TSTP Solution File: SWW474+6 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWW474+6 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 1 00:21:11 EDT 2023
% Result : Theorem 27.21s 27.39s
% Output : Proof 27.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.27 % Problem : SWW474+6 : TPTP v8.1.2. Released v5.3.0.
% 0.12/0.28 % Command : do_cvc5 %s %d
% 0.27/0.49 % Computer : n014.cluster.edu
% 0.27/0.49 % Model : x86_64 x86_64
% 0.27/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.27/0.49 % Memory : 8042.1875MB
% 0.27/0.49 % OS : Linux 3.10.0-693.el7.x86_64
% 0.27/0.49 % CPULimit : 300
% 0.27/0.49 % WCLimit : 300
% 0.27/0.49 % DateTime : Sun Aug 27 18:18:16 EDT 2023
% 0.27/0.49 % CPUTime :
% 0.34/0.79 %----Proving TF0_NAR, FOF, or CNF
% 27.21/27.39 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.QjDnEukgVt/cvc5---1.0.5_6953.p...
% 27.21/27.39 ------- get file name : TPTP file name is SWW474+6
% 27.21/27.39 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_6953.smt2...
% 27.21/27.39 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 27.21/27.39 --- Run --no-e-matching --full-saturate-quant at 5...
% 27.21/27.39 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 27.21/27.39 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 27.21/27.39 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 27.21/27.39 % SZS status Theorem for SWW474+6
% 27.21/27.39 % SZS output start Proof for SWW474+6
% 27.21/27.39 (
% 27.21/27.39 (let ((_let_1 (tptp.hoare_1656922687triple tptp.state))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.bot_bot _let_2))) (let ((_let_4 (tptp.hAPP tptp.com _let_1 tptp.hoare_Mirabelle_MGT tptp.y))) (let ((_let_5 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 (tptp.fun _let_2 _let_2) (tptp.insert _let_1) _let_4) _let_3))) (let ((_let_6 (tptp.fun tptp.pname tptp.bool))) (let ((_let_7 (tptp.option tptp.com))) (let ((_let_8 (tptp.fun tptp.pname _let_7))) (let ((_let_9 (tptp.hAPP _let_8 _let_6 (tptp.dom tptp.pname tptp.com) tptp.body))) (let ((_let_10 (tptp.fun tptp.pname _let_1))) (let ((_let_11 (tptp.fun tptp.pname tptp.com))) (let ((_let_12 (tptp.fun tptp.com _let_1))) (let ((_let_13 (tptp.hAPP _let_12 (tptp.fun _let_11 _let_10) (tptp.combb tptp.com _let_1 tptp.pname) tptp.hoare_Mirabelle_MGT))) (let ((_let_14 (tptp.image tptp.pname _let_1))) (let ((_let_15 (tptp.fun _let_6 _let_2))) (let ((_let_16 (tptp.hAPP _let_6 _let_2 (tptp.hAPP _let_10 _let_15 _let_14 (tptp.hAPP _let_11 _let_10 _let_13 tptp.body_1)) _let_9))) (let ((_let_17 (tptp.hoare_279057269derivs tptp.state))) (let ((_let_18 (tptp.fun _let_2 tptp.bool))) (let ((_let_19 (tptp.hAPP _let_2 _let_18 _let_17 _let_16))) (let ((_let_20 (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_19 _let_5)))) (let ((_let_21 (not _let_20))) (let ((_let_22 (tptp.some tptp.com))) (let ((_let_23 (= (tptp.hAPP tptp.pname _let_7 tptp.body tptp.pn) (tptp.hAPP tptp.com _let_7 _let_22 tptp.y)))) (let ((_let_24 (tptp.hBOOL tptp.wT_bodies))) (let ((_let_25 (tptp.hBOOL tptp.hoare_1924220188gleton))) (let ((_let_26 (forall ((Pn $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.option tptp.com))) (=> (tptp.hBOOL tptp.wT_bodies) (=> (= (tptp.hAPP tptp.pname _let_1 tptp.body Pn) (tptp.hAPP tptp.com _let_1 (tptp.some tptp.com) B_2)) (tptp.hBOOL (tptp.hAPP tptp.com tptp.bool tptp.wt B_2)))))))) (let ((_let_27 (forall ((C_1 $$unsorted)) (let ((_let_1 (tptp.hoare_1656922687triple tptp.state))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.bot_bot _let_2))) (=> (tptp.hBOOL tptp.hoare_1924220188gleton) (=> (tptp.hBOOL tptp.wT_bodies) (=> (tptp.hBOOL (tptp.hAPP tptp.com tptp.bool tptp.wt C_1)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.hoare_279057269derivs tptp.state) _let_3) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 (tptp.fun _let_2 _let_2) (tptp.insert _let_1) (tptp.hAPP tptp.com _let_1 tptp.hoare_Mirabelle_MGT C_1)) _let_3)))))))))))) (let ((_let_28 (forall ((X_a $$unsorted) (G_1 $$unsorted) (G_2 $$unsorted) (Ts $$unsorted)) (let ((_let_1 (tptp.hoare_279057269derivs X_a))) (let ((_let_2 (tptp.fun (tptp.hoare_1656922687triple X_a) tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.hAPP _let_2 _let_3 _let_1 G_1))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 _let_3 _let_1 G_2) Ts)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_4 G_2)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_4 Ts))))))))))) (let ((_let_29 (forall ((X_a $$unsorted) (G_1 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.hoare_1656922687triple X_a) tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.hoare_279057269derivs X_a) G_1) (tptp.bot_bot _let_1))))))) (let ((_let_30 (tptp.fun tptp.bool tptp.bool))) (let ((_let_31 (tptp.fun tptp.bool _let_30))) (let ((_let_32 (tptp.fun tptp.state tptp.bool))) (let ((_let_33 (tptp.fun tptp.com tptp.com))) (let ((_let_34 (forall ((X_a $$unsorted) (G_1 $$unsorted) (G_2 $$unsorted) (Ts $$unsorted)) (let ((_let_1 (tptp.hoare_279057269derivs X_a))) (let ((_let_2 (tptp.fun (tptp.hoare_1656922687triple X_a) tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.hAPP _let_2 _let_3 _let_1 G_1))) (or (not (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 _let_3 _let_1 G_2) Ts))) (not (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_4 G_2))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_4 Ts)))))))))) (let ((_let_35 (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_19 _let_3)))) (let ((_let_36 (not _let_35))) (let ((_let_37 (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 _let_18 _let_17 _let_3) _let_5)))) (let ((_let_38 (not _let_37))) (let ((_let_39 (or _let_38 _let_36 _let_20))) (let ((_let_40 (EQ_RESOLVE (ASSUME :args (_let_28)) (MACRO_SR_EQ_INTRO :args (_let_28 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_41 (not _let_39))) (let ((_let_42 (tptp.hBOOL (tptp.hAPP tptp.com tptp.bool tptp.wt tptp.y)))) (let ((_let_43 (not _let_42))) (let ((_let_44 (or _let_43 _let_37))) (let ((_let_45 (forall ((C_1 $$unsorted)) (let ((_let_1 (tptp.hoare_1656922687triple tptp.state))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.bot_bot _let_2))) (or (not (tptp.hBOOL (tptp.hAPP tptp.com tptp.bool tptp.wt C_1))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.hoare_279057269derivs tptp.state) _let_3) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 (tptp.fun _let_2 _let_2) (tptp.insert _let_1) (tptp.hAPP tptp.com _let_1 tptp.hoare_Mirabelle_MGT C_1)) _let_3)))))))))) (let ((_let_46 (ASSUME :args (_let_24)))) (let ((_let_47 (_let_45))) (let ((_let_48 (not _let_23))) (let ((_let_49 (or _let_48 _let_42))) (let ((_let_50 (forall ((Pn $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.option tptp.com))) (or (not (= (tptp.hAPP tptp.pname _let_1 tptp.body Pn) (tptp.hAPP tptp.com _let_1 (tptp.some tptp.com) B_2))) (tptp.hBOOL (tptp.hAPP tptp.com tptp.bool tptp.wt B_2))))))) (let ((_let_51 (_let_50))) (let ((_let_52 (_let_29))) (let ((_let_53 (ASSUME :args _let_52))) (let ((_let_54 (tptp.fun (tptp.hoare_1656922687triple X_a) tptp.bool))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_40 :args (tptp.state _let_16 _let_3 _let_5 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_34))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_39)) :args ((or _let_20 _let_36 _let_38 _let_41))) (ASSUME :args (_let_21)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_53 :args (tptp.state _let_16 QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP _let_54 (tptp.fun _let_54 tptp.bool) (tptp.hoare_279057269derivs X_a) G_1)))) :args _let_52)) _let_53 :args (_let_35 false _let_29)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_44)) :args ((or _let_43 _let_37 (not _let_44)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_49)) :args ((or _let_48 _let_42 (not _let_49)))) (ASSUME :args (_let_23)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_51) :args (tptp.pn tptp.y QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP tptp.pname _let_7 tptp.body Pn) (tptp.hAPP tptp.com _let_7 _let_22 B_2)))) :args _let_51)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (ASSUME :args (_let_26)) (MACRO_SR_EQ_INTRO :args (_let_26 SB_DEFAULT SBA_FIXPOINT))) _let_46 :args (_let_50 false _let_24)) :args (_let_49 false _let_50)) :args (_let_42 false _let_23 false _let_49)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_47) :args (tptp.y QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.hAPP tptp.com _let_1 tptp.hoare_Mirabelle_MGT C_1)))) :args _let_47)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (ASSUME :args (_let_27)) (MACRO_SR_EQ_INTRO :args (_let_27 SB_DEFAULT SBA_FIXPOINT))) (ASSUME :args (_let_25)) _let_46 :args (_let_45 false _let_25 false _let_24)) :args (_let_44 false _let_45)) :args (_let_37 false _let_42 false _let_44)) :args (_let_41 true _let_20 false _let_35 false _let_37)) _let_40 :args (false true _let_39 false _let_34)) :args ((forall ((X_b $$unsorted) (X_c $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.combb X_b X_c X_a))) (= (tptp.ti (tptp.fun (tptp.fun X_b X_c) (tptp.fun (tptp.fun X_a X_b) (tptp.fun X_a X_c))) _let_1) _let_1))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted)) (let ((_let_1 (tptp.combc X_a X_b X_c))) (= (tptp.ti (tptp.fun (tptp.fun X_a (tptp.fun X_b X_c)) (tptp.fun X_b (tptp.fun X_a X_c))) _let_1) _let_1))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.combi X_a))) (= (tptp.ti (tptp.fun X_a X_a) _let_1) _let_1))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (let ((_let_1 (tptp.combk X_a X_b))) (= (tptp.ti (tptp.fun X_a (tptp.fun X_b X_a)) _let_1) _let_1))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted)) (let ((_let_1 (tptp.combs X_a X_b X_c))) (= (tptp.ti (tptp.fun (tptp.fun X_a (tptp.fun X_b X_c)) (tptp.fun (tptp.fun X_a X_b) (tptp.fun X_a X_c))) _let_1) _let_1))) (= (tptp.ti (tptp.fun tptp.com tptp.bool) tptp.wt) tptp.wt) (= (tptp.ti tptp.bool tptp.wT_bodies) tptp.wT_bodies) (= (tptp.ti _let_8 tptp.body) tptp.body) (= (tptp.ti _let_11 tptp.body_1) tptp.body_1) (= (tptp.ti tptp.com tptp.skip) tptp.skip) (= (tptp.ti (tptp.fun tptp.com _let_33) tptp.semi) tptp.semi) (= (tptp.ti (tptp.fun _let_32 _let_33) tptp.while) tptp.while) (forall ((X_a $$unsorted) (X_b $$unsorted)) (let ((_let_1 (tptp.finite_comp_fun_idem X_a X_b))) (= (tptp.ti (tptp.fun (tptp.fun X_a (tptp.fun X_b X_b)) tptp.bool) _let_1) _let_1))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.finite_finite X_a))) (= (tptp.ti (tptp.fun (tptp.fun X_a tptp.bool) tptp.bool) _let_1) _let_1))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (let ((_let_1 (tptp.finite1357897459simple X_a X_b))) (= (tptp.ti (tptp.fun (tptp.fun X_a (tptp.fun X_a X_a)) (tptp.fun X_a (tptp.fun (tptp.fun X_b X_a) (tptp.fun (tptp.fun (tptp.fun X_b tptp.bool) X_a) tptp.bool)))) _let_1) _let_1))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (let ((_let_1 (tptp.finite908156982e_idem X_a X_b))) (= (tptp.ti (tptp.fun (tptp.fun X_a (tptp.fun X_a X_a)) (tptp.fun X_a (tptp.fun (tptp.fun X_b X_a) (tptp.fun (tptp.fun (tptp.fun X_b tptp.bool) X_a) tptp.bool)))) _let_1) _let_1))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.finite_folding_one X_a))) (= (tptp.ti (tptp.fun (tptp.fun X_a (tptp.fun X_a X_a)) (tptp.fun (tptp.fun (tptp.fun X_a tptp.bool) X_a) tptp.bool)) _let_1) _let_1))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.finite2073411215e_idem X_a))) (= (tptp.ti (tptp.fun (tptp.fun X_a (tptp.fun X_a X_a)) (tptp.fun (tptp.fun (tptp.fun X_a tptp.bool) X_a) tptp.bool)) _let_1) _let_1))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (let ((_let_1 (tptp.fun_upd X_a X_b))) (let ((_let_2 (tptp.fun X_a X_b))) (= (tptp.ti (tptp.fun _let_2 (tptp.fun X_a (tptp.fun X_b _let_2))) _let_1) _let_1)))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (let ((_let_1 (tptp.inj_on X_a X_b))) (= (tptp.ti (tptp.fun (tptp.fun X_a X_b) (tptp.fun (tptp.fun X_a tptp.bool) tptp.bool)) _let_1) _let_1))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (let ((_let_1 (tptp.override_on X_a X_b))) (let ((_let_2 (tptp.fun X_a X_b))) (= (tptp.ti (tptp.fun _let_2 (tptp.fun _let_2 (tptp.fun (tptp.fun X_a tptp.bool) _let_2))) _let_1) _let_1)))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.minus_minus X_b))) (=> (tptp.minus X_b) (= (tptp.ti (tptp.fun X_b (tptp.fun X_b X_b)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.the_1 X_a))) (= (tptp.ti (tptp.fun (tptp.fun X_a tptp.bool) X_a) _let_1) _let_1))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.undefined X_a))) (= (tptp.ti X_a _let_1) _let_1))) (= (tptp.ti _let_12 tptp.hoare_Mirabelle_MGT) tptp.hoare_Mirabelle_MGT) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.hoare_279057269derivs X_a))) (let ((_let_2 (tptp.fun (tptp.hoare_1656922687triple X_a) tptp.bool))) (= (tptp.ti (tptp.fun _let_2 (tptp.fun _let_2 tptp.bool)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.hoare_2027193591valids X_a))) (let ((_let_2 (tptp.fun (tptp.hoare_1656922687triple X_a) tptp.bool))) (= (tptp.ti (tptp.fun _let_2 (tptp.fun _let_2 tptp.bool)) _let_1) _let_1)))) (= (tptp.ti tptp.bool tptp.hoare_1924220188gleton) tptp.hoare_1924220188gleton) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.hoare_246368825triple X_a))) (let ((_let_2 (tptp.fun X_a (tptp.fun tptp.state tptp.bool)))) (= (tptp.ti (tptp.fun _let_2 (tptp.fun tptp.com (tptp.fun _let_2 (tptp.hoare_1656922687triple X_a)))) _let_1) _let_1)))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.hoare_1312322281e_case X_b X_a))) (let ((_let_2 (tptp.fun X_b (tptp.fun tptp.state tptp.bool)))) (= (tptp.ti (tptp.fun (tptp.fun _let_2 (tptp.fun tptp.com (tptp.fun _let_2 X_a))) (tptp.fun (tptp.hoare_1656922687triple X_b) X_a)) _let_1) _let_1)))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.hoare_1632998903le_rec X_b X_a))) (let ((_let_2 (tptp.fun X_b (tptp.fun tptp.state tptp.bool)))) (= (tptp.ti (tptp.fun (tptp.fun _let_2 (tptp.fun tptp.com (tptp.fun _let_2 X_a))) (tptp.fun (tptp.hoare_1656922687triple X_b) X_a)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.if X_a))) (= (tptp.ti (tptp.fun tptp.bool (tptp.fun X_a (tptp.fun X_a X_a))) _let_1) _let_1))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.semilattice_inf_inf X_a))) (=> (tptp.semilattice_inf X_a) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a X_a)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.semilattice_sup_sup X_a))) (=> (tptp.semilattice_sup X_a) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a X_a)) _let_1) _let_1)))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.dom X_b X_a))) (= (tptp.ti (tptp.fun (tptp.fun X_b (tptp.option X_a)) (tptp.fun X_b tptp.bool)) _let_1) _let_1))) (= (tptp.ti (tptp.fun tptp.com (tptp.fun tptp.state _let_32)) tptp.evalc) tptp.evalc) (forall ((X_a $$unsorted) (X_b $$unsorted)) (let ((_let_1 (tptp.fold_graph X_a X_b))) (= (tptp.ti (tptp.fun (tptp.fun X_a (tptp.fun X_b X_b)) (tptp.fun X_b (tptp.fun (tptp.fun X_a tptp.bool) (tptp.fun X_b tptp.bool)))) _let_1) _let_1))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.none X_b))) (= (tptp.ti (tptp.option X_b) _let_1) _let_1))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.some X_a))) (= (tptp.ti (tptp.fun X_a (tptp.option X_a)) _let_1) _let_1))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (let ((_let_1 (tptp.option_rec X_a X_b))) (= (tptp.ti (tptp.fun X_a (tptp.fun (tptp.fun X_b X_a) (tptp.fun (tptp.option X_b) X_a))) _let_1) _let_1))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.set X_a))) (= (tptp.ti (tptp.fun (tptp.option X_a) (tptp.fun X_a tptp.bool)) _let_1) _let_1))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.the X_a))) (= (tptp.ti (tptp.fun (tptp.option X_a) X_a) _let_1) _let_1))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.bot_bot X_a))) (=> (tptp.bot X_a) (= (tptp.ti X_a _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (=> (tptp.ord X_a) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a tptp.bool)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.partial_flat_lub X_a))) (= (tptp.ti (tptp.fun X_a (tptp.fun (tptp.fun X_a tptp.bool) X_a)) _let_1) _let_1))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.collect X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (= (tptp.ti (tptp.fun _let_2 _let_2) _let_1) _let_1)))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (let ((_let_1 (tptp.image X_a X_b))) (= (tptp.ti (tptp.fun (tptp.fun X_a X_b) (tptp.fun (tptp.fun X_a tptp.bool) (tptp.fun X_b tptp.bool))) _let_1) _let_1))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.insert X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (= (tptp.ti (tptp.fun X_a (tptp.fun _let_2 _let_2)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.the_elem X_a))) (= (tptp.ti (tptp.fun (tptp.fun X_a tptp.bool) X_a) _let_1) _let_1))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.fAll X_a))) (= (tptp.ti (tptp.fun (tptp.fun X_a tptp.bool) tptp.bool) _let_1) _let_1))) (= (tptp.ti tptp.bool tptp.fFalse) tptp.fFalse) (= (tptp.ti _let_30 tptp.fNot) tptp.fNot) (= (tptp.ti tptp.bool tptp.fTrue) tptp.fTrue) (= (tptp.ti _let_31 tptp.fconj) tptp.fconj) (= (tptp.ti _let_31 tptp.fdisj) tptp.fdisj) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.fequal X_a))) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a tptp.bool)) _let_1) _let_1))) (= (tptp.ti _let_31 tptp.fimplies) tptp.fimplies) (forall ((X_a $$unsorted) (X_c $$unsorted) (B_1_1 $$unsorted) (B_2_1 $$unsorted)) (= (tptp.hAPP X_a X_c (tptp.ti (tptp.fun X_a X_c) B_1_1) B_2_1) (tptp.hAPP X_a X_c B_1_1 B_2_1))) (forall ((X_a $$unsorted) (X_c $$unsorted) (B_1_1 $$unsorted) (B_2_1 $$unsorted)) (= (tptp.hAPP X_a X_c B_1_1 (tptp.ti X_a B_2_1)) (tptp.hAPP X_a X_c B_1_1 B_2_1))) (forall ((X_c $$unsorted) (X_a $$unsorted) (B_1_1 $$unsorted) (B_2_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a X_c B_1_1 B_2_1))) (= (tptp.ti X_c _let_1) _let_1))) (forall ((B_1_1 $$unsorted)) (= (tptp.hBOOL (tptp.ti tptp.bool B_1_1)) (tptp.hBOOL B_1_1))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.member X_a))) (= (tptp.ti (tptp.fun X_a (tptp.fun (tptp.fun X_a tptp.bool) tptp.bool)) _let_1) _let_1))) (= (tptp.ti _let_2 tptp.fa) tptp.fa) (= (tptp.ti tptp.pname tptp.pn) tptp.pn) (= (tptp.ti tptp.com tptp.y) tptp.y) _let_29 (forall ((X_a $$unsorted) (Ts $$unsorted) (G_1 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.hoare_1656922687triple X_a) tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) Ts) G_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.hoare_279057269derivs X_a) G_1) Ts)))))) (forall ((X_a $$unsorted) (Ts $$unsorted) (G_1 $$unsorted) (Ts_1 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.hoare_1656922687triple X_a) tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP _let_1 _let_2 (tptp.hoare_279057269derivs X_a) G_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 Ts_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) Ts) Ts_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 Ts)))))))) (forall ((X_a $$unsorted) (G_1 $$unsorted) (G_2 $$unsorted) (Ts $$unsorted)) (let ((_let_1 (tptp.hoare_279057269derivs X_a))) (let ((_let_2 (tptp.fun (tptp.hoare_1656922687triple X_a) tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 _let_3 _let_1 G_2) Ts)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 _let_3 (tptp.ord_less_eq _let_2) G_2) G_1)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 _let_3 _let_1 G_1) Ts)))))))) _let_28 (forall ((X_a $$unsorted) (Ts $$unsorted) (G_1 $$unsorted) (T_3 $$unsorted)) (let ((_let_1 (tptp.hoare_1656922687triple X_a))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP _let_1 (tptp.fun _let_2 _let_2) (tptp.insert _let_1) T_3))) (let ((_let_4 (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.hoare_279057269derivs X_a) G_1))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_4 (tptp.hAPP _let_2 _let_2 _let_3 (tptp.bot_bot _let_2)))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_4 Ts)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_4 (tptp.hAPP _let_2 _let_2 _let_3 Ts)))))))))) (forall ((X_a $$unsorted) (G_1 $$unsorted) (T_3 $$unsorted) (Ts $$unsorted)) (let ((_let_1 (tptp.hoare_1656922687triple X_a))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.hoare_279057269derivs X_a) G_1))) (let ((_let_4 (tptp.hAPP _let_1 (tptp.fun _let_2 _let_2) (tptp.insert _let_1) T_3))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 (tptp.hAPP _let_2 _let_2 _let_4 Ts))) (and (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 (tptp.hAPP _let_2 _let_2 _let_4 (tptp.bot_bot _let_2)))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 Ts))))))))) (forall ((Pn_1 $$unsorted) (G_1 $$unsorted)) (let ((_let_1 (tptp.hoare_1656922687triple tptp.state))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.bot_bot _let_2))) (let ((_let_4 (tptp.insert _let_1))) (let ((_let_5 (tptp.fun _let_2 _let_2))) (let ((_let_6 (tptp.hAPP _let_1 _let_5 _let_4 (tptp.hAPP tptp.com _let_1 tptp.hoare_Mirabelle_MGT (tptp.hAPP tptp.pname tptp.com tptp.body_1 Pn_1))))) (let ((_let_7 (tptp.hoare_279057269derivs tptp.state))) (let ((_let_8 (tptp.fun _let_2 tptp.bool))) (let ((_let_9 (tptp.option tptp.com))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 _let_8 _let_7 (tptp.hAPP _let_2 _let_2 _let_6 G_1)) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 _let_5 _let_4 (tptp.hAPP tptp.com _let_1 tptp.hoare_Mirabelle_MGT (tptp.hAPP _let_9 tptp.com (tptp.the tptp.com) (tptp.hAPP tptp.pname _let_9 tptp.body Pn_1)))) _let_3))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 _let_8 _let_7 G_1) (tptp.hAPP _let_2 _let_2 _let_6 _let_3)))))))))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun _let_1 _let_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_a) A_1)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite _let_1) (tptp.hAPP _let_2 _let_2 (tptp.collect _let_1) (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_3 _let_3 (tptp.combc _let_1 _let_1 tptp.bool) (tptp.ord_less_eq _let_1)) A_1))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (H $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite X_a) Fa)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun _let_2 _let_1) (tptp.image X_a X_b) H) Fa))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) (tptp.bot_bot _let_1)) A_1)))) (forall ((X_a $$unsorted) (A_3 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.finite_finite X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_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.insert X_a) A_3) A_1))))))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_a) (tptp.bot_bot _let_1))))) (forall ((X_a $$unsorted) (Q_1 $$unsorted) (P_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.bool tptp.bool))) (let ((_let_2 (tptp.fun X_a _let_1))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.collect X_a))) (let ((_let_5 (tptp.finite_finite X_a))) (=> (or (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool _let_5 (tptp.hAPP _let_3 _let_3 _let_4 P_1))) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool _let_5 (tptp.hAPP _let_3 _let_3 _let_4 Q_1)))) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool _let_5 (tptp.hAPP _let_3 _let_3 _let_4 (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_2 (tptp.fun _let_3 _let_3) (tptp.combs X_a tptp.bool tptp.bool) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun tptp.bool _let_1) (tptp.fun _let_3 _let_2) (tptp.combb tptp.bool _let_1 X_a) tptp.fconj) P_1)) Q_1))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (C_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.bot_bot _let_1))) (let ((_let_3 (tptp.fun X_a X_b))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (let ((_let_5 (tptp.hAPP _let_4 _let_1 (tptp.hAPP _let_3 (tptp.fun _let_4 _let_1) (tptp.image X_a X_b) (tptp.hAPP X_b _let_3 (tptp.combk X_b X_a) C_1)) A_1))) (let ((_let_6 (= (tptp.ti _let_4 A_1) (tptp.bot_bot _let_4)))) (and (=> _let_6 (= _let_5 _let_2)) (=> (not _let_6) (= _let_5 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) C_1) _let_2))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (C_1 $$unsorted) (X_2 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a X_b))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_a (tptp.fun _let_3 tptp.bool) (tptp.member X_a) X_2) A_1)) (= (tptp.hAPP _let_3 _let_1 (tptp.hAPP _let_2 (tptp.fun _let_3 _let_1) (tptp.image X_a X_b) (tptp.hAPP X_b _let_2 (tptp.combk X_b X_a) C_1)) A_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) C_1) (tptp.bot_bot _let_1)))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F $$unsorted) (X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.option X_a))) (let ((_let_3 (tptp.hAPP (tptp.fun X_b _let_2) _let_1 (tptp.dom X_b X_a) F))) (=> (= (tptp.hAPP X_b _let_2 F X_2) (tptp.hAPP X_a _let_2 (tptp.some X_a) Y_2)) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_2) _let_3) _let_3)))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (B $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite X_a) A_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) B) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun _let_2 _let_1) (tptp.image X_a X_b) F) A_1))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) B))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.bot_bot _let_1))) (let ((_let_3 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.insert X_a) X_2) _let_2))) (let ((_let_4 (tptp.ti _let_1 A_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) A_1) _let_3)) (or (= _let_4 _let_2) (= _let_4 _let_3)))))))) _let_27 (forall ((X_a $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) A_3) (tptp.bot_bot _let_1)))))) (forall ((X_a $$unsorted) (B_1 $$unsorted) (A_3 $$unsorted) (B $$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) A_3))) (=> (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B))) (= (tptp.ti X_a A_3) (tptp.ti X_a B_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.insert X_a) B_1) B))))))) (forall ((X_a $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted) (A_1 $$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) A_3))) (=> (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) B_1) A_1))) (=> (not (= (tptp.ti X_a A_3) (tptp.ti X_a B_1))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_1))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.ord_less_eq _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 B) A_1)) (= (tptp.ti _let_1 A_1) (tptp.ti _let_1 B)))))))) (forall ((X_a $$unsorted) (C_1 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 (tptp.member X_a) C_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_1) B)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 A_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 B)))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted) (F $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (= (tptp.ti X_a B_1) (tptp.hAPP X_b X_a F X_2)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_b (tptp.fun _let_2 tptp.bool) (tptp.member X_b) X_2) A_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) B_1) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_b X_a) (tptp.fun _let_2 _let_1) (tptp.image X_b X_a) F) A_1)))))))) (forall ((X_a $$unsorted) (A_3 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (= (tptp.ti _let_1 A_1) (tptp.bot_bot _let_1)) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) A_3) A_1)))))) (forall ((X_a $$unsorted) (P_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (= (= (tptp.hAPP _let_1 _let_1 (tptp.collect X_a) P_1) (tptp.bot_bot _let_1)) (forall ((X_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool P_1 X_1))))))) (forall ((X_a $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) C_1) (tptp.bot_bot _let_1)))))) (forall ((X_a $$unsorted) (P_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (= (= (tptp.bot_bot _let_1) (tptp.hAPP _let_1 _let_1 (tptp.collect X_a) P_1)) (forall ((X_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool P_1 X_1))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (= (exists ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_1) A_1)))) (not (= (tptp.ti _let_1 A_1) (tptp.bot_bot _let_1)))))) (forall ((X_a $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (= (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_1) A_1))))) (= (tptp.ti _let_1 A_1) (tptp.bot_bot _let_1))))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (= (tptp.bot_bot _let_1) (tptp.hAPP _let_1 _let_1 (tptp.collect X_a) (tptp.hAPP tptp.bool _let_1 (tptp.combk tptp.bool X_a) tptp.fFalse))))) (forall ((X_a $$unsorted)) (=> (tptp.finite_finite_1 X_a) (forall ((A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_a tptp.bool) tptp.bool (tptp.finite_finite X_a) A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.finite_finite_1 X_a) (forall ((A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_a tptp.bool) tptp.bool (tptp.finite_finite X_a) A_1))))) (forall ((X_a $$unsorted) (A_3 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) A_3) A_1)) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.insert X_a) A_3) A_1) (tptp.ti _let_1 A_1))))) (forall ((X_a $$unsorted) (B_1 $$unsorted) (A_3 $$unsorted) (B $$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) A_3))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B)) (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) B_1) B))))))) (forall ((X_a $$unsorted) (B $$unsorted) (X_2 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.insert X_a) X_2))) (let ((_let_3 (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2))) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 A_1))) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 B))) (= (= (tptp.hAPP _let_1 _let_1 _let_2 A_1) (tptp.hAPP _let_1 _let_1 _let_2 B)) (= (tptp.ti _let_1 A_1) (tptp.ti _let_1 B))))))))) (forall ((X_a $$unsorted) (Y_2 $$unsorted) (A_1 $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.insert X_a) Y_2) A_1) X_2)) (or (= (tptp.ti X_a Y_2) (tptp.ti X_a X_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool A_1 X_2)))))) (forall ((X_a $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted) (A_1 $$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) A_3))) (= (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) B_1) A_1))) (or (= (tptp.ti X_a A_3) (tptp.ti X_a B_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_1))))))) (forall ((X_a $$unsorted) (X_2 $$unsorted) (Y_2 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.insert X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (let ((_let_4 (tptp.hAPP X_a _let_3 _let_1 X_2))) (let ((_let_5 (tptp.hAPP X_a _let_3 _let_1 Y_2))) (= (tptp.hAPP _let_2 _let_2 _let_4 (tptp.hAPP _let_2 _let_2 _let_5 A_1)) (tptp.hAPP _let_2 _let_2 _let_5 (tptp.hAPP _let_2 _let_2 _let_4 A_1))))))))) (forall ((X_a $$unsorted) (X_2 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.insert X_a) X_2))) (let ((_let_3 (tptp.hAPP _let_1 _let_1 _let_2 A_1))) (= (tptp.hAPP _let_1 _let_1 _let_2 _let_3) _let_3))))) (forall ((X_a $$unsorted) (A_3 $$unsorted) (P_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun X_a _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.fun tptp.bool tptp.bool))) (let ((_let_5 (tptp.fun X_a _let_4))) (let ((_let_6 (tptp.collect X_a))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_3 (tptp.insert X_a) A_3) (tptp.hAPP _let_1 _let_1 _let_6 P_1)) (tptp.hAPP _let_1 _let_1 _let_6 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_5 _let_3 (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.fimplies) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_4 _let_3 (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)) A_3)))) P_1)))))))))) (forall ((X_a $$unsorted) (A_3 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.fun X_a _let_1))) (let ((_let_4 (tptp.fun tptp.bool tptp.bool))) (let ((_let_5 (tptp.fun X_a _let_4))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_2 (tptp.insert X_a) A_3) B) (tptp.hAPP _let_1 _let_1 (tptp.collect X_a) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_5 _let_2 (tptp.combs X_a tptp.bool tptp.bool) (tptp.hAPP _let_1 _let_5 (tptp.hAPP (tptp.fun tptp.bool _let_4) (tptp.fun _let_1 _let_5) (tptp.combb tptp.bool _let_4 X_a) tptp.fdisj) (tptp.hAPP X_a _let_1 (tptp.hAPP _let_3 _let_3 (tptp.combc X_a X_a tptp.bool) (tptp.fequal X_a)) A_3))) (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_a (tptp.fun _let_1 tptp.bool)) _let_2 (tptp.combc X_a _let_1 tptp.bool) (tptp.member X_a)) B)))))))))) (forall ((X_a $$unsorted) (A_3 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) A_3) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.insert X_a) A_3) B))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.ord_less_eq _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (=> (= (tptp.ti _let_1 A_1) (tptp.ti _let_1 B)) (not (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 A_1) B)) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 B) A_1)))))))))) (forall ((X_a $$unsorted) (C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.ord_less_eq _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.hAPP _let_1 _let_3 _let_2 A_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_4 B)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 B) C)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_4 C))))))))) (forall ((X_a $$unsorted) (X_2 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 (tptp.member X_a) X_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_1) B)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 A_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 B)))))))) (forall ((X_a $$unsorted) (B $$unsorted) (X_2 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 (tptp.member X_a) X_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 