_1))) (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool _let_5 (tptp.hAPP _let_1 _let_4 (tptp.listrel X_a) (tptp.hAPP _let_1 _let_1 (tptp.transitive_rtrancl X_a) R_1))))))))))) (forall ((X_a $$unsorted) (Aa $$unsorted) (R_1 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_a))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) (tptp.hAPP X_a _let_1 (tptp.hAPP X_a (tptp.fun X_a _let_1) (tptp.product_Pair X_a X_a) Aa) Aa)) (tptp.hAPP _let_2 _let_2 (tptp.transitive_rtrancl X_a) R_1)))))) (forall ((X_a $$unsorted) (P_1 $$unsorted) (R_1 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_a))) (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) P_1))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 R_1)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 (tptp.hAPP _let_2 _let_2 (tptp.transitive_rtrancl X_a) R_1)))))))) (forall ((X_a $$unsorted) (Ca $$unsorted) (Aa $$unsorted) (Ba $$unsorted) (R_1 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_a))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP _let_2 _let_2 (tptp.transitive_rtrancl X_a) R_1))) (let ((_let_4 (tptp.product_Pair X_a X_a))) (let ((_let_5 (tptp.fun X_a _let_1))) (let ((_let_6 (tptp.hAPP X_a _let_5 _let_4 Aa))) (let ((_let_7 (tptp.member _let_1))) (let ((_let_8 (tptp.fun _let_2 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 _let_8 _let_7 (tptp.hAPP X_a _let_1 _let_6 Ba)) R_1)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 _let_8 _let_7 (tptp.hAPP X_a _let_1 (tptp.hAPP X_a _let_5 _let_4 Ba) Ca)) _let_3)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 _let_8 _let_7 (tptp.hAPP X_a _let_1 _let_6 Ca)) _let_3))))))))))))) (forall ((X_a $$unsorted) (Ca $$unsorted) (Aa $$unsorted) (Ba $$unsorted) (R_1 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_a))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP _let_2 _let_2 (tptp.transitive_rtrancl X_a) R_1))) (let ((_let_4 (tptp.product_Pair X_a X_a))) (let ((_let_5 (tptp.fun X_a _let_1))) (let ((_let_6 (tptp.hAPP X_a _let_5 _let_4 Aa))) (let ((_let_7 (tptp.member _let_1))) (let ((_let_8 (tptp.fun _let_2 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 _let_8 _let_7 (tptp.hAPP X_a _let_1 _let_6 Ba)) _let_3)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 _let_8 _let_7 (tptp.hAPP X_a _let_1 (tptp.hAPP X_a _let_5 _let_4 Ba) Ca)) R_1)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 _let_8 _let_7 (tptp.hAPP X_a _let_1 _let_6 Ca)) _let_3))))))))))))) (forall ((X_a $$unsorted) (Ca $$unsorted) (Aa $$unsorted) (Ba $$unsorted) (R_1 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_a))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP _let_2 _let_2 (tptp.transitive_rtrancl X_a) R_1))) (let ((_let_4 (tptp.product_Pair X_a X_a))) (let ((_let_5 (tptp.fun X_a _let_1))) (let ((_let_6 (tptp.hAPP X_a _let_5 _let_4 Aa))) (let ((_let_7 (tptp.member _let_1))) (let ((_let_8 (tptp.fun _let_2 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 _let_8 _let_7 (tptp.hAPP X_a _let_1 _let_6 Ba)) _let_3)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 _let_8 _let_7 (tptp.hAPP X_a _let_1 (tptp.hAPP X_a _let_5 _let_4 Ba) Ca)) _let_3)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 _let_8 _let_7 (tptp.hAPP X_a _let_1 _let_6 Ca)) _let_3))))))))))))) (forall ((X_a $$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) (Y_1 $$unsorted) (X_1 $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.set X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.list X_a))) (let ((_let_4 (tptp.hAPP X_a (tptp.fun _let_2 tptp.bool) (tptp.member X_a) Y_1))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_4 (tptp.hAPP _let_3 _let_2 _let_1 (tptp.hAPP _let_3 _let_3 (tptp.hAPP X_a (tptp.fun _let_3 _let_3) (tptp.cons X_a) X_1) Xs_1)))) (or (= (tptp.ti X_a Y_1) (tptp.ti X_a X_1)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_4 (tptp.hAPP _let_3 _let_2 _let_1 Xs_1)))))))))) (forall ((X_a $$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) (X_1 $$unsorted) (N_2 $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.set X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.list X_a))) (let ((_let_4 (tptp.hAPP X_a (tptp.fun _let_2 tptp.bool) (tptp.member X_a) X_1))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_4 (tptp.hAPP _let_3 _let_2 _let_1 (tptp.hAPP _let_3 _let_3 (tptp.hAPP tptp.nat (tptp.fun _let_3 _let_3) (tptp.drop X_a) N_2) Xs_1)))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_4 (tptp.hAPP _let_3 _let_2 _let_1 Xs_1))))))))) (forall ((X_a $$unsorted) (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 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) (tptp.hAPP (tptp.list X_a) _let_1 (tptp.set X_a) Xs_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa X_2)))))))) (forall ((X_a $$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) (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 $$unsorted) (Xs_1 $$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) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a (tptp.fun _let_2 tptp.bool) (tptp.member X_a) X_1) (tptp.hAPP _let_1 _let_2 (tptp.set X_a) Xs_1))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.insert X_a) X_1) Xs_1) Xs_1))))) _let_7 (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((Ys $$unsorted) (Xs_1 $$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)) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool _let_4 Ys)) (=> (= (tptp.hAPP _let_3 _let_2 _let_1 Xs_1) (tptp.hAPP _let_3 _let_2 _let_1 Ys)) (= Xs_1 Ys)))))))))))))) (forall ((X_a $$unsorted) (Ys $$unsorted) (Pa $$unsorted) (X_1 $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.hAPP _let_3 _let_2 (tptp.takeWhile X_a) Pa))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_a (tptp.fun _let_3 tptp.bool) (tptp.member X_a) X_1) (tptp.hAPP _let_1 _let_3 (tptp.set X_a) Xs_1))) (=> (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa X_1))) (= (tptp.hAPP _let_1 _let_1 _let_4 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.append X_a) Xs_1) Ys)) (tptp.hAPP _let_1 _let_1 _let_4 Xs_1))))))))) _let_6 (forall ((X_a $$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 $$unsorted) (X_1 $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.butlast X_a))) (let ((_let_3 (tptp.set X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (let ((_let_5 (tptp.hAPP X_a (tptp.fun _let_4 tptp.bool) (tptp.member X_a) X_1))) (=> (or (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool _let_5 (tptp.hAPP _let_1 _let_4 _let_3 (tptp.hAPP _let_1 _let_1 _let_2 Xs_1)))) (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool _let_5 (tptp.hAPP _let_1 _let_4 _let_3 (tptp.hAPP _let_1 _let_1 _let_2 Ys))))) (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool _let_5 (tptp.hAPP _let_1 _let_4 _let_3 (tptp.hAPP _let_1 _let_1 _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.append X_a) Xs_1) Ys)))))))))))) (forall ((X_a $$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 $$unsorted) (Pa $$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)) (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)))))))))) (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) (R_1 $$unsorted)) (let ((_let_1 (tptp.transitive_rtrancl X_a))) (let ((_let_2 (tptp.fun (tptp.product_prod X_a X_a) tptp.bool))) (let ((_let_3 (tptp.hAPP _let_2 _let_2 _let_1 R_1))) (= (tptp.hAPP _let_2 _let_2 _let_1 _let_3) _let_3))))) (forall ((X_a $$unsorted) (Zs_1 $$unsorted) (Ys $$unsorted) (R_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_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_1))) (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 $$unsorted)) (let ((_let_1 (tptp.product_Pair X_a X_a))) (let ((_let_2 (tptp.product_prod X_a X_a))) (let ((_let_3 (tptp.fun X_a _let_2))) (let ((_let_4 (tptp.hAPP X_a _let_3 _let_1 X_2))) (let ((_let_5 (tptp.member _let_2))) (let ((_let_6 (tptp.fun _let_2 tptp.bool))) (let ((_let_7 (tptp.fun _let_6 tptp.bool))) (let ((_let_8 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_8 tptp.bool (tptp.hAPP X_a (tptp.fun _let_8 tptp.bool) (tptp.member X_a) X_2) (tptp.hAPP (tptp.list X_a) _let_8 (tptp.set X_a) Xs_1))) (=> (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP _let_2 _let_7 _let_5 (tptp.hAPP X_a _let_2 _let_4 Y_2)) R_1)) (=> (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP _let_2 _let_7 _let_5 (tptp.hAPP X_a _let_2 (tptp.hAPP X_a _let_3 _let_1 Y_2) Z)) R_1)) (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP _let_2 _let_7 _let_5 (tptp.hAPP X_a _let_2 _let_4 Z)) R_1)))))))))))))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 _let_9 _let_8 (tptp.hAPP _let_1 _let_2 _let_7 Ys)) _let_4)) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 _let_9 _let_8 (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_1 _let_6 _let_5 Ys) Zs_1)) _let_4)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 _let_9 _let_8 (tptp.hAPP _let_1 _let_2 _let_7 Zs_1)) _let_4))))))))))))))) (forall ((X_a $$unsorted) (Ys $$unsorted) (Pa $$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)) (tptp.hAPP _let_1 _let_1 _let_3 Ys))))))) (forall ((X_a $$unsorted) (Ys $$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 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) (tptp.hAPP (tptp.list X_a) _let_1 (tptp.set X_a) Xs_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa X_2))))) (= (tptp.hAPP _let_1 _let_1 _let_3 (tptp.hAPP _let_1 _let_1 _let_4 Ys)) (tptp.hAPP _let_1 _let_1 _let_4 (tptp.hAPP _let_1 _let_1 _let_3 Ys))))))))) (forall ((X_a $$unsorted) (Pa $$unsorted) (Xs_1 $$unsorted)) (=> (exists ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) (tptp.hAPP (tptp.list X_a) _let_1 (tptp.set X_a) Xs_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa X_2))))) (not (forall ((Ys_2 $$unsorted) (X_2 $$unsorted)) (=> (exists ((Zs $$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_2) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_2 (tptp.cons X_a) X_2) Zs)))))) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa X_2)))))))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_1) (tptp.hAPP (tptp.list X_a) _let_1 (tptp.set X_a) Xs_1))) (exists ((Ys_2 $$unsorted) (Zs $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (and (= Xs_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_3 (tptp.append X_a) Ys_2) (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_a _let_3 (tptp.cons X_a) X_1) Zs))) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_1) (tptp.hAPP _let_2 _let_1 (tptp.set X_a) Ys_2)))))))))))) (forall ((X_a $$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_2 $$unsorted) (Zs $$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_2) (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_a _let_3 (tptp.cons X_a) X_1) Zs))) (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)))))))))))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_1) (tptp.hAPP (tptp.list X_a) _let_1 (tptp.set X_a) Xs_1))) (exists ((Ys_2 $$unsorted) (Zs $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (= Xs_1 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.append X_a) Ys_2) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_2 (tptp.cons X_a) X_1) Zs))))))))) (forall ((X_a $$unsorted) (Q_1 $$unsorted) (Pa $$unsorted) (L_1 $$unsorted) (K_1 $$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_1 K_1) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) (tptp.hAPP (tptp.list X_a) _let_1 (tptp.set X_a) L_1))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa X_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool Q_1 X_2)))))) (= (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_4 _let_3 _let_1 Pa) L_1) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_4 _let_3 _let_1 Q_1) K_1))))))))) (forall ((X_a $$unsorted) (Q_1 $$unsorted) (Pa $$unsorted) (L_1 $$unsorted) (K_1 $$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_1 K_1) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) (tptp.hAPP (tptp.list X_a) _let_1 (tptp.set X_a) L_1))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa X_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool Q_1 X_2)))))) (= (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_4 _let_3 _let_1 Pa) L_1) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_4 _let_3 _let_1 Q_1) K_1))))))))) (forall ((X_a $$unsorted) (Pa $$unsorted) (Aa $$unsorted) (Ba $$unsorted) (R_1 $$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) Aa) Ba)) (tptp.hAPP _let_2 _let_2 (tptp.transitive_rtrancl X_a) R_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa Aa)) (=> (forall ((Y_2 $$unsorted) (Z $$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))) (=> (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 Aa) Y_2)) (tptp.hAPP _let_5 _let_5 (tptp.transitive_rtrancl X_a) R_1))) (=> (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 Y_2) Z)) R_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa Y_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa Z)))))))))))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa Ba)))))))) (forall ((X_a $$unsorted) (Pa $$unsorted) (Aa $$unsorted) (Ba $$unsorted) (R_1 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_a))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) (tptp.hAPP X_a _let_1 (tptp.hAPP X_a (tptp.fun X_a _let_1) (tptp.product_Pair X_a X_a) Aa) Ba)) (tptp.hAPP _let_2 _let_2 (tptp.transitive_rtrancl X_a) R_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa Ba)) (=> (forall ((Y_2 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_a))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.product_Pair X_a X_a))) (let ((_let_4 (tptp.fun X_a _let_1))) (let ((_let_5 (tptp.member _let_1))) (let ((_let_6 (tptp.fun _let_2 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 _let_6 _let_5 (tptp.hAPP X_a _let_1 (tptp.hAPP X_a _let_4 _let_3 Y_2) Z)) R_1)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 _let_6 _let_5 (tptp.hAPP X_a _let_1 (tptp.hAPP X_a _let_4 _let_3 Z) Ba)) (tptp.hAPP _let_2 _let_2 (tptp.transitive_rtrancl X_a) R_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa Z)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa Y_2)))))))))))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa Aa)))))))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (Z_2 $$unsorted) (R_1 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_a))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) (tptp.hAPP X_a _let_1 (tptp.hAPP X_a (tptp.fun X_a _let_1) (tptp.product_Pair X_a X_a) X_1) Z_2)) (tptp.hAPP _let_2 _let_2 (tptp.transitive_rtrancl X_a) R_1))) (=> (not (= (tptp.ti X_a X_1) (tptp.ti X_a Z_2))) (not (forall ((Y_2 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_a))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.product_Pair X_a X_a))) (let ((_let_4 (tptp.fun X_a _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 X_a _let_1 (tptp.hAPP X_a _let_4 _let_3 X_1) Y_2)) R_1)) (not (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 _let_6 _let_5 (tptp.hAPP X_a _let_1 (tptp.hAPP X_a _let_4 _let_3 Y_2) Z_2)) (tptp.hAPP _let_2 _let_2 (tptp.transitive_rtrancl X_a) R_1)))))))))))))))))) (forall ((X_a $$unsorted) (Aa $$unsorted) (Ba $$unsorted) (R_1 $$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) Aa) Ba)) (tptp.hAPP _let_2 _let_2 (tptp.transitive_rtrancl X_a) R_1))) (=> (not (= (tptp.ti X_a Aa) (tptp.ti X_a Ba))) (not (forall ((Y_2 $$unsorted)) (let ((_let_1 (tptp.product_Pair X_a X_a))) (let ((_let_2 (tptp.product_prod X_a X_a))) (let ((_let_3 (tptp.fun X_a _let_2))) (let ((_let_4 (tptp.member _let_2))) (let ((_let_5 (tptp.fun _let_2 tptp.bool))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP _let_2 _let_6 _let_4 (tptp.hAPP X_a _let_2 (tptp.hAPP X_a _let_3 _let_1 Aa) Y_2)) (tptp.hAPP _let_5 _let_5 (tptp.transitive_rtrancl X_a) R_1))) (not (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP _let_2 _let_6 _let_4 (tptp.hAPP X_a _let_2 (tptp.hAPP X_a _let_3 _let_1 Y_2) Ba)) R_1))))))))))))))))) (forall ((X_a $$unsorted) (Pa $$unsorted) (Xs_1 $$unsorted)) (=> (exists ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) (tptp.hAPP (tptp.list X_a) _let_1 (tptp.set X_a) Xs_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa X_2))))) (not (forall ((Ys_2 $$unsorted) (X_2 $$unsorted)) (=> (exists ((Zs $$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_2) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_2 (tptp.cons X_a) X_2) Zs)))))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa X_2)) (not (forall ((Xa $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) Xa) (tptp.hAPP (tptp.list X_a) _let_1 (tptp.set X_a) Ys_2))) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa Xa))))))))))))) (forall ((X_a $$unsorted) (Pa $$unsorted) (Xs_1 $$unsorted)) (=> (exists ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) (tptp.hAPP (tptp.list X_a) _let_1 (tptp.set X_a) Xs_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa X_2))))) (not (forall ((Ys_2 $$unsorted) (X_2 $$unsorted) (Zs $$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_2) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_2 (tptp.cons X_a) X_2) Zs))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa X_2)) (not (forall ((Xa $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) Xa) (tptp.hAPP (tptp.list X_a) _let_1 (tptp.set X_a) Zs))) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa Xa))))))))))))))) (forall ((X_a $$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_2 $$unsorted) (Zs $$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_2) (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_a _let_3 (tptp.cons X_a) X_1) Zs))) (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_2)))))))))))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_1) (tptp.hAPP (tptp.list X_a) _let_1 (tptp.set X_a) Xs_1))) (exists ((Ys_2 $$unsorted) (Zs $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (and (= Xs_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_3 (tptp.append X_a) Ys_2) (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_a _let_3 (tptp.cons X_a) X_1) Zs))) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_1) (tptp.hAPP _let_2 _let_1 (tptp.set X_a) Zs)))))))))))) (forall ((X_a $$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_2 $$unsorted) (Zs $$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_2) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_2 (tptp.cons X_a) X_1) Zs))))))))) (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_2 $$unsorted) (X_2 $$unsorted) (Zs $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (and (= Xs_1 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.append X_a) Ys_2) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_2 (tptp.cons X_a) X_2) Zs))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa X_2)) (forall ((Xa $$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))) (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_2 $$unsorted) (X_2 $$unsorted)) (and (exists ((Zs $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (= Xs_1 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.append X_a) Ys_2) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_2 (tptp.cons X_a) X_2) Zs)))))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa X_2)) (forall ((Xa $$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_2))) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa Xa)))))))))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (Xs_1 $$unsorted) (I_1 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.list_update X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun X_a _let_2))) (let ((_let_4 (tptp.fun tptp.nat _let_3))) (let ((_let_5 (tptp.fun tptp.nat _let_2))) (let ((_let_6 (tptp.cons X_a))) (let ((_let_7 (tptp.fun _let_2 _let_2))) (let ((_let_8 (tptp.hAPP X_a _let_7 _let_6 X_1))) (let ((_let_9 (tptp.fun _let_5 _let_5))) (= (tptp.hAPP X_a _let_2 (tptp.hAPP tptp.nat _let_3 (tptp.hAPP _let_2 _let_4 _let_1 (tptp.hAPP _let_2 _let_2 _let_8 Xs_1)) I_1) V) (tptp.hAPP tptp.nat _let_2 (tptp.hAPP _let_5 _let_5 (tptp.hAPP _let_2 _let_9 (tptp.nat_case _let_2) (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_a _let_7 _let_6 V) Xs_1)) (tptp.hAPP _let_5 _let_5 (tptp.hAPP _let_7 _let_9 (tptp.combb _let_2 _let_2 tptp.nat) _let_8) (tptp.hAPP X_a _let_5 (tptp.hAPP _let_4 (tptp.fun X_a _let_5) (tptp.combc tptp.nat X_a _let_2) (tptp.hAPP _let_2 _let_4 _let_1 Xs_1)) V))) I_1)))))))))))) (forall ((X_a $$unsorted) (N_2 $$unsorted) (X_1 $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.drop X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (let ((_let_4 (tptp.fun _let_2 _let_2))) (let ((_let_5 (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_a _let_4 (tptp.cons X_a) X_1) Xs_1))) (= (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.nat _let_4 _let_1 N_2) _let_5) (tptp.hAPP tptp.nat _let_2 (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_2 (tptp.fun _let_3 _let_3) (tptp.nat_case _let_2) _let_5) (tptp.hAPP _let_2 _let_3 (tptp.hAPP (tptp.fun tptp.nat _let_4) (tptp.fun _let_2 _let_3) (tptp.combc tptp.nat _let_2 _let_2) _let_1) Xs_1)) N_2)))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (Xa_1 $$unsorted) (Xb $$unsorted) (Za $$unsorted) (Zb $$unsorted) (R_1 $$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))) (let ((_let_4 (tptp.hAPP X_b _let_2 (tptp.hAPP X_a _let_3 _let_1 Za) Zb))) (let ((_let_5 (tptp.hAPP X_b _let_2 (tptp.hAPP X_a _let_3 _let_1 Xa_1) Xb))) (let ((_let_6 (tptp.product_prod _let_2 _let_2))) (let ((_let_7 (tptp.fun _let_6 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_7 tptp.bool (tptp.hAPP _let_6 (tptp.fun _let_7 tptp.bool) (tptp.member _let_6) (tptp.hAPP _let_2 _let_6 (tptp.hAPP _let_2 (tptp.fun _let_2 _let_6) (tptp.product_Pair _let_2 _let_2) _let_5) _let_4)) (tptp.hAPP _let_7 _let_7 (tptp.transitive_rtrancl _let_2) R_1))) (=> (not (= _let_5 _let_4)) (not (forall ((A_5 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_b))) (let ((_let_2 (tptp.product_prod _let_1 _let_1))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.product_Pair X_a X_b))) (let ((_let_5 (tptp.fun X_b _let_1))) (let ((_let_6 (tptp.hAPP X_b _let_1 (tptp.hAPP X_a _let_5 _let_4 A_5) B_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))) (=> (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 X_b _let_1 (tptp.hAPP X_a _let_5 _let_4 Xa_1) Xb)) _let_6)) R_1)) (not (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 _let_6) (tptp.hAPP X_b _let_1 (tptp.hAPP X_a _let_5 _let_4 Za) Zb))) (tptp.hAPP _let_3 _let_3 (tptp.transitive_rtrancl _let_1) R_1))))))))))))))))))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (Pa $$unsorted) (Ax $$unsorted) (Ay $$unsorted) (Bx $$unsorted) (By $$unsorted) (R_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.product_prod X_a X_b))) (let ((_let_3 (tptp.product_prod _let_2 _let_2))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.product_Pair X_a X_b))) (let ((_let_6 (tptp.fun X_b _let_2))) (=> (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) (tptp.hAPP X_b _let_2 (tptp.hAPP X_a _let_6 _let_5 Ax) Ay)) (tptp.hAPP X_b _let_2 (tptp.hAPP X_a _let_6 _let_5 Bx) By))) (tptp.hAPP _let_4 _let_4 (tptp.transitive_rtrancl _let_2) R_1))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_a _let_1 Pa Bx) By)) (=> (forall ((A_5 $$unsorted) (B_2 $$unsorted) (Aa_1 $$unsorted) (Ba_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.product_prod X_a X_b))) (let ((_let_3 (tptp.product_prod _let_2 _let_2))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.product_Pair X_a X_b))) (let ((_let_6 (tptp.fun X_b _let_2))) (let ((_let_7 (tptp.hAPP X_b _let_2 (tptp.hAPP X_a _let_6 _let_5 Aa_1) Ba_1))) (let ((_let_8 (tptp.product_Pair _let_2 _let_2))) (let ((_let_9 (tptp.fun _let_2 _let_3))) (let ((_let_10 (tptp.member _let_3))) (let ((_let_11 (tptp.fun _let_4 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP _let_3 _let_11 _let_10 (tptp.hAPP _let_2 _let_3 (tptp.hAPP _let_2 _let_9 _let_8 (tptp.hAPP X_b _let_2 (tptp.hAPP X_a _let_6 _let_5 A_5) B_2)) _let_7)) R_1)) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP _let_3 _let_11 _let_10 (tptp.hAPP _let_2 _let_3 (tptp.hAPP _let_2 _let_9 _let_8 _let_7) (tptp.hAPP X_b _let_2 (tptp.hAPP X_a _let_6 _let_5 Bx) By))) (tptp.hAPP _let_4 _let_4 (tptp.transitive_rtrancl _let_2) R_1))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_a _let_1 Pa Aa_1) Ba_1)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_a _let_1 Pa A_5) B_2))))))))))))))))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_a _let_1 Pa Ax) Ay)))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (Pa $$unsorted) (Ax $$unsorted) (Ay $$unsorted) (Bx $$unsorted) (By $$unsorted) (R_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.product_prod X_a X_b))) (let ((_let_3 (tptp.product_prod _let_2 _let_2))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.product_Pair X_a X_b))) (let ((_let_6 (tptp.fun X_b _let_2))) (=> (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) (tptp.hAPP X_b _let_2 (tptp.hAPP X_a _let_6 _let_5 Ax) Ay)) (tptp.hAPP X_b _let_2 (tptp.hAPP X_a _let_6 _let_5 Bx) By))) (tptp.hAPP _let_4 _let_4 (tptp.transitive_rtrancl _let_2) R_1))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_a _let_1 Pa Ax) Ay)) (=> (forall ((A_5 $$unsorted) (B_2 $$unsorted) (Aa_1 $$unsorted) (Ba_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.product_Pair X_a X_b))) (let ((_let_3 (tptp.product_prod X_a X_b))) (let ((_let_4 (tptp.fun X_b _let_3))) (let ((_let_5 (tptp.hAPP X_b _let_3 (tptp.hAPP X_a _let_4 _let_2 A_5) B_2))) (let ((_let_6 (tptp.product_Pair _let_3 _let_3))) (let ((_let_7 (tptp.product_prod _let_3 _let_3))) (let ((_let_8 (tptp.fun _let_3 _let_7))) (let ((_let_9 (tptp.member _let_7))) (let ((_let_10 (tptp.fun _let_7 tptp.bool))) (let ((_let_11 (tptp.fun _let_10 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_10 tptp.bool (tptp.hAPP _let_7 _let_11 _let_9 (tptp.hAPP _let_3 _let_7 (tptp.hAPP _let_3 _let_8 _let_6 (tptp.hAPP X_b _let_3 (tptp.hAPP X_a _let_4 _let_2 Ax) Ay)) _let_5)) (tptp.hAPP _let_10 _let_10 (tptp.transitive_rtrancl _let_3) R_1))) (=> (tptp.hBOOL (tptp.hAPP _let_10 tptp.bool (tptp.hAPP _let_7 _let_11 _let_9 (tptp.hAPP _let_3 _let_7 (tptp.hAPP _let_3 _let_8 _let_6 _let_5) (tptp.hAPP X_b _let_3 (tptp.hAPP X_a _let_4 _let_2 Aa_1) Ba_1))) R_1)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_a _let_1 Pa A_5) B_2)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_a _let_1 Pa Aa_1) Ba_1))))))))))))))))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_a _let_1 Pa Bx) By)))))))))))) (forall ((X_a $$unsorted) (N_2 $$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_2) (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_2))))))))) (forall ((X_a $$unsorted) (A1 $$unsorted) (A2 $$unsorted) (R_1 $$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) A1) A2)) (tptp.hAPP _let_2 _let_2 (tptp.transitive_rtrancl X_a) R_1))) (or (exists ((A_5 $$unsorted)) (let ((_let_1 (tptp.ti X_a A_5))) (and (= (tptp.ti X_a A1) _let_1) (= (tptp.ti X_a A2) _let_1)))) (exists ((A_5 $$unsorted) (B_2 $$unsorted) (C_2 $$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))) (and (= (tptp.ti X_a A1) (tptp.ti X_a A_5)) (= (tptp.ti X_a A2) (tptp.ti X_a C_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 A_5) B_2)) (tptp.hAPP _let_5 _let_5 (tptp.transitive_rtrancl X_a) R_1))) (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) C_2)) R_1))))))))))))))) (forall ((X_a $$unsorted) (R_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun (tptp.product_prod _let_1 _let_1) tptp.bool))) (let ((_let_3 (tptp.fun (tptp.product_prod X_a X_a) tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) (tptp.hAPP _let_3 _let_2 (tptp.listrel X_a) R_1)) (tptp.hAPP _let_2 _let_2 (tptp.transitive_rtrancl _let_1) (tptp.hAPP _let_3 _let_2 (tptp.listrel1 X_a) R_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))))) (exists ((Ys_2 $$unsorted) (X_2 $$unsorted)) (and (exists ((Zs $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (= Xs_1 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.append X_a) Ys_2) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_2 (tptp.cons X_a) X_2) Zs)))))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa X_2)) (forall ((Xa $$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_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_2 $$unsorted) (X_2 $$unsorted) (Zs $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (and (= Xs_1 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.append X_a) Ys_2) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_2 (tptp.cons X_a) X_2) Zs))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa X_2)) (forall ((Xa $$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))) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa Xa)))))))))))) (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 $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.ord_less_eq _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 A_2) B_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 B_1) A_2)) (= (tptp.ti _let_1 A_2) (tptp.ti _let_1 B_1)))))))) (forall ((X_a $$unsorted) (Ca $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 (tptp.member X_a) Ca))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_2) B_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 A_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 B_1)))))))) (forall ((X_a $$unsorted) (N_2 $$unsorted) (Xs_1 $$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_2) Xs_1))) (tptp.hAPP _let_3 _let_2 _let_1 Xs_1))))))) (forall ((X_a $$unsorted) (R_1 $$unsorted) (S $$unsorted)) (let ((_let_1 (tptp.listrel X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun (tptp.product_prod _let_2 _let_2) tptp.bool))) (let ((_let_4 (tptp.fun (tptp.product_prod X_a X_a) tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP _let_4 (tptp.fun _let_4 tptp.bool) (tptp.ord_less_eq _let_4) R_1) S)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_3 (tptp.fun _let_3 tptp.bool) (tptp.ord_less_eq _let_3) (tptp.hAPP _let_4 _let_3 _let_1 R_1)) (tptp.hAPP _let_4 _let_3 _let_1 S))))))))) (forall ((X_a $$unsorted) (R_1 $$unsorted) (S $$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_1) S)) (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_1)) (tptp.hAPP _let_4 _let_3 _let_1 S))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (B_1 $$unsorted) (A_4 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.pi X_a X_b))) (let ((_let_2 (tptp.fun (tptp.fun X_a X_b) tptp.bool))) (let ((_let_3 (tptp.fun X_a (tptp.fun X_b tptp.bool)))) (let ((_let_4 (tptp.fun _let_3 _let_2))) (let ((_let_5 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP _let_5 (tptp.fun _let_5 tptp.bool) (tptp.ord_less_eq _let_5) A_4) A_2)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) (tptp.hAPP _let_3 _let_2 (tptp.hAPP _let_5 _let_4 _let_1 A_2) B_1)) (tptp.hAPP _let_3 _let_2 (tptp.hAPP _let_5 _let_4 _let_1 A_4) B_1)))))))))) (forall ((X_a $$unsorted) (R_2 $$unsorted) (S_2 $$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_2)) (tptp.hAPP _let_1 _let_1 _let_4 S_2))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 R_2) S_2)))))))) (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 $$unsorted) (Q_1 $$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 $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X) Y))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X)))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.ord X_b) (forall ((X_1 $$unsorted) (F $$unsorted) (G $$unsorted)) (let ((_let_1 (tptp.fun X_a X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) F) G)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) (tptp.hAPP X_a X_b F X_1)) (tptp.hAPP X_a X_b G X_1)))))))) (forall ((X_a $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.ord_less_eq _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (=> (= (tptp.ti _let_1 A_2) (tptp.ti _let_1 B_1)) (not (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 A_2) B_1)) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 B_1) A_2)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((Z_1 $$unsorted) (Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 Z_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 X)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X) Y)) (= (tptp.ti X_a X) (tptp.ti X_a Y))))))))) (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((Z_1 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 X))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 Y)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) Z_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 Z_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X) Y)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X)) (= (tptp.ti X_a X) (tptp.ti X_a Y))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((C $$unsorted) (B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B) A_1)) (=> (= (tptp.ti X_a B) (tptp.ti X_a C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 C) A_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ord X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) A_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B)) (=> (= (tptp.ti X_a B) (tptp.ti X_a C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 C)))))))) (forall ((X_a $$unsorted) (C_1 $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.ord_less_eq _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.hAPP _let_1 _let_3 _let_2 A_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_4 B_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 B_1) C_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_4 C_1))))))))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 (tptp.member X_a) X_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_2) B_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 A_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 B_1)))))))) (forall ((X_a $$unsorted) (B_1 $$unsorted) (X_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 (tptp.member X_a) X_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 A_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_2) B_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 B_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) C))) (=> (= (tptp.ti X_a A_1) (tptp.ti X_a B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.ord X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (= (tptp.ti X_a A_1) (tptp.ti X_a B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) C))))))))) (forall ((X_a $$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 $$unsorted) (X_1 $$unsorted) (A_2 $$unsorted) (B_1 $$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 (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_2) B_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 A_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 B_1)))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.ord X_b) (forall ((X_1 $$unsorted) (F $$unsorted) (G $$unsorted)) (let ((_let_1 (tptp.fun X_a X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) F) G)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) (tptp.hAPP X_a X_b F X_1)) (tptp.hAPP X_a X_b G X_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (=> (= X Y) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X) Y)))))) (forall ((X_a $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (= (tptp.ti _let_1 A_2) (tptp.ti _let_1 B_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) B_1) A_2))))) (forall ((X_a $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (= (tptp.ti _let_1 A_2) (tptp.ti _let_1 B_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) A_2) B_1))))) (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) (A_2 $$unsorted) (B_1 $$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))) (= (= (tptp.ti _let_1 A_2) (tptp.ti _let_1 B_1)) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 A_2) B_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 B_1) A_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) (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 $$unsorted) (A_2 $$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_2) A_2)))) (forall ((X_a $$unsorted) (N $$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) _let_1) _let_1)))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (N_2 $$unsorted) (Xs_1 $$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_2) 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 $$unsorted) (I_2 $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.distinct X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 Xs)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.nat (tptp.fun _let_1 _let_1) (tptp.take X_a) I_2) Xs))))))) (forall ((X_a $$unsorted)) (=> (tptp.top X_a) (forall ((A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) A_1) (tptp.top_top X_a)))))) (forall ((X_a $$unsorted)) (=> (tptp.top X_a) (forall ((Aa $$unsorted)) (let ((_let_1 (tptp.top_top X_a))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) _let_1) Aa)) (= (tptp.ti X_a Aa) _let_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.top X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.top_top X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) _let_1) A_1)) (= (tptp.ti X_a A_1) _let_1)))))) (forall ((X_a $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) A_2) (tptp.top_top _let_1))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((N $$unsorted) (Xs $$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) Xs))))))))) (forall ((X_a $$unsorted) (R_1 $$unsorted) (S $$unsorted)) (let ((_let_1 (tptp.transitive_rtrancl X_a))) (let ((_let_2 (tptp.fun (tptp.product_prod X_a X_a) tptp.bool))) (let ((_let_3 (tptp.hAPP _let_2 _let_2 _let_1 S))) (let ((_let_4 (tptp.ord_less_eq _let_2))) (let ((_let_5 (tptp.fun _let_2 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 _let_5 _let_4 R_1) _let_3)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 _let_5 _let_4 (tptp.hAPP _let_2 _let_2 _let_1 R_1)) _let_3))))))))) (forall ((X_a $$unsorted) (R_2 $$unsorted) (S_2 $$unsorted)) (let ((_let_1 (tptp.transitive_rtrancl X_a))) (let ((_let_2 (tptp.fun (tptp.product_prod X_a X_a) tptp.bool))) (let ((_let_3 (tptp.hAPP _let_2 _let_2 _let_1 R_2))) (let ((_let_4 (tptp.ord_less_eq _let_2))) (let ((_let_5 (tptp.fun _let_2 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 _let_5 _let_4 R_2) S_2)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 _let_5 _let_4 S_2) _let_3)) (= (tptp.hAPP _let_2 _let_2 _let_1 S_2) _let_3))))))))) (forall ((X_a $$unsorted) (R_1 $$unsorted) (S $$unsorted)) (let ((_let_1 (tptp.transitive_rtrancl X_a))) (let ((_let_2 (tptp.fun (tptp.product_prod X_a X_a) tptp.bool))) (let ((_let_3 (tptp.ord_less_eq _let_2))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 _let_4 _let_3 R_1) S)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 _let_4 _let_3 (tptp.hAPP _let_2 _let_2 _let_1 R_1)) (tptp.hAPP _let_2 _let_2 _let_1 S))))))))) (forall ((X_a $$unsorted) (N $$unsorted) (Xs $$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) Xs)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.nat _let_2 (tptp.drop X_a) N) 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 $$unsorted) (X_1 $$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 $$unsorted)) (=> (tptp.linorder X_a) (forall ((Zs_2 $$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_2))) (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 $$unsorted) (Zs_1 $$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.hAPP _let_2 _let_2 (tptp.hAPP X_a _let_3 _let_1 Y_1) Zs_1))) (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 $$unsorted) (N_2 $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.set X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.list X_a))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) (tptp.hAPP _let_3 _let_2 _let_1 (tptp.hAPP _let_3 _let_3 (tptp.hAPP tptp.nat (tptp.fun _let_3 _let_3) (tptp.drop X_a) N_2) Xs_1))) (tptp.hAPP _let_3 _let_2 _let_1 Xs_1))))))) (forall ((X_a $$unsorted) (I_1 $$unsorted) (X_1 $$unsorted) (Xs_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun X_a _let_1))) (let ((_let_3 (tptp.set X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (let ((_let_5 (tptp.ord_less_eq _let_4))) (let ((_let_6 (tptp.fun _let_4 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP _let_4 _let_6 _let_5 (tptp.hAPP _let_1 _let_4 _let_3 Xs_1)) A_2)) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP X_a _let_6 (tptp.member X_a) X_1) A_2)) (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP _let_4 _let_6 _let_5 (tptp.hAPP _let_1 _let_4 _let_3 (tptp.hAPP X_a _let_1 (tptp.hAPP tptp.nat _let_2 (tptp.hAPP _let_1 (tptp.fun tptp.nat _let_2) (tptp.list_update X_a) Xs_1) I_1) X_1))) A_2))))))))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (Ys $$unsorted) (Zs_1 $$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) Zs_1) (and (= Xs_1 (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.nat _let_3 (tptp.take X_a) _let_2) Zs_1)) (= Ys (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.nat _let_3 (tptp.drop X_a) _let_2) Zs_1)))))))) (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 $$unsorted)) (let ((_let_1 (tptp.linorder_sorted X_a))) (let ((_let_2 (tptp.list X_a))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 (tptp.fun _let_2 _let_2) (tptp.append X_a) Xs_1) Ys))) (and (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 Xs_1)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 Ys)) (forall ((X_2 $$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 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) Xa) (tptp.hAPP (tptp.list X_a) _let_1 (tptp.set X_a) Ys))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) X_2) Xa))))))))))))))) (forall ((X_a $$unsorted) (R_1 $$unsorted)) (let ((_let_1 (tptp.listrel1 X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun (tptp.product_prod _let_2 _let_2) tptp.bool))) (let ((_let_4 (tptp.fun (tptp.product_prod X_a X_a) tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_3 (tptp.fun _let_3 tptp.bool) (tptp.ord_less_eq _let_3) (tptp.hAPP _let_4 _let_3 _let_1 (tptp.hAPP _let_4 _let_4 (tptp.transitive_rtrancl X_a) R_1))) (tptp.hAPP _let_3 _let_3 (tptp.transitive_rtrancl _let_2) (tptp.hAPP _let_4 _let_3 _let_1 R_1))))))))) (forall ((X_a $$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 $$unsorted) (B_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (forall ((X_2 $$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_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B_1)))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) A_2) B_1))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (B_1 $$unsorted) (C_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.fun X_a X_b) tptp.bool))) (let ((_let_2 (tptp.fun X_a (tptp.fun X_b tptp.bool)))) (let ((_let_3 (tptp.hAPP (tptp.fun X_a tptp.bool) (tptp.fun _let_2 _let_1) (tptp.pi X_a X_b) A_2))) (=> (forall ((X_2 $$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_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 X_a _let_1 B_1 X_2)) (tptp.hAPP X_a _let_1 C_1 X_2))))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) (tptp.hAPP _let_2 _let_1 _let_3 B_1)) (tptp.hAPP _let_2 _let_1 _let_3 C_1)))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.ord X_b) (forall ((F $$unsorted) (G $$unsorted)) (let ((_let_1 (tptp.fun X_a X_b))) (=> (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) (tptp.hAPP X_a X_b F X_2)) (tptp.hAPP X_a X_b G X_2)))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) F) G))))))) (forall ((X_a $$unsorted) (R_1 $$unsorted) (R_3 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun (tptp.product_prod _let_1 _let_1) tptp.bool))) (let ((_let_3 (tptp.fun (tptp.product_prod X_a X_a) tptp.bool))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_3 _let_5 (tptp.ord_less_eq _let_3) R_1) R_3)) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_4 _let_5 (tptp.refl_on X_a) (tptp.top_top _let_4)) R_3)) (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.listrel1 X_a) R_1)) (tptp.hAPP _let_3 _let_2 (tptp.listrel X_a) R_3))))))))))) (forall ((X_a $$unsorted) (X $$unsorted) (Xs $$unsorted) (Ys_1 $$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 Xs)) (tptp.hAPP _let_1 tptp.nat _let_2 Ys_1))) (not (= Xs (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.cons X_a) X) Ys_1))))))) (forall ((X_a $$unsorted) (Xs $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.list X_a))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) Xs)) N)) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.nat (tptp.fun _let_1 _let_1) (tptp.take X_a) N) Xs) Xs)))) (forall ((X_a $$unsorted) (X $$unsorted) (Xs $$unsorted) (I_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun X_a _let_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) Xs)) I_2)) (= (tptp.hAPP X_a _let_1 (tptp.hAPP tptp.nat _let_2 (tptp.hAPP _let_1 (tptp.fun tptp.nat _let_2) (tptp.list_update X_a) Xs) I_2) X) Xs))))) (forall ((X_a $$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 $$unsorted) (Pa $$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) (X_b $$unsorted) (R_2 $$unsorted) (S_2 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.fun X_b _let_3))) (let ((_let_5 (tptp.fun X_b _let_1))) (let ((_let_6 (tptp.fun _let_5 _let_4))) (let ((_let_7 (tptp.fun X_a _let_4))) (let ((_let_8 (tptp.fun X_a _let_5))) (let ((_let_9 (tptp.fun X_b tptp.bool))) (let ((_let_10 (tptp.fun _let_2 _let_9))) (let ((_let_11 (tptp.fun X_a _let_10))) (let ((_let_12 (tptp.fun X_a _let_9))) (let ((_let_13 (tptp.hAPP _let_11 (tptp.fun _let_2 _let_12) (tptp.combc X_a _let_2 _let_9) (tptp.hAPP _let_7 _let_11 (tptp.hAPP (tptp.fun _let_4 _let_10) (tptp.fun _let_7 _let_11) (tptp.combb _let_4 _let_10 X_a) (tptp.combc X_b _let_2 tptp.bool)) (tptp.hAPP _let_8 _let_7 (tptp.hAPP _let_6 (tptp.fun _let_8 _let_7) (tptp.combb _let_5 _let_4 X_a) (tptp.hAPP (tptp.fun _let_1 _let_3) _let_6 (tptp.combb _let_1 _let_3 X_b) (tptp.member _let_1))) (tptp.product_Pair X_a X_b)))))) (= (tptp.hBOOL (tptp.hAPP _let_12 tptp.bool (tptp.hAPP _let_12 (tptp.fun _let_12 tptp.bool) (tptp.ord_less_eq _let_12) (tptp.hAPP _let_2 _let_12 _let_13 R_2)) (tptp.hAPP _let_2 _let_12 _let_13 S_2))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 _let_3 (tptp.ord_less_eq _let_2) R_2) S_2))))))))))))))))) (forall ((X_a $$unsorted) (R_1 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.product_prod X_a X_a) tptp.bool))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_1 tptp.bool) (tptp.refl_on X_a) (tptp.top_top _let_2)) (tptp.hAPP _let_1 _let_1 (tptp.transitive_rtrancl X_a) R_1)))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (M_2 $$unsorted) (N_2 $$unsorted)) (let ((_let_1 (tptp.take X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (let ((_let_4 (tptp.set X_a))) (let ((_let_5 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M_2) N_2)) (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP _let_5 (tptp.fun _let_5 tptp.bool) (tptp.ord_less_eq _let_5) (tptp.hAPP _let_2 _let_5 _let_4 (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 M_2) Xs_1))) (tptp.hAPP _let_2 _let_5 _let_4 (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 N_2) Xs_1))))))))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (N_2 $$unsorted) (M_2 $$unsorted)) (let ((_let_1 (tptp.drop X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (let ((_let_4 (tptp.set X_a))) (let ((_let_5 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N_2) M_2)) (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP _let_5 (tptp.fun _let_5 tptp.bool) (tptp.ord_less_eq _let_5) (tptp.hAPP _let_2 _let_5 _let_4 (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 M_2) Xs_1))) (tptp.hAPP _let_2 _let_5 _let_4 (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 N_2) Xs_1))))))))))) (forall ((X_a $$unsorted) (Xs $$unsorted) (N $$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)) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.nat (tptp.fun _let_1 _let_1) (tptp.drop X_a) N) Xs) (tptp.nil X_a))))) (forall ((X_a $$unsorted) (N_2 $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (= (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.nat (tptp.fun _let_1 _let_1) (tptp.drop X_a) N_2) Xs_1) (tptp.nil X_a)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) Xs_1)) N_2))))) (forall ((X_a $$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 $$unsorted) (R_1 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_a))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.fun X_a _let_3))) (= (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.reflp X_a) R_1)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_3 (tptp.fun _let_2 tptp.bool) (tptp.refl_on X_a) (tptp.top_top _let_3)) (tptp.hAPP _let_2 _let_2 (tptp.collect _let_1) (tptp.hAPP _let_4 _let_2 (tptp.product_prod_case X_a X_a tptp.bool) R_1)))))))))) (forall ((X_a $$unsorted) (Aa $$unsorted) (A_2 $$unsorted) (R_1 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_a))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_4 _let_3 (tptp.refl_on X_a) A_2) R_1)) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP X_a (tptp.fun _let_4 tptp.bool) (tptp.member X_a) Aa) A_2)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 _let_3 (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) Aa) Aa)) R_1))))))))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted) (A_2 $$unsorted) (R_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.product_prod X_a X_a))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_1 _let_4 (tptp.refl_on X_a) A_2) R_1)) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 _let_4 (tptp.member _let_2) (tptp.hAPP X_a _let_2 (tptp.hAPP X_a (tptp.fun X_a _let_2) (tptp.product_Pair X_a X_a) X_1) Y_1)) R_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_1) A_2))))))))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted) (A_2 $$unsorted) (R_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.product_prod X_a X_a))) (let ((_let_3 (tptp.fun _let_2 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 (tptp.refl_on X_a) A_2) R_1)) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 _let_4 (tptp.member _let_2) (tptp.hAPP X_a _let_2 (tptp.hAPP X_a (tptp.fun X_a _let_2) (tptp.product_Pair X_a X_a) X_1) Y_1)) R_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) Y_1) A_2))))))))) (forall ((X_a $$unsorted) (N $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.take X_a))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (=> (not (= Xs (tptp.nil X_a))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.nat tptp.nat tptp.suc N)) Xs) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_3 (tptp.cons X_a) (tptp.hAPP _let_1 X_a (tptp.hd X_a) Xs)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.nat _let_3 _let_2 N) (tptp.hAPP _let_1 _let_1 (tptp.tl X_a) Xs))))))))) (forall ((X_b $$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) (X_b $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted) (Pa $$unsorted) (Q_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a _let_1))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) Pa) Q_1)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_a _let_1 Pa X_1) Y_1)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_a _let_1 Q_1 X_1) Y_1))))))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (R_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_a _let_1) tptp.bool (tptp.reflp X_a) R_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 R_1 X_1) X_1))))) (forall ((X_a $$unsorted) (N $$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)) (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) Xs)))))))) (forall ((X_a $$unsorted) (N $$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)) (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) Xs)))))) (forall ((X_a $$unsorted) (X $$unsorted) (Xs $$unsorted) (I_2 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.list_update X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun X_a _let_2))) (let ((_let_4 (tptp.fun tptp.nat _let_3))) (let ((_let_5 (tptp.hAPP X_a (tptp.fun _let_2 _let_2) (tptp.cons X_a) X))) (= (tptp.hAPP X_a _let_2 (tptp.hAPP tptp.nat _let_3 (tptp.hAPP _let_2 _let_4 _let_1 (tptp.hAPP _let_2 _let_2 _let_5 Xs)) (tptp.hAPP tptp.nat tptp.nat tptp.suc I_2)) Y) (tptp.hAPP _let_2 _let_2 _let_5 (tptp.hAPP X_a _let_2 (tptp.hAPP tptp.nat _let_3 (tptp.hAPP _let_2 _let_4 _let_1 Xs) I_2) Y))))))))) (forall ((X_a $$unsorted) (N $$unsorted) (X $$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)) 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) X))))))) (forall ((X_a $$unsorted) (N $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.take X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (let ((_let_4 (tptp.tl X_a))) (= (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 N) (tptp.hAPP _let_2 _let_2 _let_4 Xs)) (tptp.hAPP _let_2 _let_2 _let_4 (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N)) Xs)))))))) (forall ((X_a $$unsorted) (N $$unsorted) (Xs $$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)) Xs) (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.nat _let_3 _let_2 N) (tptp.hAPP _let_1 _let_1 (tptp.tl X_a) Xs))))))) (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_a $$unsorted) (N_2 $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (= (= (tptp.hAPP tptp.nat tptp.nat tptp.suc N_2) (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) Xs_1)) (exists ((Y_2 $$unsorted) (Ys_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (and (= Xs_1 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.cons X_a) Y_2) Ys_2)) (= (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) Ys_2) N_2))))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (N_2 $$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_2)) (exists ((Y_2 $$unsorted) (Ys_2 $$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_2)) (= (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) Ys_2) N_2))))))) (forall ((X_a $$unsorted) (N $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.take X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N) (tptp.hAPP _let_2 tptp.nat (tptp.size_size _let_2) Xs))) (= (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_3 (tptp.append X_a) (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 N) Xs)) (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_a _let_3 (tptp.cons X_a) (tptp.hAPP _let_2 X_a (tptp.hd X_a) (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.nat _let_3 (tptp.drop X_a) N) Xs))) (tptp.nil X_a))) (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N)) Xs))))))) (forall ((X $$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)) (=> (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_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 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (or (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) X) Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) Y) X))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((X_1 $$unsorted) (Y_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.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 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) X_1) Y_1)) (or (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) X_1) Y_1)) (= (tptp.ti X_a X_1) (tptp.ti X_a Y_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) X) Y))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) Y) X))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) Y) X))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) X) Y))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X_1 $$unsorted) (Y_1 $$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 $$unsorted)) (=> (tptp.order X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (not (= (tptp.ti X_a A_1) (tptp.ti X_a B))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) A_1) B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) A_1) B)))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (not (= (tptp.ti X_a A_1) (tptp.ti X_a B))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) B) A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) B) A_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) Y) X)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) X) Y)))))))) (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) X) Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) X) Y))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X_1 $$unsorted) (Y_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.order X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) X) Y)) (or (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) X) Y)) (= (tptp.ti X_a X) (tptp.ti X_a Y)))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a 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(tptp.order X_a) (forall ((Z_1 $$unsorted) (Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) Z_1) Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Z_1) X))))))))) (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((Z_1 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) X) Y)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) Z_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X) Z_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((Z_1 $$unsorted) (Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) Z_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) Y) X)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_2 Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_2 X))))))))) (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((X $$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 $$unsorted)) (=> (tptp.preorder X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B) A_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((B $$unsorted) (A_1 $$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 B) A_1)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ord X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (= (tptp.ti X_a A_1) (tptp.ti X_a B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) C))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) C))) (=> (= (tptp.ti X_a A_1) (tptp.ti X_a B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.ord X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) A_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B)) (=> (= (tptp.ti X_a B) (tptp.ti X_a C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 C)))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((C $$unsorted) (B $$unsorted) (A_1 $$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 B) A_1)) (=> (= (tptp.ti X_a B) (tptp.ti X_a C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 C) A_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((Z_1 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 X))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 Y)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) Z_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 Z_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((Z_1 $$unsorted) (Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 Z_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 X)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((X $$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 $$unsorted)) (=> (tptp.top X_a) (forall ((A_1 $$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_1)))))) (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 $$unsorted) (X_1 $$unsorted) (N_2 $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun X_a _let_1))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N_2) (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) Xs_1))) (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) (tptp.hAPP X_a _let_1 (tptp.hAPP tptp.nat _let_2 (tptp.hAPP _let_1 (tptp.fun tptp.nat _let_2) (tptp.list_update X_a) Xs_1) N_2) X_1))))))))) (forall ((X_a $$unsorted) (Ys_1 $$unsorted) (X $$unsorted) (I_2 $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.list_update X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun X_a _let_2))) (let ((_let_4 (tptp.fun tptp.nat _let_3))) (let ((_let_5 (tptp.append X_a))) (let ((_let_6 (tptp.fun _let_2 _let_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I_2) (tptp.hAPP _let_2 tptp.nat (tptp.size_size _let_2) Xs))) (= (tptp.hAPP X_a _let_2 (tptp.hAPP tptp.nat _let_3 (tptp.hAPP _let_2 _let_4 _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_6 _let_5 Xs) Ys_1)) I_2) X) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_6 _let_5 (tptp.hAPP X_a _let_2 (tptp.hAPP tptp.nat _let_3 (tptp.hAPP _let_2 _let_4 _let_1 Xs) I_2) X)) Ys_1)))))))))) (forall ((X_a $$unsorted) (N $$unsorted) (Xs $$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))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N) (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 $$unsorted) (N $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.last X_a))) (let ((_let_2 (tptp.list X_a))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N) (tptp.hAPP _let_2 tptp.nat (tptp.size_size _let_2) Xs))) (= (tptp.hAPP _let_2 X_a _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.nat (tptp.fun _let_2 _let_2) (tptp.drop X_a) N) Xs)) (tptp.hAPP _let_2 X_a _let_1 Xs)))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (I_2 $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.fun X_a _let_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I_2) (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) Xs))) (= (tptp.hAPP X_a _let_1 (tptp.hAPP tptp.nat _let_3 (tptp.hAPP _let_1 (tptp.fun tptp.nat _let_3) (tptp.list_update X_a) Xs) I_2) A_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.append X_a) (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.nat _let_2 (tptp.take X_a) I_2) Xs)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_2 (tptp.cons X_a) A_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.nat _let_2 (tptp.drop X_a) (tptp.hAPP tptp.nat tptp.nat tptp.suc I_2)) Xs))))))))) (forall ((N $$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) (tptp.hAPP tptp.nat tptp.nat tptp.suc N)))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M)) (tptp.hAPP tptp.nat tptp.nat tptp.suc N))))))) (forall ((X_a $$unsorted) (R_1 $$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.fun (tptp.product_prod X_a X_a) tptp.bool))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.fun _let_1 _let_2))) (let ((_let_8 (tptp.fun _let_7 _let_6))) (let ((_let_9 (tptp.fun _let_1 _let_6))) (let ((_let_10 (tptp.fun _let_1 _let_7))) (let ((_let_11 (tptp.fun _let_1 tptp.bool))) (let ((_let_12 (tptp.fun _let_3 _let_11))) (let ((_let_13 (tptp.fun _let_1 _let_12))) (let ((_let_14 (tptp.fun _let_1 _let_11))) (let ((_let_15 (tptp.size_size _let_1))) (let ((_let_16 (tptp.fun tptp.nat tptp.bool))) (let ((_let_17 (tptp.combb tptp.nat _let_16 _let_1))) (let ((_let_18 (tptp.fun _let_1 _let_16))) (let ((_let_19 (tptp.fun _let_1 tptp.nat))) (let ((_let_20 (tptp.fun _let_19 _let_18))) (let ((_let_21 (tptp.fun tptp.nat _let_16))) (let ((_let_22 (tptp.fun _let_19 _let_11))) (let ((_let_23 (tptp.fun _let_1 _let_22))) (let ((_let_24 (tptp.hAPP (tptp.fun _let_16 _let_22) (tptp.fun _let_18 _let_23) (tptp.combb _let_16 _let_22 _let_1) (tptp.combb tptp.nat tptp.bool _let_1)))) (let ((_let_25 (tptp.combc _let_1 _let_19 _let_11))) (let ((_let_26 (tptp.fun _let_19 _let_14))) (let ((_let_27 (tptp.fun tptp.bool tptp.bool))) (let ((_let_28 (tptp.combb tptp.bool _let_27 _let_1))) (let ((_let_29 (tptp.fun _let_1 _let_27))) (let ((_let_30 (tptp.fun _let_11 _let_29))) (let ((_let_31 (tptp.fun tptp.bool _let_27))) (let ((_let_32 (tptp.combb _let_11 _let_29 _let_1))) (let ((_let_33 (tptp.fun _let_1 _let_29))) (let ((_let_34 (tptp.fun _let_14 _let_33))) (let ((_let_35 (tptp.fun _let_11 _let_11))) (let ((_let_36 (tptp.fun _let_1 _let_35))) (let ((_let_37 (tptp.hAPP (tptp.fun _let_29 _let_35) (tptp.fun _let_33 _let_36) (tptp.combb _let_29 _let_35 _let_1) (tptp.combs _let_1 tptp.bool tptp.bool)))) (let ((_let_38 (tptp.combs _let_1 _let_11 _let_11))) (let ((_let_39 (tptp.fun _let_14 _let_14))) (= (tptp.hAPP _let_4 _let_3 (tptp.lenlex X_a) R_1) (tptp.hAPP _let_3 _let_3 (tptp.collect _let_2) (tptp.hAPP _let_14 _let_3 (tptp.product_prod_case _let_1 _let_1 tptp.bool) (tptp.hAPP _let_14 _let_14 (tptp.hAPP _let_36 _let_39 _let_38 (tptp.hAPP _let_33 _let_36 _let_37 (tptp.hAPP _let_14 _let_33 (tptp.hAPP _let_30 _let_34 _let_32 (tptp.hAPP _let_31 _let_30 _let_28 tptp.fdisj)) (tptp.hAPP _let_19 _let_14 (tptp.hAPP _let_23 _let_26 _let_25 (tptp.hAPP _let_18 _let_23 _let_24 (tptp.hAPP _let_19 _let_18 (tptp.hAPP _let_21 _let_20 _let_17 (tptp.ord_less tptp.nat)) _let_15))) _let_15)))) (tptp.hAPP _let_14 _let_14 (tptp.hAPP _let_36 _let_39 _let_38 (tptp.hAPP _let_33 _let_36 _let_37 (tptp.hAPP _let_14 _let_33 (tptp.hAPP _let_30 _let_34 _let_32 (tptp.hAPP _let_31 _let_30 _let_28 tptp.fconj)) (tptp.hAPP _let_19 _let_14 (tptp.hAPP _let_23 _let_26 _let_25 (tptp.hAPP _let_18 _let_23 _let_24 (tptp.hAPP _let_19 _let_18 (tptp.hAPP _let_21 _let_20 _let_17 (tptp.fequal tptp.nat)) _let_15))) _let_15)))) (tptp.hAPP _let_3 _let_14 (tptp.hAPP _let_13 (tptp.fun _let_3 _let_14) (tptp.combc _let_1 _let_3 _let_11) (tptp.hAPP _let_9 _let_13 (tptp.hAPP (tptp.fun _let_6 _let_12) (tptp.fun _let_9 _let_13) (tptp.combb _let_6 _let_12 _let_1) (tptp.combc _let_1 _let_3 tptp.bool)) (tptp.hAPP _let_10 _let_9 (tptp.hAPP _let_8 (tptp.fun _let_10 _let_9) (tptp.combb _let_7 _let_6 _let_1) (tptp.hAPP (tptp.fun _let_2 _let_5) _let_8 (tptp.combb _let_2 _let_5 _let_1) (tptp.member _let_2))) (tptp.product_Pair _let_1 _let_1)))) (tptp.hAPP _let_4 _let_3 (tptp.lex X_a) R_1))))))))))))))))))))))))))))))))))))))))))))))) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) X_2) (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc X_2))))) (forall ((X_a $$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_2 $$unsorted) (B_1 $$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_2) B_1)) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_2) B_1)) (not (= (tptp.ti _let_1 A_2) (tptp.ti _let_1 B_1)))))))) (forall ((X_a $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_2) B_1)) (or (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less _let_1) A_2) B_1)) (= (tptp.ti _let_1 A_2) (tptp.ti _let_1 B_1))))))) (forall ((X_a $$unsorted) (A_2 $$unsorted) (B_1 $$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_2) B_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_2) B_1)))))) (forall ((X_a $$unsorted) (C_1 $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP _let_1 _let_2 (tptp.ord_less _let_1) A_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 B_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) B_1) C_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 C_1)))))))) (forall ((X_a $$unsorted) (C_1 $$unsorted) (A_2 $$unsorted) (B_1 $$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_2) B_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 B_1) C_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 A_2) C_1)))))))) (forall ((N $$unsorted)) (not (= N (tptp.hAPP tptp.nat tptp.nat tptp.suc N)))) (forall ((N $$unsorted)) (not (= (tptp.hAPP tptp.nat tptp.nat tptp.suc N) N))) (forall ((Nat_4 $$unsorted) (Nat_5 $$unsorted)) (= (= (tptp.hAPP tptp.nat tptp.nat tptp.suc Nat_4) (tptp.hAPP tptp.nat tptp.nat tptp.suc Nat_5)) (= Nat_4 Nat_5))) (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 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N) N)))) (forall ((M_2 $$unsorted) (N_2 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (not (= M_2 N_2)) (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M_2) N_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 N_2) M_2))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (not (= X Y)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 X) Y))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Y) X))))))) (forall ((N $$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) N)))) (forall ((N $$unsorted) (M $$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) M)) (not (= M N)))) (forall ((S_1 $$unsorted) (T_3 $$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_1) T_3)) (not (= S_1 T_3)))) (forall ((Pa $$unsorted) (M_2 $$unsorted) (N_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 Pa N_2) M_2)))) (let ((_let_3 (tptp.ord_less tptp.nat))) (=> (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 _let_3 M_2) N_2)) _let_2) (=> (=> (= M_2 N_2) _let_2) (=> (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 _let_3 N_2) M_2)) _let_2) _let_2))))))) (forall ((N $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N) N))) (forall ((M $$unsorted) (N $$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) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 N) M)))))) (forall ((M $$unsorted) (N $$unsorted)) (=> (= M N) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M) N)))) (forall ((K $$unsorted) (I_2 $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 I_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 J)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 J) K)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 K)))))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) N)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 N) M)) (= M N)))))) (forall ((M $$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 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M)) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) N)))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 N))) (= M N))))) (forall ((K $$unsorted) (I_2 $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 I_2) J)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 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_2)) K))))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M))) (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) N)) (=> (not (= _let_1 N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 _let_1) 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 N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N)))))) (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))) (= M N))))) (forall ((N_2 $$unsorted) (M_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N_2))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 M_2))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M_2))) (= N_2 M_2))))) (forall ((M_2 $$unsorted) (N_2 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M_2)) (tptp.hAPP tptp.nat tptp.nat tptp.suc N_2))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M_2) N_2)))))) (forall ((M_2 $$unsorted) (N_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M_2))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N_2))) (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 N_2)) (= M_2 N_2))))) (forall ((M_2 $$unsorted) (N_2 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M_2) N_2))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 N_2) (tptp.hAPP tptp.nat tptp.nat tptp.suc M_2))))))) (forall ((N $$unsorted)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc N)) N)))) (forall ((M_2 $$unsorted) (N_2 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M_2) N_2))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N_2)) M_2)))))) (forall ((M_2 $$unsorted) (N_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N_2))) (let ((_let_2 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M_2))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 _let_1)) (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 N_2)) (= M_2 _let_1)))))) (forall ((N_2 $$unsorted) (M_2 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N_2)) (tptp.hAPP tptp.nat tptp.nat tptp.suc M_2))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 N_2) M_2)))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N)))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N))) (let ((_let_2 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 _let_1)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 N))) (= M _let_1)))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M)) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) N)))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) M) N)) (= M N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) M) N))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) M) N)) (=> (not (= M N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) M) N)))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) M) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) M) N))))) (forall ((M_2 $$unsorted) (N_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) M_2) N_2)) (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) M_2) N_2)) (= M_2 N_2))))) (forall ((M_2 $$unsorted) (N_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) M_2) N_2)) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) M_2) N_2)) (not (= M_2 N_2)))))) (forall ((X_a $$unsorted) (F1 $$unsorted) (F2 $$unsorted) (Nat_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat X_a))) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.nat_case X_a) F1) F2) (tptp.hAPP tptp.nat tptp.nat tptp.suc Nat_4)) (tptp.hAPP tptp.nat X_a F2 Nat_4)))) (forall ((N_2 $$unsorted) (M_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) N_2) M_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc N_2)) M_2))))) (forall ((M_2 $$unsorted) (N_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) M_2) (tptp.hAPP tptp.nat tptp.nat tptp.suc N_2))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) M_2) N_2))))) (forall ((M_2 $$unsorted) (N_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc M_2)) N_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) M_2) N_2))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) M) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) M) (tptp.hAPP tptp.nat tptp.nat tptp.suc N)))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) M) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc M)) N))))) (forall ((M_2 $$unsorted) (N_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) M_2) N_2)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) N_2) (tptp.hAPP tptp.nat tptp.nat tptp.suc M_2))) (= N_2 M_2))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc M)) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) M) N))))) (forall ((Pa $$unsorted) (I_1 $$unsorted) (J_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) I_1) J_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa J_2)) (=> (forall ((I $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I) J_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa (tptp.hAPP tptp.nat tptp.nat tptp.suc I))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa I))))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa I_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((N_2 $$unsorted) (N_3 $$unsorted) (F $$unsorted)) (=> (forall ((N_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP tptp.nat X_a F N_1)) (tptp.hAPP tptp.nat X_a F (tptp.hAPP tptp.nat tptp.nat tptp.suc 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) N_2) N_3)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP tptp.nat X_a F N_2)) (tptp.hAPP tptp.nat X_a F N_3)))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((N_2 $$unsorted) (N_3 $$unsorted) (F $$unsorted)) (=> (forall ((N_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.hAPP tptp.nat X_a F N_1)) (tptp.hAPP tptp.nat X_a F (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1))))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N_2) N_3)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.hAPP tptp.nat X_a F N_2)) (tptp.hAPP tptp.nat X_a F N_3)))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((N_2 $$unsorted) (M_2 $$unsorted) (F $$unsorted)) (=> (forall ((N_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.hAPP tptp.nat X_a F N_1)) (tptp.hAPP tptp.nat X_a F (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1))))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.hAPP tptp.nat X_a F N_2)) (tptp.hAPP tptp.nat X_a F M_2))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N_2) M_2))))))) (forall ((X_a $$unsorted) (Ca $$unsorted) (A_2 $$unsorted) (B_1 $$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) Ca))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less _let_1) A_2) B_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 A_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 B_1)))))))) (forall ((X_a $$unsorted) (C_1 $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.ord_less _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.hAPP _let_1 _let_3 _let_2 A_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_4 B_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 B_1) C_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_4 C_1))))))))) (forall ((M_2 $$unsorted) (N_2 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M_2)) N_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.bool (tptp.fun _let_2 _let_2) (tptp.nat_case tptp.bool) tptp.fFalse) (tptp.hAPP tptp.nat _let_2 _let_1 M_2)) N_2)))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (S $$unsorted) (R_1 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.product_prod X_a X_b) tptp.bool))) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.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) Y_2)))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 R_1)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 S))))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) R_1) S))))) (forall ((I_1 $$unsorted) (J_2 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (forall ((I $$unsorted) (J_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 I) J_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat F I)) (tptp.hAPP tptp.nat tptp.nat F J_1))))))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 I_1) J_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat F I_1)) (tptp.hAPP tptp.nat tptp.nat F J_2)))))))) (forall ((N $$unsorted) (M_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc N)) M_3)) (exists ((M_1 $$unsorted)) (= M_3 (tptp.hAPP tptp.nat tptp.nat tptp.suc M_1))))) (forall ((I_2 $$unsorted) (K $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I_2) K)) (=> (not (= K (tptp.hAPP tptp.nat tptp.nat tptp.suc I_2))) (not (forall ((J_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I_2) J_1)) (not (= K (tptp.hAPP tptp.nat tptp.nat tptp.suc J_1))))))))) (forall ((I_2 $$unsorted) (K $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc I_2)) K)) (not (forall ((J_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I_2) J_1)) (not (= K (tptp.hAPP tptp.nat tptp.nat tptp.suc J_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.dense_linorder X_a) (forall ((Z_1 $$unsorted) (Y $$unsorted)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) X_2) Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) X_2) Z_1))))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) Y) Z_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.dense_linorder X_a) (forall ((Z_1 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) X) Y)) (=> (forall ((W $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.ord_less X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 _let_2 X) W)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 _let_2 W) Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) W) Z_1))))))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) Y) Z_1)))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (and (tptp.order X_a) (tptp.ord X_b)) (forall ((Ca $$unsorted) (F $$unsorted) (Ba $$unsorted) (Aa $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) (tptp.hAPP X_b X_a F Ba)) Aa)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) Ca) Ba)) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) Y_2) X_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.hAPP X_b X_a F Y_2)) (tptp.hAPP X_b X_a F X_2))))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) (tptp.hAPP X_b X_a F Ca)) Aa))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (and (tptp.order X_a) (tptp.order X_b)) (forall ((Ca $$unsorted) (F $$unsorted) (Ba $$unsorted) (Aa $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_b X_a F Ba)) Aa)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) Ca) Ba)) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) Y_2) X_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP X_b X_a F Y_2)) (tptp.hAPP X_b X_a F X_2))))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_b X_a F Ca)) Aa)))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (and (tptp.order X_b) (tptp.order X_a)) (forall ((Ca $$unsorted) (Aa $$unsorted) (F $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) Aa) (tptp.hAPP X_b X_a F Ba))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) Ba) Ca)) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) X_2) Y_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.hAPP X_b X_a F X_2)) (tptp.hAPP X_b X_a F Y_2))))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) Aa) (tptp.hAPP X_b X_a F Ca)))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (and (tptp.order X_a) (tptp.order X_b)) (forall ((Ca $$unsorted) (F $$unsorted) (Ba $$unsorted) (Aa $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) Ba) Aa)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less_eq X_b) Ca) (tptp.hAPP X_a X_b F Ba))) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) Y_2) X_2)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) (tptp.hAPP X_a X_b F Y_2)) (tptp.hAPP X_a X_b F X_2))))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less X_b) Ca) (tptp.hAPP X_a X_b F Aa)))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (and (tptp.order X_a) (tptp.order X_b)) (forall ((Ca $$unsorted) (F $$unsorted) (Ba $$unsorted) (Aa $$unsorted)) (let ((_let_1 (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) Ca))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) Ba) Aa)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool _let_1 (tptp.hAPP X_a X_b F Ba))) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) Y_2) X_2)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) (tptp.hAPP X_a X_b F Y_2)) (tptp.hAPP X_a X_b F X_2))))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool _let_1 (tptp.hAPP X_a X_b F Aa)))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (and (tptp.order X_b) (tptp.order X_a)) (forall ((F $$unsorted) (Ca $$unsorted) (Aa $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) Aa) Ba)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less_eq X_b) (tptp.hAPP X_a X_b F Ba)) Ca)) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) X_2) Y_2)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) (tptp.hAPP X_a X_b F X_2)) (tptp.hAPP X_a X_b F Y_2))))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less X_b) (tptp.hAPP X_a X_b F Aa)) Ca))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (and (tptp.order X_b) (tptp.order X_a)) (forall ((Ca $$unsorted) (Aa $$unsorted) (F $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) Aa))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_b X_a F Ba))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) Ba) Ca)) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) X_2) Y_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP X_b X_a F X_2)) (tptp.hAPP X_b X_a F Y_2))))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_b X_a F Ca)))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (and (tptp.order X_b) (tptp.order X_a)) (forall ((F $$unsorted) (Ca $$unsorted) (Aa $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.ord_less X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) Aa) Ba)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 (tptp.hAPP X_a X_b F Ba)) Ca)) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X_2) Y_2)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) (tptp.hAPP X_a X_b F X_2)) (tptp.hAPP X_a X_b F Y_2))))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 (tptp.hAPP X_a X_b F Aa)) Ca)))))))))) (forall ((X_a $$unsorted) (I_2 $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I_2) (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) Xs))) (= Xs (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) I_2) Xs)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_2 (tptp.cons X_a) (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_1 (tptp.fun tptp.nat X_a) (tptp.nth X_a) Xs) I_2)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.nat _let_2 (tptp.drop X_a) (tptp.hAPP tptp.nat tptp.nat tptp.suc I_2)) Xs)))))))) (forall ((X_a $$unsorted) (Xs $$unsorted) (I_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun X_a _let_1))) (= (tptp.hAPP X_a _let_1 (tptp.hAPP tptp.nat _let_2 (tptp.hAPP _let_1 (tptp.fun tptp.nat _let_2) (tptp.list_update X_a) Xs) I_2) (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_1 (tptp.fun tptp.nat X_a) (tptp.nth X_a) Xs) I_2)) Xs)))) (forall ((X_a $$unsorted) (Xs $$unsorted) (X $$unsorted) (I_2 $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.nth X_a))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (let ((_let_3 (tptp.list X_a))) (let ((_let_4 (tptp.fun X_a _let_3))) (=> (not (= I_2 J)) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_3 _let_2 _let_1 (tptp.hAPP X_a _let_3 (tptp.hAPP tptp.nat _let_4 (tptp.hAPP _let_3 (tptp.fun tptp.nat _let_4) (tptp.list_update X_a) Xs) I_2) X)) J) (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_3 _let_2 _let_1 Xs) J)))))))) (forall ((X_a $$unsorted) (X $$unsorted) (Xs $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.nth X_a))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (let ((_let_3 (tptp.list X_a))) (= (tptp.hAPP tptp.nat X_a (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) Xs)) (tptp.hAPP tptp.nat tptp.nat tptp.suc N)) (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_3 _let_2 _let_1 Xs) N)))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (Ys $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.size_size _let_1))) (= (= Xs_1 Ys) (and (= (tptp.hAPP _let_1 tptp.nat _let_2 Xs_1) (tptp.hAPP _let_1 tptp.nat _let_2 Ys)) (forall ((I $$unsorted)) (let ((_let_1 (tptp.nth X_a))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (let ((_let_3 (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) I) (tptp.hAPP _let_3 tptp.nat (tptp.size_size _let_3) Xs_1))) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_3 _let_2 _let_1 Xs_1) I) (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_3 _let_2 _let_1 Ys) I)))))))))))) (forall ((X_a $$unsorted) (Xs $$unsorted) (I_2 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.nth X_a))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (let ((_let_3 (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) I_2) N)) (= (tptp.hAPP tptp.nat X_a (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)) I_2) (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_3 _let_2 _let_1 Xs) I_2))))))) (forall ((X_a $$unsorted) (N $$unsorted) (Xs $$unsorted) (Y $$unsorted) (Ys_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (=> (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.nat _let_2 (tptp.drop X_a) N) Xs) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_2 (tptp.cons X_a) Y) Ys_1)) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_1 (tptp.fun tptp.nat X_a) (tptp.nth X_a) Xs) N) (tptp.ti X_a Y)))))) (forall ((X_a $$unsorted) (X $$unsorted) (I_2 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.list X_a))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I_2) N)) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_1 (tptp.fun tptp.nat X_a) (tptp.nth X_a) (tptp.hAPP X_a _let_1 (tptp.hAPP tptp.nat (tptp.fun X_a _let_1) (tptp.replicate X_a) N) X)) I_2) (tptp.ti X_a X))))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (Xs_1 $$unsorted) (N_2 $$unsorted)) (let ((_let_1 (tptp.nth X_a))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (let ((_let_3 (tptp.list X_a))) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_3 _let_2 _let_1 (tptp.hAPP _let_3 _let_3 (tptp.hAPP X_a (tptp.fun _let_3 _let_3) (tptp.cons X_a) X_1) Xs_1)) N_2) (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_a (tptp.fun _let_2 _let_2) (tptp.nat_case X_a) X_1) (tptp.hAPP _let_3 _let_2 _let_1 Xs_1)) N_2)))))) (forall ((X_a $$unsorted) (N_2 $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (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_2) (tptp.hAPP _let_2 tptp.nat (tptp.size_size _let_2) Xs_1))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_2 (tptp.fun tptp.nat X_a) (tptp.nth X_a) Xs_1) N_2)) (tptp.hAPP _let_2 _let_1 (tptp.set X_a) Xs_1))))))) (forall ((X_a $$unsorted) (Pa $$unsorted) (Xs_1 $$unsorted)) (= (forall ((X_2 $$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 ((I $$unsorted)) (let ((_let_1 (tptp.list X_a))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I) (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) Xs_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_1 (tptp.fun tptp.nat X_a) (tptp.nth X_a) Xs_1) I)))))))) (forall ((X_a $$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 ((I $$unsorted)) (let ((_let_1 (tptp.list X_a))) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I) (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) Xs_1))) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_1 (tptp.fun tptp.nat X_a) (tptp.nth X_a) Xs_1) I) (tptp.ti X_a X_1)))))))) (forall ((X_a $$unsorted) (Xs $$unsorted) (X $$unsorted) (Ys_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_1 (tptp.fun tptp.nat X_a) (tptp.nth X_a) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.append X_a) Xs) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_2 (tptp.cons X_a) X) Ys_1))) (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) Xs)) (tptp.ti X_a X))))) (forall ((X_a $$unsorted) (J_2 $$unsorted) (I_1 $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.hAPP _let_1 (tptp.fun tptp.nat X_a) (tptp.nth X_a) Xs_1))) (let ((_let_3 (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) Xs_1))) (let ((_let_4 (tptp.ord_less tptp.nat))) (let ((_let_5 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.distinct X_a) Xs_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_5 _let_4 I_1) _let_3)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_5 _let_4 J_2) _let_3)) (= (= (tptp.hAPP tptp.nat X_a _let_2 I_1) (tptp.hAPP tptp.nat X_a _let_2 J_2)) (= I_1 J_2))))))))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.list X_a) tptp.bool (tptp.distinct X_a) Xs_1)) (forall ((I $$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 tptp.nat) I) (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) Xs_1))) (forall ((J_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.hAPP _let_1 (tptp.fun tptp.nat X_a) (tptp.nth X_a) Xs_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) J_1) (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) Xs_1))) (=> (not (= I J_1)) (not (= (tptp.hAPP tptp.nat X_a _let_2 I) (tptp.hAPP tptp.nat X_a _let_2 J_1))))))))))))) (forall ((X_a $$unsorted) (X $$unsorted) (J $$unsorted) (I_2 $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.nth X_a))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (let ((_let_3 (tptp.list X_a))) (let ((_let_4 (tptp.fun X_a _let_3))) (let ((_let_5 (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_3 _let_2 _let_1 (tptp.hAPP X_a _let_3 (tptp.hAPP tptp.nat _let_4 (tptp.hAPP _let_3 (tptp.fun tptp.nat _let_4) (tptp.list_update X_a) Xs) I_2) X)) J))) (let ((_let_6 (= I_2 J))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I_2) (tptp.hAPP _let_3 tptp.nat (tptp.size_size _let_3) Xs))) (and (=> _let_6 (= _let_5 (tptp.ti X_a X))) (=> (not _let_6) (= _let_5 (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_3 _let_2 _let_1 Xs) J)))))))))))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (I_1 $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun X_a _let_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I_1) (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) Xs_1))) (= (= (tptp.hAPP X_a _let_1 (tptp.hAPP tptp.nat _let_2 (tptp.hAPP _let_1 (tptp.fun tptp.nat _let_2) (tptp.list_update X_a) Xs_1) I_1) X_1) Xs_1) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_1 (tptp.fun tptp.nat X_a) (tptp.nth X_a) Xs_1) I_1) (tptp.ti X_a X_1))))))) (forall ((X_a $$unsorted) (X $$unsorted) (I_2 $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun X_a _let_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I_2) (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) Xs))) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_1 (tptp.fun tptp.nat X_a) (tptp.nth X_a) (tptp.hAPP X_a _let_1 (tptp.hAPP tptp.nat _let_2 (tptp.hAPP _let_1 (tptp.fun tptp.nat _let_2) (tptp.list_update X_a) Xs) I_2) X)) I_2) (tptp.ti X_a X)))))) (forall ((X_a $$unsorted) (Pa $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.size_size _let_1))) (let ((_let_3 (tptp.hAPP _let_1 tptp.nat _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_a tptp.bool) (tptp.fun _let_1 _let_1) (tptp.takeWhile X_a) Pa) Xs_1)))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) _let_3) (tptp.hAPP _let_1 tptp.nat _let_2 Xs_1))) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_1 (tptp.fun tptp.nat X_a) (tptp.nth X_a) Xs_1) _let_3))))))))) (forall ((X_a $$unsorted) (J_2 $$unsorted) (Pa $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.nth X_a))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (let ((_let_3 (tptp.list X_a))) (let ((_let_4 (tptp.hAPP _let_3 _let_3 (tptp.hAPP (tptp.fun X_a tptp.bool) (tptp.fun _let_3 _let_3) (tptp.takeWhile X_a) Pa) Xs_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) J_2) (tptp.hAPP _let_3 tptp.nat (tptp.size_size _let_3) _let_4))) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_3 _let_2 _let_1 _let_4) J_2) (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_3 _let_2 _let_1 Xs_1) J_2)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((I_2 $$unsorted) (J $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.hAPP _let_1 (tptp.fun tptp.nat X_a) (tptp.nth X_a) Xs))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.linorder_sorted X_a) Xs)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 (tptp.ord_less_eq tptp.nat) I_2) J)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 (tptp.ord_less tptp.nat) J) (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) Xs))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP tptp.nat X_a _let_2 I_2)) (tptp.hAPP tptp.nat X_a _let_2 J)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((Xs_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.list X_a) tptp.bool (tptp.linorder_sorted X_a) Xs_1)) (forall ((J_1 $$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 tptp.nat) J_1) (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) Xs_1))) (forall ((I $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.list X_a) (tptp.fun tptp.nat X_a) (tptp.nth X_a) Xs_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) I) J_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP tptp.nat X_a _let_1 I)) (tptp.hAPP tptp.nat X_a _let_1 J_1))))))))))))) (forall ((X_a $$unsorted) (I_2 $$unsorted) (Xs $$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.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I_2) (tptp.hAPP _let_2 tptp.nat (tptp.size_size _let_2) Xs))) (= (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_a _let_3 (tptp.cons X_a) (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_2 (tptp.fun tptp.nat X_a) (tptp.nth X_a) Xs) I_2)) (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc I_2)) Xs)) (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 I_2) Xs))))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (Ys $$unsorted) (R_1 $$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)) (tptp.hAPP (tptp.fun (tptp.product_prod X_a X_a) tptp.bool) _let_4 (tptp.listrel X_a) R_1))) (and (= (tptp.hAPP _let_1 tptp.nat _let_2 Xs_1) (tptp.hAPP _let_1 tptp.nat _let_2 Ys)) (forall ((N_1 $$unsorted)) (let ((_let_1 (tptp.nth X_a))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (let ((_let_3 (tptp.list X_a))) (let ((_let_4 (tptp.product_prod X_a X_a))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N_1) (tptp.hAPP _let_3 tptp.nat (tptp.size_size _let_3) Xs_1))) (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP _let_4 (tptp.fun _let_5 tptp.bool) (tptp.member _let_4) (tptp.hAPP X_a _let_4 (tptp.hAPP X_a (tptp.fun X_a _let_4) (tptp.product_Pair X_a X_a) (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_3 _let_2 _let_1 Xs_1) N_1)) (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_3 _let_2 _let_1 Ys) N_1))) R_1)))))))))))))))) (forall ((X_a $$unsorted) (N $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.list X_a))) (=> (not (= Xs (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 tptp.nat) N) (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) Xs))) (= (tptp.hAPP _let_1 X_a (tptp.hd X_a) (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.nat (tptp.fun _let_1 _let_1) (tptp.drop X_a) N) Xs)) (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_1 (tptp.fun tptp.nat X_a) (tptp.nth X_a) Xs) N)))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((I_2 $$unsorted) (J $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.hAPP _let_1 (tptp.fun tptp.nat X_a) (tptp.nth X_a) Xs))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.linorder_sorted X_a) (tptp.hAPP _let_1 _let_1 (tptp.rev X_a) Xs))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 (tptp.ord_less_eq tptp.nat) I_2) J)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 (tptp.ord_less tptp.nat) J) (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) Xs))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP tptp.nat X_a _let_2 J)) (tptp.hAPP tptp.nat X_a _let_2 I_2)))))))))))) (forall ((X_a $$unsorted) (I_2 $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.take X_a))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I_2) (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) Xs))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.nat _let_2 _let_3 (tptp.hAPP tptp.nat tptp.nat tptp.suc I_2)) Xs) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.append X_a) (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.nat _let_2 _let_3 I_2) Xs)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_2 (tptp.cons X_a) (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_1 (tptp.fun tptp.nat X_a) (tptp.nth X_a) Xs) I_2)) (tptp.nil X_a))))))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (Ys $$unsorted) (R_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.product_prod _let_1 _let_1))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_3 tptp.bool) (tptp.member _let_2) (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_2) (tptp.product_Pair _let_1 _let_1) Xs_1) Ys)) (tptp.hAPP (tptp.fun (tptp.product_prod X_a X_a) tptp.bool) _let_3 (tptp.listrel1 X_a) R_1))) (exists ((Y_2 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun X_a _let_1))) (let ((_let_3 (tptp.product_prod X_a X_a))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (and (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP _let_3 (tptp.fun _let_4 tptp.bool) (tptp.member _let_3) (tptp.hAPP X_a _let_3 (tptp.hAPP X_a (tptp.fun X_a _let_3) (tptp.product_Pair X_a X_a) (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_1 (tptp.fun tptp.nat X_a) (tptp.nth X_a) Xs_1) N_1)) Y_2)) R_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N_1) (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) Xs_1))) (= Ys (tptp.hAPP X_a _let_1 (tptp.hAPP tptp.nat _let_2 (tptp.hAPP _let_1 (tptp.fun tptp.nat _let_2) (tptp.list_update X_a) Xs_1) N_1) Y_2))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((Xs $$unsorted)) (=> (forall ((I $$unsorted) (J_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.hAPP _let_1 (tptp.fun tptp.nat X_a) (tptp.nth X_a) Xs))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 (tptp.ord_less_eq tptp.nat) I) J_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 (tptp.ord_less tptp.nat) J_1) (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) Xs))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP tptp.nat X_a _let_2 I)) (tptp.hAPP tptp.nat X_a _let_2 J_1))))))))) (tptp.hBOOL (tptp.hAPP (tptp.list X_a) tptp.bool (tptp.linorder_sorted X_a) Xs)))))) (forall ((X_a $$unsorted) (Pa $$unsorted) (Xs_1 $$unsorted) (N_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (=> (forall ((I $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 N_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) Xs_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_1 (tptp.fun tptp.nat X_a) (tptp.nth X_a) Xs_1) I)))))))) (=> (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N_2) (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) Xs_1))) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_1 (tptp.fun tptp.nat X_a) (tptp.nth X_a) Xs_1) N_2))))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_a tptp.bool) _let_2 (tptp.takeWhile X_a) Pa) Xs_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.nat _let_2 (tptp.take X_a) N_2) Xs_1))))))) (forall ((X_a $$unsorted) (Pa $$unsorted) (Xs_1 $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.size_size _let_1))) (let ((_let_3 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) J_2))) (=> (forall ((I $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I) J_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa (tptp.hAPP tptp.nat X_a (tptp.hAPP (tptp.list X_a) (tptp.fun tptp.nat X_a) (tptp.nth X_a) Xs_1) I))))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 (tptp.hAPP _let_1 tptp.nat _let_2 Xs_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 (tptp.hAPP _let_1 tptp.nat _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_a tptp.bool) (tptp.fun _let_1 _let_1) (tptp.takeWhile X_a) Pa) Xs_1)))))))))) (forall ((X_a $$unsorted) (Ys_1 $$unsorted) (K $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.hAPP tptp.nat (tptp.fun _let_1 _let_1) (tptp.take X_a) K))) (let ((_let_3 (tptp.size_size _let_1))) (let ((_let_4 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_4 (tptp.hAPP _let_1 tptp.nat _let_3 Xs))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_4 (tptp.hAPP _let_1 tptp.nat _let_3 Ys_1))) (=> (forall ((I $$unsorted)) (let ((_let_1 (tptp.nth X_a))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (let ((_let_3 (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) I) K)) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_3 _let_2 _let_1 Xs) I) (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_3 _let_2 _let_1 Ys_1) I))))))) (= (tptp.hAPP _let_1 _let_1 _let_2 Xs) (tptp.hAPP _let_1 _let_1 _let_2 Ys_1)))))))))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (Pa $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (forall ((I $$unsorted)) (let ((_let_1 (tptp.list X_a))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I) (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) Xs_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_1 (tptp.fun tptp.nat X_a) (tptp.nth X_a) Xs_1) I)))))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_1) (tptp.hAPP (tptp.list X_a) _let_1 (tptp.set X_a) Xs_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa X_1)))))) (forall ((X_a $$unsorted) (Pa $$unsorted) (N_2 $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N_2) (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) Xs_1))) (=> (forall ((X_2 $$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 Pa X_2))))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_1 (tptp.fun tptp.nat X_a) (tptp.nth X_a) Xs_1) N_2))))))) (forall ((X_a $$unsorted) (Xs $$unsorted) (Ys_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.size_size _let_1))) (=> (= (tptp.hAPP _let_1 tptp.nat _let_2 Xs) (tptp.hAPP _let_1 tptp.nat _let_2 Ys_1)) (=> (forall ((I $$unsorted)) (let ((_let_1 (tptp.nth X_a))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (let ((_let_3 (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) I) (tptp.hAPP _let_3 tptp.nat (tptp.size_size _let_3) Xs))) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_3 _let_2 _let_1 Xs) I) (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_3 _let_2 _let_1 Ys_1) I))))))) (= Xs Ys_1)))))) (forall ((X_a $$unsorted) (Pa $$unsorted) (K_1 $$unsorted)) (= (forall ((I $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I) K_1)) (exists ((X1 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP tptp.nat (tptp.fun X_a tptp.bool) Pa I) X1))))) (exists ((Xs_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (and (= (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) Xs_2) K_1) (forall ((I $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I) K_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP tptp.nat (tptp.fun X_a tptp.bool) Pa I) (tptp.hAPP tptp.nat X_a (tptp.hAPP (tptp.list X_a) (tptp.fun tptp.nat X_a) (tptp.nth X_a) Xs_2) I)))))))))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted) (R_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.size_size _let_1))) (let ((_let_3 (tptp.hAPP _let_1 tptp.nat _let_2 X_1))) (let ((_let_4 (tptp.product_prod _let_1 _let_1))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP _let_4 (tptp.fun _let_5 tptp.bool) (tptp.member _let_4) (tptp.hAPP _let_1 _let_4 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_4) (tptp.product_Pair _let_1 _let_1) X_1) Y_1)) (tptp.hAPP (tptp.fun (tptp.product_prod X_a X_a) tptp.bool) _let_5 (tptp.lexord X_a) R_1))) (or (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) _let_3) (tptp.hAPP _let_1 tptp.nat _let_2 Y_1))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.nat (tptp.fun _let_1 _let_1) (tptp.take X_a) _let_3) Y_1) X_1)) (exists ((I $$unsorted)) (let ((_let_1 (tptp.nth X_a))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (let ((_let_3 (tptp.list X_a))) (let ((_let_4 (tptp.product_prod X_a X_a))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (let ((_let_6 (tptp.hAPP tptp.nat (tptp.fun _let_3 _let_3) (tptp.take X_a) I))) (let ((_let_7 (tptp.size_size _let_3))) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.ord_min tptp.nat) (tptp.hAPP _let_3 tptp.nat _let_7 X_1)) (tptp.hAPP _let_3 tptp.nat _let_7 Y_1)))) (= (tptp.hAPP _let_3 _let_3 _let_6 X_1) (tptp.hAPP _let_3 _let_3 _let_6 Y_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) (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_3 _let_2 _let_1 X_1) I)) (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_3 _let_2 _let_1 Y_1) I))) R_1))))))))))))))))))) (forall ((X_a $$unsorted) (R_1 $$unsorted)) (=> (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) R_1 X_2) X_2))) (tptp.hBOOL (tptp.hAPP (tptp.fun X_a (tptp.fun X_a tptp.bool)) tptp.bool (tptp.reflp X_a) R_1)))) (forall ((X_a $$unsorted) (J_2 $$unsorted) (Pa $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.size_size _let_1))) (let ((_let_5 (tptp.nth X_a))) (let ((_let_6 (tptp.fun tptp.nat X_a))) (let ((_let_7 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_3 _let_2 (tptp.dropWhile X_a) Pa) Xs_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) J_2) (tptp.hAPP _let_1 tptp.nat _let_4 _let_7))) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_1 _let_6 _let_5 _let_7) J_2) (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_1 _let_6 _let_5 Xs_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) J_2) (tptp.hAPP _let_1 tptp.nat _let_4 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_3 _let_2 (tptp.takeWhile X_a) Pa) Xs_1)))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((Z_2 $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) Z_2))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_min X_a) X_1) Y_1))) (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 X_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 Y_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (Z_2 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_min X_a) X_1) Y_1)) Z_2)) (or (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X_1) Z_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y_1) Z_2))))))))) (forall ((Z_1 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) X))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) Y) Z_1)))))) (forall ((Y $$unsorted) (X $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) X))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 Z_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) Y) Z_1)))))) (forall ((I_2 $$unsorted) (J $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) I_2) J)) K)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 I_2) K)))))) (forall ((M $$unsorted) (N $$unsorted) (K $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.plus_plus tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 K) L)) (=> (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_4 _let_3 M) L) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_4 _let_3 K) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) N))))))))) (forall ((K $$unsorted) (L $$unsorted) (I_2 $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.ord_less tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 I_2) J)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 K) L)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 I_2) K)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 J) L)))))))))) (forall ((K $$unsorted) (I_2 $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.ord_less tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 I_2) J)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 I_2) K)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 J) K))))))))) (forall ((M $$unsorted) (I_2 $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 J)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M) J)))))) (forall ((M $$unsorted) (I_2 $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 J)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) J) M)))))) (forall ((K_1 $$unsorted) (M_2 $$unsorted) (N_2 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) K_1))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 M_2)) (tptp.hAPP tptp.nat tptp.nat _let_3 N_2))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M_2) N_2))))))) (forall ((J $$unsorted) (I_2 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) J) I_2)) I_2)))) (forall ((I_2 $$unsorted) (J $$unsorted)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) I_2) J)) I_2)))) (forall ((X_a $$unsorted) (N $$unsorted) (M $$unsorted) (Xs $$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 N) (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 M) Xs)) (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) N) M)) Xs)))))) (forall ((X_a $$unsorted) (N $$unsorted) (M $$unsorted) (Xs $$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.hAPP _let_2 _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 N) (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 M) Xs)) (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.ord_min tptp.nat) N) M)) Xs)))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (Z_2 $$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 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_min X_a) X_1) Y_1)) Z_2)) (or (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X_1) Z_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y_1) Z_2))))))))) (forall ((Z_1 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) X))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) Y) Z_1)))))) (forall ((Y $$unsorted) (X $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) X))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 Z_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) Y) Z_1)))))) (forall ((N $$unsorted) (M $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M) N)))) (forall ((N $$unsorted) (M $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) N) M)))) (forall ((M_2 $$unsorted) (N_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M_2) N_2)) (exists ((K_2 $$unsorted)) (= N_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M_2) K_2))))) (forall ((K_1 $$unsorted) (M_2 $$unsorted) (N_2 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) K_1))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 M_2)) (tptp.hAPP tptp.nat tptp.nat _let_3 N_2))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M_2) N_2))))))) (forall ((M $$unsorted) (I_2 $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) I_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 J)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) J) M)))))) (forall ((M $$unsorted) (I_2 $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) I_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 J)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M) J)))))) (forall ((K $$unsorted) (I_2 $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.ord_less_eq tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 I_2) J)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 I_2) K)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 J) K))))))))) (forall ((K $$unsorted) (L $$unsorted) (I_2 $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.ord_less_eq tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 I_2) J)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 K) L)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 I_2) K)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 J) L)))))))))) (forall ((M $$unsorted) (K $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M) K)) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 K) N)))))) (forall ((M $$unsorted) (K $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M) K)) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) N)))))) (forall ((M $$unsorted) (K $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M) K)) N)) (not (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) N)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 K) N))))))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M))) (= (tptp.hAPP tptp.nat tptp.nat _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N)) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat _let_1 N))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M)) N) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M) N)))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M)) N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M) (tptp.hAPP tptp.nat tptp.nat tptp.suc N)))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_min tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M)) (tptp.hAPP tptp.nat tptp.nat tptp.suc N)) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M) N)))))) (forall ((M_2 $$unsorted) (K_1 $$unsorted) (N_2 $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M_2) K_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 N_2) K_1)) (= M_2 N_2))))) (forall ((K_1 $$unsorted) (M_2 $$unsorted) (N_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) K_1))) (= (= (tptp.hAPP tptp.nat tptp.nat _let_1 M_2) (tptp.hAPP tptp.nat tptp.nat _let_1 N_2)) (= M_2 N_2)))) (forall ((M $$unsorted) (N $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 M))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 N)) K) (tptp.hAPP tptp.nat tptp.nat _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 N) K))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 X))) (let ((_let_4 (tptp.hAPP tptp.nat _let_2 _let_1 Y))) (= (tptp.hAPP tptp.nat tptp.nat _let_3 (tptp.hAPP tptp.nat tptp.nat _let_4 Z_1)) (tptp.hAPP tptp.nat tptp.nat _let_4 (tptp.hAPP tptp.nat tptp.nat _let_3 Z_1)))))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M) N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 N) M))))) (forall ((X_a $$unsorted) (N $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.size_size _let_1))) (= (tptp.hAPP _let_1 tptp.nat _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.nat (tptp.fun _let_1 _let_1) (tptp.take X_a) N) Xs)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.ord_min tptp.nat) (tptp.hAPP _let_1 tptp.nat _let_2 Xs)) N))))) (forall ((M_2 $$unsorted) (N_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M_2) N_2)) (exists ((K_2 $$unsorted)) (= N_2 (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M_2) K_2)))))) (forall ((I_2 $$unsorted) (M $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I_2) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M) I_2))))) (forall ((I_2 $$unsorted) (M $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I_2) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) I_2) M))))) (forall ((X_a $$unsorted) (Xs $$unsorted) (Ys_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.size_size _let_1))) (= (tptp.hAPP _let_1 tptp.nat _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.append X_a) Xs) Ys_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) (tptp.hAPP _let_1 tptp.nat _let_2 Xs)) (tptp.hAPP _let_1 tptp.nat _let_2 Ys_1)))))) (forall ((X_a $$unsorted) (I_2 $$unsorted) (K $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.replicate X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun X_a _let_2))) (= (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.nat (tptp.fun _let_2 _let_2) (tptp.take X_a) I_2) (tptp.hAPP X_a _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 K) X)) (tptp.hAPP X_a _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.ord_min tptp.nat) I_2) K)) X)))))) (forall ((X_a $$unsorted) (N $$unsorted) (M $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.replicate X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun X_a _let_2))) (= (tptp.hAPP X_a _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) N) M)) X) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 (tptp.fun _let_2 _let_2) (tptp.append X_a) (tptp.hAPP X_a _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 N) X)) (tptp.hAPP X_a _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 M) X))))))) (forall ((X_a $$unsorted) (N $$unsorted) (M $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.take X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (let ((_let_4 (tptp.hAPP tptp.nat _let_3 (tptp.drop X_a) M))) (= (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 N) (tptp.hAPP _let_2 _let_2 _let_4 Xs)) (tptp.hAPP _let_2 _let_2 _let_4 (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) N) M)) Xs)))))))) (forall ((X_a $$unsorted) (Xs $$unsorted) (Ys_1 $$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.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.splice X_a) Xs) Ys_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) (tptp.hAPP _let_1 tptp.nat _let_2 Xs)) (tptp.hAPP _let_1 tptp.nat _let_2 Ys_1)))))) (forall ((X_a $$unsorted) (Xs $$unsorted) (Ys_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.nth X_a))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (let ((_let_3 (tptp.list X_a))) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_3 _let_2 _let_1 (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_3 (tptp.fun _let_3 _let_3) (tptp.append X_a) Xs) Ys_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) (tptp.hAPP _let_3 tptp.nat (tptp.size_size _let_3) Xs)) N)) (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_3 _let_2 _let_1 Ys_1) N)))))) (forall ((X_a $$unsorted) (I_2 $$unsorted) (J $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.take X_a))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.nat _let_2 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) I_2) J)) Xs) (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 _let_3 I_2) Xs)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.nat _let_2 _let_3 J) (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.nat _let_2 (tptp.drop X_a) I_2) Xs)))))))) (forall ((X_a $$unsorted) (N $$unsorted) (I_2 $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) N) I_2))) (let ((_let_2 (tptp.nth X_a))) (let ((_let_3 (tptp.fun tptp.nat X_a))) (let ((_let_4 (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) _let_1) (tptp.hAPP _let_4 tptp.nat (tptp.size_size _let_4) Xs))) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_4 _let_3 _let_2 (tptp.hAPP _let_4 _let_4 (tptp.hAPP tptp.nat (tptp.fun _let_4 _let_4) (tptp.drop X_a) N) Xs)) I_2) (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_4 _let_3 _let_2 Xs) _let_1)))))))) (forall ((M_2 $$unsorted) (K_1 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (=> (forall ((M_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M_1) N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat F M_1)) (tptp.hAPP tptp.nat tptp.nat F N_1))))))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat F M_2)) K_1)) (tptp.hAPP tptp.nat tptp.nat F (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M_2) K_1)))))))) (forall ((M $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M) N)) (exists ((K_2 $$unsorted)) (= N (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M) K_2)))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere223160158up_add X_a) (forall ((C $$unsorted) (D_1 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 (tptp.ord_less_eq X_a) C) D_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) D_1)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.cancel_semigroup_add X_a) (forall ((B $$unsorted) (A_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (=> (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) A_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 C) A_1)) (= (tptp.ti X_a B) (tptp.ti X_a C)))))))) (forall ((X_a $$unsorted)) (=> (tptp.cancel146912293up_add X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1))) (=> (= (tptp.hAPP X_a X_a _let_1 B) (tptp.hAPP X_a X_a _let_1 C)) (= (tptp.ti X_a B) (tptp.ti X_a C))))))) (forall ((X_a $$unsorted)) (=> (tptp.cancel_semigroup_add X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1))) (=> (= (tptp.hAPP X_a X_a _let_1 B) (tptp.hAPP X_a X_a _let_1 C)) (= (tptp.ti X_a B) (tptp.ti X_a C))))))) (forall ((X_a $$unsorted)) (=> (tptp.cancel_semigroup_add X_a) (forall ((Ba $$unsorted) (Aa $$unsorted) (Ca $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (= (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Ba) Aa) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Ca) Aa)) (= (tptp.ti X_a Ba) (tptp.ti X_a Ca)))))))) (forall ((X_a $$unsorted)) (=> (tptp.cancel_semigroup_add X_a) (forall ((Aa $$unsorted) (Ba $$unsorted) (Ca $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) Aa))) (= (= (tptp.hAPP X_a X_a _let_1 Ba) (tptp.hAPP X_a X_a _let_1 Ca)) (= (tptp.ti X_a Ba) (tptp.ti X_a Ca))))))) (forall ((X_a $$unsorted)) (=> (tptp.ab_semigroup_add X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 A_1))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 B)) C) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) C))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere236663937imp_le X_a) (forall ((Aa $$unsorted) (Ca $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.plus_plus X_a))) (let ((_let_4 (tptp.fun X_a X_a))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 Aa) Ca)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 Ba) Ca))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Aa) Ba)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere236663937imp_le X_a) (forall ((Ca $$unsorted) (Aa $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) Ca))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 Aa)) (tptp.hAPP X_a X_a _let_3 Ba))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Aa) Ba))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere779506340up_add X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less_eq X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 A_1) B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) C))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere779506340up_add X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) C))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 A_1)) (tptp.hAPP X_a X_a _let_1 B)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere779506340up_add X_a) (forall ((C $$unsorted) (D_1 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less_eq X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 C) D_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) D_1)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere236663937imp_le X_a) (forall ((A_1 $$unsorted) (C $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.plus_plus X_a))) (let ((_let_4 (tptp.fun X_a X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 B) C))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere236663937imp_le X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) C))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 A_1)) (tptp.hAPP X_a X_a _let_3 B))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere236663937imp_le X_a) (forall ((Aa $$unsorted) (Ca $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.plus_plus X_a))) (let ((_let_4 (tptp.fun X_a X_a))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 Aa) Ca)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 Ba) Ca))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Aa) Ba)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere236663937imp_le X_a) (forall ((Ca $$unsorted) (Aa $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) Ca))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 Aa)) (tptp.hAPP X_a X_a _let_3 Ba))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Aa) Ba))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere223160158up_add X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 A_1) B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) C))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere223160158up_add X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) C))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 A_1)) (tptp.hAPP X_a X_a _let_1 B)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere223160158up_add X_a) (forall ((C $$unsorted) (D_1 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 C) D_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) D_1)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere236663937imp_le X_a) (forall ((A_1 $$unsorted) (C $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.plus_plus X_a))) (let ((_let_4 (tptp.fun X_a X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 B) C))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere236663937imp_le X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) C))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 A_1)) (tptp.hAPP X_a X_a _let_3 B))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere236663937imp_le X_a) (forall ((X $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_min X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 X) Y)) Z_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 X) Z_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Y) Z_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere223160158up_add X_a) (forall ((C $$unsorted) (D_1 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 (tptp.ord_less_eq