A_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_1) B)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 B)))))))) (forall ((X_a $$unsorted) (X_2 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 (tptp.member X_a) X_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_1) B)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 A_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 B)))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (= (tptp.ti _let_1 A_1) (tptp.ti _let_1 B)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) B) A_1))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (= (tptp.ti _let_1 A_1) (tptp.ti _let_1 B)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) A_1) B))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.ord_less_eq _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (= (tptp.ti _let_1 A_1) (tptp.ti _let_1 B)) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 A_1) B)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 B) A_1)))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) A_1) A_1)))) (forall ((X_b $$unsorted) (X_a $$unsorted) (B_1 $$unsorted) (F $$unsorted) (X_2 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a (tptp.fun _let_2 tptp.bool) (tptp.member X_a) X_2) A_1)) (=> (= (tptp.ti X_b B_1) (tptp.hAPP X_a X_b F X_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) B_1) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun _let_2 _let_1) (tptp.image X_a X_b) F) A_1)))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F $$unsorted) (X_2 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a (tptp.fun _let_2 tptp.bool) (tptp.member X_a) X_2) A_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) (tptp.hAPP X_a X_b F X_2)) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun _let_2 _let_1) (tptp.image X_a X_b) F) A_1))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (Z $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) Z) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_b X_a) (tptp.fun _let_2 _let_1) (tptp.image X_b X_a) F) A_1))) (exists ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_1) A_1)) (= (tptp.ti X_a Z) (tptp.hAPP X_b X_a F X_1))))))))) (forall ((X_a $$unsorted) (P_1 $$unsorted) (Q_1 $$unsorted)) (let ((_let_1 (tptp.collect X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.finite_finite X_a))) (let ((_let_4 (tptp.fun tptp.bool tptp.bool))) (let ((_let_5 (tptp.fun X_a _let_4))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 (tptp.hAPP _let_2 _let_2 _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_5 (tptp.fun _let_2 _let_2) (tptp.combs X_a tptp.bool tptp.bool) (tptp.hAPP _let_2 _let_5 (tptp.hAPP (tptp.fun tptp.bool _let_4) (tptp.fun _let_2 _let_5) (tptp.combb tptp.bool _let_4 X_a) tptp.fdisj) P_1)) Q_1)))) (and (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 (tptp.hAPP _let_2 _let_2 _let_1 P_1))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 (tptp.hAPP _let_2 _let_2 _let_1 Q_1))))))))))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (Xa $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.fun X_a _let_1))) (let ((_let_4 (tptp.fun tptp.bool tptp.bool))) (let ((_let_5 (tptp.fun X_a _let_4))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_2 (tptp.insert X_a) X_1) Xa) (tptp.hAPP _let_1 _let_1 (tptp.collect X_a) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_5 _let_2 (tptp.combs X_a tptp.bool tptp.bool) (tptp.hAPP _let_1 _let_5 (tptp.hAPP (tptp.fun tptp.bool _let_4) (tptp.fun _let_1 _let_5) (tptp.combb tptp.bool _let_4 X_a) tptp.fdisj) (tptp.hAPP X_a _let_1 (tptp.hAPP _let_3 _let_3 (tptp.combc X_a X_a tptp.bool) (tptp.fequal X_a)) X_1))) (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_a (tptp.fun _let_1 tptp.bool)) _let_2 (tptp.combc X_a _let_1 tptp.bool) (tptp.member X_a)) Xa)))))))))) (forall ((X_a $$unsorted) (Y_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_a X_a) (tptp.fun _let_1 _let_1) (tptp.image X_a X_a) (tptp.combi X_a)) Y_3) (tptp.ti _let_1 Y_3)))) (forall ((X_b $$unsorted) (X_a $$unsorted) (X_c $$unsorted) (F $$unsorted) (G $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c X_a))) (let ((_let_2 (tptp.fun X_c X_b))) (let ((_let_3 (tptp.fun X_b X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (let ((_let_5 (tptp.fun X_c tptp.bool))) (let ((_let_6 (tptp.fun X_b tptp.bool))) (= (tptp.hAPP _let_6 _let_4 (tptp.hAPP _let_3 (tptp.fun _let_6 _let_4) (tptp.image X_b X_a) F) (tptp.hAPP _let_5 _let_6 (tptp.hAPP _let_2 (tptp.fun _let_5 _let_6) (tptp.image X_c X_b) G) A_1)) (tptp.hAPP _let_5 _let_4 (tptp.hAPP _let_1 (tptp.fun _let_5 _let_4) (tptp.image X_c X_a) (tptp.hAPP _let_2 _let_1 (tptp.hAPP _let_3 (tptp.fun _let_2 _let_1) (tptp.combb X_b X_a X_c) F) G)) A_1))))))))) (forall ((X_a $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.bot_bot _let_1))) (let ((_let_3 (tptp.insert X_a))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (=> (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_4 _let_3 A_3) _let_2) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_4 _let_3 B_1) _let_2)) (= (tptp.ti X_a A_3) (tptp.ti X_a B_1)))))))) (forall ((X_a $$unsorted) (B_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) B_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.insert X_a) A_3) (tptp.bot_bot _let_1)))) (= (tptp.ti X_a B_1) (tptp.ti X_a A_3))))) (forall ((X_a $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted) (C_1 $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.ti X_a C_1))) (let ((_let_2 (tptp.ti X_a B_1))) (let ((_let_3 (tptp.ti X_a D))) (let ((_let_4 (tptp.ti X_a A_3))) (let ((_let_5 (tptp.fun X_a tptp.bool))) (let ((_let_6 (tptp.bot_bot _let_5))) (let ((_let_7 (tptp.insert X_a))) (let ((_let_8 (tptp.fun _let_5 _let_5))) (= (= (tptp.hAPP _let_5 _let_5 (tptp.hAPP X_a _let_8 _let_7 A_3) (tptp.hAPP _let_5 _let_5 (tptp.hAPP X_a _let_8 _let_7 B_1) _let_6)) (tptp.hAPP _let_5 _let_5 (tptp.hAPP X_a _let_8 _let_7 C_1) (tptp.hAPP _let_5 _let_5 (tptp.hAPP X_a _let_8 _let_7 D) _let_6))) (or (and (= _let_4 _let_1) (= _let_2 _let_3)) (and (= _let_4 _let_3) (= _let_2 _let_1))))))))))))) (forall ((X_a $$unsorted) (B_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) B_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.insert X_a) A_3) (tptp.bot_bot _let_1)))) (= (tptp.ti X_a B_1) (tptp.ti X_a A_3))))) (forall ((X_a $$unsorted) (A_3 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (not (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.insert X_a) A_3) A_1) (tptp.bot_bot _let_1))))) (forall ((X_a $$unsorted) (A_3 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (not (= (tptp.bot_bot _let_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.insert X_a) A_3) A_1))))) (forall ((X_a $$unsorted) (A_3 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.finite_finite X_a))) (let ((_let_2 (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.insert X_a) A_3) A_1))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 A_1)))))) (forall ((X_a $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.bot_bot _let_1))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) A_1) _let_2)) (= (tptp.ti _let_1 A_1) _let_2))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (= (= (tptp.hAPP _let_1 _let_2 (tptp.hAPP (tptp.fun X_b X_a) (tptp.fun _let_1 _let_2) (tptp.image X_b X_a) F) A_1) (tptp.bot_bot _let_2)) (= (tptp.ti _let_1 A_1) (tptp.bot_bot _let_1)))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (= (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_b X_a) (tptp.fun _let_2 _let_1) (tptp.image X_b X_a) F) (tptp.bot_bot _let_2)) (tptp.bot_bot _let_1))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (= (= (tptp.bot_bot _let_2) (tptp.hAPP _let_1 _let_2 (tptp.hAPP (tptp.fun X_b X_a) (tptp.fun _let_1 _let_2) (tptp.image X_b X_a) F) A_1)) (= (tptp.ti _let_1 A_1) (tptp.bot_bot _let_1)))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.finite_finite X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) A_1) B)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 B)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 A_1))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.finite_finite X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 B)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) A_1) B)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 A_1))))))) (forall ((X_a $$unsorted) (A_3 $$unsorted) (C $$unsorted) (D_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.insert X_a) A_3))) (let ((_let_3 (tptp.ord_less_eq _let_1))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_4 _let_3 C) D_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_4 _let_3 (tptp.hAPP _let_1 _let_1 _let_2 C)) (tptp.hAPP _let_1 _let_1 _let_2 D_1))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (F $$unsorted) (G $$unsorted)) (let ((_let_1 (tptp.fun X_a X_b))) (=> (forall ((X_1 $$unsorted)) (= (tptp.hAPP X_a X_b F X_1) (tptp.hAPP X_a X_b G X_1))) (= (tptp.ti _let_1 F) (tptp.ti _let_1 G))))) (forall ((X_a $$unsorted) (X_2 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool A_1 X_2))))) (forall ((X_a $$unsorted) (P_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (= (tptp.hAPP _let_1 _let_1 (tptp.collect X_a) P_1) (tptp.ti _let_1 P_1)))) (forall ((X_a $$unsorted) (B_1 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) A_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.insert X_a) B_1) B))))))) (forall ((X_a $$unsorted) (B $$unsorted) (X_2 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_1))) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a _let_2 (tptp.member X_a) X_2) A_1))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.insert X_a) X_2) B))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 B)))))))) (forall ((X_a $$unsorted) (X_2 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.ord_less_eq _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.insert X_a) X_2) A_1)) B)) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a _let_3 (tptp.member X_a) X_2) B)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 A_1) B)))))))) (forall ((X_a $$unsorted) (B $$unsorted) (A_3 $$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) B) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.insert X_a) A_3) B))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F $$unsorted) (X_2 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun _let_2 _let_1) (tptp.image X_a X_b) F) A_1))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a (tptp.fun _let_2 tptp.bool) (tptp.member X_a) X_2) A_1)) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) (tptp.hAPP X_a X_b F X_2)) _let_3) _let_3)))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F $$unsorted) (A_3 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.hAPP (tptp.fun X_b X_a) (tptp.fun _let_2 _let_1) (tptp.image 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.insert X_b) A_3) B)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.insert X_a) (tptp.hAPP X_b X_a F A_3)) (tptp.hAPP _let_2 _let_1 _let_3 B))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun _let_2 _let_1) (tptp.image X_a X_b) F))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) A_1) B)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) (tptp.hAPP _let_2 _let_1 _let_3 A_1)) (tptp.hAPP _let_2 _let_1 _let_3 B)))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (B $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) B) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_b X_a) (tptp.fun _let_2 _let_1) (tptp.image X_b X_a) F) A_1))) (exists ((AA $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (and (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) AA) A_1)) (= (tptp.ti _let_1 B) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_b X_a) (tptp.fun _let_2 _let_1) (tptp.image X_b X_a) F) AA)))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (M $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.option X_a))) (=> (= (tptp.hAPP X_b _let_2 M A_3) (tptp.hAPP X_a _let_2 (tptp.some X_a) B_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_3) (tptp.hAPP (tptp.fun X_b _let_2) _let_1 (tptp.dom X_b X_a) M))))))) (forall ((X_a $$unsorted) (P_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.bot_bot _let_1))) (let ((_let_3 (tptp.fun X_a _let_1))) (let ((_let_4 (tptp.fun tptp.bool tptp.bool))) (let ((_let_5 (tptp.fun X_a _let_4))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (let ((_let_7 (tptp.hAPP _let_1 _let_1 (tptp.collect X_a) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_5 _let_6 (tptp.combs X_a tptp.bool tptp.bool) (tptp.hAPP _let_1 _let_5 (tptp.hAPP (tptp.fun tptp.bool _let_4) (tptp.fun _let_1 _let_5) (tptp.combb tptp.bool _let_4 X_a) tptp.fconj) (tptp.hAPP X_a _let_1 (tptp.hAPP _let_3 _let_3 (tptp.combc X_a X_a tptp.bool) (tptp.fequal X_a)) A_3))) P_1)))) (let ((_let_8 (tptp.hBOOL (tptp.hAPP X_a tptp.bool P_1 A_3)))) (and (=> _let_8 (= _let_7 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_6 (tptp.insert X_a) A_3) _let_2))) (=> (not _let_8) (= _let_7 _let_2)))))))))))) (forall ((X_a $$unsorted) (P_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.bot_bot _let_1))) (let ((_let_3 (tptp.fun tptp.bool tptp.bool))) (let ((_let_4 (tptp.fun X_a _let_3))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (let ((_let_6 (tptp.hAPP _let_1 _let_1 (tptp.collect X_a) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_4 _let_5 (tptp.combs X_a tptp.bool tptp.bool) (tptp.hAPP _let_1 _let_4 (tptp.hAPP (tptp.fun tptp.bool _let_3) (tptp.fun _let_1 _let_4) (tptp.combb tptp.bool _let_3 X_a) tptp.fconj) (tptp.hAPP X_a _let_1 (tptp.fequal X_a) A_3))) P_1)))) (let ((_let_7 (tptp.hBOOL (tptp.hAPP X_a tptp.bool P_1 A_3)))) (and (=> _let_7 (= _let_6 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_5 (tptp.insert X_a) A_3) _let_2))) (=> (not _let_7) (= _let_6 _let_2))))))))))) (forall ((X_a $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun X_a _let_1))) (= (tptp.hAPP _let_1 _let_1 (tptp.collect X_a) (tptp.hAPP X_a _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc X_a X_a tptp.bool) (tptp.fequal X_a)) A_3)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.insert X_a) A_3) (tptp.bot_bot _let_1)))))) (forall ((X_a $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (= (tptp.hAPP _let_1 _let_1 (tptp.collect X_a) (tptp.hAPP X_a _let_1 (tptp.fequal X_a) A_3)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.insert X_a) A_3) (tptp.bot_bot _let_1))))) (forall ((C_1 $$unsorted) (G_1 $$unsorted)) (let ((_let_1 (tptp.hoare_1656922687triple tptp.state))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL tptp.hoare_1924220188gleton) (=> (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.hoare_1656922687triple tptp.state))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun tptp.pname tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP tptp.pname (tptp.fun _let_3 tptp.bool) (tptp.member tptp.pname) X_1) (tptp.hAPP (tptp.fun tptp.pname (tptp.option tptp.com)) _let_3 (tptp.dom tptp.pname tptp.com) tptp.body))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.hoare_279057269derivs tptp.state) G_1) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 (tptp.fun _let_2 _let_2) (tptp.insert _let_1) (tptp.hAPP tptp.com _let_1 tptp.hoare_Mirabelle_MGT (tptp.hAPP tptp.pname tptp.com tptp.body_1 X_1))) (tptp.bot_bot _let_2))))))))) (=> (tptp.hBOOL (tptp.hAPP tptp.com tptp.bool tptp.wt C_1)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.hoare_279057269derivs tptp.state) G_1) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 (tptp.fun _let_2 _let_2) (tptp.insert _let_1) (tptp.hAPP tptp.com _let_1 tptp.hoare_Mirabelle_MGT C_1)) (tptp.bot_bot _let_2)))))))))) _let_26 (forall ((X_a $$unsorted) (X_b $$unsorted) (B_1 $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) B_1) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_b X_a) (tptp.fun _let_2 _let_1) (tptp.image X_b X_a) F) A_1))) (not (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (= (tptp.ti X_a B_1) (tptp.hAPP X_b X_a F X_1)) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_1) A_1))))))))))) (forall ((X_a $$unsorted) (P_1 $$unsorted) (A_1 $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_a) Fa)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) Fa) A_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool P_1 (tptp.bot_bot _let_1))) (=> (forall ((A_5 $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) A_5))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_a) F_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_1)) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 F_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool P_1 F_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool P_1 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.insert X_a) A_5) F_1)))))))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool P_1 Fa)))))))) (forall ((P $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.com tptp.bool tptp.wt (tptp.hAPP tptp.pname tptp.com tptp.body_1 P))) (not (forall ((Y_1 $$unsorted)) (let ((_let_1 (tptp.option tptp.com))) (not (= (tptp.hAPP tptp.pname _let_1 tptp.body P) (tptp.hAPP tptp.com _let_1 (tptp.some tptp.com) Y_1)))))))) (forall ((X_a $$unsorted) (B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B)))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) A_1) B))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_a) B)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) B) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_b X_a) (tptp.fun _let_2 _let_1) (tptp.image X_b X_a) F) A_1))) (exists ((C_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (and (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) C_3) A_1)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite X_b) C_3)) (= (tptp.ti _let_1 B) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_b X_a) (tptp.fun _let_2 _let_1) (tptp.image X_b X_a) F) C_3))))))))))) (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.finite_finite tptp.pname) _let_9)) (forall ((X_a $$unsorted) (P_1 $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_a) Fa)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool P_1 (tptp.bot_bot _let_1))) (=> (forall ((X_1 $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_a) F_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) F_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool P_1 F_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool P_1 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.insert X_a) X_1) F_1)))))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool P_1 Fa))))))) (forall ((X_a $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_a) A_3)) (or (= (tptp.ti _let_1 A_3) (tptp.bot_bot _let_1)) (exists ((A_4 $$unsorted) (A_5 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (and (= (tptp.ti _let_1 A_3) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.insert X_a) A_5) A_4)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_a) A_4))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (not (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite X_a) A_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun _let_2 _let_1) (tptp.image X_a X_b) F) A_1))) (exists ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a _let_1))) (let ((_let_3 (tptp.fun X_a X_b))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (let ((_let_5 (tptp.member X_a))) (let ((_let_6 (tptp.fun _let_4 _let_4))) (let ((_let_7 (tptp.fun _let_4 tptp.bool))) (let ((_let_8 (tptp.fun tptp.bool tptp.bool))) (let ((_let_9 (tptp.fun X_a _let_8))) (and (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP X_a _let_7 _let_5 X_1) A_1)) (not (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.finite_finite X_a) (tptp.hAPP _let_4 _let_4 (tptp.collect X_a) (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_9 _let_6 (tptp.combs X_a tptp.bool tptp.bool) (tptp.hAPP _let_4 _let_9 (tptp.hAPP (tptp.fun tptp.bool _let_8) (tptp.fun _let_4 _let_9) (tptp.combb tptp.bool _let_8 X_a) tptp.fconj) (tptp.hAPP _let_4 _let_4 (tptp.hAPP (tptp.fun X_a _let_7) _let_6 (tptp.combc X_a _let_4 tptp.bool) _let_5) A_1))) (tptp.hAPP X_b _let_4 (tptp.hAPP _let_2 (tptp.fun X_b _let_4) (tptp.combc X_a X_b tptp.bool) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun X_b _let_1) (tptp.fun _let_3 _let_2) (tptp.combb X_b _let_1 X_a) (tptp.fequal X_b)) F)) (tptp.hAPP X_a X_b F X_1))))))))))))))))))))))) (forall ((Pname_2 $$unsorted) (Pname_1 $$unsorted)) (= (= (tptp.hAPP tptp.pname tptp.com tptp.body_1 Pname_2) (tptp.hAPP tptp.pname tptp.com tptp.body_1 Pname_1)) (= (tptp.ti tptp.pname Pname_2) (tptp.ti tptp.pname Pname_1)))) (forall ((G_1 $$unsorted) (Procs $$unsorted)) (let ((_let_1 (tptp.hoare_1656922687triple tptp.state))) (let ((_let_2 (tptp.fun tptp.pname _let_1))) (let ((_let_3 (tptp.fun tptp.pname tptp.com))) (let ((_let_4 (tptp.hAPP (tptp.fun tptp.com _let_1) (tptp.fun _let_3 _let_2) (tptp.combb tptp.com _let_1 tptp.pname) tptp.hoare_Mirabelle_MGT))) (let ((_let_5 (tptp.image tptp.pname _let_1))) (let ((_let_6 (tptp.fun _let_1 tptp.bool))) (let ((_let_7 (tptp.fun tptp.pname tptp.bool))) (let ((_let_8 (tptp.fun _let_7 _let_6))) (let ((_let_9 (tptp.hAPP _let_7 _let_6 (tptp.hAPP _let_2 _let_8 _let_5 (tptp.hAPP _let_3 _let_2 _let_4 tptp.body_1)) Procs))) (let ((_let_10 (tptp.hoare_279057269derivs tptp.state))) (let ((_let_11 (tptp.fun _let_6 tptp.bool))) (let ((_let_12 (tptp.option tptp.com))) (let ((_let_13 (tptp.fun tptp.pname _let_12))) (=> (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP _let_6 _let_11 _let_10 (tptp.hAPP _let_6 _let_6 (tptp.hAPP _let_6 (tptp.fun _let_6 _let_6) (tptp.semilattice_sup_sup _let_6) G_1) _let_9)) (tptp.hAPP _let_7 _let_6 (tptp.hAPP _let_2 _let_8 _let_5 (tptp.hAPP _let_3 _let_2 _let_4 (tptp.hAPP _let_13 _let_3 (tptp.hAPP (tptp.fun _let_12 tptp.com) (tptp.fun _let_13 _let_3) (tptp.combb _let_12 tptp.com tptp.pname) (tptp.the tptp.com)) tptp.body))) Procs))) (=> (tptp.hBOOL (tptp.hAPP _let_7 tptp.bool (tptp.finite_finite tptp.pname) Procs)) (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP _let_6 _let_11 _let_10 G_1) _let_9)))))))))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (A_3 $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) A_3) (tptp.hAPP (tptp.fun X_a (tptp.option X_b)) _let_1 (tptp.dom X_a X_b) M))) (exists ((B_4 $$unsorted)) (let ((_let_1 (tptp.option X_b))) (= (tptp.hAPP X_a _let_1 M A_3) (tptp.hAPP X_b _let_1 (tptp.some X_b) B_4))))))) (forall ((X_a $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (= (tptp.hAPP _let_1 X_a (tptp.the_elem X_a) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.insert X_a) X_2) (tptp.bot_bot _let_1))) (tptp.ti X_a X_2)))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F $$unsorted) (B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a (tptp.fun _let_2 tptp.bool) (tptp.member X_a) X_1) A_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) (tptp.hAPP X_a X_b F X_1)) B)))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun _let_2 _let_1) (tptp.image X_a X_b) F) A_1)) B)))))) (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 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (= (not (= (tptp.ti _let_1 A_1) (tptp.bot_bot _let_1))) (exists ((X_1 $$unsorted) (B_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (and (= (tptp.ti _let_1 A_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.insert X_a) X_1) B_3)) (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) B_3))))))))) (forall ((X_a $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.option X_a))) (= (tptp.hAPP _let_1 X_a (tptp.the X_a) (tptp.hAPP X_a _let_1 (tptp.some X_a) X)) (tptp.ti X_a X)))) (forall ((X_a $$unsorted) (G_1 $$unsorted) (P_1 $$unsorted) (Pn_1 $$unsorted) (Q_1 $$unsorted)) (let ((_let_1 (tptp.hoare_1656922687triple X_a))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.bot_bot _let_2))) (let ((_let_4 (tptp.fun X_a (tptp.fun tptp.state tptp.bool)))) (let ((_let_5 (tptp.fun _let_4 _let_1))) (let ((_let_6 (tptp.hAPP _let_4 (tptp.fun tptp.com _let_5) (tptp.hoare_246368825triple X_a) P_1))) (let ((_let_7 (tptp.insert _let_1))) (let ((_let_8 (tptp.fun _let_2 _let_2))) (let ((_let_9 (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.hoare_279057269derivs X_a) G_1))) (let ((_let_10 (tptp.option tptp.com))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_9 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 _let_8 _let_7 (tptp.hAPP _let_4 _let_1 (tptp.hAPP tptp.com _let_5 _let_6 (tptp.hAPP _let_10 tptp.com (tptp.the tptp.com) (tptp.hAPP tptp.pname _let_10 tptp.body Pn_1))) Q_1)) _let_3))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_9 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 _let_8 _let_7 (tptp.hAPP _let_4 _let_1 (tptp.hAPP tptp.com _let_5 _let_6 (tptp.hAPP tptp.pname tptp.com tptp.body_1 Pn_1)) Q_1)) _let_3))))))))))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (C_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) C_1))) (=> (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_1))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_sup_sup _let_1) A_1) B))))))) (forall ((X_a $$unsorted) (C_1 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) C_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_sup_sup _let_1) A_1) B))) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_1))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B))))))) (forall ((X_a $$unsorted) (P_1 $$unsorted) (Q_1 $$unsorted)) (let ((_let_1 (tptp.collect X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (let ((_let_4 (tptp.fun tptp.bool tptp.bool))) (let ((_let_5 (tptp.fun X_a _let_4))) (= (tptp.hAPP _let_2 _let_2 _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_5 _let_3 (tptp.combs X_a tptp.bool tptp.bool) (tptp.hAPP _let_2 _let_5 (tptp.hAPP (tptp.fun tptp.bool _let_4) (tptp.fun _let_2 _let_5) (tptp.combb tptp.bool _let_4 X_a) tptp.fdisj) P_1)) Q_1)) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_3 (tptp.semilattice_sup_sup _let_2) (tptp.hAPP _let_2 _let_2 _let_1 P_1)) (tptp.hAPP _let_2 _let_2 _let_1 Q_1))))))))) (forall ((X_a $$unsorted) (Fun1_1 $$unsorted) (Com_2 $$unsorted) (Fun2_1 $$unsorted) (Fun1_2 $$unsorted) (Com_1 $$unsorted) (Fun2_2 $$unsorted)) (let ((_let_1 (tptp.hoare_246368825triple X_a))) (let ((_let_2 (tptp.hoare_1656922687triple X_a))) (let ((_let_3 (tptp.fun X_a (tptp.fun tptp.state tptp.bool)))) (let ((_let_4 (tptp.fun _let_3 _let_2))) (let ((_let_5 (tptp.fun tptp.com _let_4))) (= (= (tptp.hAPP _let_3 _let_2 (tptp.hAPP tptp.com _let_4 (tptp.hAPP _let_3 _let_5 _let_1 Fun1_1) Com_2) Fun2_1) (tptp.hAPP _let_3 _let_2 (tptp.hAPP tptp.com _let_4 (tptp.hAPP _let_3 _let_5 _let_1 Fun1_2) Com_1) Fun2_2)) (and (= Fun1_1 Fun1_2) (= Com_2 Com_1) (= Fun2_1 Fun2_2))))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (C_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) C_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_sup_sup _let_1) A_1) B))))))) (forall ((X_a $$unsorted) (B $$unsorted) (C_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) C_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_sup_sup _let_1) A_1) B))))))) (forall ((X_a $$unsorted) (P_1 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (= (forall ((X_1 $$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.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_sup_sup _let_1) A_1) B))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool P_1 X_1))))) (and (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_1) A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool P_1 X_1))))) (forall ((X_1 $$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) B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool P_1 X_1)))))))) (forall ((X_a $$unsorted) (P_1 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (= (exists ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_sup_sup _let_1) A_1) B))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool P_1 X_1))))) (or (exists ((X_1 $$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_1) A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool P_1 X_1))))) (exists ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_1) B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool P_1 X_1)))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.semilattice_sup_sup _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.hAPP _let_1 _let_3 _let_2 A_1))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 (tptp.hAPP _let_1 _let_1 _let_4 B)) C) (tptp.hAPP _let_1 _let_1 _let_4 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 B) C)))))))) (forall ((X_a $$unsorted) (C_1 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) C_1))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_sup_sup _let_1) A_1) B))) (or (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.semilattice_sup_sup _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.hAPP _let_1 _let_3 _let_2 A_1))) (let ((_let_5 (tptp.hAPP _let_1 _let_3 _let_2 B))) (= (tptp.hAPP _let_1 _let_1 _let_4 (tptp.hAPP _let_1 _let_1 _let_5 C)) (tptp.hAPP _let_1 _let_1 _let_5 (tptp.hAPP _let_1 _let_1 _let_4 C))))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_sup_sup _let_1) A_1))) (let ((_let_3 (tptp.hAPP _let_1 _let_1 _let_2 B))) (= (tptp.hAPP _let_1 _let_1 _let_2 _let_3) _let_3))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.semilattice_sup_sup _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 A_1) B) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 B) A_1)))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (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.semilattice_sup_sup _let_1) A_1) B) (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.fdisj) (tptp.hAPP _let_1 _let_1 _let_3 A_1))) (tptp.hAPP _let_1 _let_1 _let_3 B)))))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_sup_sup _let_1) A_1) A_1) (tptp.ti _let_1 A_1)))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.bot_bot _let_1))) (= (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_sup_sup _let_1) A_1) B) _let_2) (and (= (tptp.ti _let_1 A_1) _let_2) (= (tptp.ti _let_1 B) _let_2)))))) (forall ((X_a $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_sup_sup _let_1) A_1) (tptp.bot_bot _let_1)) (tptp.ti _let_1 A_1)))) (forall ((X_a $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_sup_sup _let_1) (tptp.bot_bot _let_1)) B) (tptp.ti _let_1 B)))) (forall ((X_a $$unsorted) (G_1 $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.finite_finite X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 Fa)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 G_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.semilattice_sup_sup _let_1) Fa) G_1)))))))) (forall ((X_a $$unsorted) (Fa $$unsorted) (G_1 $$unsorted)) (let ((_let_1 (tptp.finite_finite X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 (tptp.fun _let_2 _let_2) (tptp.semilattice_sup_sup _let_2) Fa) G_1))) (and (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 Fa)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 G_1))))))) (forall ((X_a $$unsorted) (A_3 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.semilattice_sup_sup _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.hAPP X_a _let_3 (tptp.insert X_a) A_3))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 (tptp.hAPP _let_1 _let_1 _let_4 B)) C) (tptp.hAPP _let_1 _let_1 _let_4 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 B) C)))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (A_3 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP _let_1 _let_2 (tptp.semilattice_sup_sup _let_1) A_1))) (let ((_let_4 (tptp.hAPP X_a _let_2 (tptp.insert X_a) A_3))) (= (tptp.hAPP _let_1 _let_1 _let_3 (tptp.hAPP _let_1 _let_1 _let_4 B)) (tptp.hAPP _let_1 _let_1 _let_4 (tptp.hAPP _let_1 _let_1 _let_3 B)))))))) (forall ((X_a $$unsorted) (B $$unsorted) (D_1 $$unsorted) (A_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.semilattice_sup_sup _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_1) C)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_5 _let_4 B) D_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_1) B)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 C) D_1))))))))))) (forall ((X_a $$unsorted) (B $$unsorted) (A_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.ord_less_eq _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 A_1) C)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 B) C)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_sup_sup _let_1) A_1) B)) C)))))))) (forall ((X_a $$unsorted) (B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) B) A_1)) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_sup_sup _let_1) A_1) B) (tptp.ti _let_1 A_1))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) A_1) B)) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_sup_sup _let_1) A_1) B) (tptp.ti _let_1 B))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) A_1) B)) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_sup_sup _let_1) A_1) B) (tptp.ti _let_1 B))))) (forall ((X_a $$unsorted) (B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) B) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_sup_sup _let_1) A_1) B))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) A_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_sup_sup _let_1) A_1) B))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.hAPP (tptp.fun X_b X_a) (tptp.fun _let_2 _let_1) (tptp.image X_b X_a) F))) (= (tptp.hAPP _let_2 _let_1 _let_3 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 (tptp.fun _let_2 _let_2) (tptp.semilattice_sup_sup _let_2) A_1) B)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_sup_sup _let_1) (tptp.hAPP _let_2 _let_1 _let_3 A_1)) (tptp.hAPP _let_2 _let_1 _let_3 B))))))) (forall ((X_a $$unsorted) (A_3 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun X_a _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_3 (tptp.insert X_a) A_3) B) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 (tptp.semilattice_sup_sup _let_1) (tptp.hAPP _let_1 _let_1 (tptp.collect X_a) (tptp.hAPP X_a _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc X_a X_a tptp.bool) (tptp.fequal X_a)) A_3))) B)))))) (forall ((X_a $$unsorted) (A_3 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP X_a _let_2 (tptp.insert X_a) A_3))) (= (tptp.hAPP _let_1 _let_1 _let_3 A_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.semilattice_sup_sup _let_1) (tptp.hAPP _let_1 _let_1 _let_3 (tptp.bot_bot _let_1))) A_1)))))) (forall ((X_a $$unsorted) (G_1 $$unsorted) (P_1 $$unsorted) (Q_1 $$unsorted) (Procs $$unsorted)) (let ((_let_1 (tptp.hoare_1656922687triple X_a))) (let ((_let_2 (tptp.fun X_a (tptp.fun tptp.state tptp.bool)))) (let ((_let_3 (tptp.fun _let_2 _let_1))) (let ((_let_4 (tptp.fun tptp.com _let_3))) (let ((_let_5 (tptp.fun tptp.pname _let_4))) (let ((_let_6 (tptp.fun tptp.pname _let_2))) (let ((_let_7 (tptp.fun tptp.pname _let_3))) (let ((_let_8 (tptp.fun tptp.pname tptp.com))) (let ((_let_9 (tptp.hAPP _let_5 (tptp.fun _let_8 _let_7) (tptp.combs tptp.pname tptp.com _let_3) (tptp.hAPP _let_6 _let_5 (tptp.hAPP (tptp.fun _let_2 _let_4) (tptp.fun _let_6 _let_5) (tptp.combb _let_2 _let_4 tptp.pname) (tptp.hoare_246368825triple X_a)) P_1)))) (let ((_let_10 (tptp.combs tptp.pname _let_2 _let_1))) (let ((_let_11 (tptp.fun tptp.pname _let_1))) (let ((_let_12 (tptp.fun _let_6 _let_11))) (let ((_let_13 (tptp.image tptp.pname _let_1))) (let ((_let_14 (tptp.fun _let_1 tptp.bool))) (let ((_let_15 (tptp.fun tptp.pname tptp.bool))) (let ((_let_16 (tptp.fun _let_15 _let_14))) (let ((_let_17 (tptp.hAPP _let_15 _let_14 (tptp.hAPP _let_11 _let_16 _let_13 (tptp.hAPP _let_6 _let_11 (tptp.hAPP _let_7 _let_12 _let_10 (tptp.hAPP _let_8 _let_7 _let_9 tptp.body_1)) Q_1)) Procs))) (let ((_let_18 (tptp.hoare_279057269derivs X_a))) (let ((_let_19 (tptp.fun _let_14 tptp.bool))) (let ((_let_20 (tptp.option tptp.com))) (let ((_let_21 (tptp.fun tptp.pname _let_20))) (=> (tptp.hBOOL (tptp.hAPP _let_14 tptp.bool (tptp.hAPP _let_14 _let_19 _let_18 (tptp.hAPP _let_14 _let_14 (tptp.hAPP _let_14 (tptp.fun _let_14 _let_14) (tptp.semilattice_sup_sup _let_14) G_1) _let_17)) (tptp.hAPP _let_15 _let_14 (tptp.hAPP _let_11 _let_16 _let_13 (tptp.hAPP _let_6 _let_11 (tptp.hAPP _let_7 _let_12 _let_10 (tptp.hAPP _let_8 _let_7 _let_9 (tptp.hAPP _let_21 _let_8 (tptp.hAPP (tptp.fun _let_20 tptp.com) (tptp.fun _let_21 _let_8) (tptp.combb _let_20 tptp.com tptp.pname) (tptp.the tptp.com)) tptp.body))) Q_1)) Procs))) (tptp.hBOOL (tptp.hAPP _let_14 tptp.bool (tptp.hAPP _let_14 _let_19 _let_18 G_1) _let_17))))))))))))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X) Y))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X)))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((Z_1 $$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 $$unsorted)) (=> (tptp.order X_a) (forall ((C_2 $$unsorted) (B_2 $$unsorted) (A_6 $$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_2) A_6)) (=> (= (tptp.ti X_a B_2) (tptp.ti X_a C_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 C_2) A_6))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ord X_a) (forall ((C_2 $$unsorted) (A_6 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) A_6))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B_2)) (=> (= B_2 C_2) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 C_2)))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((C_2 $$unsorted) (A_6 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) C_2))) (=> (= (tptp.ti X_a A_6) (tptp.ti X_a B_2)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_6)))))))) (forall ((X_a $$unsorted)) (=> (tptp.ord X_a) (forall ((C_2 $$unsorted) (A_6 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (= A_6 B_2) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B_2) C_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_6) C_2))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((Y_2 $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y_2) X_2)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X_2) Y_2)) (= (tptp.ti X_a X_2) (tptp.ti X_a Y_2))))))))) (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((X 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_let_3)))))))))))))))))))))) (forall ((X_a $$unsorted) (Pn_1 $$unsorted) (G_1 $$unsorted) (P_1 $$unsorted) (Q_1 $$unsorted) (Procs $$unsorted)) (let ((_let_1 (tptp.hoare_1656922687triple X_a))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun X_a (tptp.fun tptp.state tptp.bool)))) (let ((_let_4 (tptp.hoare_246368825triple X_a))) (let ((_let_5 (tptp.fun _let_3 _let_1))) (let ((_let_6 (tptp.fun tptp.com _let_5))) (let ((_let_7 (tptp.fun _let_2 _let_2))) (let ((_let_8 (tptp.hoare_279057269derivs X_a))) (let ((_let_9 (tptp.fun _let_2 tptp.bool))) (let ((_let_10 (tptp.fun tptp.pname tptp.bool))) (let ((_let_11 (tptp.option tptp.com))) (let ((_let_12 (tptp.fun tptp.pname tptp.com))) (let ((_let_13 (tptp.fun tptp.pname _let_11))) (let ((_let_14 (tptp.fun tptp.pname _let_6))) (let ((_let_15 (tptp.fun tptp.pname _let_3))) (let ((_let_16 (tptp.fun tptp.pname _let_5))) (let ((_let_17 (tptp.hAPP _let_14 (tptp.fun _let_12 _let_16) (tptp.combs tptp.pname tptp.com _let_5) (tptp.hAPP _let_15 _let_14 (tptp.hAPP (tptp.fun _let_3 _let_6) (tptp.fun _let_15 _let_14) (tptp.combb _let_3 _let_6 tptp.pname) _let_4) P_1)))) (let ((_let_18 (tptp.combs tptp.pname _let_3 _let_1))) (let ((_let_19 (tptp.fun tptp.pname _let_1))) (let ((_let_20 (tptp.fun _let_15 _let_19))) (let ((_let_21 (tptp.image tptp.pname _let_1))) (let ((_let_22 (tptp.fun _let_10 _let_2))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 _let_9 _let_8 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_7 (tptp.semilattice_sup_sup _let_2) G_1) (tptp.hAPP _let_10 _let_2 (tptp.hAPP _let_19 _let_22 _let_21 (tptp.hAPP _let_15 _let_19 (tptp.hAPP _let_16 _let_20 _let_18 (tptp.hAPP _let_12 _let_16 _let_17 tptp.body_1)) Q_1)) Procs))) (tptp.hAPP _let_10 _let_2 (tptp.hAPP _let_19 _let_22 _let_21 (tptp.hAPP _let_15 _let_19 (tptp.hAPP _let_16 _let_20 _let_18 (tptp.hAPP _let_12 _let_16 _let_17 (tptp.hAPP _let_13 _let_12 (tptp.hAPP (tptp.fun _let_11 tptp.com) (tptp.fun _let_13 _let_12) (tptp.combb _let_11 tptp.com tptp.pname) (tptp.the tptp.com)) tptp.body))) Q_1)) Procs))) (=> (tptp.hBOOL (tptp.hAPP _let_10 tptp.bool (tptp.hAPP tptp.pname (tptp.fun _let_10 tptp.bool) (tptp.member tptp.pname) Pn_1) Procs)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 _let_9 _let_8 G_1) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 _let_7 (tptp.insert _let_1) (tptp.hAPP _let_3 _let_1 (tptp.hAPP tptp.com _let_5 (tptp.hAPP _let_3 _let_6 _let_4 (tptp.hAPP tptp.pname _let_3 P_1 Pn_1)) (tptp.hAPP tptp.pname tptp.com tptp.body_1 Pn_1)) (tptp.hAPP tptp.pname _let_3 Q_1 Pn_1))) (tptp.bot_bot _let_2))))))))))))))))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.bot X_a) (forall ((A_6 $$unsorted)) (let ((_let_1 (tptp.bot_bot 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) A_6) _let_1)) (= (tptp.ti X_a A_6) _let_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.bot X_a) (forall ((A_3 $$unsorted)) (let ((_let_1 (tptp.bot_bot X_a))) (= 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(tptp.bot_bot X_b))))) (forall ((X_a $$unsorted) (P_1 $$unsorted) (Pn_1 $$unsorted) (Q_1 $$unsorted) (G_1 $$unsorted)) (let ((_let_1 (tptp.hoare_1656922687triple X_a))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.bot_bot _let_2))) (let ((_let_4 (tptp.fun X_a (tptp.fun tptp.state tptp.bool)))) (let ((_let_5 (tptp.fun _let_4 _let_1))) (let ((_let_6 (tptp.hAPP _let_4 (tptp.fun tptp.com _let_5) (tptp.hoare_246368825triple X_a) P_1))) (let ((_let_7 (tptp.insert _let_1))) (let ((_let_8 (tptp.fun _let_2 _let_2))) (let ((_let_9 (tptp.hAPP _let_1 _let_8 _let_7 (tptp.hAPP _let_4 _let_1 (tptp.hAPP tptp.com _let_5 _let_6 (tptp.hAPP tptp.pname tptp.com tptp.body_1 Pn_1)) Q_1)))) (let ((_let_10 (tptp.hoare_279057269derivs X_a))) (let ((_let_11 (tptp.fun _let_2 tptp.bool))) (let ((_let_12 (tptp.option tptp.com))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 _let_11 _let_10 (tptp.hAPP _let_2 _let_2 _let_9 G_1)) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 _let_8 _let_7 (tptp.hAPP _let_4 _let_1 (tptp.hAPP tptp.com _let_5 _let_6 (tptp.hAPP _let_12 tptp.com (tptp.the tptp.com) (tptp.hAPP tptp.pname _let_12 tptp.body Pn_1))) Q_1)) _let_3))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 _let_11 _let_10 G_1) (tptp.hAPP _let_2 _let_2 _let_9 _let_3))))))))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (P_1 $$unsorted) (Q_1 $$unsorted) (G_1 $$unsorted) (P_2 $$unsorted) (C0_1 $$unsorted) (Q_2 $$unsorted) (U_1 $$unsorted)) (let ((_let_1 (tptp.hoare_1656922687triple X_b))) (let ((_let_2 (tptp.fun X_b (tptp.fun tptp.state tptp.bool)))) (let ((_let_3 (tptp.fun _let_2 _let_1))) (let ((_let_4 (tptp.fun tptp.com _let_3))) (let ((_let_5 (tptp.fun X_a _let_4))) (let ((_let_6 (tptp.fun X_a _let_2))) (let ((_let_7 (tptp.hAPP (tptp.fun _let_2 _let_4) (tptp.fun _let_6 _let_5) (tptp.combb _let_2 _let_4 X_a) (tptp.hoare_246368825triple X_b)))) (let ((_let_8 (tptp.combs X_a tptp.com _let_3))) (let ((_let_9 (tptp.fun X_a _let_3))) (let ((_let_10 (tptp.fun X_a tptp.com))) (let ((_let_11 (tptp.fun _let_10 _let_9))) (let ((_let_12 (tptp.combs X_a _let_2 _let_1))) (let ((_let_13 (tptp.fun X_a _let_1))) (let ((_let_14 (tptp.fun _let_6 _let_13))) (let ((_let_15 (tptp.image X_a _let_1))) (let ((_let_16 (tptp.fun _let_1 tptp.bool))) (let ((_let_17 (tptp.fun X_a tptp.bool))) (let ((_let_18 (tptp.fun _let_17 _let_16))) (let ((_let_19 (tptp.hAPP _let_16 (tptp.fun _let_16 tptp.bool) (tptp.hoare_279057269derivs X_b) G_1))) (=> (tptp.hBOOL (tptp.hAPP _let_17 tptp.bool (tptp.finite_finite X_a) U_1)) (=> (forall ((P_3 $$unsorted)) (let ((_let_1 (tptp.hoare_1656922687triple X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.bot_bot _let_2))) (let ((_let_4 (tptp.fun X_b (tptp.fun tptp.state tptp.bool)))) (let ((_let_5 (tptp.hAPP X_a tptp.com C0_1 P_3))) (let ((_let_6 (tptp.hoare_246368825triple X_b))) (let ((_let_7 (tptp.fun _let_4 _let_1))) (let ((_let_8 (tptp.fun tptp.com _let_7))) (let ((_let_9 (tptp.insert _let_1))) (let ((_let_10 (tptp.fun _let_2 _let_2))) (let ((_let_11 (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.hoare_279057269derivs X_b) G_1))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_11 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 _let_10 _let_9 (tptp.hAPP _let_4 _let_1 (tptp.hAPP tptp.com _let_7 (tptp.hAPP _let_4 _let_8 _let_6 (tptp.hAPP X_a _let_4 P_2 P_3)) _let_5) (tptp.hAPP X_a _let_4 Q_2 P_3))) _let_3))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_11 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 _let_10 _let_9 (tptp.hAPP _let_4 _let_1 (tptp.hAPP tptp.com _let_7 (tptp.hAPP _let_4 _let_8 _let_6 (tptp.hAPP X_a _let_4 P_1 P_3)) _let_5) (tptp.hAPP X_a _let_4 Q_1 P_3))) _let_3)))))))))))))))) (=> (tptp.hBOOL (tptp.hAPP _let_16 tptp.bool _let_19 (tptp.hAPP _let_17 _let_16 (tptp.hAPP _let_13 _let_18 _let_15 (tptp.hAPP _let_6 _let_13 (tptp.hAPP _let_9 _let_14 _let_12 (tptp.hAPP _let_10 _let_9 (tptp.hAPP _let_5 _let_11 _let_8 (tptp.hAPP _let_6 _let_5 _let_7 P_2)) C0_1)) Q_2)) U_1))) (tptp.hBOOL (tptp.hAPP _let_16 tptp.bool _let_19 (tptp.hAPP _let_17 _let_16 (tptp.hAPP _let_13 _let_18 _let_15 (tptp.hAPP _let_6 _let_13 (tptp.hAPP _let_9 _let_14 _let_12 (tptp.hAPP _let_10 _let_9 (tptp.hAPP _let_5 _let_11 _let_8 (tptp.hAPP _let_6 _let_5 _let_7 P_1)) C0_1)) Q_1)) U_1)))))))))))))))))))))))))) (forall ((X_a $$unsorted) (G_1 $$unsorted) (C_1 $$unsorted) (Q_1 $$unsorted) (P_1 $$unsorted)) (let ((_let_1 (tptp.hoare_1656922687triple X_a))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun X_a (tptp.fun tptp.state tptp.bool)))) (let ((_let_4 (tptp.fun _let_3 _let_1))) (=> (forall ((Z_3 $$unsorted) (S_3 $$unsorted)) (let ((_let_1 (tptp.hoare_1656922687triple X_a))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun tptp.state tptp.bool))) (let ((_let_4 (tptp.combk _let_3 X_a))) (let ((_let_5 (tptp.fun X_a _let_3))) (let ((_let_6 (tptp.fun tptp.state _let_3))) (let ((_let_7 (tptp.fun _let_5 _let_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP X_a _let_3 P_1 Z_3) S_3)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.hoare_279057269derivs X_a) G_1) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 (tptp.fun _let_2 _let_2) (tptp.insert _let_1) (tptp.hAPP _let_5 _let_1 (tptp.hAPP tptp.com _let_7 (tptp.hAPP _let_5 (tptp.fun tptp.com _let_7) (tptp.hoare_246368825triple X_a) (tptp.hAPP _let_3 _let_5 _let_4 (tptp.hAPP tptp.state _let_3 (tptp.hAPP _let_6 _let_6 (tptp.combc tptp.state tptp.state tptp.bool) (tptp.fequal tptp.state)) S_3))) C_1) (tptp.hAPP _let_3 _let_5 _let_4 (tptp.hAPP X_a _let_3 Q_1 Z_3)))) (tptp.bot_bot _let_2))))))))))))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.hoare_279057269derivs X_a) G_1) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 (tptp.fun _let_2 _let_2) (tptp.insert _let_1) (tptp.hAPP _let_3 _let_1 (tptp.hAPP tptp.com _let_4 (tptp.hAPP _let_3 (tptp.fun tptp.com _let_4) (tptp.hoare_246368825triple X_a) P_1) C_1) Q_1)) (tptp.bot_bot _let_2)))))))))) (forall ((X_a $$unsorted) (G_1 $$unsorted) (P_1 $$unsorted) (Q_1 $$unsorted) (Procs $$unsorted)) (let ((_let_1 (tptp.hoare_1656922687triple X_a))) (let ((_let_2 (tptp.fun X_a (tptp.fun tptp.state tptp.bool)))) (let ((_let_3 (tptp.fun _let_2 _let_1))) (let ((_let_4 (tptp.fun tptp.com _let_3))) (let ((_let_5 (tptp.fun tptp.pname _let_4))) (let ((_let_6 (tptp.fun tptp.pname _let_2))) (let ((_let_7 (tptp.fun tptp.pname _let_3))) (let ((_let_8 (tptp.fun tptp.pname tptp.com))) (let ((_let_9 (tptp.hAPP _let_5 (tptp.fun _let_8 _let_7) (tptp.combs tptp.pname tptp.com _let_3) (tptp.hAPP _let_6 _let_5 (tptp.hAPP (tptp.fun _let_2 _let_4) (tptp.fun _let_6 _let_5) (tptp.combb _let_2 _let_4 tptp.pname) (tptp.hoare_246368825triple X_a)) P_1)))) (let ((_let_10 (tptp.combs tptp.pname _let_2 _let_1))) (let ((_let_11 (tptp.fun tptp.pname _let_1))) (let ((_let_12 (tptp.fun _let_6 _let_11))) (let ((_let_13 (tptp.image tptp.pname _let_1))) (let ((_let_14 (tptp.fun _let_1 tptp.bool))) (let ((_let_15 (tptp.fun tptp.pname tptp.bool))) (let ((_let_16 (tptp.fun _let_15 _let_14))) (let ((_let_17 (tptp.hAPP _let_15 _let_14 (tptp.hAPP _let_11 _let_16 _let_13 (tptp.hAPP _let_6 _let_11 (tptp.hAPP _let_7 _let_12 _let_10 (tptp.hAPP _let_8 _let_7 _let_9 tptp.body_1)) Q_1)) Procs))) (let ((_let_18 (tptp.hoare_2027193591valids X_a))) (let ((_let_19 (tptp.fun _let_14 tptp.bool))) (let ((_let_20 (tptp.option tptp.com))) (let ((_let_21 (tptp.fun tptp.pname _let_20))) (=> (tptp.hBOOL (tptp.hAPP _let_14 tptp.bool (tptp.hAPP _let_14 _let_19 _let_18 (tptp.hAPP _let_14 _let_14 (tptp.hAPP _let_14 (tptp.fun _let_14 _let_14) (tptp.semilattice_sup_sup _let_14) G_1) _let_17)) (tptp.hAPP _let_15 _let_14 (tptp.hAPP _let_11 _let_16 _let_13 (tptp.hAPP _let_6 _let_11 (tptp.hAPP _let_7 _let_12 _let_10 (tptp.hAPP _let_8 _let_7 _let_9 (tptp.hAPP _let_21 _let_8 (tptp.hAPP (tptp.fun _let_20 tptp.com) (tptp.fun _let_21 _let_8) (tptp.combb _let_20 tptp.com tptp.pname) (tptp.the tptp.com)) tptp.body))) Q_1)) Procs))) (tptp.hBOOL (tptp.hAPP _let_14 tptp.bool (tptp.hAPP _let_14 _let_19 _let_18 G_1) _let_17))))))))))))))))))))))))) (forall ((X_a $$unsorted) (P_1 $$unsorted) (G_1 $$unsorted) (P_2 $$unsorted) (C_1 $$unsorted) (Q_1 $$unsorted)) (let ((_let_1 (tptp.hoare_1656922687triple X_a))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.bot_bot _let_2))) (let ((_let_4 (tptp.hoare_246368825triple X_a))) (let ((_let_5 (tptp.fun X_a (tptp.fun tptp.state tptp.bool)))) (let ((_let_6 (tptp.fun _let_5 _let_1))) (let ((_let_7 (tptp.fun tptp.com _let_6))) (let ((_let_8 (tptp.insert _let_1))) (let ((_let_9 (tptp.fun _let_2 _let_2))) (let ((_let_10 (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.hoare_279057269derivs X_a) G_1))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_10 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 _let_9 _let_8 (tptp.hAPP _let_5 _let_1 (tptp.hAPP tptp.com _let_6 (tptp.hAPP _let_5 _let_7 _let_4 P_2) C_1) Q_1)) _let_3))) (=> (forall ((Z_3 $$unsorted) (S_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.state tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP X_a _let_1 P_1 Z_3) S_3)) (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP X_a _let_1 P_2 Z_3) S_3))))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_10 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 _let_9 _let_8 (tptp.hAPP _let_5 _let_1 (tptp.hAPP tptp.com _let_6 (tptp.hAPP _let_5 _let_7 _let_4 P_1) C_1) Q_1)) _let_3)))))))))))))))) (forall ((X_a $$unsorted) (Q_1 $$unsorted) (G_1 $$unsorted) (P_1 $$unsorted) (C_1 $$unsorted) (Q_2 $$unsorted)) (let ((_let_1 (tptp.hoare_1656922687triple X_a))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.bot_bot _let_2))) (let ((_let_4 (tptp.fun X_a (tptp.fun tptp.state tptp.bool)))) (let ((_let_5 (tptp.fun _let_4 _let_1))) (let ((_let_6 (tptp.hAPP tptp.com _let_5 (tptp.hAPP _let_4 (tptp.fun tptp.com _let_5) (tptp.hoare_246368825triple X_a) P_1) C_1))) (let ((_let_7 (tptp.insert _let_1))) (let ((_let_8 (tptp.fun _let_2 _let_2))) (let ((_let_9 (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.hoare_279057269derivs X_a) G_1))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_9 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 _let_8 _let_7 (tptp.hAPP _let_4 _let_1 _let_6 Q_2)) _let_3))) (=> (forall ((Z_3 $$unsorted) (S_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.state tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP X_a _let_1 Q_2 Z_3) S_3)) (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP X_a _let_1 Q_1 Z_3) S_3))))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_9 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 _let_8 _let_7 (tptp.hAPP _let_4 _let_1 _let_6 Q_1)) _let_3))))))))))))))) (forall ((P_1 $$unsorted) (Q_1 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.hoare_1656922687triple tptp.state))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.bot_bot _let_2))) (let ((_let_4 (tptp.fun tptp.state (tptp.fun tptp.state tptp.bool)))) (let ((_let_5 (tptp.fun _let_4 _let_1))) (let ((_let_6 (tptp.insert _let_1))) (let ((_let_7 (tptp.fun _let_2 _let_2))) (let ((_let_8 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 _let_7 _let_6 (tptp.hAPP _let_4 _let_1 (tptp.hAPP tptp.com _let_5 (tptp.hAPP _let_4 (tptp.fun tptp.com _let_5) (tptp.hoare_246368825triple tptp.state) P_1) C_1) Q_1)) _let_3))) (let ((_let_9 (tptp.fun _let_2 tptp.bool))) (let ((_let_10 (tptp.hAPP _let_2 _let_9 (tptp.hoare_279057269derivs tptp.state) _let_3))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_10 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 _let_7 _let_6 (tptp.hAPP tptp.com _let_1 tptp.hoare_Mirabelle_MGT C_1)) _let_3))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 _let_9 (tptp.hoare_2027193591valids tptp.state) _let_3) _let_8)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_10 _let_8))))))))))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_sup_sup _let_1) A_1) B) X_2)) (=> (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool A_1 X_2))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool B X_2)))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (=> (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool B X_2))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool A_1 X_2))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_sup_sup _let_1) A_1) B) X_2))))) (forall ((X_a $$unsorted) (G_1 $$unsorted) (Ts $$unsorted)) (let ((_let_1 (tptp.fun (tptp.hoare_1656922687triple X_a) tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.hoare_279057269derivs X_a) G_1) Ts)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.hoare_2027193591valids X_a) G_1) Ts)))))) (forall ((X_a $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.bot_bot _let_1))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_2 X_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_1) _let_2)))))) (forall ((X_a $$unsorted) (Q_1 $$unsorted) (P_1 $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool P_1 X_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) P_1) Q_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool Q_1 X_2)))))) (forall ((X_a $$unsorted) (X_2 $$unsorted) (P_1 $$unsorted) (Q_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) P_1) Q_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool P_1 X_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool Q_1 X_2)))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool B X_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_sup_sup _let_1) A_1) B) X_2))))) (forall ((X_a $$unsorted) (B $$unsorted) (A_1 $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool A_1 X_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_sup_sup _let_1) A_1) B) X_2))))) (forall ((X_a $$unsorted) (R_1 $$unsorted) (S $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.ord_less_eq _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.hAPP (tptp.fun X_a _let_3) (tptp.fun _let_1 _let_1) (tptp.combc X_a _let_1 tptp.bool) (tptp.member X_a)))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 (tptp.hAPP _let_1 _let_1 _let_4 R_1)) (tptp.hAPP _let_1 _let_1 _let_4 S))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 R_1) S)))))))) (forall ((X_a $$unsorted) (R_1 $$unsorted) (S $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.semilattice_sup_sup _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.member X_a))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.hAPP (tptp.fun X_a _let_5) _let_3 (tptp.combc X_a _let_1 tptp.bool) _let_4))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 (tptp.hAPP _let_1 _let_1 _let_6 R_1)) (tptp.hAPP _let_1 _let_1 _let_6 S)) X_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a _let_5 _let_4 X_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 R_1) S))))))))))) (forall ((X_a $$unsorted) (Q_1 $$unsorted) (P_1 $$unsorted) (G_1 $$unsorted) (P_2 $$unsorted) (C_1 $$unsorted) (Q_2 $$unsorted)) (let ((_let_1 (tptp.hoare_1656922687triple X_a))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.bot_bot _let_2))) (let ((_let_4 (tptp.hoare_246368825triple X_a))) (let ((_let_5 (tptp.fun X_a (tptp.fun tptp.state tptp.bool)))) (let ((_let_6 (tptp.fun _let_5 _let_1))) (let ((_let_7 (tptp.fun tptp.com _let_6))) (let ((_let_8 (tptp.insert _let_1))) (let ((_let_9 (tptp.fun _let_2 _let_2))) (let ((_let_10 (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.hoare_279057269derivs X_a) G_1))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_10 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 _let_9 _let_8 (tptp.hAPP _let_5 _let_1 (tptp.hAPP tptp.com _let_6 (tptp.hAPP _let_5 _let_7 _let_4 P_2) C_1) Q_2)) _let_3))) (=> (forall ((Z_3 $$unsorted) (S_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP X_a (tptp.fun tptp.state tptp.bool) P_1 Z_3) S_3)) (forall ((S_4 $$unsorted)) (=> (forall ((Z_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.state tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP X_a _let_1 P_2 Z_4) S_3)) (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP X_a _let_1 Q_2 Z_4) S_4))))) (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP X_a (tptp.fun tptp.state tptp.bool) Q_1 Z_3) S_4)))))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_10 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 _let_9 _let_8 (tptp.hAPP _let_5 _let_1 (tptp.hAPP tptp.com _let_6 (tptp.hAPP _let_5 _let_7 _let_4 P_1) C_1) Q_1)) _let_3)))))))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.ord X_b) (forall ((F $$unsorted) (G $$unsorted)) (let ((_let_1 (tptp.fun X_a X_b))) (=> (forall ((X_1 $$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_1)) (tptp.hAPP X_a X_b G 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) F) G))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F1 $$unsorted) (Fun1_1 $$unsorted) (Com_2 $$unsorted) (Fun2_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b (tptp.fun tptp.state tptp.bool)))) (let ((_let_2 (tptp.fun _let_1 X_a))) (let ((_let_3 (tptp.fun tptp.com _let_2))) (let ((_let_4 (tptp.hoare_1656922687triple X_b))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (= (tptp.hAPP _let_4 X_a (tptp.hAPP (tptp.fun _let_1 _let_3) (tptp.fun _let_4 X_a) (tptp.hoare_1312322281e_case X_b X_a) F1) (tptp.hAPP _let_1 _let_4 (tptp.hAPP tptp.com _let_5 (tptp.hAPP _let_1 (tptp.fun tptp.com _let_5) (tptp.hoare_246368825triple X_b) Fun1_1) Com_2) Fun2_1)) (tptp.hAPP _let_1 X_a (tptp.hAPP tptp.com _let_2 (tptp.hAPP _let_1 _let_3 F1 Fun1_1) Com_2) Fun2_1)))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F1 $$unsorted) (Fun1_1 $$unsorted) (Com_2 $$unsorted) (Fun2_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b (tptp.fun tptp.state tptp.bool)))) (let ((_let_2 (tptp.fun _let_1 X_a))) (let ((_let_3 (tptp.fun tptp.com _let_2))) (let ((_let_4 (tptp.hoare_1656922687triple X_b))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (= (tptp.hAPP _let_4 X_a (tptp.hAPP (tptp.fun _let_1 _let_3) (tptp.fun _let_4 X_a) (tptp.hoare_1632998903le_rec X_b X_a) F1) (tptp.hAPP _let_1 _let_4 (tptp.hAPP tptp.com _let_5 (tptp.hAPP _let_1 (tptp.fun tptp.com _let_5) (tptp.hoare_246368825triple X_b) Fun1_1) Com_2) Fun2_1)) (tptp.hAPP _let_1 X_a (tptp.hAPP tptp.com _let_2 (tptp.hAPP _let_1 _let_3 F1 Fun1_1) Com_2) Fun2_1)))))))) (forall ((X_a $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.option X_a))) (= (tptp.hAPP _let_2 _let_1 (tptp.set X_a) (tptp.hAPP X_a _let_2 (tptp.some X_a) X_2)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.insert X_a) X_2) (tptp.bot_bot _let_1)))))) (forall ((X_a $$unsorted) (X_2 $$unsorted) (Xo $$unsorted)) (let ((_let_1 (tptp.option X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a (tptp.fun _let_2 tptp.bool) (tptp.member X_a) X_2) (tptp.hAPP _let_1 _let_2 (tptp.set X_a) Xo))) (= (tptp.ti _let_1 Xo) (tptp.hAPP X_a _let_1 (tptp.some X_a) X_2)))))) (forall ((X_a $$unsorted) (X_2 $$unsorted) (P_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.option X_a))) (=> (forall ((X_1 $$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.hAPP (tptp.option X_a) _let_1 (tptp.set X_a) A_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool P_1 X_1))))) (=> (= (tptp.ti _let_1 A_1) (tptp.hAPP X_a _let_1 (tptp.some X_a) X_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool P_1 X_2)))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.lattice X_b) (forall ((F $$unsorted) (G $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_b))) (= (tptp.hAPP X_a X_b (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_sup_sup _let_1) F) G) X_1) (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.semilattice_sup_sup X_b) (tptp.hAPP X_a X_b F X_1)) (tptp.hAPP X_a X_b G X_1))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (tptp.lattice X_a) (forall ((F $$unsorted) (G $$unsorted) (X_2 $$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.semilattice_sup_sup _let_1) F) G) X_2) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.semilattice_sup_sup X_a) (tptp.hAPP X_b X_a F X_2)) (tptp.hAPP X_b X_a G X_2))))))) (=> _let_25 (forall ((T_5 $$unsorted)) (not (forall ((S_3 $$unsorted)) (= S_3 T_5))))) (= _let_25 (exists ((S_3 $$unsorted) (T_5 $$unsorted)) (not (= S_3 T_5)))) (forall ((X_a $$unsorted)) (=> (tptp.semilattice_sup X_a) (forall ((X $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.semilattice_sup_sup 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 $$unsorted)) (=> (tptp.lattice X_a) (forall ((X $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.semilattice_sup_sup 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 $$unsorted)) (=> (tptp.semilattice_sup X_a) (forall ((A_6 $$unsorted) (B_2 $$unsorted) (C_2 $$unsorted)) (let ((_let_1 (tptp.semilattice_sup_sup X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 A_6))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 B_2)) C_2) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B_2) C_2))))))))) (forall ((X_a $$unsorted)) (=> (tptp.semilattice_sup X_a) (forall ((X $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.semilattice_sup_sup 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 $$unsorted)) (=> (tptp.lattice X_a) (forall ((X $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.semilattice_sup_sup 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 $$unsorted)) (=> (tptp.semilattice_sup X_a) (forall ((B_2 $$unsorted) (A_6 $$unsorted) (C_2 $$unsorted)) (let ((_let_1 (tptp.semilattice_sup_sup X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 B_2))) (let ((_let_4 (tptp.hAPP X_a _let_2 _let_1 A_6))) (= (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a _let_4 C_2)) (tptp.hAPP X_a X_a _let_4 (tptp.hAPP X_a X_a _let_3 C_2)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.semilattice_sup X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.semilattice_sup_sup X_a) X))) (let ((_let_2 (tptp.hAPP X_a X_a _let_1 Y))) (= (tptp.hAPP X_a X_a _let_1 _let_2) _let_2)))))) (forall ((X_a $$unsorted)) (=> (tptp.lattice X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.semilattice_sup_sup 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 $$unsorted)) (=> (tptp.semilattice_sup X_a) (forall ((A_6 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.semilattice_sup_sup X_a) A_6))) (let ((_let_2 (tptp.hAPP X_a X_a _let_1 B_2))) (= (tptp.hAPP X_a X_a _let_1 _let_2) _let_2)))))) (forall ((X_a $$unsorted)) (=> (tptp.semilattice_sup X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.semilattice_sup_sup 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 $$unsorted)) (=> (tptp.lattice X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.semilattice_sup_sup X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 X) Y) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Y) X))))))) (forall ((X_a $$unsorted)) (=> (tptp.semilattice_sup X_a) (forall ((A_6 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.semilattice_sup_sup 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_6) B_2) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B_2) A_6))))))) (forall ((X_a $$unsorted)) (=> (tptp.semilattice_sup X_a) (forall ((X $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.semilattice_sup_sup X_a) X) X) (tptp.ti X_a X))))) (forall ((X_a $$unsorted)) (=> (tptp.semilattice_sup X_a) (forall ((A_6 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.semilattice_sup_sup X_a) A_6) A_6) (tptp.ti X_a A_6))))) (forall ((X_a $$unsorted)) (=> (tptp.semilattice_sup X_a) (forall ((A_6 $$unsorted) (B_2 $$unsorted) (X $$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 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.semilattice_sup_sup X_a) A_6) B_2)) X)) (not (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_6) X)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B_2) X))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.semilattice_sup X_a) (forall ((B_2 $$unsorted) (D_2 $$unsorted) (A_6 $$unsorted) (C_2 $$unsorted)) (let ((_let_1 (tptp.semilattice_sup_sup X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less_eq X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 A_6) C_2)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 B_2) D_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_6) B_2)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 C_2) D_2)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.semilattice_sup X_a) (forall ((Z_1 $$unsorted) (Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Z_1) X)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.semilattice_sup_sup X_a) Y) Z_1)) X))))))))) (forall ((X_a $$unsorted)) (=> (tptp.semilattice_sup X_a) (forall ((B_2 $$unsorted) (A_6 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_6) X)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B_2) X)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.semilattice_sup_sup X_a) A_6) B_2)) X))))))))) (forall ((X_a $$unsorted)) (=> (tptp.semilattice_sup 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.semilattice_sup_sup X_a) X) Y) (tptp.ti X_a X)))))) (forall ((X_a $$unsorted)) (=> (tptp.semilattice_sup X_a) (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X) Y)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.semilattice_sup_sup X_a) X) Y) (tptp.ti X_a Y)))))) (forall ((X_a $$unsorted)) (=> (tptp.semilattice_sup X_a) (forall ((A_6 $$unsorted) (X $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.semilattice_sup_sup X_a) A_6) B_2)))))))) (forall ((X_a $$unsorted)) (=> (tptp.semilattice_sup X_a) (forall ((B_2 $$unsorted) (X $$unsorted) (A_6 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_6)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.semilattice_sup_sup X_a) A_6) B_2)))))))) (forall ((X_a $$unsorted)) (=> (tptp.semilattice_sup X_a) (forall ((X_2 $$unsorted) (Y_2 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.semilattice_sup_sup X_a) X_2) Y_2)) Z)) (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X_2) Z)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y_2) Z))))))))) (forall ((X_a $$unsorted)) (=> (tptp.semilattice_sup X_a) (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.