X_a) A_1) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 C) D_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) D_1)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ord X_a) (forall ((X $$unsorted) (Least $$unsorted)) (=> (forall ((X_2 $$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) Least) X_2))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_min X_a) Least) X) (tptp.ti X_a Least)))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((X $$unsorted) (Least $$unsorted)) (=> (forall ((X_2 $$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) Least) X_2))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_min X_a) X) Least) (tptp.ti X_a Least)))))) (forall ((X_a $$unsorted)) (=> (tptp.ord X_a) (= (tptp.ord_min X_a) (tptp.hAPP (tptp.fun X_a (tptp.fun X_a tptp.bool)) (tptp.fun X_a (tptp.fun X_a X_a)) (tptp.min X_a) (tptp.ord_less_eq X_a))))) (forall ((X_a $$unsorted) (I_1 $$unsorted) (K_1 $$unsorted) (F $$unsorted) (R_1 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_a))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (forall ((I $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_a))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) (tptp.hAPP X_a _let_1 (tptp.hAPP X_a (tptp.fun X_a _let_1) (tptp.product_Pair X_a X_a) (tptp.hAPP tptp.nat X_a F (tptp.hAPP tptp.nat tptp.nat tptp.suc I))) (tptp.hAPP tptp.nat X_a F I))) (tptp.hAPP _let_2 _let_2 (tptp.transitive_rtrancl X_a) R_1)))))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) (tptp.hAPP X_a _let_1 (tptp.hAPP X_a (tptp.fun X_a _let_1) (tptp.product_Pair X_a X_a) (tptp.hAPP tptp.nat X_a F (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) I_1) K_1))) (tptp.hAPP tptp.nat X_a F I_1))) (tptp.hAPP _let_2 _let_2 (tptp.transitive_rtrancl X_a) R_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B) X)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_min X_a) A_1) B)) X)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((B $$unsorted) (A_1 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) X)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_min X_a) A_1) B)) X)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.ord_min X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 X))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 Y)) Z_1) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Y) Z_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.ord_min X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 A_1))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 B)) C) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) C))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.ord_min X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 X))) (let ((_let_4 (tptp.hAPP X_a _let_2 _let_1 Y))) (= (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a _let_4 Z_1)) (tptp.hAPP X_a X_a _let_4 (tptp.hAPP X_a X_a _let_3 Z_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((B $$unsorted) (A_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.ord_min X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 B))) (let ((_let_4 (tptp.hAPP X_a _let_2 _let_1 A_1))) (= (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a _let_4 C)) (tptp.hAPP X_a X_a _let_4 (tptp.hAPP X_a X_a _let_3 C)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_min X_a) X))) (let ((_let_2 (tptp.hAPP X_a X_a _let_1 Y))) (= (tptp.hAPP X_a X_a _let_1 _let_2) _let_2)))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_min X_a) A_1))) (let ((_let_2 (tptp.hAPP X_a X_a _let_1 B))) (= (tptp.hAPP X_a X_a _let_1 _let_2) _let_2)))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_min X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 X) Y) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Y) X))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_min X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) B) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) A_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_min X_a) A_1) A_1) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder 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_eq X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_min X_a) X) Y)) X))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_min X_a) X) Y)) Y))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder 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.ord_less_eq X_a) X_1) Y_1)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_min X_a) X_1) Y_1) (tptp.ti X_a X_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (Z_2 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X_1))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_min X_a) Y_1) Z_2))) (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 Y_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 Z_2)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((B $$unsorted) (A_1 $$unsorted) (X $$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 A_1) X)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_min X_a) A_1) B)) X)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (X $$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 B) X)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_min X_a) A_1) B)) X)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X) Y)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_min X_a) X) Y) (tptp.ti X_a X)))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((Y $$unsorted) (X $$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) Y) X)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_min X_a) X) Y) (tptp.ti X_a Y)))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((B $$unsorted) (X $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_min X_a) A_1) B))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((Z_1 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 Y)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 Z_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_min X_a) Y) Z_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((B $$unsorted) (D_1 $$unsorted) (A_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.ord_min X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less_eq X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 A_1) C)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 B) D_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) B)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 C) D_1)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_min X_a) A_1) B))) (not (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_1)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B)))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (Aa $$unsorted) (Ba $$unsorted) (A_3 $$unsorted) (B_3 $$unsorted) (R_1 $$unsorted) (S $$unsorted)) (let ((_let_1 (tptp.product_prod X_b X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.product_prod X_a X_a))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.product_prod X_a X_b))) (let ((_let_6 (tptp.product_prod _let_5 _let_5))) (let ((_let_7 (tptp.fun _let_6 tptp.bool))) (let ((_let_8 (tptp.product_Pair X_a X_b))) (let ((_let_9 (tptp.fun X_b _let_5))) (= (tptp.hBOOL (tptp.hAPP _let_7 tptp.bool (tptp.hAPP _let_6 (tptp.fun _let_7 tptp.bool) (tptp.member _let_6) (tptp.hAPP _let_5 _let_6 (tptp.hAPP _let_5 (tptp.fun _let_5 _let_6) (tptp.product_Pair _let_5 _let_5) (tptp.hAPP X_b _let_5 (tptp.hAPP X_a _let_9 _let_8 Aa) Ba)) (tptp.hAPP X_b _let_5 (tptp.hAPP X_a _let_9 _let_8 A_3) B_3))) (tptp.hAPP _let_2 _let_7 (tptp.hAPP _let_4 (tptp.fun _let_2 _let_7) (tptp.lex_prod X_a X_b) R_1) S))) (or (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP _let_3 (tptp.fun _let_4 tptp.bool) (tptp.member _let_3) (tptp.hAPP X_a _let_3 (tptp.hAPP X_a (tptp.fun X_a _let_3) (tptp.product_Pair X_a X_a) Aa) A_3)) R_1)) (and (= (tptp.ti X_a Aa) (tptp.ti X_a A_3)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) (tptp.hAPP X_b _let_1 (tptp.hAPP X_b (tptp.fun X_b _let_1) (tptp.product_Pair X_b X_b) Ba) B_3)) S))))))))))))))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_a))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) (tptp.hAPP X_a _let_1 (tptp.hAPP X_a (tptp.fun X_a _let_1) (tptp.product_Pair X_a X_a) X_1) Y_1)) (tptp.hAPP (tptp.fun X_a tptp.nat) _let_2 (tptp.measure X_a) F))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP X_a tptp.nat F X_1)) (tptp.hAPP X_a tptp.nat F Y_1))))))) (forall ((F $$unsorted)) (=> (forall ((I $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat F (tptp.hAPP tptp.nat tptp.nat tptp.suc I))) (tptp.hAPP tptp.nat tptp.nat F I)))) (exists ((I $$unsorted)) (forall ((K_2 $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat F (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) I) K_2)) (tptp.hAPP tptp.nat tptp.nat F I)))))) (forall ((X_a $$unsorted) (R_2 $$unsorted) (F $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_a))) (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_a _let_1 (tptp.hAPP X_a (tptp.fun X_a _let_1) (tptp.product_Pair X_a X_a) X_1) Y_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 X_a tptp.nat F X_1)) (tptp.hAPP X_a tptp.nat F Y_1))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 R_2)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 (tptp.hAPP _let_2 _let_2 (tptp.hAPP (tptp.fun X_a tptp.nat) (tptp.fun _let_2 _let_2) (tptp.mlex_prod X_a) F) R_2))))))))) (forall ((X_a $$unsorted) (R_2 $$unsorted) (F $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_a))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP X_a tptp.nat F X_1)) (tptp.hAPP X_a tptp.nat F Y_1))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) (tptp.hAPP X_a _let_1 (tptp.hAPP X_a (tptp.fun X_a _let_1) (tptp.product_Pair X_a X_a) X_1) Y_1)) (tptp.hAPP _let_2 _let_2 (tptp.hAPP (tptp.fun X_a tptp.nat) (tptp.fun _let_2 _let_2) (tptp.mlex_prod X_a) F) R_2))))))) (forall ((X_a $$unsorted) (L_1 $$unsorted) (L_2 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (let ((_let_4 (tptp.fun tptp.nat tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (let ((_let_6 (tptp.fun tptp.nat _let_5))) (let ((_let_7 (tptp.sublist X_a))) (let ((_let_8 (tptp.fun _let_4 _let_1))) (let ((_let_9 (tptp.append X_a))) (let ((_let_10 (tptp.fun _let_1 _let_1))) (= (tptp.hAPP _let_4 _let_1 (tptp.hAPP _let_1 _let_8 _let_7 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_10 _let_9 L_1) L_2)) A_2) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_10 _let_9 (tptp.hAPP _let_4 _let_1 (tptp.hAPP _let_1 _let_8 _let_7 L_1) A_2)) (tptp.hAPP _let_4 _let_1 (tptp.hAPP _let_1 _let_8 _let_7 L_2) (tptp.hAPP _let_4 _let_4 (tptp.collect tptp.nat) (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_6 (tptp.fun _let_4 _let_4) (tptp.combc tptp.nat _let_4 tptp.bool) (tptp.hAPP _let_2 _let_6 (tptp.hAPP _let_6 (tptp.fun _let_2 _let_6) (tptp.combb tptp.nat _let_5 tptp.nat) (tptp.member tptp.nat)) (tptp.hAPP tptp.nat _let_2 (tptp.hAPP _let_3 _let_3 (tptp.combc tptp.nat tptp.nat tptp.nat) (tptp.plus_plus tptp.nat)) (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) L_1)))) A_2)))))))))))))))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (Xs_1 $$unsorted) (I_3 $$unsorted)) (let ((_let_1 (tptp.set X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.list X_a))) (let ((_let_4 (tptp.hAPP X_a (tptp.fun _let_2 tptp.bool) (tptp.member X_a) X_1))) (let ((_let_5 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_4 (tptp.hAPP _let_3 _let_2 _let_1 (tptp.hAPP _let_5 _let_3 (tptp.hAPP _let_3 (tptp.fun _let_5 _let_3) (tptp.sublist X_a) Xs_1) I_3)))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_4 (tptp.hAPP _let_3 _let_2 _let_1 Xs_1)))))))))) (forall ((X_a $$unsorted) (I_3 $$unsorted) (X_1 $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.set X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (let ((_let_5 (tptp.hAPP X_a (tptp.fun _let_4 tptp.bool) (tptp.member X_a) X_1))) (=> (not (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool _let_5 (tptp.hAPP _let_1 _let_4 _let_3 Xs_1)))) (not (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool _let_5 (tptp.hAPP _let_1 _let_4 _let_3 (tptp.hAPP _let_2 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_2 _let_1) (tptp.sublist X_a) Xs_1) I_3)))))))))))) (forall ((X_a $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.nil X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hAPP _let_3 _let_2 (tptp.hAPP _let_2 (tptp.fun _let_3 _let_2) (tptp.sublist X_a) _let_1) A_2) _let_1))))) (forall ((X_a $$unsorted) (I_3 $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.distinct X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 Xs_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 (tptp.hAPP _let_2 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_2 _let_1) (tptp.sublist X_a) Xs_1) I_3)))))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (I_3 $$unsorted)) (let ((_let_1 (tptp.set X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.list X_a))) (let ((_let_4 (tptp.fun tptp.nat tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) (tptp.hAPP _let_3 _let_2 _let_1 (tptp.hAPP _let_4 _let_3 (tptp.hAPP _let_3 (tptp.fun _let_4 _let_3) (tptp.sublist X_a) Xs_1) I_3))) (tptp.hAPP _let_3 _let_2 _let_1 Xs_1)))))))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (L_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.member tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.fun tptp.nat _let_3))) (let ((_let_5 (tptp.fun tptp.nat tptp.nat))) (let ((_let_6 (tptp.sublist X_a))) (let ((_let_7 (tptp.list X_a))) (let ((_let_8 (tptp.fun _let_2 _let_7))) (let ((_let_9 (tptp.nil X_a))) (let ((_let_10 (tptp.fun _let_7 _let_7))) (let ((_let_11 (tptp.hAPP X_a _let_10 (tptp.cons X_a) X_1))) (= (tptp.hAPP _let_2 _let_7 (tptp.hAPP _let_7 _let_8 _let_6 (tptp.hAPP _let_7 _let_7 _let_11 L_1)) A_2) (tptp.hAPP _let_7 _let_7 (tptp.hAPP _let_7 _let_10 (tptp.append X_a) (tptp.hAPP _let_7 _let_7 (tptp.hAPP _let_7 _let_10 (tptp.hAPP tptp.bool (tptp.fun _let_7 _let_10) (tptp.if _let_7) (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.nat _let_3 _let_1 (tptp.zero_zero tptp.nat)) A_2)) (tptp.hAPP _let_7 _let_7 _let_11 _let_9)) _let_9)) (tptp.hAPP _let_2 _let_7 (tptp.hAPP _let_7 _let_8 _let_6 L_1) (tptp.hAPP _let_2 _let_2 (tptp.collect tptp.nat) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_4 (tptp.fun _let_2 _let_2) (tptp.combc tptp.nat _let_2 tptp.bool) (tptp.hAPP _let_5 _let_4 (tptp.hAPP _let_4 (tptp.fun _let_5 _let_4) (tptp.combb tptp.nat _let_3 tptp.nat) _let_1) tptp.suc)) A_2))))))))))))))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (I_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.list X_a))) (let ((_let_5 (tptp.fun tptp.nat _let_1))) (let ((_let_6 (tptp.fun tptp.bool tptp.bool))) (let ((_let_7 (tptp.fun tptp.nat _let_6))) (let ((_let_8 (tptp.fun _let_1 _let_7))) (let ((_let_9 (tptp.hAPP (tptp.fun tptp.bool _let_6) _let_8 (tptp.combb tptp.bool _let_6 tptp.nat) tptp.fconj))) (let ((_let_10 (tptp.combs tptp.nat tptp.bool tptp.bool))) (let ((_let_11 (tptp.fun tptp.nat X_a))) (let ((_let_12 (tptp.fun _let_11 _let_1))) (let ((_let_13 (tptp.fun X_a tptp.bool))) (let ((_let_14 (tptp.fun X_a _let_12))) (let ((_let_15 (tptp.fun X_a _let_13))) (let ((_let_16 (tptp.fun X_a _let_1))) (let ((_let_17 (tptp.fun X_a _let_7))) (let ((_let_18 (tptp.fun X_a _let_2))) (= (tptp.hAPP _let_4 _let_13 (tptp.set X_a) (tptp.hAPP _let_1 _let_4 (tptp.hAPP _let_4 (tptp.fun _let_1 _let_4) (tptp.sublist X_a) Xs_1) I_3)) (tptp.hAPP _let_13 _let_13 (tptp.collect X_a) (tptp.hAPP _let_16 _let_13 (tptp.hAPP _let_3 (tptp.fun _let_16 _let_13) (tptp.combb _let_1 tptp.bool X_a) (tptp.fEx tptp.nat)) (tptp.hAPP _let_1 _let_16 (tptp.hAPP _let_18 (tptp.fun _let_1 _let_16) (tptp.combc X_a _let_1 _let_1) (tptp.hAPP _let_17 _let_18 (tptp.hAPP (tptp.fun _let_7 _let_2) (tptp.fun _let_17 _let_18) (tptp.combb _let_7 _let_2 X_a) _let_10) (tptp.hAPP _let_16 _let_17 (tptp.hAPP _let_8 (tptp.fun _let_16 _let_17) (tptp.combb _let_1 _let_7 X_a) _let_9) (tptp.hAPP _let_11 _let_16 (tptp.hAPP _let_14 (tptp.fun _let_11 _let_16) (tptp.combc X_a _let_11 _let_1) (tptp.hAPP _let_15 _let_14 (tptp.hAPP (tptp.fun _let_13 _let_12) (tptp.fun _let_15 _let_14) (tptp.combb _let_13 _let_12 X_a) (tptp.combb X_a tptp.bool tptp.nat)) (tptp.fequal X_a))) (tptp.hAPP _let_4 _let_11 (tptp.nth X_a) Xs_1))))) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_7 _let_2 _let_10 (tptp.hAPP _let_1 _let_7 _let_9 (tptp.hAPP tptp.nat _let_1 (tptp.hAPP _let_5 _let_5 (tptp.combc tptp.nat tptp.nat tptp.bool) (tptp.ord_less tptp.nat)) (tptp.hAPP _let_4 tptp.nat (tptp.size_size _let_4) Xs_1)))) (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun tptp.nat _let_3) _let_2 (tptp.combc tptp.nat _let_1 tptp.bool) (tptp.member tptp.nat)) I_3))))))))))))))))))))))))) (forall ((X_a $$unsorted) (N $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) Xs))) (let ((_let_3 (tptp.nth X_a))) (let ((_let_4 (tptp.fun tptp.nat X_a))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N) _let_2)) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_1 _let_4 _let_3 (tptp.hAPP _let_1 _let_1 (tptp.rev X_a) Xs)) N) (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_1 _let_4 _let_3 Xs) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) _let_2) (tptp.hAPP tptp.nat tptp.nat tptp.suc N)))))))))) (forall ((N $$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) (tptp.zero_zero tptp.nat))))) (forall ((N $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.zero_zero tptp.nat)) N))) (forall ((N $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) (tptp.hAPP tptp.nat tptp.nat tptp.suc N)))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (tptp.minus X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b X_a))) (= (tptp.hAPP X_b X_a (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) A_2) B_1) X_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.minus_minus X_a) (tptp.hAPP X_b X_a A_2 X_1)) (tptp.hAPP X_b X_a B_1 X_1))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.minus X_b) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_b))) (= (tptp.hAPP X_a X_b (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) A_2) B_1) X_2) (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.minus_minus X_b) (tptp.hAPP X_a X_b A_2 X_2)) (tptp.hAPP X_a X_b B_1 X_2))))))) (forall ((Pa $$unsorted) (Aa $$unsorted) (Ba $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) Aa) Ba))) (and (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) Aa) Ba)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa (tptp.zero_zero tptp.nat)))) (forall ((D_3 $$unsorted)) (=> (= Aa (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) Ba) D_3)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa D_3))))))) (forall ((Pa $$unsorted) (Aa $$unsorted) (Ba $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) Aa) Ba))) (not (or (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) Aa) Ba)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa (tptp.zero_zero tptp.nat))))) (exists ((D_3 $$unsorted)) (and (= Aa (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) Ba) D_3)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa D_3))))))))) (forall ((X_a $$unsorted)) (=> (tptp.monoid_add X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) (tptp.zero_zero X_a)) A_1) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_monoid_add X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) (tptp.zero_zero X_a)) A_1) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.linord219039673up_add X_a) (forall ((Aa $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (= _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) Aa) Aa)) (= (tptp.ti X_a Aa) _let_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.monoid_add X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) (tptp.zero_zero X_a)) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_monoid_add X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) (tptp.zero_zero X_a)) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.group_add X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.plus_plus X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.minus_minus X_a) A_1) B)) B) (tptp.ti X_a A_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.group_add X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.minus_minus X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.plus_plus X_a) A_1) B)) B) (tptp.ti X_a A_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ab_group_add X_a) (forall ((X $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.minus_minus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_min X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 X) Y)) Z_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 X) Z_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Y) Z_1))))))))) (forall ((M $$unsorted) (N $$unsorted)) (=> (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M) N) M) (= N (tptp.zero_zero tptp.nat)))) (forall ((M $$unsorted) (I_2 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_min tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.minus_minus tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 M) I_2)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 N) I_2)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M) N)) I_2)))))) (forall ((M $$unsorted) (K $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.plus_plus tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 M) K)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 N) K)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M) N)))))) (forall ((K $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 (tptp.plus_plus tptp.nat) K))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 M)) (tptp.hAPP tptp.nat tptp.nat _let_3 N)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M) N)))))) (forall ((I_2 $$unsorted) (J $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.minus_minus tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat _let_1 _let_2 I_2))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.hAPP tptp.nat tptp.nat _let_3 J)) K) (tptp.hAPP tptp.nat tptp.nat _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) J) K))))))) (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) N) M)) N) M))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) M) N)) N) M))) (forall ((M_2 $$unsorted) (N_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M_2) N_2) _let_1) (and (= M_2 _let_1) (= N_2 _let_1))))) (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) N) M)) (tptp.zero_zero tptp.nat)))) (forall ((M $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M) (tptp.zero_zero tptp.nat)) M)) (forall ((N $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.ord_min tptp.nat) N) _let_1) _let_1))) (forall ((N $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) (tptp.zero_zero tptp.nat)) N) N)) (forall ((N $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.ord_min tptp.nat) _let_1) N) _let_1))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ab_group_add X_a) (forall ((Aa $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Aa) Ba)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.minus_minus X_a) Aa) Ba)) (tptp.zero_zero X_a))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ab_group_add X_a) (forall ((Aa $$unsorted) (Ba $$unsorted) (Ca $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.minus_minus X_a))) (let ((_let_4 (tptp.fun X_a X_a))) (=> (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 Aa) Ba) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 Ca) D)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Aa) Ba)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Ca) D))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ab_group_add X_a) (forall ((Aa $$unsorted) (Ba $$unsorted) (Ca $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.minus_minus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (=> (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Aa) Ba) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Ca) D)) (= (= (tptp.ti X_a Aa) (tptp.ti X_a Ba)) (= (tptp.ti X_a Ca) (tptp.ti X_a D))))))))) (forall ((X_a $$unsorted)) (=> (tptp.group_add X_a) (forall ((Aa $$unsorted) (Ba $$unsorted)) (= (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.minus_minus X_a) Aa) Ba) (tptp.zero_zero X_a)) (= (tptp.ti X_a Aa) (tptp.ti X_a Ba)))))) (forall ((X_a $$unsorted)) (=> (tptp.ab_group_add X_a) (forall ((Aa $$unsorted) (Ba $$unsorted)) (= (= (tptp.ti X_a Aa) (tptp.ti X_a Ba)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.minus_minus X_a) Aa) Ba) (tptp.zero_zero X_a)))))) (forall ((X_a $$unsorted)) (=> (tptp.group_add X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.minus_minus X_a) A_1) A_1) (tptp.zero_zero X_a))))) (forall ((X_a $$unsorted)) (=> (tptp.group_add X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.minus_minus X_a) A_1) (tptp.zero_zero X_a)) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.zero X_a) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ti X_a X_1))) (= (= _let_1 _let_2) (= _let_2 _let_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ab_group_add X_a) (forall ((Aa $$unsorted) (Ba $$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 Aa) Ba)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.minus_minus X_a) Aa) Ba)) (tptp.zero_zero X_a))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ab_group_add X_a) (forall ((Aa $$unsorted) (Ba $$unsorted) (Ca $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.minus_minus X_a))) (let ((_let_4 (tptp.fun X_a X_a))) (=> (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 Aa) Ba) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 Ca) D)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Aa) Ba)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Ca) D))))))))))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) _let_1) N)) (= (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) N) (tptp.hAPP tptp.nat tptp.nat tptp.suc _let_1))) N)))) (forall ((I_2 $$unsorted) (N $$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.zero_zero tptp.nat)) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) N) (tptp.hAPP tptp.nat tptp.nat tptp.suc I_2))) N)))))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (=> (not (= N _let_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) _let_1) N))))) (forall ((L $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) L))) (let ((_let_2 (tptp.ord_less tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (let ((_let_4 (tptp.hAPP tptp.nat _let_3 _let_2 M))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_4 N)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_4 L)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.nat tptp.nat _let_1 N)) (tptp.hAPP tptp.nat tptp.nat _let_1 M)))))))))) (forall ((N $$unsorted) (J $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 J) K)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) J) N)) K)))))) (forall ((M $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M) N)) (not (= N (tptp.zero_zero tptp.nat))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.zero_zero tptp.nat)))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 N)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 M)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) M) N)) M)))))))) (forall ((N $$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) (tptp.zero_zero tptp.nat))))) (forall ((N_2 $$unsorted) (M_2 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.zero_zero tptp.nat)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) N_2) M_2))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M_2) N_2)))))) (forall ((N_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (= (not (= N_2 _let_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) _let_1) N_2))))) (forall ((N $$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) (tptp.zero_zero tptp.nat))))) (forall ((X_a $$unsorted) (M_2 $$unsorted) (X_1 $$unsorted) (N_2 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.replicate X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun X_a _let_2))) (= (= (tptp.hAPP X_a _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 M_2) X_1) (tptp.hAPP X_a _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 N_2) Y_1)) (and (= M_2 N_2) (=> (not (= M_2 (tptp.zero_zero tptp.nat))) (= (tptp.ti X_a X_1) (tptp.ti X_a Y_1))))))))) (forall ((X_a $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.list X_a))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.nat (tptp.fun _let_1 _let_1) (tptp.drop X_a) (tptp.zero_zero tptp.nat)) Xs) Xs))) (forall ((N $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.zero_zero tptp.nat)) N))) (forall ((N_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N_2) _let_1)) (= N_2 _let_1)))) (forall ((M $$unsorted) (N $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) M) N)) M))) (forall ((M_2 $$unsorted) (N_2 $$unsorted)) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) M_2) N_2) (tptp.zero_zero tptp.nat)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M_2) N_2)))) (forall ((M $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M) N)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) M) N) (tptp.zero_zero tptp.nat)))) (forall ((L $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) L))) (let ((_let_2 (tptp.ord_less_eq 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) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.nat tptp.nat _let_1 N)) (tptp.hAPP tptp.nat tptp.nat _let_1 M)))))))) (forall ((L $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.ord_less_eq tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 M) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M) L)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 N) L))))))))) (forall ((I_2 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) N))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) I_2) N)) (= (tptp.hAPP tptp.nat tptp.nat _let_1 (tptp.hAPP tptp.nat tptp.nat _let_1 I_2)) I_2)))) (forall ((N_2 $$unsorted) (K_1 $$unsorted) (M_2 $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 M_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 N_2)) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M_2) K_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 N_2) K_1)) (= M_2 N_2)))))))) (forall ((N $$unsorted) (K $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 M))) (let ((_let_4 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_4 M)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_4 N)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 K)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 N) K)) (tptp.hAPP tptp.nat tptp.nat _let_3 N))))))))) (forall ((N_2 $$unsorted) (K_1 $$unsorted) (M_2 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.minus_minus tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.nat))) (let ((_let_5 (tptp.hAPP tptp.nat _let_2 _let_1 K_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_5 M_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_5 N_2)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_4 _let_3 M_2) K_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_4 _let_3 N_2) K_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M_2) N_2))))))))))) (forall ((M $$unsorted)) (not (= (tptp.zero_zero tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc M)))) (forall ((Nat_3 $$unsorted)) (not (= (tptp.zero_zero tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc Nat_3)))) (forall ((M $$unsorted)) (not (= (tptp.hAPP tptp.nat tptp.nat tptp.suc M) (tptp.zero_zero tptp.nat)))) (forall ((Nat_2 $$unsorted)) (not (= (tptp.hAPP tptp.nat tptp.nat tptp.suc Nat_2) (tptp.zero_zero tptp.nat)))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M)) (tptp.hAPP tptp.nat tptp.nat tptp.suc N)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M) N))))) (forall ((M $$unsorted) (N $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M)) N)) (tptp.hAPP tptp.nat tptp.nat tptp.suc K)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M) N)) K))))) (forall ((M $$unsorted)) (not (= (tptp.zero_zero tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc M)))) (forall ((M $$unsorted)) (not (= (tptp.hAPP tptp.nat tptp.nat tptp.suc M) (tptp.zero_zero tptp.nat)))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (let ((_let_2 (tptp.minus_minus tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.nat))) (=> (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_2 M) N) _let_1) (=> (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_2 N) M) _let_1) (= M N))))))) (forall ((I_2 $$unsorted) (J $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 I_2))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 J)) K) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 K)) J)))))) (forall ((M $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) M) M) (tptp.zero_zero tptp.nat))) (forall ((M $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) M) (tptp.zero_zero tptp.nat)) M)) (forall ((N $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) _let_1) N) _let_1))) (forall ((X_a $$unsorted) (F1 $$unsorted) (F2 $$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.zero_zero tptp.nat)) (tptp.ti X_a F1)))) (forall ((M_2 $$unsorted) (N_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) M_2))) (= (tptp.hAPP tptp.nat tptp.nat _let_2 (tptp.hAPP tptp.nat tptp.nat tptp.suc N_2)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.nat (tptp.fun _let_1 _let_1) (tptp.nat_case tptp.nat) (tptp.zero_zero tptp.nat)) (tptp.combi tptp.nat)) (tptp.hAPP tptp.nat tptp.nat _let_2 N_2)))))) (forall ((I_2 $$unsorted) (K $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.plus_plus tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K) J)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 J) I_2)) K) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 J) K)) I_2))))))) (forall ((I_2 $$unsorted) (K $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.minus_minus tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K) J)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 J) K)) I_2) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 J) I_2)) K))))))) (forall ((I_2 $$unsorted) (K $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 (tptp.plus_plus tptp.nat) I_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K) J)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 J)) K) (tptp.hAPP tptp.nat tptp.nat _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 J) K)))))))) (forall ((K_1 $$unsorted) (I_1 $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) I_1) J_2)) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) J_2) I_1) K_1) (= J_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) K_1) I_1)))))) (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N) M)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) M) N)) N) M)))) (forall ((I_1 $$unsorted) (K_1 $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.ord_less_eq tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 K_1) J_2)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 I_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) J_2) K_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) I_1) K_1)) J_2)))))))) (forall ((I_2 $$unsorted) (K $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) I_2))) (let ((_let_3 (tptp.minus_minus tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K) J)) (= (tptp.hAPP tptp.nat tptp.nat _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 J) K)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat _let_2 J)) K))))))) (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N) M)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) M) N)) M)))) (forall ((M $$unsorted) (K $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.ord_less_eq tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 K) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 M) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) N) M)) K)))))))) (forall ((J_2 $$unsorted) (K_1 $$unsorted) (I_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.ord_less_eq 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 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) J_2) K_1)) I_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 J_2) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) I_1) K_1)))))))) (forall ((I_2 $$unsorted) (K $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.minus_minus tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K) J)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 I_2) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 J) K)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) I_2) K)) J)))))) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.ord_less tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 (tptp.ord_less_eq tptp.nat) C) A_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 A_1) C)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 B) C)))))))))) (forall ((N_2 $$unsorted) (K_1 $$unsorted) (M_2 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.minus_minus tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.nat))) (let ((_let_5 (tptp.hAPP tptp.nat _let_2 (tptp.ord_less_eq tptp.nat) K_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_5 M_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_5 N_2)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_4 _let_3 M_2) K_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_4 _let_3 N_2) K_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M_2) N_2))))))))))) (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N) M)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M)) N) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M) N))))))) (forall ((I_1 $$unsorted) (J_2 $$unsorted) (K_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (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 I_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) J_2) K_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) I_1) K_1)) J_2))))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M) N))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) M) N)) M)))) (forall ((M $$unsorted) (N $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) M) N)) (tptp.hAPP tptp.nat tptp.nat tptp.suc M)))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) _let_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) B)) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.zero_zero X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) B))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord219039673up_add X_a) (forall ((Aa $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) Aa) Aa)) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 Aa) _let_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord219039673up_add X_a) (forall ((Aa $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.zero_zero X_a)))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) Aa) Aa))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 Aa))))))) (forall ((X_a $$unsorted) (N $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.size_size _let_1))) (= (tptp.hAPP _let_1 tptp.nat _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.nat (tptp.fun _let_1 _let_1) (tptp.drop X_a) N) Xs)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) (tptp.hAPP _let_1 tptp.nat _let_2 Xs)) N))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) _let_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) B)) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B $$unsorted) (A_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 B))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.zero_zero X_a)) C)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) C))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B $$unsorted) (C $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 B))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.zero_zero X_a)) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) C))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) _let_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_2 X_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_2 Y_1)) (= (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) X_1) Y_1) _let_1) (and (= (tptp.ti X_a X_1) _let_1) (= (tptp.ti X_a Y_1) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) B))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord219039673up_add X_a) (forall ((Aa $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) Aa) Aa)) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 Aa) _let_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord219039673up_add X_a) (forall ((Aa $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) Aa) Aa))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 Aa))))))) (forall ((X_a $$unsorted) (N $$unsorted) (M $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 (tptp.drop X_a) N))) (let ((_let_4 (tptp.take X_a))) (= (tptp.hAPP _let_1 _let_1 _let_3 (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.nat _let_2 _let_4 M) Xs)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.nat _let_2 _let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) M) N)) (tptp.hAPP _let_1 _let_1 _let_3 Xs)))))))) (forall ((X_a $$unsorted) (I_2 $$unsorted) (K $$unsorted) (X $$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 _let_2 _let_2 (tptp.hAPP tptp.nat (tptp.fun _let_2 _let_2) (tptp.drop X_a) I_2) (tptp.hAPP X_a _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 K) X)) (tptp.hAPP X_a _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) K) I_2)) X)))))) (forall ((M_2 $$unsorted) (N_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M_2) (tptp.hAPP tptp.nat tptp.nat tptp.suc N_2))) (or (= M_2 (tptp.zero_zero tptp.nat)) (exists ((J_1 $$unsorted)) (and (= M_2 (tptp.hAPP tptp.nat tptp.nat tptp.suc J_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) J_1) N_2))))))) (forall ((N_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N_2) (tptp.hAPP tptp.nat tptp.nat tptp.suc _let_1))) (= N_2 _let_1)))) (forall ((N_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N_2)) (exists ((M_1 $$unsorted)) (= N_2 (tptp.hAPP tptp.nat tptp.nat tptp.suc M_1))))) (forall ((M_2 $$unsorted) (N_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.nat tptp.nat tptp.suc _let_1))) (= (= _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M_2) N_2)) (or (and (= M_2 _let_2) (= N_2 _let_1)) (and (= M_2 _let_1) (= N_2 _let_2))))))) (forall ((M_2 $$unsorted) (N_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.nat tptp.nat tptp.suc _let_1))) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M_2) N_2) _let_2) (or (and (= M_2 _let_2) (= N_2 _let_1)) (and (= M_2 _let_1) (= N_2 _let_2))))))) (forall ((M_2 $$unsorted) (N_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M_2) N_2))) (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 M_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 N_2)))))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.list X_a))) (= (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) (tptp.nil X_a)) (tptp.zero_zero tptp.nat)))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (= (= (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) Xs_1) (tptp.zero_zero tptp.nat)) (= Xs_1 (tptp.nil X_a))))) (forall ((X_a $$unsorted) (X $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.list X_a))) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_1 (tptp.fun tptp.nat X_a) (tptp.nth 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.zero_zero tptp.nat)) (tptp.ti X_a X)))) (forall ((X_a $$unsorted) (Xs $$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.take X_a) (tptp.zero_zero tptp.nat)) Xs) (tptp.nil X_a)))) (forall ((X_a $$unsorted) (N_2 $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.nil X_a))) (let ((_let_2 (tptp.list X_a))) (= (= (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.nat (tptp.fun _let_2 _let_2) (tptp.take X_a) N_2) Xs_1) _let_1) (or (= N_2 (tptp.zero_zero tptp.nat)) (= Xs_1 _let_1)))))) (forall ((X_a $$unsorted) (X $$unsorted) (Xs $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cons X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (let ((_let_4 (tptp.fun X_a _let_2))) (= (tptp.hAPP X_a _let_2 (tptp.hAPP tptp.nat _let_4 (tptp.hAPP _let_2 (tptp.fun tptp.nat _let_4) (tptp.list_update X_a) (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_a _let_3 _let_1 X) Xs)) (tptp.zero_zero tptp.nat)) Y) (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_a _let_3 _let_1 Y) Xs))))))) (forall ((X_a $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.list X_a))) (= (tptp.hAPP X_a _let_1 (tptp.hAPP tptp.nat (tptp.fun X_a _let_1) (tptp.replicate X_a) (tptp.zero_zero tptp.nat)) X) (tptp.nil X_a)))) (forall ((X_a $$unsorted) (N_2 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (= (= (tptp.nil X_a) (tptp.hAPP X_a _let_1 (tptp.hAPP tptp.nat (tptp.fun X_a _let_1) (tptp.replicate X_a) N_2) X_1)) (= N_2 (tptp.zero_zero tptp.nat))))) (forall ((X_a $$unsorted) (N_2 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (= (= (tptp.hAPP X_a _let_1 (tptp.hAPP tptp.nat (tptp.fun X_a _let_1) (tptp.replicate X_a) N_2) X_1) (tptp.nil X_a)) (= N_2 (tptp.zero_zero tptp.nat))))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (N_2 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a (tptp.fun _let_2 tptp.bool) (tptp.member X_a) X_1) (tptp.hAPP _let_1 _let_2 (tptp.set X_a) (tptp.hAPP X_a _let_1 (tptp.hAPP tptp.nat (tptp.fun X_a _let_1) (tptp.replicate X_a) N_2) Y_1)))) (and (= (tptp.ti X_a X_1) (tptp.ti X_a Y_1)) (not (= N_2 (tptp.zero_zero tptp.nat)))))))) (forall ((X_a $$unsorted) (Pa $$unsorted) (N_2 $$unsorted) (Aa $$unsorted)) (= (exists ((X_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (and (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a (tptp.fun _let_2 tptp.bool) (tptp.member X_a) X_2) (tptp.hAPP _let_1 _let_2 (tptp.set X_a) (tptp.hAPP X_a _let_1 (tptp.hAPP tptp.nat (tptp.fun X_a _let_1) (tptp.replicate X_a) N_2) Aa)))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa X_2)))))) (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa Aa)) (not (= N_2 (tptp.zero_zero tptp.nat)))))) (forall ((X_a $$unsorted) (Pa $$unsorted) (N_2 $$unsorted) (Aa $$unsorted)) (= (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a (tptp.fun _let_2 tptp.bool) (tptp.member X_a) X_2) (tptp.hAPP _let_1 _let_2 (tptp.set X_a) (tptp.hAPP X_a _let_1 (tptp.hAPP tptp.nat (tptp.fun X_a _let_1) (tptp.replicate X_a) N_2) Aa)))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa X_2)))))) (or (tptp.hBOOL (tptp.hAPP X_a tptp.bool Pa Aa)) (= N_2 (tptp.zero_zero tptp.nat))))) (forall ((X_a $$unsorted) (X $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.list X_a))) (=> (not (= N (tptp.zero_zero tptp.nat))) (= (tptp.hAPP _let_1 X_a (tptp.last X_a) (tptp.hAPP X_a _let_1 (tptp.hAPP tptp.nat (tptp.fun X_a _let_1) (tptp.replicate X_a) N) X)) (tptp.ti X_a X))))) (forall ((X_a $$unsorted) (X $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.list X_a))) (=> (not (= N (tptp.zero_zero tptp.nat))) (= (tptp.hAPP _let_1 X_a (tptp.hd X_a) (tptp.hAPP X_a _let_1 (tptp.hAPP tptp.nat (tptp.fun X_a _let_1) (tptp.replicate X_a) N) X)) (tptp.ti X_a X))))) (forall ((N_2 $$unsorted) (M_2 $$unsorted)) (let ((_let_1 (tptp.ord_min tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N_2)) M_2) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.nat _let_3 (tptp.nat_case tptp.nat) (tptp.zero_zero tptp.nat)) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_3 (tptp.combb tptp.nat tptp.nat tptp.nat) tptp.suc) (tptp.hAPP tptp.nat _let_2 _let_1 N_2))) M_2)))))) (forall ((M_2 $$unsorted) (N_2 $$unsorted)) (let ((_let_1 (tptp.ord_min tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (let ((_let_4 (tptp.fun _let_2 _let_2))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M_2) (tptp.hAPP tptp.nat tptp.nat tptp.suc N_2)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.nat _let_4 (tptp.nat_case tptp.nat) (tptp.zero_zero tptp.nat)) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_4 (tptp.combb tptp.nat tptp.nat tptp.nat) tptp.suc) (tptp.hAPP tptp.nat _let_2 (tptp.hAPP _let_3 _let_3 (tptp.combc tptp.nat tptp.nat tptp.nat) _let_1) N_2))) M_2))))))) (forall ((M $$unsorted) (K $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.minus_minus tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K) J)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 M) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 J) K))) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) M) K)) (tptp.hAPP tptp.nat tptp.nat tptp.suc J))))))) (forall ((M $$unsorted) (K $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.minus_minus tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K) J)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 J) K))) M) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.hAPP tptp.nat tptp.nat tptp.suc J)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) K) M))))))) (forall ((X_a $$unsorted) (N $$unsorted) (Xs $$unsorted) (Ys_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.take X_a))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.hAPP tptp.nat _let_3 _let_2 N))) (let ((_let_5 (tptp.append X_a))) (= (tptp.hAPP _let_1 _let_1 _let_4 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_5 Xs) Ys_1)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_5 (tptp.hAPP _let_1 _let_1 _let_4 Xs)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) N) (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) Xs))) Ys_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 (tptp.ord_less X_a) _let_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) _let_1) B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) B))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 (tptp.ord_less X_a) _let_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) _let_1) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) B))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B $$unsorted) (C $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.zero_zero X_a)) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) B) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) C)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B $$unsorted) (C $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) B))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_2 C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) C)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) _let_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 (tptp.ord_less_eq X_a) B) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) B)) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 (tptp.ord_less_eq X_a) A_1) _let_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) B)) _let_1)))))))))) (forall ((X_a $$unsorted) (N $$unsorted) (Xs $$unsorted) (Ys_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.drop X_a))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.hAPP tptp.nat _let_3 _let_2 N))) (let ((_let_5 (tptp.append X_a))) (= (tptp.hAPP _let_1 _let_1 _let_4 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_5 Xs) Ys_1)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_5 (tptp.hAPP _let_1 _let_1 _let_4 Xs)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) N) (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) Xs))) Ys_1))))))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) Xs_1))) (not (= Xs_1 (tptp.nil X_a)))))) (forall ((X_a $$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.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) Xs_1))))))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.nil X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_a (tptp.fun _let_2 _let_2) (tptp.cons X_a) X_1) _let_1))) (let ((_let_4 (tptp.fun tptp.nat tptp.bool))) (let ((_let_5 (tptp.hAPP _let_4 _let_2 (tptp.hAPP _let_2 (tptp.fun _let_4 _let_2) (tptp.sublist X_a) _let_3) A_2))) (let ((_let_6 (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP tptp.nat (tptp.fun _let_4 tptp.bool) (tptp.member tptp.nat) (tptp.zero_zero tptp.nat)) A_2)))) (and (=> _let_6 (= _let_5 _let_3)) (=> (not _let_6) (= _let_5 _let_1)))))))))) (forall ((X_a $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.list X_a))) (=> (not (= Xs (tptp.nil X_a))) (= (tptp.hAPP _let_1 X_a (tptp.hd X_a) Xs) (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_1 (tptp.fun tptp.nat X_a) (tptp.nth X_a) Xs) (tptp.zero_zero tptp.nat)))))) (forall ((X_a $$unsorted) (Ys_1 $$unsorted) (N $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) Xs))) (let ((_let_3 (tptp.nth X_a))) (let ((_let_4 (tptp.fun tptp.nat X_a))) (let ((_let_5 (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_1 _let_4 _let_3 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.append X_a) Xs) Ys_1)) N))) (let ((_let_6 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N) _let_2)))) (and (=> _let_6 (= _let_5 (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_1 _let_4 _let_3 Xs) N))) (=> (not _let_6) (= _let_5 (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_1 _let_4 _let_3 Ys_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) N) _let_2)))))))))))) (forall ((X_a $$unsorted) (Ys_1 $$unsorted) (X $$unsorted) (N $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) Xs))) (let ((_let_3 (tptp.list_update X_a))) (let ((_let_4 (tptp.fun X_a _let_1))) (let ((_let_5 (tptp.fun tptp.nat _let_4))) (let ((_let_6 (tptp.append X_a))) (let ((_let_7 (tptp.fun _let_1 _let_1))) (let ((_let_8 (tptp.hAPP _let_1 _let_7 _let_6 Xs))) (let ((_let_9 (tptp.hAPP X_a _let_1 (tptp.hAPP tptp.nat _let_4 (tptp.hAPP _let_1 _let_5 _let_3 (tptp.hAPP _let_1 _let_1 _let_8 Ys_1)) N) X))) (let ((_let_10 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N) _let_2)))) (and (=> _let_10 (= _let_9 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_7 _let_6 (tptp.hAPP X_a _let_1 (tptp.hAPP tptp.nat _let_4 (tptp.hAPP _let_1 _let_5 _let_3 Xs) N) X)) Ys_1))) (=> (not _let_10) (= _let_9 (tptp.hAPP _let_1 _let_1 _let_8 (tptp.hAPP X_a _let_1 (tptp.hAPP tptp.nat _let_4 (tptp.hAPP _let_1 _let_5 _let_3 Ys_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) N) _let_2)) X)))))))))))))))) (forall ((X_a $$unsorted) (I_2 $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.rev X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (= (tptp.hAPP _let_2 _let_2 _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.nat _let_3 (tptp.drop X_a) I_2) Xs)) (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.nat _let_3 (tptp.take X_a) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) (tptp.hAPP _let_2 tptp.nat (tptp.size_size _let_2) Xs)) I_2)) (tptp.hAPP _let_2 _let_2 _let_1 Xs))))))) (forall ((X_a $$unsorted) (I_2 $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.rev X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (= (tptp.hAPP _let_2 _let_2 _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.nat _let_3 (tptp.take X_a) I_2) Xs)) (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.nat _let_3 (tptp.drop X_a) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) (tptp.hAPP _let_2 tptp.nat (tptp.size_size _let_2) Xs)) I_2)) (tptp.hAPP _let_2 _let_2 _let_1 Xs))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (List_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.size_size _let_1))) (= (tptp.hAPP _let_1 tptp.nat _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.cons X_a) A_1) List_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) (tptp.hAPP _let_1 tptp.nat _let_2 List_1)) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat))))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (let ((_let_4 (tptp.fun tptp.nat X_a))) (let ((_let_5 (tptp.fun _let_4 _let_2))) (let ((_let_6 (tptp.fun X_a tptp.bool))) (let ((_let_7 (tptp.fun X_a _let_5))) (let ((_let_8 (tptp.fun X_a _let_6))) (let ((_let_9 (tptp.fun X_a _let_2))) (let ((_let_10 (tptp.fun tptp.bool tptp.bool))) (let ((_let_11 (tptp.fun tptp.nat _let_10))) (let ((_let_12 (tptp.fun _let_2 _let_11))) (let ((_let_13 (tptp.fun X_a _let_11))) (let ((_let_14 (tptp.fun _let_2 _let_2))) (let ((_let_15 (tptp.fun X_a _let_14))) (= (tptp.hAPP _let_1 _let_6 (tptp.set X_a) Xs_1) (tptp.hAPP _let_6 _let_6 (tptp.collect X_a) (tptp.hAPP _let_9 _let_6 (tptp.hAPP (tptp.fun _let_2 tptp.bool) (tptp.fun _let_9 _let_6) (tptp.combb _let_2 tptp.bool X_a) (tptp.fEx tptp.nat)) (tptp.hAPP _let_2 _let_9 (tptp.hAPP _let_15 (tptp.fun _let_2 _let_9) (tptp.combc X_a _let_2 _let_2) (tptp.hAPP _let_13 _let_15 (tptp.hAPP (tptp.fun _let_11 _let_14) (tptp.fun _let_13 _let_15) (tptp.combb _let_11 _let_14 X_a) (tptp.combs tptp.nat tptp.bool tptp.bool)) (tptp.hAPP _let_9 _let_13 (tptp.hAPP _let_12 (tptp.fun _let_9 _let_13) (tptp.combb _let_2 _let_11 X_a) (tptp.hAPP (tptp.fun tptp.bool _let_10) _let_12 (tptp.combb tptp.bool _let_10 tptp.nat) tptp.fconj)) (tptp.hAPP _let_4 _let_9 (tptp.hAPP _let_7 (tptp.fun _let_4 _let_9) (tptp.combc X_a _let_4 _let_2) (tptp.hAPP _let_8 _let_7 (tptp.hAPP (tptp.fun _let_6 _let_5) (tptp.fun _let_8 _let_7) (tptp.combb _let_6 _let_5 X_a) (tptp.combb X_a tptp.bool tptp.nat)) (tptp.fequal X_a))) (tptp.hAPP _let_1 _let_4 (tptp.nth X_a) Xs_1))))) (tptp.hAPP tptp.nat _let_2 (tptp.hAPP _let_3 _let_3 (tptp.combc tptp.nat tptp.nat tptp.bool) (tptp.ord_less tptp.nat)) (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) Xs_1)))))))))))))))))))))) (forall ((N_2 $$unsorted) (Pa $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa (tptp.zero_zero tptp.nat)))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa N_2)) (exists ((K_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K_2) N_2)) (forall ((I $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I) K_2)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa I))))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa K_2))))))) (forall ((I_2 $$unsorted) (J $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I_2) J)) (exists ((K_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) K_2)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) I_2) K_2) J))))) (forall ((X_a $$unsorted) (C_1 $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.minus_minus _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.ord_less_eq _let_1))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_5 _let_4 A_2) B_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_5 _let_4 B_1) C_1)) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 B_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 C_1) A_2)) (tptp.ti _let_1 A_2)))))))))) (forall ((X_a $$unsorted) (D_2 $$unsorted) (B_1 $$unsorted) (A_2 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.minus_minus _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.ord_less_eq _let_1))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_5 _let_4 A_2) C_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_5 _let_4 D_2) B_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_5 _let_4 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 A_2) B_1)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 C_1) D_2))))))))))) (forall ((X_a $$unsorted) (A_2 $$unsorted) (B_1 $$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) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) A_2) B_1)) A_2)))) (forall ((N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N)) (exists ((M_1 $$unsorted)) (= N (tptp.hAPP tptp.nat tptp.nat tptp.suc M_1))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((Aa $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) Aa) Aa)) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 Aa) _let_1))))))))) (forall ((X_a $$unsorted) (Ca $$unsorted) (A_2 $$unsorted) (B_1 $$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) Ca))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) A_2) B_1))) (not (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B_1)))))))) (forall ((X_a $$unsorted) (B_1 $$unsorted) (Ca $$unsorted) (A_2 $$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) Ca))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_2)) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B_1))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) A_2) B_1)))))))) (forall ((X_a $$unsorted) (Ca $$unsorted) (A_2 $$unsorted) (B_1 $$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) Ca))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) A_2) B_1))) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B_1))))))) (forall ((X_a $$unsorted) (Ca $$unsorted) (A_2 $$unsorted) (B_1 $$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) Ca))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) A_2) B_1))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_2)))))) (forall ((X_a $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.minus_minus _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 A_2) B_1))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 _let_4) B_1) _let_4)))))) (forall ((X_a $$unsorted) (Ca $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) Ca))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) A_2) B_1))) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_2)) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B_1)))))))) (forall ((X_a $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP (tptp.fun X_a (tptp.fun _let_1 tptp.bool)) _let_2 (tptp.combc X_a _let_1 tptp.bool) (tptp.member X_a)))) (let ((_let_4 (tptp.fun tptp.bool tptp.bool))) (let ((_let_5 (tptp.fun X_a _let_4))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.minus_minus _let_1) A_2) B_1) (tptp.hAPP _let_1 _let_1 (tptp.collect X_a) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_5 _let_2 (tptp.combs X_a tptp.bool tptp.bool) (tptp.hAPP _let_1 _let_5 (tptp.hAPP (tptp.fun tptp.bool _let_4) (tptp.fun _let_1 _let_5) (tptp.combb tptp.bool _let_4 X_a) tptp.fconj) (tptp.hAPP _let_1 _let_1 _let_3 A_2))) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_4 _let_2 (tptp.combb tptp.bool tptp.bool X_a) tptp.fNot) (tptp.hAPP _let_1 _let_1 _let_3 B_1))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord219039673up_add X_a) (forall ((Aa $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) Aa) Aa) _let_1) (= (tptp.ti X_a Aa) _let_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((B $$unsorted) (C $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 B))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.zero_zero X_a)) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) C))))))))))) (forall ((Nat $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat tptp.nat_size (tptp.hAPP tptp.nat tptp.nat tptp.suc Nat)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.nat_size Nat)) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (not (= (tptp.ti X_a X) (tptp.ti X_a Y))) (=> (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X) Y))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X))))))))) (= (tptp.hAPP tptp.nat tptp.nat tptp.nat_size _let_4) _let_4) (forall ((X_a $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less _let_1) A_2) B_1)) (exists ((B_2 $$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) B_2) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) B_1) A_2)))))))) (forall ((I_1 $$unsorted) (Pa $$unsorted) (K_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa K_1)) (=> (forall ((N_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa N_1)))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) K_1) I_1)))))) (forall ((N $$unsorted)) (=> (not (= N (tptp.zero_zero tptp.nat))) (exists ((M_1 $$unsorted)) (= N (tptp.hAPP tptp.nat tptp.nat tptp.suc M_1))))) (forall ((N_2 $$unsorted) (Pa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa (tptp.zero_zero tptp.nat))) (=> (forall ((N_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1))))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa N_2))))) (forall ((Y $$unsorted)) (=> (not (= Y (tptp.zero_zero tptp.nat))) (not (forall ((Nat_1 $$unsorted)) (not (= Y (tptp.hAPP tptp.nat tptp.nat tptp.suc Nat_1))))))) (forall ((Pa $$unsorted) (K_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa K_1)) (=> (forall ((N_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa N_1)))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa (tptp.zero_zero tptp.nat)))))) (forall ((Nat $$unsorted)) (let ((_let_1 (tptp.size_size tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc Nat)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) (tptp.hAPP tptp.nat tptp.nat _let_1 Nat)) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat)))))) (forall ((X_a $$unsorted) (Fa $$unsorted) (Aa $$unsorted) (List $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.hAPP (tptp.fun X_a tptp.nat) (tptp.fun _let_1 tptp.nat) (tptp.list_size X_a) Fa))) (let ((_let_3 (tptp.plus_plus tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP _let_1 tptp.nat _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.cons X_a) Aa) List)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_4 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_4 _let_3 (tptp.hAPP X_a tptp.nat Fa Aa)) (tptp.hAPP _let_1 tptp.nat _let_2 List))) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat))))))))) (= (tptp.hAPP tptp.nat tptp.nat _let_5 _let_4) _let_4) (forall ((N $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.size_size tptp.nat) N) N)) (forall ((X_a $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.list X_a))) (= (tptp.hAPP _let_1 tptp.nat (tptp.hAPP (tptp.fun X_a tptp.nat) (tptp.fun _let_1 tptp.nat) (tptp.list_size X_a) Fa) (tptp.nil X_a)) (tptp.zero_zero tptp.nat)))) (forall ((X_a $$unsorted) (Y_1 $$unsorted) (F $$unsorted) (X_1 $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) Y_1))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_a (tptp.fun _let_3 tptp.bool) (tptp.member X_a) X_1) (tptp.hAPP _let_1 _let_3 (tptp.set X_a) Xs_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 (tptp.hAPP X_a tptp.nat F X_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 (tptp.hAPP _let_1 tptp.nat (tptp.hAPP (tptp.fun X_a tptp.nat) (tptp.fun _let_1 tptp.nat) (tptp.list_size X_a) F) Xs_1))))))))) (forall ((X_a $$unsorted) (Y_1 $$unsorted) (F $$unsorted) (X_1 $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) Y_1))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (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.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 (tptp.hAPP X_a tptp.nat F X_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 (tptp.hAPP _let_1 tptp.nat (tptp.hAPP (tptp.fun X_a tptp.nat) (tptp.fun _let_1 tptp.nat) (tptp.list_size X_a) F) Xs_1))))))))) (forall ((X_a $$unsorted) (F $$unsorted) (G $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.list_size X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun _let_2 tptp.nat))) (let ((_let_4 (tptp.fun X_a tptp.nat))) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) (tptp.hAPP (tptp.list X_a) _let_1 (tptp.set X_a) Xs_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP X_a tptp.nat F X_2)) (tptp.hAPP X_a tptp.nat G X_2)))))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP _let_2 tptp.nat (tptp.hAPP _let_4 _let_3 _let_1 F) Xs_1)) (tptp.hAPP _let_2 tptp.nat (tptp.hAPP _let_4 _let_3 _let_1 G) Xs_1))))))))) (forall ((X_a $$unsorted) (A_2 $$unsorted) (XS $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (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.fun _let_5 tptp.bool))) (let ((_let_7 (tptp.fun tptp.bool tptp.bool))) (let ((_let_8 (tptp.fun X_a _let_7))) (let ((_let_9 (tptp.fun tptp.bool _let_7))) (let ((_let_10 (tptp.fun X_a _let_3))) (let ((_let_11 (tptp.fun X_a _let_2))) (let ((_let_12 (tptp.fun _let_1 _let_1))) (let ((_let_13 (tptp.fun _let_12 _let_2))) (let ((_let_14 (tptp.fun _let_1 _let_13))) (let ((_let_15 (tptp.fun _let_1 _let_2))) (let ((_let_16 (tptp.fun X_a _let_12))) (let ((_let_17 (tptp.fun _let_16 _let_11))) (let ((_let_18 (tptp.fun _let_1 _let_17))) (let ((_let_19 (tptp.fun _let_1 _let_11))) (let ((_let_20 (tptp.fun _let_1 _let_7))) (let ((_let_21 (tptp.fun _let_2 _let_20))) (let ((_let_22 (tptp.fun X_a _let_20))) (let ((_let_23 (tptp.fun _let_11 _let_22))) (let ((_let_24 (tptp.fun _let_1 _let_22))) (let ((_let_25 (tptp.fun _let_22 _let_10))) (let ((_let_26 (tptp.fun _let_1 _let_10))) (let ((_let_27 (tptp.fun _let_11 _let_11))) (let ((_let_28 (tptp.fun _let_1 _let_27))) (let ((_let_29 (tptp.fun _let_11 _let_5))) (let ((_let_30 (tptp.fun _let_1 _let_5))) (= (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_5 _let_3 (tptp.set_Cons X_a) A_2) XS) (tptp.hAPP _let_2 _let_2 (tptp.collect _let_1) (tptp.hAPP _let_30 _let_2 (tptp.hAPP _let_6 (tptp.fun _let_30 _let_2) (tptp.combb _let_5 tptp.bool _let_1) (tptp.fEx X_a)) (tptp.hAPP _let_19 _let_30 (tptp.hAPP _let_29 (tptp.fun _let_19 _let_30) (tptp.combb _let_11 _let_5 _let_1) (tptp.hAPP _let_4 _let_29 (tptp.combb _let_2 tptp.bool X_a) (tptp.fEx _let_1))) (tptp.hAPP _let_11 _let_19 (tptp.hAPP _let_28 (tptp.fun _let_11 _let_19) (tptp.combc _let_1 _let_11 _let_11) (tptp.hAPP _let_26 _let_28 (tptp.hAPP (tptp.fun _let_10 _let_27) (tptp.fun _let_26 _let_28) (tptp.combb _let_10 _let_27 _let_1) (tptp.combs X_a _let_2 _let_2)) (tptp.hAPP _let_24 _let_26 (tptp.hAPP _let_25 (tptp.fun _let_24 _let_26) (tptp.combb _let_22 _let_10 _let_1) (tptp.hAPP (tptp.fun _let_20 _let_3) _let_25 (tptp.combb _let_20 _let_3 X_a) (tptp.combs _let_1 tptp.bool tptp.bool))) (tptp.hAPP _let_19 _let_24 (tptp.hAPP _let_23 (tptp.fun _let_19 _let_24) (tptp.combb _let_11 _let_22 _let_1) (tptp.hAPP _let_21 _let_23 (tptp.combb _let_2 _let_20 X_a) (tptp.hAPP _let_9 _let_21 (tptp.combb tptp.bool _let_7 _let_1) tptp.fconj))) (tptp.hAPP _let_16 _let_19 (tptp.hAPP _let_18 (tptp.fun _let_16 _let_19) (tptp.combc _let_1 _let_16 _let_11) (tptp.hAPP _let_14 _let_18 (tptp.hAPP (tptp.fun _let_13 _let_17) (tptp.fun _let_14 _let_18) (tptp.combb _let_13 _let_17 _let_1) (tptp.combb _let_12 _let_2 X_a)) (tptp.hAPP _let_15 _let_14 (tptp.hAPP (tptp.fun _let_2 _let_13) (tptp.fun _let_15 _let_14) (tptp.combb _let_2 _let_13 _let_1) (tptp.combb _let_1 tptp.bool _let_1)) (tptp.fequal _let_1)))) (tptp.cons X_a)))))) (tptp.hAPP _let_2 _let_11 (tptp.hAPP _let_10 (tptp.fun _let_2 _let_11) (tptp.combc X_a _let_2 _let_2) (tptp.hAPP _let_8 _let_10 (tptp.hAPP (tptp.fun _let_7 _let_3) (tptp.fun _let_8 _let_10) (tptp.combb _let_7 _let_3 X_a) (tptp.combb tptp.bool tptp.bool _let_1)) (tptp.hAPP _let_5 _let_8 (tptp.hAPP _let_9 (tptp.fun _let_5 _let_8) (tptp.combb tptp.bool _let_7 X_a) tptp.fconj) (tptp.hAPP _let_5 _let_5 (tptp.hAPP (tptp.fun X_a _let_6) (tptp.fun _let_5 _let_5) (tptp.combc X_a _let_5 tptp.bool) (tptp.member X_a)) A_2)))) (tptp.hAPP _let_2 _let_2 (tptp.hAPP (tptp.fun _let_1 _let_4) _let_3 (tptp.combc _let_1 _let_2 tptp.bool) (tptp.member _let_1)) XS)))))))))))))))))))))))))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) (tptp.zero_zero X_a)) A_1) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) (tptp.zero_zero X_a)) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted) (D_1 $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 A_1))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 B)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 C) D_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) D_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 A_1))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 B)) C) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 C)) B)))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 A_1))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 B)) C) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) C))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (C $$unsorted) (D_1 $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 A_1))) (= (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 C) D_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 C)) D_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (C $$unsorted) (D_1 $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 A_1))) (let ((_let_4 (tptp.hAPP X_a _let_2 _let_1 C))) (= (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a _let_4 D_1)) (tptp.hAPP X_a X_a _let_4 (tptp.hAPP X_a X_a _let_3 D_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 C) A_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiri456707255roduct X_a) (forall ((Ba $$unsorted) (Aa $$unsorted)) (= (= (tptp.ti X_a Ba) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) Ba) Aa)) (= (tptp.ti X_a Aa) (tptp.zero_zero X_a)))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_field X_a) (forall ((X $$unsorted) (Y $$unsorted)) (=> (forall ((E $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) (tptp.zero_zero X_a)) E)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) X) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) Y) E)))))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X) Y)))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (Xs_1 $$unsorted) (Ys $$unsorted)) (let ((_let_1 (tptp.list X_b))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (let ((_let_4 (tptp.fun tptp.nat _let_3))) (let ((_let_5 (tptp.fun tptp.nat X_b))) (let ((_let_6 (tptp.fun tptp.nat X_a))) (let ((_let_7 (tptp.product_prod X_a X_b))) (let ((_let_8 (tptp.fun X_b _let_7))) (let ((_let_9 (tptp.fun tptp.nat _let_8))) (let ((_let_10 (tptp.fun tptp.nat _let_7))) (let ((_let_11 (tptp.fun _let_10 _let_3))) (let ((_let_12 (tptp.fun _let_7 tptp.bool))) (let ((_let_13 (tptp.fun _let_7 _let_11))) (let ((_let_14 (tptp.fun _let_7 _let_12))) (let ((_let_15 (tptp.fun _let_7 _let_3))) (let ((_let_16 (tptp.fun tptp.bool tptp.bool))) (let ((_let_17 (tptp.fun tptp.nat _let_16))) (let ((_let_18 (tptp.fun _let_3 _let_17))) (let ((_let_19 (tptp.fun _let_7 _let_17))) (let ((_let_20 (tptp.fun _let_3 _let_3))) (let ((_let_21 (tptp.fun _let_7 _let_20))) (let ((_let_22 (tptp.list _let_7))) (= (tptp.hAPP _let_22 _let_12 (tptp.set _let_7) (tptp.hAPP _let_1 _let_22 (tptp.hAPP _let_2 (tptp.fun _let_1 _let_22) (tptp.zip X_a X_b) Xs_1) Ys)) (tptp.hAPP _let_12 _let_12 (tptp.collect _let_7) (tptp.hAPP _let_15 _let_12 (tptp.hAPP (tptp.fun _let_3 tptp.bool) (tptp.fun _let_15 _let_12) (tptp.combb _let_3 tptp.bool _let_7) (tptp.fEx tptp.nat)) (tptp.hAPP _let_3 _let_15 (tptp.hAPP _let_21 (tptp.fun _let_3 _let_15) (tptp.combc _let_7 _let_3 _let_3) (tptp.hAPP _let_19 _let_21 (tptp.hAPP (tptp.fun _let_17 _let_20) (tptp.fun _let_19 _let_21) (tptp.combb _let_17 _let_20 _let_7) (tptp.combs tptp.nat tptp.bool tptp.bool)) (tptp.hAPP _let_15 _let_19 (tptp.hAPP _let_18 (tptp.fun _let_15 _let_19) (tptp.combb _let_3 _let_17 _let_7) (tptp.hAPP (tptp.fun tptp.bool _let_16) _let_18 (tptp.combb tptp.bool _let_16 tptp.nat) tptp.fconj)) (tptp.hAPP _let_10 _let_15 (tptp.hAPP _let_13 (tptp.fun _let_10 _let_15) (tptp.combc _let_7 _let_10 _let_3) (tptp.hAPP _let_14 _let_13 (tptp.hAPP (tptp.fun _let_12 _let_11) (tptp.fun _let_14 _let_13) (tptp.combb _let_12 _let_11 _let_7) (tptp.combb _let_7 tptp.bool tptp.nat)) (tptp.fequal _let_7))) (tptp.hAPP _let_5 _let_10 (tptp.hAPP _let_9 (tptp.fun _let_5 _let_10) (tptp.combs tptp.nat X_b _let_7) (tptp.hAPP _let_6 _let_9 (tptp.hAPP (tptp.fun X_a _let_8) (tptp.fun _let_6 _let_9) (tptp.combb X_a _let_8 tptp.nat) (tptp.product_Pair X_a X_b)) (tptp.hAPP _let_2 _let_6 (tptp.nth X_a) Xs_1))) (tptp.hAPP _let_1 _let_5 (tptp.nth X_b) Ys)))))) (tptp.hAPP tptp.nat _let_3 (tptp.hAPP _let_4 _let_4 (tptp.combc tptp.nat tptp.nat tptp.bool) (tptp.ord_less tptp.nat)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.ord_min tptp.nat) (tptp.hAPP _let_2 tptp.nat (tptp.size_size _let_2) Xs_1)) (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) Ys)))))))))))))))))))))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (Xs $$unsorted) (Ys_1 $$unsorted)) (let ((_let_1 (tptp.list X_b))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.list (tptp.product_prod X_a X_b)))) (= (tptp.hAPP _let_3 tptp.nat (tptp.size_size _let_3) (tptp.hAPP _let_1 _let_3 (tptp.hAPP _let_2 (tptp.fun _let_1 _let_3) (tptp.zip X_a X_b) Xs) Ys_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.ord_min tptp.nat) (tptp.hAPP _let_2 tptp.nat (tptp.size_size _let_2) Xs)) (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) Ys_1))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (Xs $$unsorted) (Ys_1 $$unsorted)) (let ((_let_1 (tptp.zip X_a X_b))) (let ((_let_2 (tptp.product_prod X_a X_b))) (let ((_let_3 (tptp.list _let_2))) (let ((_let_4 (tptp.list X_b))) (let ((_let_5 (tptp.fun _let_4 _let_3))) (let ((_let_6 (tptp.list X_a))) (=> (= (tptp.hAPP _let_6 tptp.nat (tptp.size_size _let_6) Xs) (tptp.hAPP _let_4 tptp.nat (tptp.size_size _let_4) Ys_1)) (= (tptp.hAPP _let_4 _let_3 (tptp.hAPP _let_6 _let_5 _let_1 (tptp.hAPP _let_6 _let_6 (tptp.rev X_a) Xs)) (tptp.hAPP _let_4 _let_4 (tptp.rev X_b) Ys_1)) (tptp.hAPP _let_3 _let_3 (tptp.rev _let_2) (tptp.hAPP _let_4 _let_3 (tptp.hAPP _let_6 _let_5 _let_1 Xs) Ys_1))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (Ys_1 $$unsorted) (Vs_2 $$unsorted) (Xs $$unsorted) (Us_2 $$unsorted)) (let ((_let_1 (tptp.zip X_a X_b))) (let ((_let_2 (tptp.product_prod X_a X_b))) (let ((_let_3 (tptp.list _let_2))) (let ((_let_4 (tptp.list X_b))) (let ((_let_5 (tptp.fun _let_4 _let_3))) (let ((_let_6 (tptp.list X_a))) (let ((_let_7 (tptp.size_size _let_4))) (let ((_let_8 (tptp.size_size _let_6))) (=> (= (tptp.hAPP _let_6 tptp.nat _let_8 Xs) (tptp.hAPP _let_4 tptp.nat _let_7 Us_2)) (=> (= (tptp.hAPP _let_6 tptp.nat _let_8 Ys_1) (tptp.hAPP _let_4 tptp.nat _let_7 Vs_2)) (= (tptp.hAPP _let_4 _let_3 (tptp.hAPP _let_6 _let_5 _let_1 (tptp.hAPP _let_6 _let_6 (tptp.hAPP _let_6 (tptp.fun _let_6 _let_6) (tptp.append X_a) Xs) Ys_1)) (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_4 (tptp.fun _let_4 _let_4) (tptp.append X_b) Us_2) Vs_2)) (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_3 (tptp.fun _let_3 _let_3) (tptp.append _let_2) (tptp.hAPP _let_4 _let_3 (tptp.hAPP _let_6 _let_5 _let_1 Xs) Us_2)) (tptp.hAPP _let_4 _let_3 (tptp.hAPP _let_6 _let_5 _let_1 Ys_1) Vs_2)))))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (X_1 $$unsorted) (Xs_1 $$unsorted) (Ys $$unsorted)) (let ((_let_1 (tptp.zip X_a X_b))) (let ((_let_2 (tptp.product_prod X_a X_b))) (let ((_let_3 (tptp.list _let_2))) (let ((_let_4 (tptp.list X_b))) (let ((_let_5 (tptp.fun _let_4 _let_3))) (let ((_let_6 (tptp.list X_a))) (let ((_let_7 (tptp.fun X_b _let_2))) (let ((_let_8 (tptp.fun _let_3 _let_3))) (let ((_let_9 (tptp.fun X_b _let_8))) (let ((_let_10 (tptp.fun _let_5 _let_5))) (let ((_let_11 (tptp.fun X_b _let_10))) (let ((_let_12 (tptp.fun X_b _let_5))) (= (tptp.hAPP _let_4 _let_3 (tptp.hAPP _let_6 _let_5 _let_1 (tptp.hAPP _let_6 _let_6 (tptp.hAPP X_a (tptp.fun _let_6 _let_6) (tptp.cons X_a) X_1) Xs_1)) Ys) (tptp.hAPP _let_4 _let_3 (tptp.hAPP _let_12 _let_5 (tptp.hAPP _let_3 (tptp.fun _let_12 _let_5) (tptp.list_case _let_3 X_b) (tptp.nil _let_2)) (tptp.hAPP _let_5 _let_12 (tptp.hAPP _let_11 (tptp.fun _let_5 _let_12) (tptp.combc X_b _let_5 _let_5) (tptp.hAPP _let_9 _let_11 (tptp.hAPP (tptp.fun _let_8 _let_10) (tptp.fun _let_9 _let_11) (tptp.combb _let_8 _let_10 X_b) (tptp.combb _let_3 _let_3 _let_4)) (tptp.hAPP _let_7 _let_9 (tptp.hAPP (tptp.fun _let_2 _let_8) (tptp.fun _let_7 _let_9) (tptp.combb _let_2 _let_8 X_b) (tptp.cons _let_2)) (tptp.hAPP X_a _let_7 (tptp.product_Pair X_a X_b) X_1)))) (tptp.hAPP _let_6 _let_5 _let_1 Xs_1))) Ys))))))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (Xs_1 $$unsorted) (Y_1 $$unsorted) (Ys $$unsorted)) (let ((_let_1 (tptp.zip X_a X_b))) (let ((_let_2 (tptp.product_prod X_a X_b))) (let ((_let_3 (tptp.list _let_2))) (let ((_let_4 (tptp.list X_b))) (let ((_let_5 (tptp.list X_a))) (let ((_let_6 (tptp.fun _let_5 _let_3))) (let ((_let_7 (tptp.fun _let_4 _let_3))) (let ((_let_8 (tptp.fun X_a _let_2))) (let ((_let_9 (tptp.fun _let_3 _let_3))) (let ((_let_10 (tptp.fun X_a _let_9))) (let ((_let_11 (tptp.fun _let_6 _let_6))) (let ((_let_12 (tptp.fun X_a _let_11))) (let ((_let_13 (tptp.fun X_a _let_6))) (= (tptp.hAPP _let_4 _let_3 (tptp.hAPP _let_5 _let_7 _let_1 Xs_1) (tptp.hAPP _let_4 _let_4 (tptp.hAPP X_b (tptp.fun _let_4 _let_4) (tptp.cons X_b) Y_1) Ys)) (tptp.hAPP _let_5 _let_3 (tptp.hAPP _let_13 _let_6 (tptp.hAPP _let_3 (tptp.fun _let_13 _let_6) (tptp.list_case _let_3 X_a) (tptp.nil _let_2)) (tptp.hAPP _let_6 _let_13 (tptp.hAPP _let_12 (tptp.fun _let_6 _let_13) (tptp.combc X_a _let_6 _let_6) (tptp.hAPP _let_10 _let_12 (tptp.hAPP (tptp.fun _let_9 _let_11) (tptp.fun _let_10 _let_12) (tptp.combb _let_9 _let_11 X_a) (tptp.combb _let_3 _let_3 _let_5)) (tptp.hAPP _let_8 _let_10 (tptp.hAPP (tptp.fun _let_2 _let_9) (tptp.fun _let_8 _let_10) (tptp.combb _let_2 _let_9 X_a) (tptp.cons _let_2)) (tptp.hAPP X_b _let_8 (tptp.hAPP (tptp.fun X_a (tptp.fun X_b _let_2)) (tptp.fun X_b _let_8) (tptp.combc X_a X_b _let_2) (tptp.product_Pair X_a X_b)) Y_1)))) (tptp.hAPP _let_4 _let_6 (tptp.hAPP (tptp.fun _let_5 _let_7) (tptp.fun _let_4 _let_6) (tptp.combc _let_5 _let_4 _let_3) _let_1) Ys))) Xs_1)))))))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (Xs $$unsorted) (I_2 $$unsorted) (X $$unsorted) (Ys_1 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_b))) (let ((_let_2 (tptp.zip X_a X_b))) (let ((_let_3 (tptp.list _let_1))) (let ((_let_4 (tptp.list X_b))) (let ((_let_5 (tptp.fun _let_4 _let_3))) (let ((_let_6 (tptp.list X_a))) (let ((_let_7 (tptp.fun _let_1 _let_3))) (let ((_let_8 (tptp.fun X_b _let_4))) (let ((_let_9 (tptp.fun X_a _let_6))) (= (tptp.hAPP _let_4 _let_3 (tptp.hAPP _let_6 _let_5 _let_2 (tptp.hAPP X_a _let_6 (tptp.hAPP tptp.nat _let_9 (tptp.hAPP _let_6 (tptp.fun tptp.nat _let_9) (tptp.list_update X_a) Xs) I_2) X)) (tptp.hAPP X_b _let_4 (tptp.hAPP tptp.nat _let_8 (tptp.hAPP _let_4 (tptp.fun tptp.nat _let_8) (tptp.list_update X_b) Ys_1) I_2) Y)) (tptp.hAPP _let_1 _let_3 (tptp.hAPP tptp.nat _let_7 (tptp.hAPP _let_3 (tptp.fun tptp.nat _let_7) (tptp.list_update _let_1) (tptp.hAPP _let_4 _let_3 (tptp.hAPP _let_6 _let_5 _let_2 Xs) Ys_1)) I_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) Y))))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (X $$unsorted) (Xs $$unsorted) (Y $$unsorted) (Ys_1 $$unsorted)) (let ((_let_1 (tptp.zip X_a X_b))) (let ((_let_2 (tptp.product_prod X_a X_b))) (let ((_let_3 (tptp.list _let_2))) (let ((_let_4 (tptp.list X_b))) (let ((_let_5 (tptp.fun _let_4 _let_3))) (let ((_let_6 (tptp.list X_a))) (= (tptp.hAPP _let_4 _let_3 (tptp.hAPP _let_6 _let_5 _let_1 (tptp.hAPP _let_6 _let_6 (tptp.hAPP X_a (tptp.fun _let_6 _let_6) (tptp.cons X_a) X) Xs)) (tptp.hAPP _let_4 _let_4 (tptp.hAPP X_b (tptp.fun _let_4 _let_4) (tptp.cons X_b) Y) Ys_1)) (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_2 (tptp.fun _let_3 _let_3) (tptp.cons _let_2) (tptp.hAPP X_b _let_2 (tptp.hAPP X_a (tptp.fun X_b _let_2) (tptp.product_Pair X_a X_b) X) Y)) (tptp.hAPP _let_4 _let_3 (tptp.hAPP _let_6 _let_5 _let_1 Xs) Ys_1)))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted) (Xs_1 $$unsorted) (Ys $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.list X_b))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.list X_a))) (let ((_let_5 (tptp.product_prod X_a X_b))) (let ((_let_6 (tptp.list _let_5))) (let ((_let_7 (tptp.fun _let_5 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_7 tptp.bool (tptp.hAPP _let_5 (tptp.fun _let_7 tptp.bool) (tptp.member _let_5) (tptp.hAPP X_b _let_5 (tptp.hAPP X_a (tptp.fun X_b _let_5) (tptp.product_Pair X_a X_b) X_1) Y_1)) (tptp.hAPP _let_6 _let_7 (tptp.set _let_5) (tptp.hAPP _let_2 _let_6 (tptp.hAPP _let_4 (tptp.fun _let_2 _let_6) (tptp.zip X_a X_b) Xs_1) Ys)))) (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_4 _let_3 (tptp.set X_a) Xs_1))) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) Y_1) (tptp.hAPP _let_2 _let_1 (tptp.set X_b) Ys))))))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted) (Xs_1 $$unsorted) (Ys $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.list X_b))) (let ((_let_3 (tptp.product_prod X_a X_b))) (let ((_let_4 (tptp.list _let_3))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP _let_3 (tptp.fun _let_5 tptp.bool) (tptp.member _let_3) (tptp.hAPP X_b _let_3 (tptp.hAPP X_a (tptp.fun X_b _let_3) (tptp.product_Pair X_a X_b) X_1) Y_1)) (tptp.hAPP _let_4 _let_5 (tptp.set _let_3) (tptp.hAPP _let_2 _let_4 (tptp.hAPP (tptp.list X_a) (tptp.fun _let_2 _let_4) (tptp.zip X_a X_b) Xs_1) Ys)))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) Y_1) (tptp.hAPP _let_2 _let_1 (tptp.set X_b) Ys)))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted) (Xs_1 $$unsorted) (Ys $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.product_prod X_a X_b))) (let ((_let_4 (tptp.list _let_3))) (let ((_let_5 (tptp.list X_b))) (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) (tptp.hAPP X_b _let_3 (tptp.hAPP X_a (tptp.fun X_b _let_3) (tptp.product_Pair X_a X_b) X_1) Y_1)) (tptp.hAPP _let_4 _let_6 (tptp.set _let_3) (tptp.hAPP _let_5 _let_4 (tptp.hAPP _let_2 (tptp.fun _let_5 _let_4) (tptp.zip X_a X_b) Xs_1) Ys)))) (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) Xs_1))))))))))) (forall ((X_a $$unsorted) (Aa $$unsorted) (Ba $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.product_prod X_a X_a))) (let ((_let_4 (tptp.list _let_3))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP _let_3 (tptp.fun _let_5 tptp.bool) (tptp.member _let_3) (tptp.hAPP X_a _let_3 (tptp.hAPP X_a (tptp.fun X_a _let_3) (tptp.product_Pair X_a X_a) Aa) Ba)) (tptp.hAPP _let_4 _let_5 (tptp.set _let_3) (tptp.hAPP _let_2 _let_4 (tptp.hAPP _let_2 (tptp.fun _let_2 _let_4) (tptp.zip X_a X_a) Xs_1) Xs_1)))) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) Aa) (tptp.hAPP _let_2 _let_1 (tptp.set X_a) Xs_1))) (= (tptp.ti X_a Aa) (tptp.ti X_a Ba)))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_b))) (let ((_let_2 (tptp.list _let_1))) (let ((_let_3 (tptp.list X_b))) (= (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.list X_a) (tptp.fun _let_3 _let_2) (tptp.zip X_a X_b) Xs) (tptp.nil X_b)) (tptp.nil _let_1)))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (Ys_1 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_b))) (let ((_let_2 (tptp.list _let_1))) (let ((_let_3 (tptp.list X_b))) (= (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.list X_a) (tptp.fun _let_3 _let_2) (tptp.zip X_a X_b) (tptp.nil X_a)) Ys_1) (tptp.nil _let_1)))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (Xs $$unsorted) (Ys_1 $$unsorted)) (let ((_let_1 (tptp.product_prod X_b X_a))) (let ((_let_2 (tptp.list _let_1))) (let ((_let_3 (tptp.list X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.distinct X_a) Ys_1)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.distinct _let_1) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.list X_b) (tptp.fun _let_3 _let_2) (tptp.zip X_b X_a) Xs) Ys_1)))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (Ys_1 $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_b))) (let ((_let_2 (tptp.list _let_1))) (let ((_let_3 (tptp.list X_b))) (let ((_let_4 (tptp.list X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.distinct X_a) Xs)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.distinct _let_1) (tptp.hAPP _let_3 _let_2 (tptp.hAPP _let_4 (tptp.fun _let_3 _let_2) (tptp.zip X_a X_b) Xs) Ys_1))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (N $$unsorted) (Xs $$unsorted) (Ys_1 $$unsorted)) (let ((_let_1 (tptp.list X_b))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.zip X_a X_b))) (let ((_let_4 (tptp.product_prod X_a X_b))) (let ((_let_5 (tptp.list _let_4))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (= (tptp.hAPP _let_5 _let_5 (tptp.hAPP tptp.nat (tptp.fun _let_5 _let_5) (tptp.take _let_4) N) (tptp.hAPP _let_1 _let_5 (tptp.hAPP _let_2 _let_6 _let_3 Xs) Ys_1)) (tptp.hAPP _let_1 _let_5 (tptp.hAPP _let_2 _let_6 _let_3 (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.nat (tptp.fun _let_2 _let_2) (tptp.take X_a) N) Xs)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.nat (tptp.fun _let_1 _let_1) (tptp.take X_b) N) Ys_1)))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (N $$unsorted) (Xs $$unsorted) (Ys_1 $$unsorted)) (let ((_let_1 (tptp.list X_b))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.zip X_a X_b))) (let ((_let_4 (tptp.product_prod X_a X_b))) (let ((_let_5 (tptp.list _let_4))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (= (tptp.hAPP _let_5 _let_5 (tptp.hAPP tptp.nat (tptp.fun _let_5 _let_5) (tptp.drop _let_4) N) (tptp.hAPP _let_1 _let_5 (tptp.hAPP _let_2 _let_6 _let_3 Xs) Ys_1)) (tptp.hAPP _let_1 _let_5 (tptp.hAPP _let_2 _let_6 _let_3 (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.nat (tptp.fun _let_2 _let_2) (tptp.drop X_a) N) Xs)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.nat (tptp.fun _let_1 _let_1) (tptp.drop X_b) N) Ys_1)))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (I_2 $$unsorted) (X $$unsorted) (J $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_b))) (let ((_let_2 (tptp.list _let_1))) (let ((_let_3 (tptp.list X_b))) (let ((_let_4 (tptp.list X_a))) (= (tptp.hAPP _let_3 _let_2 (tptp.hAPP _let_4 (tptp.fun _let_3 _let_2) (tptp.zip X_a X_b) (tptp.hAPP X_a _let_4 (tptp.hAPP tptp.nat (tptp.fun X_a _let_4) (tptp.replicate X_a) I_2) X)) (tptp.hAPP X_b _let_3 (tptp.hAPP tptp.nat (tptp.fun X_b _let_3) (tptp.replicate X_b) J) Y)) (tptp.hAPP _let_1 _let_2 (tptp.hAPP tptp.nat (tptp.fun _let_1 _let_2) (tptp.replicate _let_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.ord_min tptp.nat) I_2) J)) (tptp.hAPP X_b _let_1 (tptp.hAPP X_a (tptp.fun X_b _let_1) (tptp.product_Pair X_a X_b) X) Y)))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (Ys_1 $$unsorted) (I_2 $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.list X_b))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.product_prod X_a X_b))) (let ((_let_4 (tptp.list _let_3))) (let ((_let_5 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_5 (tptp.hAPP _let_2 tptp.nat (tptp.size_size _let_2) Xs))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_5 (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) Ys_1))) (= (tptp.hAPP tptp.nat _let_3 (tptp.hAPP _let_4 (tptp.fun tptp.nat _let_3) (tptp.nth _let_3) (tptp.hAPP _let_1 _let_4 (tptp.hAPP _let_2 (tptp.fun _let_1 _let_4) (tptp.zip X_a X_b) Xs) Ys_1)) I_2) (tptp.hAPP X_b _let_3 (tptp.hAPP X_a (tptp.fun X_b _let_3) (tptp.product_Pair X_a X_b) (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_2 (tptp.fun tptp.nat X_a) (tptp.nth X_a) Xs) I_2)) (tptp.hAPP tptp.nat X_b (tptp.hAPP _let_1 (tptp.fun tptp.nat X_b) (tptp.nth X_b) Ys_1) I_2))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (Xs $$unsorted) (Ys_1 $$unsorted) (Zs_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) Xs))) (let ((_let_3 (tptp.list X_b))) (let ((_let_4 (tptp.fun _let_3 _let_3))) (let ((_let_5 (tptp.zip X_a X_b))) (let ((_let_6 (tptp.product_prod X_a X_b))) (let ((_let_7 (tptp.list _let_6))) (let ((_let_8 (tptp.fun _let_3 _let_7))) (= (tptp.hAPP _let_3 _let_7 (tptp.hAPP _let_1 _let_8 _let_5 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.append X_a) Xs) Ys_1)) Zs_2) (tptp.hAPP _let_7 _let_7 (tptp.hAPP _let_7 (tptp.fun _let_7 _let_7) (tptp.append _let_6) (tptp.hAPP _let_3 _let_7 (tptp.hAPP _let_1 _let_8 _let_5 Xs) (tptp.hAPP _let_3 _let_3 (tptp.hAPP tptp.nat _let_4 (tptp.take X_b) _let_2) Zs_2))) (tptp.hAPP _let_3 _let_7 (tptp.hAPP _let_1 _let_8 _let_5 Ys_1) (tptp.hAPP _let_3 _let_3 (tptp.hAPP tptp.nat _let_4 (tptp.drop X_b) _let_2) Zs_2))))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (Xs $$unsorted) (Ys_1 $$unsorted) (Zs_2 $$unsorted)) (let ((_let_1 (tptp.list X_b))) (let ((_let_2 (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) Ys_1))) (let ((_let_3 (tptp.list X_a))) (let ((_let_4 (tptp.fun _let_3 _let_3))) (let ((_let_5 (tptp.zip X_a X_b))) (let ((_let_6 (tptp.product_prod X_a X_b))) (let ((_let_7 (tptp.list _let_6))) (let ((_let_8 (tptp.fun _let_1 _let_7))) (= (tptp.hAPP _let_1 _let_7 (tptp.hAPP _let_3 _let_8 _let_5 Xs) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.append X_b) Ys_1) Zs_2)) (tptp.hAPP _let_7 _let_7 (tptp.hAPP _let_7 (tptp.fun _let_7 _let_7) (tptp.append _let_6) (tptp.hAPP _let_1 _let_7 (tptp.hAPP _let_3 _let_8 _let_5 (tptp.hAPP _let_3 _let_3 (tptp.hAPP tptp.nat _let_4 (tptp.take X_a) _let_2) Xs)) Ys_1)) (tptp.hAPP _let_1 _let_7 (tptp.hAPP _let_3 _let_8 _let_5 (tptp.hAPP _let_3 _let_3 (tptp.hAPP tptp.nat _let_4 (tptp.drop X_a) _let_2) Xs)) Zs_2)))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (Pa $$unsorted) (Xs_1 $$unsorted) (Ys $$unsorted)) (let ((_let_1 (tptp.list (tptp.product_prod X_a X_b)))) (let ((_let_2 (tptp.list X_b))) (=> (forall ((Zs $$unsorted) (Ws $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.list (tptp.product_prod X_a X_b)))) (let ((_let_2 (tptp.list X_b))) (let ((_let_3 (tptp.list X_a))) (let ((_let_4 (tptp.size_size _let_2))) (let ((_let_5 (tptp.size_size _let_3))) (=> (= (tptp.hAPP _let_3 tptp.nat _let_5 Zs) (tptp.hAPP _let_2 tptp.nat _let_4 Ws)) (=> (= N_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.ord_min tptp.nat) (tptp.hAPP _let_3 tptp.nat _let_5 Xs_1)) (tptp.hAPP _let_2 tptp.nat _let_4 Ys))) (=> (= Zs (tptp.hAPP _let_3 _let_3 (tptp.hAPP tptp.nat (tptp.fun _let_3 _let_3) (tptp.take X_a) N_1) Xs_1)) (=> (= Ws (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.nat (tptp.fun _let_2 _let_2) (tptp.take X_b) N_1) Ys)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa (tptp.hAPP _let_2 _let_1 (tptp.hAPP _let_3 (tptp.fun _let_2 _let_1) (tptp.zip X_a X_b) Zs) Ws))))))))))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.list X_a) (tptp.fun _let_2 _let_1) (tptp.zip X_a X_b) Xs_1) Ys))))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (Ys $$unsorted) (R_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.size_size _let_1))) (let ((_let_3 (tptp.product_prod _let_1 _let_1))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP _let_3 (tptp.fun _let_4 tptp.bool) (tptp.member _let_3) (tptp.hAPP _let_1 _let_3 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_3) (tptp.product_Pair _let_1 _let_1) Xs_1) Ys)) (tptp.hAPP (tptp.fun (tptp.product_prod X_a X_a) tptp.bool) _let_4 (tptp.listrel X_a) R_1))) (and (= (tptp.hAPP _let_1 tptp.nat _let_2 Xs_1) (tptp.hAPP _let_1 tptp.nat _let_2 Ys)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_a))) (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))) (let ((_let_5 (tptp.fun X_a _let_4))) (let ((_let_6 (tptp.fun X_a _let_1))) (let ((_let_7 (tptp.fun _let_6 _let_5))) (let ((_let_8 (tptp.fun X_a _let_5))) (let ((_let_9 (tptp.fun X_a _let_6))) (let ((_let_10 (tptp.fun X_a tptp.bool))) (let ((_let_11 (tptp.fun _let_3 _let_10))) (let ((_let_12 (tptp.fun X_a _let_11))) (let ((_let_13 (tptp.fun X_a _let_10))) (let ((_let_14 (tptp.list _let_1))) (let ((_let_15 (tptp.list X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_1 _let_4 _let_2 X_2) (tptp.hAPP _let_14 _let_3 (tptp.set _let_1) (tptp.hAPP _let_15 _let_14 (tptp.hAPP _let_15 (tptp.fun _let_15 _let_14) (tptp.zip X_a X_a) Xs_1) Ys)))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_13 _let_3 (tptp.product_prod_case X_a X_a tptp.bool) (tptp.hAPP _let_3 _let_13 (tptp.hAPP _let_12 (tptp.fun _let_3 _let_13) (tptp.combc X_a _let_3 _let_10) (tptp.hAPP _let_8 _let_12 (tptp.hAPP (tptp.fun _let_5 _let_11) (tptp.fun _let_8 _let_12) (tptp.combb _let_5 _let_11 X_a) (tptp.combc X_a _let_3 tptp.bool)) (tptp.hAPP _let_9 _let_8 (tptp.hAPP _let_7 (tptp.fun _let_9 _let_8) (tptp.combb _let_6 _let_5 X_a) (tptp.hAPP (tptp.fun _let_1 _let_4) _let_7 (tptp.combb _let_1 _let_4 X_a) _let_2)) (tptp.product_Pair X_a X_a)))) R_1)) X_2)))))))))))))))))))))))))) (forall ((X_a $$unsorted) (A_2 $$unsorted) (R_1 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.product_prod X_a X_a) tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP (tptp.fun X_a tptp.bool) (tptp.fun _let_1 tptp.bool) (tptp.refl_on X_a) A_2) R_1)) (and (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (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.fun _let_1 tptp.bool)) _let_2 (tptp.combc X_a _let_1 tptp.bool) (tptp.member X_a)) A_2))) (let ((_let_4 (tptp.fun tptp.bool tptp.bool))) (let ((_let_5 (tptp.fun X_a _let_4))) (let ((_let_6 (tptp.fun X_a _let_2))) (let ((_let_7 (tptp.fun X_a _let_1))) (let ((_let_8 (tptp.product_prod X_a X_a))) (let ((_let_9 (tptp.fun _let_8 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_9 tptp.bool (tptp.hAPP _let_8 (tptp.fun _let_9 tptp.bool) (tptp.member _let_8) X_2) R_1)) (tptp.hBOOL (tptp.hAPP _let_8 tptp.bool (tptp.hAPP _let_7 _let_9 (tptp.product_prod_case X_a X_a tptp.bool) (tptp.hAPP _let_1 _let_7 (tptp.hAPP _let_6 (tptp.fun _let_1 _let_7) (tptp.combc X_a _let_1 _let_1) (tptp.hAPP _let_5 _let_6 (tptp.hAPP (tptp.fun _let_4 _let_2) (tptp.fun _let_5 _let_6) (tptp.combb _let_4 _let_2 X_a) (tptp.combb tptp.bool tptp.bool X_a)) (tptp.hAPP _let_1 _let_5 (tptp.hAPP (tptp.fun tptp.bool _let_4) (tptp.fun _let_1 _let_5) (tptp.combb tptp.bool _let_4 X_a) tptp.fconj) _let_3))) _let_3)) X_2))))))))))))) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_a))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_a (tptp.fun _let_3 tptp.bool) (tptp.member X_a) X_2) A_2)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) (tptp.hAPP X_a _let_1 (tptp.hAPP X_a (tptp.fun X_a _let_1) (tptp.product_Pair X_a X_a) X_2) X_2)) R_1))))))))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (Ys $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.size_size _let_1))) (= (= Xs_1 Ys) (and (= (tptp.hAPP _let_1 tptp.nat _let_2 Xs_1) (tptp.hAPP _let_1 tptp.nat _let_2 Ys)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_a))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.list _let_1))) (let ((_let_4 (tptp.list X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) X_2) (tptp.hAPP _let_3 _let_2 (tptp.set _let_1) (tptp.hAPP _let_4 _let_3 (tptp.hAPP _let_4 (tptp.fun _let_4 _let_3) (tptp.zip X_a X_a) Xs_1) Ys)))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP (tptp.fun X_a (tptp.fun X_a tptp.bool)) _let_2 (tptp.product_prod_case X_a X_a tptp.bool) (tptp.fequal X_a)) X_2))))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (Pa $$unsorted) (Xs_1 $$unsorted) (Ys $$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.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_2 _let_3 (tptp.hAPP (tptp.fun X_a (tptp.fun X_b tptp.bool)) (tptp.fun _let_2 _let_3) (tptp.list_all2 X_a X_b) Pa) Xs_1) Ys)) (and (= (tptp.hAPP _let_2 tptp.nat (tptp.size_size _let_2) Xs_1) (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) Ys)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.list _let_1))) (let ((_let_4 (tptp.list X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) X_2) (tptp.hAPP _let_3 _let_2 (tptp.set _let_1) (tptp.hAPP _let_4 _let_3 (tptp.hAPP (tptp.list X_a) (tptp.fun _let_4 _let_3) (tptp.zip X_a X_b) Xs_1) Ys)))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP (tptp.fun X_a (tptp.fun X_b tptp.bool)) _let_2 (tptp.product_prod_case X_a X_b tptp.bool) Pa) X_2)))))))))))))) (forall ((X_a $$unsorted) (A_2 $$unsorted) (As_1 $$unsorted)) (let ((_let_1 (tptp.listset X_a))) (let ((_let_2 (tptp.fun (tptp.list X_a) tptp.bool))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.list _let_3))) (= (tptp.hAPP _let_4 _let_2 _let_1 (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_3 (tptp.fun _let_4 _let_4) (tptp.cons _let_3) A_2) As_1)) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_3 (tptp.fun _let_2 _let_2) (tptp.set_Cons X_a) A_2) (tptp.hAPP _let_4 _let_2 _let_1 As_1)))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (Ca $$unsorted) (D $$unsorted) (Pa $$unsorted) (Aa $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.list X_b))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.hAPP (tptp.fun X_a (tptp.fun X_b tptp.bool)) (tptp.fun _let_2 _let_3) (tptp.list_all2 X_a X_b) Pa))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_2 _let_3 _let_4 Aa) Ba)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_2 _let_3 _let_4 Ca) D)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_2 _let_3 _let_4 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 (tptp.fun _let_2 _let_2) (tptp.append X_a) Aa) Ca)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.append X_b) Ba) D)))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (Pa $$unsorted) (Ys $$unsorted)) (let ((_let_1 (tptp.list X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.list X_a))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun X_a (tptp.fun X_b tptp.bool)) (tptp.fun _let_3 _let_2) (tptp.list_all2 X_a X_b) Pa) (tptp.nil X_a)) Ys)) (= Ys (tptp.nil X_b))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (Pa $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.list X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.list X_a))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun X_a (tptp.fun X_b tptp.bool)) (tptp.fun _let_3 _let_2) (tptp.list_all2 X_a X_b) Pa) Xs_1) (tptp.nil X_b))) (= Xs_1 (tptp.nil X_a))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (Pa $$unsorted) (X_1 $$unsorted) (Xs_1 $$unsorted) (Y_1 $$unsorted) (Ys $$unsorted)) (let ((_let_1 (tptp.list X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.list X_a))) (let ((_let_4 (tptp.fun X_b tptp.bool))) (let ((_let_5 (tptp.hAPP (tptp.fun X_a _let_4) (tptp.fun _let_3 _let_2) (tptp.list_all2 X_a X_b) Pa))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_3 _let_2 _let_5 (tptp.hAPP _let_3 _let_3 (tptp.hAPP X_a (tptp.fun _let_3 _let_3) (tptp.cons X_a) X_1) Xs_1)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.cons X_b) Y_1) Ys))) (and (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_a _let_4 Pa X_1) Y_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_3 _let_2 _let_5 Xs_1) Ys)))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (N_2 $$unsorted) (Pa $$unsorted) (As $$unsorted) (Bs $$unsorted)) (let ((_let_1 (tptp.list X_b))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.hAPP (tptp.fun X_a (tptp.fun X_b tptp.bool)) (tptp.fun _let_2 _let_3) (tptp.list_all2 X_a X_b) Pa))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_2 _let_3 _let_4 As) Bs)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_2 _let_3 _let_4 (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.nat (tptp.fun _let_2 _let_2) (tptp.drop X_a) N_2) As)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.nat (tptp.fun _let_1 _let_1) (tptp.drop X_b) N_2) Bs))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (Pa $$unsorted) (Xs_1 $$unsorted) (Ys $$unsorted)) (let ((_let_1 (tptp.list X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.list X_a))) (let ((_let_4 (tptp.hAPP (tptp.fun X_a (tptp.fun X_b tptp.bool)) (tptp.fun _let_3 _let_2) (tptp.list_all2 X_a X_b) Pa))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_3 _let_2 _let_4 (tptp.hAPP _let_3 _let_3 (tptp.rev X_a) Xs_1)) (tptp.hAPP _let_1 _let_1 (tptp.rev X_b) Ys))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_3 _let_2 _let_4 Xs_1) Ys)))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (Pa $$unsorted) (Xs_1 $$unsorted) (Ys $$unsorted)) (let ((_let_1 (tptp.list X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.list X_a))) (let ((_let_4 (tptp.hAPP (tptp.fun X_a (tptp.fun X_b tptp.bool)) (tptp.fun _let_3 _let_2) (tptp.list_all2 X_a X_b) Pa))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_3 _let_2 _let_4 (tptp.hAPP _let_3 _let_3 (tptp.rev X_a) Xs_1)) Ys)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_3 _let_2 _let_4 Xs_1) (tptp.hAPP _let_1 _let_1 (tptp.rev X_b) Ys))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (N_2 $$unsorted) (Pa $$unsorted) (Xs_1 $$unsorted) (Ys $$unsorted)) (let ((_let_1 (tptp.list X_b))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.hAPP (tptp.fun X_a (tptp.fun X_b tptp.bool)) (tptp.fun _let_2 _let_3) (tptp.list_all2 X_a X_b) Pa))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_2 _let_3 _let_4 Xs_1) Ys)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_2 _let_3 _let_4 (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.nat (tptp.fun _let_2 _let_2) (tptp.take X_a) N_2) Xs_1)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.nat (tptp.fun _let_1 _let_1) (tptp.take X_b) N_2) Ys))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (Pa $$unsorted) (Xs_1 $$unsorted) (Ys $$unsorted)) (let ((_let_1 (tptp.list X_b))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_2 _let_3 (tptp.hAPP (tptp.fun X_a (tptp.fun X_b tptp.bool)) (tptp.fun _let_2 _let_3) (tptp.list_all2 X_a X_b) Pa) Xs_1) Ys)) (= (tptp.hAPP _let_2 tptp.nat (tptp.size_size _let_2) Xs_1) (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) Ys))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (Pa $$unsorted) (Us_1 $$unsorted) (Vs_1 $$unsorted) (Xs_1 $$unsorted) (Ys $$unsorted)) (let ((_let_1 (tptp.list X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.list X_a))) (let ((_let_4 (tptp.hAPP (tptp.fun X_a (tptp.fun X_b tptp.bool)) (tptp.fun _let_3 _let_2) (tptp.list_all2 X_a X_b) Pa))) (=> (= (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)) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_3 _let_2 _let_4 (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_3 (tptp.fun _let_3 _let_3) (tptp.append X_a) Xs_1) Us_1)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.append X_b) Ys) Vs_1))) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_3 _let_2 _let_4 Xs_1) Ys)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_3 _let_2 _let_4 Us_1) Vs_1)))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (Pa $$unsorted) (Xs_1 $$unsorted) (Ys $$unsorted)) (let ((_let_1 (tptp.list X_b))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_2 _let_3 (tptp.hAPP (tptp.fun X_a (tptp.fun X_b tptp.bool)) (tptp.fun _let_2 _let_3) (tptp.list_all2 X_a X_b) Pa) Xs_1) Ys)) (and (= (tptp.hAPP _let_2 tptp.nat (tptp.size_size _let_2) Xs_1) (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) Ys)) (forall ((I $$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 tptp.nat) I) (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) Xs_1))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_a (tptp.fun X_b tptp.bool) Pa (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_1 (tptp.fun tptp.nat X_a) (tptp.nth X_a) Xs_1) I)) (tptp.hAPP tptp.nat X_b (tptp.hAPP (tptp.list X_b) (tptp.fun tptp.nat X_b) (tptp.nth X_b) Ys) I)))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (P_1 $$unsorted) (Pa $$unsorted) (Xs_1 $$unsorted) (Ys $$unsorted)) (let ((_let_1 (tptp.list X_b))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun X_b tptp.bool))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_2 _let_4 (tptp.hAPP (tptp.fun X_a _let_3) (tptp.fun _let_2 _let_4) (tptp.list_all2 X_a X_b) Pa) Xs_1) Ys)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) P_1) (tptp.hAPP _let_2 tptp.nat (tptp.size_size _let_2) Xs_1))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_a _let_3 Pa (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_2 (tptp.fun tptp.nat X_a) (tptp.nth X_a) Xs_1) P_1)) (tptp.hAPP tptp.nat X_b (tptp.hAPP _let_1 (tptp.fun tptp.nat X_b) (tptp.nth X_b) Ys) P_1)))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (P_1 $$unsorted) (Pa $$unsorted) (Xs_1 $$unsorted) (Ys $$unsorted)) (let ((_let_1 (tptp.list X_b))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun X_b tptp.bool))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_2 _let_4 (tptp.hAPP (tptp.fun X_a _let_3) (tptp.fun _let_2 _let_4) (tptp.list_all2 X_a X_b) Pa) Xs_1) Ys)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) P_1) (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) Ys))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_a _let_3 Pa (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_2 (tptp.fun tptp.nat X_a) (tptp.nth X_a) Xs_1) P_1)) (tptp.hAPP tptp.nat X_b (tptp.hAPP _let_1 (tptp.fun tptp.nat X_b) (tptp.nth X_b) Ys) P_1)))))))))) (forall ((X_a $$unsorted) (Xs_1 $$unsorted) (Ys $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (= Xs_1 Ys) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.hAPP (tptp.fun X_a (tptp.fun X_a tptp.bool)) (tptp.fun _let_1 _let_2) (tptp.list_all2 X_a X_a) (tptp.fequal X_a)) Xs_1) Ys)))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (I_1 $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted) (Pa $$unsorted) (Xs_1 $$unsorted) (Ys $$unsorted)) (let ((_let_1 (tptp.list X_b))) (let ((_let_2 (tptp.fun X_b _let_1))) (let ((_let_3 (tptp.list X_a))) (let ((_let_4 (tptp.fun X_a _let_3))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.fun X_b tptp.bool))) (let ((_let_7 (tptp.hAPP (tptp.fun X_a _let_6) (tptp.fun _let_3 _let_5) (tptp.list_all2 X_a X_b) Pa))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_3 _let_5 _let_7 Xs_1) Ys)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_a _let_6 Pa X_1) Y_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I_1) (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) Ys))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_3 _let_5 _let_7 (tptp.hAPP X_a _let_3 (tptp.hAPP tptp.nat _let_4 (tptp.hAPP _let_3 (tptp.fun tptp.nat _let_4) (tptp.list_update X_a) Xs_1) I_1) X_1)) (tptp.hAPP X_b _let_1 (tptp.hAPP tptp.nat _let_2 (tptp.hAPP _let_1 (tptp.fun tptp.nat _let_2) (tptp.list_update X_b) Ys) I_1) Y_1)))))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted) (Pa $$unsorted) (Ys $$unsorted) (I_1 $$unsorted) (Xs_1 $$unsorted)) (let ((_let_1 (tptp.list X_b))) (let ((_let_2 (tptp.fun X_b _let_1))) (let ((_let_3 (tptp.list X_a))) (let ((_let_4 (tptp.fun X_a _let_3))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.fun X_b tptp.bool))) (let ((_let_7 (tptp.hAPP (tptp.fun X_a _let_6) (tptp.fun _let_3 _let_5) (tptp.list_all2 X_a X_b) Pa))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I_1) (tptp.hAPP _let_3 tptp.nat (tptp.size_size _let_3) Xs_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_3 _let_5 _let_7 Xs_1) Ys)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_a _let_6 Pa X_1) Y_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_3 _let_5 _let_7 (tptp.hAPP X_a _let_3 (tptp.hAPP tptp.nat _let_4 (tptp.hAPP _let_3 (tptp.fun tptp.nat _let_4) (tptp.list_update X_a) Xs_1) I_1) X_1)) (tptp.hAPP X_b _let_1 (tptp.hAPP tptp.nat _let_2 (tptp.hAPP _let_1 (tptp.fun tptp.nat _let_2) (tptp.list_update X_b) Ys) I_1) Y_1)))))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (Pa $$unsorted) (Aa $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.list X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.list X_a))) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.list _let_1))) (let ((_let_4 (tptp.list X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) X_2) (tptp.hAPP _let_3 _let_2 (tptp.set _let_1) (tptp.hAPP _let_4 _let_3 (tptp.hAPP (tptp.list X_a) (tptp.fun _let_4 _let_3) (tptp.zip X_a X_b) Aa) Ba)))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP (tptp.fun X_a (tptp.fun X_b tptp.bool)) _let_2 (tptp.product_prod_case X_a X_b tptp.bool) Pa) X_2)))))))) (=> (= (tptp.hAPP _let_3 tptp.nat (tptp.size_size _let_3) Aa) (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) Ba)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun X_a (tptp.fun X_b tptp.bool)) (tptp.fun _let_3 _let_2) (tptp.list_all2 X_a X_b) Pa) Aa) Ba)))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (Pa $$unsorted) (Aa $$unsorted) (Ba $$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) Aa) (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) Ba)) (=> (forall ((N_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N_1) (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) Aa))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_a (tptp.fun X_b tptp.bool) Pa (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_1 (tptp.fun tptp.nat X_a) (tptp.nth X_a) Aa) N_1)) (tptp.hAPP tptp.nat X_b (tptp.hAPP (tptp.list X_b) (tptp.fun tptp.nat X_b) (tptp.nth X_b) Ba) N_1)))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun X_a (tptp.fun X_b tptp.bool)) (tptp.fun _let_3 _let_2) (tptp.list_all2 X_a X_b) Pa) Aa) Ba)))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (Pa $$unsorted) (Xs_1 $$unsorted) (Ys $$unsorted) (Zs_1 $$unsorted)) (let ((_let_1 (tptp.list X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.list X_a))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun X_a (tptp.fun X_b tptp.bool)) (tptp.fun _let_3 _let_2) (tptp.list_all2 X_a X_b) Pa) Xs_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.append X_b) Ys) Zs_1))) (exists ((Us $$unsorted) (Vs $$unsorted)) (let ((_let_1 (tptp.list X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.list X_a))) (let ((_let_4 (tptp.hAPP (tptp.fun X_a (tptp.fun X_b tptp.bool)) (tptp.fun _let_3 _let_2) (tptp.list_all2 X_a X_b) Pa))) (let ((_let_5 (tptp.size_size _let_1))) (let ((_let_6 (tptp.size_size _let_3))) (and (= Xs_1 (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_3 (tptp.fun _let_3 _let_3) (tptp.append X_a) Us) Vs)) (= (tptp.hAPP _let_3 tptp.nat _let_6 Us) (tptp.hAPP _let_1 tptp.nat _let_5 Ys)) (= (tptp.hAPP _let_3 tptp.nat _let_6 Vs) (tptp.hAPP _let_1 tptp.nat _let_5 Zs_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_3 _let_2 _let_4 Us) Ys)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_3 _let_2 _let_4 Vs) Zs_1))))))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (Pa $$unsorted) (Xs_1 $$unsorted) (Ys $$unsorted) (Zs_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.list X_b))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 _let_3 (tptp.hAPP (tptp.fun X_a (tptp.fun X_b tptp.bool)) (tptp.fun _let_1 _let_3) (tptp.list_all2 X_a X_b) Pa) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.append X_a) Xs_1) Ys)) Zs_1)) (exists ((Us $$unsorted) (Vs $$unsorted)) (let ((_let_1 (tptp.list X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.list X_a))) (let ((_let_4 (tptp.hAPP (tptp.fun X_a (tptp.fun X_b tptp.bool)) (tptp.fun _let_3 _let_2) (tptp.list_all2 X_a X_b) Pa))) (let ((_let_5 (tptp.size_size _let_3))) (let ((_let_6 (tptp.size_size _let_1))) (and (= Zs_1 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.append X_b) Us) Vs)) (= (tptp.hAPP _let_1 tptp.nat _let_6 Us) (tptp.hAPP _let_3 tptp.nat _let_5 Xs_1)) (= (tptp.hAPP _let_1 tptp.nat _let_6 Vs) (tptp.hAPP _let_3 tptp.nat _let_5 Ys)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_3 _let_2 _let_4 Xs_1) Us)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_3 _let_2 _let_4 Ys) Vs))))))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (Pa $$unsorted) (Xs_1 $$unsorted) (Y_1 $$unsorted) (Ys $$unsorted)) (let ((_let_1 (tptp.list X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.list X_a))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun X_a (tptp.fun X_b tptp.bool)) (tptp.fun _let_3 _let_2) (tptp.list_all2 X_a X_b) Pa) Xs_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.cons X_b) Y_1) Ys))) (exists ((Z $$unsorted) (Zs $$unsorted)) (let ((_let_1 (tptp.list X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.list X_a))) (let ((_let_4 (tptp.fun X_b tptp.bool))) (and (= Xs_1 (tptp.hAPP _let_3 _let_3 (tptp.hAPP X_a (tptp.fun _let_3 _let_3) (tptp.cons X_a) Z) Zs)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_a _let_4 Pa Z) Y_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun X_a _let_4) (tptp.fun _let_3 _let_2) (tptp.list_all2 X_a X_b) Pa) Zs) Ys))))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (Pa $$unsorted) (X_1 $$unsorted) (Xs_1 $$unsorted) (Ys $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.list X_b))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 _let_3 (tptp.hAPP (tptp.fun X_a (tptp.fun X_b tptp.bool)) (tptp.fun _let_1 _let_3) (tptp.list_all2 X_a X_b) Pa) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.cons X_a) X_1) Xs_1)) Ys)) (exists ((Z $$unsorted) (Zs $$unsorted)) (let ((_let_1 (tptp.list X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.list X_a))) (let ((_let_4 (tptp.fun X_b tptp.bool))) (and (= Ys (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.cons X_b) Z) Zs)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_a _let_4 Pa X_1) Z)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun X_a _let_4) (tptp.fun _let_3 _let_2) (tptp.list_all2 X_a X_b) Pa) Xs_1) Zs))))))))))))) (forall ((X_a $$unsorted) (X $$unsorted) (K $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.last X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun X_a _let_2))) (let ((_let_4 (tptp.hAPP _let_2 X_a _let_1 (tptp.hAPP X_a _let_2 (tptp.hAPP tptp.nat _let_3 (tptp.hAPP _let_2 (tptp.fun tptp.nat _let_3) (tptp.list_update X_a) Xs) K) X)))) (let ((_let_5 (= K (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) (tptp.hAPP _let_2 tptp.nat (tptp.size_size _let_2) Xs)) (tptp.one_one tptp.nat))))) (=> (not (= Xs (tptp.nil X_a))) (and (=> _let_5 (= _let_4 (tptp.ti X_a X))) (=> (not _let_5) (= _let_4 (tptp.hAPP _let_2 X_a _let_1 Xs))))))))))) (forall ((X_a $$unsorted) (N $$unsorted) (Xs $$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_eq tptp.nat) N) (tptp.hAPP _let_2 tptp.nat (tptp.size_size _let_2) Xs))) (= (tptp.hAPP _let_2 _let_2 (tptp.butlast X_a) (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 N) Xs)) (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) N) (tptp.one_one tptp.nat))) Xs))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) A_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) (tptp.one_one X_a))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.one_one X_a)) (tptp.zero_zero X_a)))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) (tptp.one_one X_a))))) (forall ((X_a $$unsorted)) (=> (tptp.zero_neq_one X_a) (not (= (tptp.zero_zero X_a) (tptp.one_one X_a))))) (forall ((X_a $$unsorted)) (=> (tptp.zero_neq_one X_a) (not (= (tptp.one_one X_a) (tptp.zero_zero X_a))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.one_one X_a)) (tptp.zero_zero X_a)))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.zero_zero X_a)) (tptp.one_one X_a))))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (=> (tptp.linordered_semidom X_a) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.zero_zero X_a)) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) _let_1) _let_1)))))) (= (tptp.one_one tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc _let_4)) (forall ((X_a $$unsorted)) (=> (tptp.one X_a) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (let ((_let_2 (tptp.ti X_a X_1))) (= (= _let_1 _let_2) (= _let_2 _let_1))))))) (forall ((N $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat tptp.suc N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) N) (tptp.one_one tptp.nat)))) (forall ((N $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat tptp.suc N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) (tptp.one_one tptp.nat)) N))) (forall ((N $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc N)) (tptp.one_one tptp.nat)) N)) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 M))) (= (tptp.hAPP tptp.nat tptp.nat _let_3 (tptp.hAPP tptp.nat tptp.nat tptp.suc N)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 (tptp.one_one tptp.nat))) N)))))) (forall ((X_a $$unsorted) (X $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP X_a _let_2 (tptp.cons X_a) X))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.nat _let_2 (tptp.take X_a) (tptp.one_one tptp.nat)) (tptp.hAPP _let_1 _let_1 _let_3 Xs)) (tptp.hAPP _let_1 _let_1 _let_3 (tptp.nil X_a))))))) (forall ((X_a $$unsorted) (X $$unsorted) (Xs $$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 tptp.nat _let_2 (tptp.drop X_a) (tptp.one_one tptp.nat)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_2 (tptp.cons X_a) X) Xs)) 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.butlast X_a) Xs)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) (tptp.hAPP _let_1 tptp.nat _let_2 Xs)) (tptp.one_one tptp.nat)))))) (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.tl X_a) Xs)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) (tptp.hAPP _let_1 tptp.nat _let_2 Xs)) (tptp.one_one tptp.nat)))))) (forall ((X_a $$unsorted) (N $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.tl X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.take X_a))) (let ((_let_4 (tptp.fun _let_2 _let_2))) (= (tptp.hAPP _let_2 _let_2 _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.nat _let_4 _let_3 N) Xs)) (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.nat _let_4 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) N) (tptp.one_one tptp.nat))) (tptp.hAPP _let_2 _let_2 _let_1 Xs)))))))) (forall ((X_a $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.list X_a))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) Xs)) (tptp.one_one tptp.nat))) (= (tptp.hAPP _let_1 _let_1 (tptp.rotate1 X_a) Xs) Xs)))) (forall ((N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N)) (= N (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) N) (tptp.one_one tptp.nat)))))) (forall ((N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N)) (= (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) N) (tptp.one_one tptp.nat))) N))) (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.plus_plus tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 M) N))) (let ((_let_4 (= M (tptp.zero_zero tptp.nat)))) (and (=> _let_4 (= _let_3 N)) (=> (not _let_4) (= _let_3 (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) M) (tptp.one_one tptp.nat))) N)))))))))) (forall ((X_a $$unsorted) (X $$unsorted) (Xs $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.nth X_a))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (let ((_let_3 (tptp.list X_a))) (let ((_let_4 (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_3 _let_2 _let_1 (tptp.hAPP _let_3 _let_3 (tptp.hAPP X_a (tptp.fun _let_3 _let_3) (tptp.cons X_a) X) Xs)) N))) (let ((_let_5 (= N (tptp.zero_zero tptp.nat)))) (and (=> _let_5 (= _let_4 (tptp.ti X_a X))) (=> (not _let_5) (= _let_4 (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_3 _let_2 _let_1 Xs) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) N) (tptp.one_one tptp.nat)))))))))))) (forall ((X_a $$unsorted) (X $$unsorted) (Xs $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.drop X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (let ((_let_4 (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_a _let_3 (tptp.cons X_a) X) Xs))) (let ((_let_5 (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 N) _let_4))) (let ((_let_6 (= N (tptp.zero_zero tptp.nat)))) (and (=> _let_6 (= _let_5 _let_4)) (=> (not _let_6) (= _let_5 (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) N) (tptp.one_one tptp.nat))) Xs))))))))))) (forall ((X_a $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.list X_a))) (= (tptp.hAPP _let_1 _let_1 (tptp.butlast X_a) Xs) (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.nat (tptp.fun _let_1 _let_1) (tptp.take X_a) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) Xs)) (tptp.one_one tptp.nat))) Xs)))) (forall ((X_a $$unsorted) (X $$unsorted) (K $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.butlast X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.hAPP _let_2 _let_2 _let_1 Xs))) (let ((_let_4 (tptp.list_update X_a))) (let ((_let_5 (tptp.fun X_a _let_2))) (let ((_let_6 (tptp.fun tptp.nat _let_5))) (let ((_let_7 (tptp.hAPP _let_2 _let_2 _let_1 (tptp.hAPP X_a _let_2 (tptp.hAPP tptp.nat _let_5 (tptp.hAPP _let_2 _let_6 _let_4 Xs) K) X)))) (let ((_let_8 (= K (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) (tptp.hAPP _let_2 tptp.nat (tptp.size_size _let_2) Xs)) (tptp.one_one tptp.nat))))) (and (=> _let_8 (= _let_7 _let_3)) (=> (not _let_8) (= _let_7 (tptp.hAPP X_a _let_2 (tptp.hAPP tptp.nat _let_5 (tptp.hAPP _let_2 _let_6 _let_4 _let_3) K) X))))))))))))) (forall ((X_a $$unsorted) (X $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.replicate X_a))) (let ((_let_2 (tptp.list X_a))) (let ((_let_3 (tptp.fun X_a _let_2))) (=> (not (= N (tptp.zero_zero tptp.nat))) (= (tptp.hAPP _let_2 _let_2 (tptp.tl X_a) (tptp.hAPP X_a _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 N) X)) (tptp.hAPP X_a _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) N) (tptp.one_one tptp.nat))) X))))))) (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)) (=> (tptp.minus T_1) (tptp.minus (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.semiri456707255roduct tptp.nat) (tptp.ordere223160158up_add tptp.nat) (tptp.ordere236663937imp_le tptp.nat) (tptp.ordere779506340up_add tptp.nat) (tptp.ordere216010020id_add tptp.nat) (tptp.cancel146912293up_add tptp.nat) (tptp.cancel_semigroup_add tptp.nat) (tptp.linordered_semidom tptp.nat) (tptp.ab_semigroup_add tptp.nat) (tptp.comm_monoid_add tptp.nat) (tptp.comm_semiring_1 tptp.nat) (tptp.zero_neq_one tptp.nat) (tptp.preorder tptp.nat) (tptp.linorder tptp.nat) (tptp.monoid_add tptp.nat) (tptp.order tptp.nat) (tptp.ord tptp.nat) (tptp.minus tptp.nat) (tptp.zero tptp.nat) (tptp.one 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.minus 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 ((X_a $$unsorted) (P $$unsorted) (X $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool P X))) (tptp.hBOOL (tptp.hAPP (tptp.fun X_a tptp.bool) tptp.bool (tptp.fEx X_a) P)))) (forall ((P $$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 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.combi X_a) P) (tptp.ti X_a P))) _let_3 (forall ((X_a $$unsorted) (X_c $$unsorted) (X_b $$unsorted) (P $$unsorted) (Q $$unsorted) (R $$unsorted)) (let ((_let_1 (tptp.fun X_b X_c))) (let ((_let_2 (tptp.fun X_a X_c))) (let ((_let_3 (tptp.fun X_a X_b))) (= (tptp.hAPP X_a X_c (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun X_a _let_1) (tptp.fun _let_3 _let_2) (tptp.combs X_a X_b X_c) P) Q) R) (tptp.hAPP X_b X_c (tptp.hAPP X_a _let_1 P R) (tptp.hAPP X_a X_b Q R))))))) (tptp.hBOOL tptp.fTrue) (forall ((P $$unsorted)) (let ((_let_1 (tptp.ti tptp.bool P))) (or (= _let_1 tptp.fTrue) (= _let_1 tptp.fFalse)))) (forall ((Q $$unsorted) (P $$unsorted)) (or (not (tptp.hBOOL P)) (not (tptp.hBOOL Q)) (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fconj P) Q)))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fconj P) Q))) (tptp.hBOOL P))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fconj P) Q))) (tptp.hBOOL Q))) (forall ((Q $$unsorted) (P $$unsorted)) (or (not (tptp.hBOOL P)) (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fdisj P) Q)))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL Q)) (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fdisj P) Q)))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fdisj P) Q))) (tptp.hBOOL P) (tptp.hBOOL Q))) (not (tptp.hBOOL tptp.fFalse)) (forall ((P $$unsorted)) (let ((_let_1 (tptp.ti tptp.bool P))) (or (= _let_1 tptp.fTrue) (= _let_1 tptp.fFalse)))) (forall ((X_a $$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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 167.82/168.10 )
% 167.82/168.10 % SZS output end Proof for SCT170+7
% 167.82/168.10 % cvc5---1.0.5 exiting
% 167.82/168.10 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------