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.semilattice_sup_sup X_a) X_2) Y_2) (tptp.ti X_a Y_2)))))) (forall ((X_a $$unsorted)) (=> (tptp.semilattice_sup X_a) (forall ((Y $$unsorted) (X $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) Y) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.semilattice_sup_sup X_a) X) Y)))))) (forall ((X_a $$unsorted)) (=> (tptp.lattice 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) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.semilattice_sup_sup X_a) X) Y)))))) (forall ((X_a $$unsorted)) (=> (tptp.semilattice_sup X_a) (forall ((X $$unsorted) (Y $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.semilattice_sup_sup X_a) X) Y)))))) (forall ((X_a $$unsorted)) (=> (tptp.lattice 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) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.semilattice_sup_sup X_a) X) Y)))))) (forall ((X_a $$unsorted)) (=> (tptp.bounded_lattice_bot X_a) (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.bot_bot X_a))) (= (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.semilattice_sup_sup X_a) X_2) Y_2) _let_1) (and (= (tptp.ti X_a X_2) _let_1) (= (tptp.ti X_a Y_2) _let_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.bounded_lattice_bot X_a) (forall ((X $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.semilattice_sup_sup X_a) X) (tptp.bot_bot X_a)) (tptp.ti X_a X))))) (forall ((X_a $$unsorted)) (=> (tptp.bounded_lattice_bot X_a) (forall ((X $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.semilattice_sup_sup X_a) (tptp.bot_bot X_a)) X) (tptp.ti X_a X))))) (forall ((X_a $$unsorted) (B $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.bot_bot _let_1))) (let ((_let_4 (tptp.finite_finite X_a))) (let ((_let_5 (tptp.fun _let_1 X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP (tptp.fun X_a _let_2) (tptp.fun _let_5 tptp.bool) (tptp.finite2073411215e_idem X_a) F) Fa)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_4 A_1)) (=> (not (= (tptp.ti _let_1 A_1) _let_3)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_4 B)) (=> (not (= (tptp.ti _let_1 B) _let_3)) (= (tptp.hAPP _let_1 X_a Fa (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_sup_sup _let_1) A_1) B)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 F (tptp.hAPP _let_1 X_a Fa A_1)) (tptp.hAPP _let_1 X_a Fa B)))))))))))))) (forall ((X_a $$unsorted) (B $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP _let_1 X_a Fa A_1))) (let ((_let_3 (tptp.fun X_a X_a))) (let ((_let_4 (tptp.fun _let_1 X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP (tptp.fun X_a _let_3) (tptp.fun _let_4 tptp.bool) (tptp.finite2073411215e_idem X_a) F) Fa)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_a) A_1)) (=> (not (= (tptp.ti _let_1 B) (tptp.bot_bot _let_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) B) A_1)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 F (tptp.hAPP _let_1 X_a Fa B)) _let_2) _let_2)))))))))) (forall ((X_a $$unsorted) (G_1 $$unsorted) (P_1 $$unsorted)) (let ((_let_1 (tptp.hoare_1656922687triple X_a))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun X_a (tptp.fun tptp.state tptp.bool)))) (let ((_let_4 (tptp.fun _let_3 _let_1))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.hoare_279057269derivs X_a) G_1) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 (tptp.fun _let_2 _let_2) (tptp.insert _let_1) (tptp.hAPP _let_3 _let_1 (tptp.hAPP tptp.com _let_4 (tptp.hAPP _let_3 (tptp.fun tptp.com _let_4) (tptp.hoare_246368825triple X_a) P_1) tptp.skip) P_1)) (tptp.bot_bot _let_2))))))))) (forall ((X_a $$unsorted) (X_2 $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.fun _let_1 X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP (tptp.fun X_a _let_2) (tptp.fun _let_3 tptp.bool) (tptp.finite2073411215e_idem X_a) F) Fa)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_a) A_1)) (=> (not (= (tptp.ti _let_1 A_1) (tptp.bot_bot _let_1))) (= (tptp.hAPP _let_1 X_a Fa (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.insert X_a) X_2) A_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 F X_2) (tptp.hAPP _let_1 X_a Fa A_1)))))))))) (forall ((X_a $$unsorted) (P_1 $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_a) Fa)) (=> (not (= (tptp.ti _let_1 Fa) (tptp.bot_bot _let_1))) (=> (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool P_1 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.insert X_a) X_1) (tptp.bot_bot _let_1)))))) (=> (forall ((X_1 $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_a) F_1)) (=> (not (= (tptp.ti _let_1 F_1) (tptp.bot_bot _let_1))) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_1) F_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool P_1 F_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool P_1 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.insert X_a) X_1) F_1))))))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool P_1 Fa)))))))) (forall ((X_a $$unsorted) (X_2 $$unsorted) (F $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.fun (tptp.fun X_a tptp.bool) X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP (tptp.fun X_a _let_1) (tptp.fun _let_2 tptp.bool) (tptp.finite2073411215e_idem X_a) F) Fa)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 F X_2) X_2) (tptp.ti X_a X_2)))))) (forall ((Pname $$unsorted)) (not (= (tptp.hAPP tptp.pname tptp.com tptp.body_1 Pname) tptp.skip))) (forall ((Pname $$unsorted)) (not (= tptp.skip (tptp.hAPP tptp.pname tptp.com tptp.body_1 Pname)))) (tptp.hBOOL (tptp.hAPP tptp.com tptp.bool tptp.wt tptp.skip)) (forall ((X_a $$unsorted) (X_2 $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP _let_1 X_a Fa A_1))) (let ((_let_3 (tptp.fun X_a X_a))) (let ((_let_4 (tptp.fun _let_1 X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP (tptp.fun X_a _let_3) (tptp.fun _let_4 tptp.bool) (tptp.finite2073411215e_idem X_a) F) Fa)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_a) A_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) A_1)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 F X_2) _let_2) _let_2))))))))) (forall ((X_a $$unsorted) (N_1 $$unsorted) (H $$unsorted) (F $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.fun _let_1 X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP (tptp.fun X_a _let_2) (tptp.fun _let_3 tptp.bool) (tptp.finite2073411215e_idem X_a) F) Fa)) (=> (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a H (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 F X_1) Y_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 F (tptp.hAPP X_a X_a H X_1)) (tptp.hAPP X_a X_a H Y_1))))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_a) N_1)) (=> (not (= (tptp.ti _let_1 N_1) (tptp.bot_bot _let_1))) (= (tptp.hAPP X_a X_a H (tptp.hAPP _let_1 X_a Fa N_1)) (tptp.hAPP _let_1 X_a Fa (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_2 (tptp.fun _let_1 _let_1) (tptp.image X_a X_a) H) N_1))))))))))) (forall ((X_a $$unsorted) (G_1 $$unsorted) (P_1 $$unsorted) (B_1 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.hoare_1656922687triple X_a))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun tptp.state tptp.bool))) (let ((_let_4 (tptp.fun _let_3 _let_3))) (let ((_let_5 (tptp.fun tptp.bool tptp.bool))) (let ((_let_6 (tptp.fun tptp.state _let_5))) (let ((_let_7 (tptp.fun _let_3 _let_6))) (let ((_let_8 (tptp.fun X_a _let_6))) (let ((_let_9 (tptp.fun X_a _let_3))) (let ((_let_10 (tptp.fun X_a _let_4))) (let ((_let_11 (tptp.fun _let_9 _let_1))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.hoare_279057269derivs X_a) G_1) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 (tptp.fun _let_2 _let_2) (tptp.insert _let_1) (tptp.hAPP _let_9 _let_1 (tptp.hAPP tptp.com _let_11 (tptp.hAPP _let_9 (tptp.fun tptp.com _let_11) (tptp.hoare_246368825triple X_a) (tptp.hAPP _let_3 _let_9 (tptp.hAPP _let_10 (tptp.fun _let_3 _let_9) (tptp.combc X_a _let_3 _let_3) (tptp.hAPP _let_8 _let_10 (tptp.hAPP (tptp.fun _let_6 _let_4) (tptp.fun _let_8 _let_10) (tptp.combb _let_6 _let_4 X_a) (tptp.combs tptp.state tptp.bool tptp.bool)) (tptp.hAPP _let_9 _let_8 (tptp.hAPP _let_7 (tptp.fun _let_9 _let_8) (tptp.combb _let_3 _let_6 X_a) (tptp.hAPP (tptp.fun tptp.bool _let_5) _let_7 (tptp.combb tptp.bool _let_5 tptp.state) tptp.fconj)) P_1))) (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_5 _let_4 (tptp.combb tptp.bool tptp.bool tptp.state) tptp.fNot) B_1))) (tptp.hAPP tptp.com tptp.com (tptp.hAPP _let_3 (tptp.fun tptp.com tptp.com) tptp.while B_1) C_1)) P_1)) (tptp.bot_bot _let_2)))))))))))))))) (forall ((X_a $$unsorted) (D $$unsorted) (R_1 $$unsorted) (G_1 $$unsorted) (P_1 $$unsorted) (C_1 $$unsorted) (Q_1 $$unsorted)) (let ((_let_1 (tptp.hoare_1656922687triple X_a))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.bot_bot _let_2))) (let ((_let_4 (tptp.hoare_246368825triple X_a))) (let ((_let_5 (tptp.fun X_a (tptp.fun tptp.state tptp.bool)))) (let ((_let_6 (tptp.fun _let_5 _let_1))) (let ((_let_7 (tptp.fun tptp.com _let_6))) (let ((_let_8 (tptp.hAPP _let_5 _let_7 _let_4 P_1))) (let ((_let_9 (tptp.insert _let_1))) (let ((_let_10 (tptp.fun _let_2 _let_2))) (let ((_let_11 (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.hoare_279057269derivs X_a) G_1))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_11 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 _let_10 _let_9 (tptp.hAPP _let_5 _let_1 (tptp.hAPP tptp.com _let_6 _let_8 C_1) Q_1)) _let_3))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_11 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 _let_10 _let_9 (tptp.hAPP _let_5 _let_1 (tptp.hAPP tptp.com _let_6 (tptp.hAPP _let_5 _let_7 _let_4 Q_1) D) R_1)) _let_3))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_11 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 _let_10 _let_9 (tptp.hAPP _let_5 _let_1 (tptp.hAPP tptp.com _let_6 _let_8 (tptp.hAPP tptp.com tptp.com (tptp.hAPP tptp.com (tptp.fun tptp.com tptp.com) tptp.semi C_1) D)) R_1)) _let_3))))))))))))))))) (forall ((X_a $$unsorted) (X_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun X_a _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.hAPP _let_1 X_a (tptp.the_elem X_a) X_3) (tptp.hAPP _let_1 X_a (tptp.the_1 X_a) (tptp.hAPP _let_2 _let_1 (tptp.hAPP _let_3 (tptp.fun _let_2 _let_1) (tptp.combb _let_1 tptp.bool X_a) (tptp.hAPP _let_1 _let_3 (tptp.fequal _let_1) X_3)) (tptp.hAPP _let_1 _let_2 (tptp.hAPP (tptp.fun X_a (tptp.fun _let_1 _let_1)) (tptp.fun _let_1 _let_2) (tptp.combc X_a _let_1 _let_1) (tptp.insert X_a)) (tptp.bot_bot _let_1))))))))) (forall ((B_1 $$unsorted) (C_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.com tptp.bool tptp.wt (tptp.hAPP tptp.com tptp.com (tptp.hAPP (tptp.fun tptp.state tptp.bool) (tptp.fun tptp.com tptp.com) tptp.while B_1) C_1))) (tptp.hBOOL (tptp.hAPP tptp.com tptp.bool tptp.wt C_1)))) (forall ((C1 $$unsorted) (C2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.com tptp.bool tptp.wt (tptp.hAPP tptp.com tptp.com (tptp.hAPP tptp.com (tptp.fun tptp.com tptp.com) tptp.semi C1) C2))) (not (=> (tptp.hBOOL (tptp.hAPP tptp.com tptp.bool tptp.wt C1)) (not (tptp.hBOOL (tptp.hAPP tptp.com tptp.bool tptp.wt C2))))))) (forall ((Com1_3 $$unsorted) (Com2_3 $$unsorted) (Fun $$unsorted) (Com_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.com tptp.com))) (not (= (tptp.hAPP tptp.com tptp.com (tptp.hAPP tptp.com _let_1 tptp.semi Com1_3) Com2_3) (tptp.hAPP tptp.com tptp.com (tptp.hAPP (tptp.fun tptp.state tptp.bool) _let_1 tptp.while Fun) Com_1))))) (forall ((Fun $$unsorted) (Com_1 $$unsorted) (Com1_3 $$unsorted) (Com2_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.com tptp.com))) (not (= (tptp.hAPP tptp.com tptp.com (tptp.hAPP (tptp.fun tptp.state tptp.bool) _let_1 tptp.while Fun) Com_1) (tptp.hAPP tptp.com tptp.com (tptp.hAPP tptp.com _let_1 tptp.semi Com1_3) Com2_3))))) (forall ((Com1_3 $$unsorted) (Com2_3 $$unsorted) (Com1_2 $$unsorted) (Com2_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.com tptp.com))) (= (= (tptp.hAPP tptp.com tptp.com (tptp.hAPP tptp.com _let_1 tptp.semi Com1_3) Com2_3) (tptp.hAPP tptp.com tptp.com (tptp.hAPP tptp.com _let_1 tptp.semi Com1_2) Com2_2)) (and (= Com1_3 Com1_2) (= Com2_3 Com2_2))))) (forall ((Fun_1 $$unsorted) (Com_2 $$unsorted) (Fun $$unsorted) (Com_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.com tptp.com))) (let ((_let_2 (tptp.fun tptp.state tptp.bool))) (= (= (tptp.hAPP tptp.com tptp.com (tptp.hAPP _let_2 _let_1 tptp.while Fun_1) Com_2) (tptp.hAPP tptp.com tptp.com (tptp.hAPP _let_2 _let_1 tptp.while Fun) Com_1)) (and (= Fun_1 Fun) (= Com_2 Com_1)))))) (forall ((Pname_1 $$unsorted) (Fun_1 $$unsorted) (Com_2 $$unsorted)) (not (= (tptp.hAPP tptp.pname tptp.com tptp.body_1 Pname_1) (tptp.hAPP tptp.com tptp.com (tptp.hAPP (tptp.fun tptp.state tptp.bool) (tptp.fun tptp.com tptp.com) tptp.while Fun_1) Com_2)))) (forall ((Fun_1 $$unsorted) (Com_2 $$unsorted) (Pname_1 $$unsorted)) (not (= (tptp.hAPP tptp.com tptp.com (tptp.hAPP (tptp.fun tptp.state tptp.bool) (tptp.fun tptp.com tptp.com) tptp.while Fun_1) Com_2) (tptp.hAPP tptp.pname tptp.com tptp.body_1 Pname_1)))) (forall ((B_1 $$unsorted) (C_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.com tptp.bool tptp.wt C_1)) (tptp.hBOOL (tptp.hAPP tptp.com tptp.bool tptp.wt (tptp.hAPP tptp.com tptp.com (tptp.hAPP (tptp.fun tptp.state tptp.bool) (tptp.fun tptp.com tptp.com) tptp.while B_1) C_1))))) (forall ((Fun $$unsorted) (Com_1 $$unsorted)) (not (= tptp.skip (tptp.hAPP tptp.com tptp.com (tptp.hAPP (tptp.fun tptp.state tptp.bool) (tptp.fun tptp.com tptp.com) tptp.while Fun) Com_1)))) (forall ((Fun $$unsorted) (Com_1 $$unsorted)) (not (= (tptp.hAPP tptp.com tptp.com (tptp.hAPP (tptp.fun tptp.state tptp.bool) (tptp.fun tptp.com tptp.com) tptp.while Fun) Com_1) tptp.skip))) (forall ((Pname $$unsorted) (Com1_1 $$unsorted) (Com2_1 $$unsorted)) (not (= (tptp.hAPP tptp.pname tptp.com tptp.body_1 Pname) (tptp.hAPP tptp.com tptp.com (tptp.hAPP tptp.com (tptp.fun tptp.com tptp.com) tptp.semi Com1_1) Com2_1)))) (forall ((Com1_1 $$unsorted) (Com2_1 $$unsorted) (Pname $$unsorted)) (not (= (tptp.hAPP tptp.com tptp.com (tptp.hAPP tptp.com (tptp.fun tptp.com tptp.com) tptp.semi Com1_1) Com2_1) (tptp.hAPP tptp.pname tptp.com tptp.body_1 Pname)))) (forall ((C1 $$unsorted) (C0 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.com tptp.bool tptp.wt C0)) (=> (tptp.hBOOL (tptp.hAPP tptp.com tptp.bool tptp.wt C1)) (tptp.hBOOL (tptp.hAPP tptp.com tptp.bool tptp.wt (tptp.hAPP tptp.com tptp.com (tptp.hAPP tptp.com (tptp.fun tptp.com tptp.com) tptp.semi C0) C1)))))) (forall ((Com1 $$unsorted) (Com2 $$unsorted)) (not (= tptp.skip (tptp.hAPP tptp.com tptp.com (tptp.hAPP tptp.com (tptp.fun tptp.com tptp.com) tptp.semi Com1) Com2)))) (forall ((Com1 $$unsorted) (Com2 $$unsorted)) (not (= (tptp.hAPP tptp.com tptp.com (tptp.hAPP tptp.com (tptp.fun tptp.com tptp.com) tptp.semi Com1) Com2) tptp.skip))) (forall ((X_a $$unsorted) (X_2 $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.fun _let_1 X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP (tptp.fun X_a _let_2) (tptp.fun _let_3 tptp.bool) (tptp.finite_folding_one X_a) F) Fa)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_a) A_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_2) A_1))) (=> (not (= (tptp.ti _let_1 A_1) (tptp.bot_bot _let_1))) (= (tptp.hAPP _let_1 X_a Fa (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.insert X_a) X_2) A_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 F X_2) (tptp.hAPP _let_1 X_a Fa A_1))))))))))) (forall ((X_a $$unsorted) (X_2 $$unsorted) (Y_2 $$unsorted) (P_1 $$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_2 _let_2 (tptp.combc X_a X_a tptp.bool) (tptp.fequal X_a)))) (let ((_let_4 (tptp.fun tptp.bool tptp.bool))) (let ((_let_5 (tptp.combb tptp.bool tptp.bool X_a))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (let ((_let_7 (tptp.fun X_a _let_4))) (let ((_let_8 (tptp.hAPP _let_1 X_a (tptp.the_1 X_a) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_7 _let_6 (tptp.combs X_a tptp.bool tptp.bool) (tptp.hAPP _let_1 _let_7 (tptp.hAPP (tptp.fun tptp.bool _let_4) (tptp.fun _let_1 _let_7) (tptp.combb tptp.bool _let_4 X_a) tptp.fconj) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_4 _let_6 _let_5 (tptp.hAPP tptp.bool _let_4 tptp.fimplies P_1)) (tptp.hAPP X_a _let_1 _let_3 X_2)))) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_4 _let_6 _let_5 (tptp.hAPP tptp.bool _let_4 tptp.fimplies (tptp.hAPP tptp.bool tptp.bool tptp.fNot P_1))) (tptp.hAPP X_a _let_1 _let_3 Y_2)))))) (let ((_let_9 (tptp.hBOOL P_1))) (and (=> _let_9 (= (tptp.ti X_a X_2) _let_8)) (=> (not _let_9) (= (tptp.ti X_a Y_2) _let_8))))))))))))) (forall ((X_a $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun X_a _let_1))) (= (tptp.hAPP _let_1 X_a (tptp.the_1 X_a) (tptp.hAPP X_a _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc X_a X_a tptp.bool) (tptp.fequal X_a)) A_3)) (tptp.ti X_a A_3))))) (forall ((X_a $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (= (tptp.hAPP _let_1 X_a (tptp.the_1 X_a) (tptp.hAPP X_a _let_1 (tptp.fequal X_a) X_2)) (tptp.ti X_a X_2)))) (forall ((X_a $$unsorted) (X_2 $$unsorted) (F $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP (tptp.fun X_a (tptp.fun X_a X_a)) (tptp.fun _let_2 tptp.bool) (tptp.finite_folding_one X_a) F) Fa)) (= (tptp.hAPP _let_1 X_a Fa (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.insert X_a) X_2) (tptp.bot_bot _let_1))) (tptp.ti X_a X_2)))))) (forall ((X_a $$unsorted) (P_1 $$unsorted) (A_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool P_1 A_3)) (=> (forall ((X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool P_1 X_1)) (= (tptp.ti X_a X_1) (tptp.ti X_a A_3)))) (= (tptp.hAPP (tptp.fun X_a tptp.bool) X_a (tptp.the_1 X_a) P_1) (tptp.ti X_a A_3))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP (tptp.fun X_a (tptp.fun X_a X_a)) (tptp.fun _let_2 tptp.bool) (tptp.finite_folding_one X_a) F) Fa)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_a) A_1)) (=> (not (= (tptp.ti _let_1 A_1) (tptp.bot_bot _let_1))) (=> (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.insert X_a))) (let ((_let_3 (tptp.fun _let_1 _let_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 X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) F X_1) Y_1)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_3 _let_2 X_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_3 _let_2 Y_1) (tptp.bot_bot _let_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 _let_1 X_a Fa A_1)) A_1))))))))) (forall ((X_a $$unsorted) (P_1 $$unsorted)) (=> (exists ((X_1 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool P_1 X_1)) (forall ((Y_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool P_1 Y_1)) (= (tptp.ti X_a Y_1) (tptp.ti X_a X_1)))))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool P_1 (tptp.hAPP (tptp.fun X_a tptp.bool) X_a (tptp.the_1 X_a) P_1))))) (forall ((X_a $$unsorted) (A_3 $$unsorted) (P_1 $$unsorted)) (=> (exists ((X_1 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool P_1 X_1)) (forall ((Y_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool P_1 Y_1)) (= (tptp.ti X_a Y_1) (tptp.ti X_a X_1)))))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool P_1 A_3)) (= (tptp.hAPP (tptp.fun X_a tptp.bool) X_a (tptp.the_1 X_a) P_1) (tptp.ti X_a A_3))))) (forall ((X_a $$unsorted) (P_1 $$unsorted) (A_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool P_1 A_3)) (=> (forall ((X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool P_1 X_1)) (= (tptp.ti X_a X_1) (tptp.ti X_a A_3)))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool P_1 (tptp.hAPP (tptp.fun X_a tptp.bool) X_a (tptp.the_1 X_a) P_1)))))) (forall ((X_a $$unsorted) (Y_2 $$unsorted)) (not (forall ((Fun1 $$unsorted) (Com $$unsorted) (Fun2 $$unsorted)) (let ((_let_1 (tptp.hoare_1656922687triple X_a))) (let ((_let_2 (tptp.fun X_a (tptp.fun tptp.state tptp.bool)))) (let ((_let_3 (tptp.fun _let_2 _let_1))) (not (= Y_2 (tptp.hAPP _let_2 _let_1 (tptp.hAPP tptp.com _let_3 (tptp.hAPP _let_2 (tptp.fun tptp.com _let_3) (tptp.hoare_246368825triple X_a) Fun1) Com) Fun2))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (B $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Z $$unsorted) (G $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.finite_finite X_b))) (let ((_let_4 (tptp.fun _let_1 X_a))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (let ((_let_6 (tptp.fun X_b X_a))) (let ((_let_7 (tptp.fun _let_6 _let_5))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP _let_6 _let_5 (tptp.hAPP X_a _let_7 (tptp.hAPP (tptp.fun X_a _let_2) (tptp.fun X_a _let_7) (tptp.finite908156982e_idem X_a X_b) F) Z) G) Fa)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 A_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 B)) (= (tptp.hAPP _let_1 X_a Fa (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_sup_sup _let_1) A_1) B)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 F (tptp.hAPP _let_1 X_a Fa A_1)) (tptp.hAPP _let_1 X_a Fa B)))))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (B $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Z $$unsorted) (G $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP _let_1 X_a Fa A_1))) (let ((_let_3 (tptp.fun X_a X_a))) (let ((_let_4 (tptp.fun _let_1 X_a))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (let ((_let_6 (tptp.fun X_b X_a))) (let ((_let_7 (tptp.fun _let_6 _let_5))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP _let_6 _let_5 (tptp.hAPP X_a _let_7 (tptp.hAPP (tptp.fun X_a _let_3) (tptp.fun X_a _let_7) (tptp.finite908156982e_idem X_a X_b) F) Z) G) Fa)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) A_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) B) A_1)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 F (tptp.hAPP _let_1 X_a Fa B)) _let_2) _let_2)))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (X_2 $$unsorted) (F $$unsorted) (Z $$unsorted) (G $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.fun (tptp.fun X_b tptp.bool) X_a))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.fun X_b X_a))) (let ((_let_5 (tptp.fun _let_4 _let_3))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_4 _let_3 (tptp.hAPP X_a _let_5 (tptp.hAPP (tptp.fun X_a _let_1) (tptp.fun X_a _let_5) (tptp.finite908156982e_idem X_a X_b) F) Z) G) Fa)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 F X_2) X_2) (tptp.ti X_a X_2))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (X_2 $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Z $$unsorted) (G $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP _let_1 X_a Fa A_1))) (let ((_let_3 (tptp.fun X_a X_a))) (let ((_let_4 (tptp.fun _let_1 X_a))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (let ((_let_6 (tptp.fun X_b X_a))) (let ((_let_7 (tptp.fun _let_6 _let_5))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP _let_6 _let_5 (tptp.hAPP X_a _let_7 (tptp.hAPP (tptp.fun X_a _let_3) (tptp.fun X_a _let_7) (tptp.finite908156982e_idem X_a X_b) F) Z) G) Fa)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) A_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_2) A_1)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 F (tptp.hAPP X_b X_a G X_2)) _let_2) _let_2)))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (X_2 $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Z $$unsorted) (G $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.fun _let_1 X_a))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.fun X_b X_a))) (let ((_let_6 (tptp.fun _let_5 _let_4))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_5 _let_4 (tptp.hAPP X_a _let_6 (tptp.hAPP (tptp.fun X_a _let_2) (tptp.fun X_a _let_6) (tptp.finite908156982e_idem X_a X_b) F) Z) G) Fa)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) A_1)) (= (tptp.hAPP _let_1 X_a Fa (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_2) A_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 F (tptp.hAPP X_b X_a G X_2)) (tptp.hAPP _let_1 X_a Fa A_1)))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F1 $$unsorted) (F2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.option X_b))) (let ((_let_2 (tptp.fun _let_1 X_a))) (let ((_let_3 (tptp.fun X_b 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.option_rec X_a X_b) F1) F2) (tptp.hAPP X_b _let_1 (tptp.some X_b) A_3)) (tptp.hAPP X_b X_a F2 A_3)))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F $$unsorted) (G $$unsorted) (M_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.image X_a X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.fun _let_3 _let_2))) (let ((_let_5 (tptp.fun X_a X_b))) (=> (= (tptp.ti _let_3 M_1) (tptp.ti _let_3 N_1)) (=> (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_1) N_1)) (= (tptp.hAPP X_a X_b F X_1) (tptp.hAPP X_a X_b G X_1))))) (= (tptp.hAPP _let_3 _let_2 (tptp.hAPP _let_5 _let_4 _let_1 F) M_1) (tptp.hAPP _let_3 _let_2 (tptp.hAPP _let_5 _let_4 _let_1 G) N_1)))))))))) (forall ((X_a $$unsorted) (Q_1 $$unsorted) (P_1 $$unsorted)) (let ((_let_1 (tptp.collect X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (forall ((X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool P_1 X_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool Q_1 X_1)))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) (tptp.hAPP _let_2 _let_2 _let_1 P_1)) (tptp.hAPP _let_2 _let_2 _let_1 Q_1))))))) (forall ((X_a $$unsorted) (Q_1 $$unsorted) (P_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (forall ((X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool P_1 X_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool Q_1 X_1)))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) P_1) Q_1))))) (forall ((X_a $$unsorted) (A_3 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) A_3) A_1)) (exists ((B_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (and (= (tptp.ti _let_1 A_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.insert X_a) A_3) B_3)) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) A_3) B_3))))))))) (forall ((X_a $$unsorted) (X_2 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) A_1)) (not (forall ((B_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (= (tptp.ti _let_1 A_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.insert X_a) X_2) B_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) B_3))))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (forall ((Y_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) Y_1) A_1))))) (= (tptp.ti _let_1 A_1) (tptp.bot_bot _let_1))))) (forall ((G_1 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.hoare_1656922687triple tptp.state))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.bot_bot _let_2))) (let ((_let_4 (tptp.insert _let_1))) (let ((_let_5 (tptp.fun _let_2 _let_2))) (let ((_let_6 (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.hoare_279057269derivs tptp.state) G_1))) (let ((_let_7 (tptp.fequal tptp.state))) (let ((_let_8 (tptp.fun tptp.state tptp.bool))) (let ((_let_9 (tptp.fun tptp.state _let_8))) (let ((_let_10 (tptp.fun tptp.bool tptp.bool))) (let ((_let_11 (tptp.fun tptp.state _let_10))) (let ((_let_12 (tptp.fun _let_8 _let_11))) (let ((_let_13 (tptp.fun tptp.state _let_11))) (let ((_let_14 (tptp.fun _let_8 _let_8))) (let ((_let_15 (tptp.fun tptp.state _let_14))) (let ((_let_16 (tptp.fun _let_8 _let_9))) (let ((_let_17 (tptp.fun tptp.state _let_9))) (let ((_let_18 (tptp.fun _let_9 _let_8))) (let ((_let_19 (tptp.fun _let_9 _let_1))) (=> (tptp.hBOOL tptp.hoare_1924220188gleton) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_6 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 _let_5 _let_4 (tptp.hAPP _let_9 _let_1 (tptp.hAPP tptp.com _let_19 (tptp.hAPP _let_9 (tptp.fun tptp.com _let_19) (tptp.hoare_246368825triple tptp.state) (tptp.hAPP _let_17 _let_9 (tptp.hAPP _let_18 (tptp.fun _let_17 _let_9) (tptp.combb _let_9 _let_8 tptp.state) (tptp.hAPP (tptp.fun _let_8 tptp.bool) _let_18 (tptp.combb _let_8 tptp.bool tptp.state) (tptp.fAll tptp.state))) (tptp.hAPP _let_9 _let_17 (tptp.hAPP _let_16 (tptp.fun _let_9 _let_17) (tptp.combb _let_8 _let_9 tptp.state) (tptp.hAPP _let_15 _let_16 (tptp.combc tptp.state _let_8 _let_8) (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 tptp.state) (tptp.combs tptp.state tptp.bool tptp.bool)) (tptp.hAPP _let_9 _let_13 (tptp.hAPP _let_12 (tptp.fun _let_9 _let_13) (tptp.combb _let_8 _let_11 tptp.state) (tptp.hAPP (tptp.fun tptp.bool _let_10) _let_12 (tptp.combb tptp.bool _let_10 tptp.state) tptp.fimplies)) (tptp.hAPP tptp.com _let_9 tptp.evalc C_1))))) _let_7))) C_1) _let_7)) _let_3))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_6 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 _let_5 _let_4 (tptp.hAPP tptp.com _let_1 tptp.hoare_Mirabelle_MGT C_1)) _let_3))))))))))))))))))))))))) (forall ((G_1 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.hoare_1656922687triple tptp.state))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.bot_bot _let_2))) (let ((_let_4 (tptp.fequal tptp.state))) (let ((_let_5 (tptp.fun tptp.state tptp.bool))) (let ((_let_6 (tptp.fun tptp.state _let_5))) (let ((_let_7 (tptp.fun tptp.bool tptp.bool))) (let ((_let_8 (tptp.fun tptp.state _let_7))) (let ((_let_9 (tptp.fun _let_5 _let_8))) (let ((_let_10 (tptp.fun tptp.state _let_8))) (let ((_let_11 (tptp.fun _let_5 _let_5))) (let ((_let_12 (tptp.fun tptp.state _let_11))) (let ((_let_13 (tptp.fun _let_5 _let_6))) (let ((_let_14 (tptp.fun tptp.state _let_6))) (let ((_let_15 (tptp.fun _let_6 _let_5))) (let ((_let_16 (tptp.fun _let_6 _let_1))) (let ((_let_17 (tptp.insert _let_1))) (let ((_let_18 (tptp.fun _let_2 _let_2))) (let ((_let_19 (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.hoare_279057269derivs tptp.state) G_1))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_19 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 _let_18 _let_17 (tptp.hAPP tptp.com _let_1 tptp.hoare_Mirabelle_MGT C_1)) _let_3))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_19 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 _let_18 _let_17 (tptp.hAPP _let_6 _let_1 (tptp.hAPP tptp.com _let_16 (tptp.hAPP _let_6 (tptp.fun tptp.com _let_16) (tptp.hoare_246368825triple tptp.state) (tptp.hAPP _let_14 _let_6 (tptp.hAPP _let_15 (tptp.fun _let_14 _let_6) (tptp.combb _let_6 _let_5 tptp.state) (tptp.hAPP (tptp.fun _let_5 tptp.bool) _let_15 (tptp.combb _let_5 tptp.bool tptp.state) (tptp.fAll tptp.state))) (tptp.hAPP _let_6 _let_14 (tptp.hAPP _let_13 (tptp.fun _let_6 _let_14) (tptp.combb _let_5 _let_6 tptp.state) (tptp.hAPP _let_12 _let_13 (tptp.combc tptp.state _let_5 _let_5) (tptp.hAPP _let_10 _let_12 (tptp.hAPP (tptp.fun _let_8 _let_11) (tptp.fun _let_10 _let_12) (tptp.combb _let_8 _let_11 tptp.state) (tptp.combs tptp.state tptp.bool tptp.bool)) (tptp.hAPP _let_6 _let_10 (tptp.hAPP _let_9 (tptp.fun _let_6 _let_10) (tptp.combb _let_5 _let_8 tptp.state) (tptp.hAPP (tptp.fun tptp.bool _let_7) _let_9 (tptp.combb tptp.bool _let_7 tptp.state) tptp.fimplies)) (tptp.hAPP tptp.com _let_6 tptp.evalc C_1))))) _let_4))) C_1) _let_4)) _let_3)))))))))))))))))))))))) (forall ((C_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.state (tptp.fun tptp.state tptp.bool)))) (let ((_let_2 (tptp.hoare_1656922687triple tptp.state))) (let ((_let_3 (tptp.fun _let_1 _let_2))) (= (tptp.hAPP tptp.com _let_2 tptp.hoare_Mirabelle_MGT C_1) (tptp.hAPP _let_1 _let_2 (tptp.hAPP tptp.com _let_3 (tptp.hAPP _let_1 (tptp.fun tptp.com _let_3) (tptp.hoare_246368825triple tptp.state) (tptp.fequal tptp.state)) C_1) (tptp.hAPP tptp.com _let_1 tptp.evalc C_1))))))) (forall ((Pn $$unsorted) (S0 $$unsorted) (S1_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.state tptp.bool))) (let ((_let_2 (tptp.fun tptp.state _let_1))) (let ((_let_3 (tptp.option tptp.com))) (=> (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP tptp.state _let_1 (tptp.hAPP tptp.com _let_2 tptp.evalc (tptp.hAPP _let_3 tptp.com (tptp.the tptp.com) (tptp.hAPP tptp.pname _let_3 tptp.body Pn))) S0) S1_1)) (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP tptp.state _let_1 (tptp.hAPP tptp.com _let_2 tptp.evalc (tptp.hAPP tptp.pname tptp.com tptp.body_1 Pn)) S0) S1_1))))))) (forall ((P $$unsorted) (S_2 $$unsorted) (S1_1 $$unsorted)) (let ((_let_1 (tptp.option tptp.com))) (let ((_let_2 (tptp.fun tptp.state tptp.bool))) (let ((_let_3 (tptp.fun tptp.state _let_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP tptp.state _let_2 (tptp.hAPP tptp.com _let_3 tptp.evalc (tptp.hAPP tptp.pname tptp.com tptp.body_1 P)) S_2) S1_1)) (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP tptp.state _let_2 (tptp.hAPP tptp.com _let_3 tptp.evalc (tptp.hAPP _let_1 tptp.com (tptp.the tptp.com) (tptp.hAPP tptp.pname _let_1 tptp.body P))) S_2) S1_1))))))) (forall ((S_2 $$unsorted) (T_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.state tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP tptp.state _let_1 (tptp.hAPP tptp.com (tptp.fun tptp.state _let_1) tptp.evalc tptp.skip) S_2) T_4)) (= T_4 S_2)))) (forall ((C_1 $$unsorted) (B_1 $$unsorted) (S_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.state tptp.bool))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool B_1 S_1))) (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP tptp.state _let_1 (tptp.hAPP tptp.com (tptp.fun tptp.state _let_1) tptp.evalc (tptp.hAPP tptp.com tptp.com (tptp.hAPP _let_1 (tptp.fun tptp.com tptp.com) tptp.while B_1) C_1)) S_1) S_1))))) (forall ((S2_1 $$unsorted) (C_1 $$unsorted) (S1_2 $$unsorted) (B_1 $$unsorted) (S0_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.state tptp.bool))) (let ((_let_2 (tptp.fun tptp.state _let_1))) (let ((_let_3 (tptp.hAPP tptp.com _let_2 tptp.evalc (tptp.hAPP tptp.com tptp.com (tptp.hAPP _let_1 (tptp.fun tptp.com tptp.com) tptp.while B_1) C_1)))) (=> (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool B_1 S0_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP tptp.state _let_1 (tptp.hAPP tptp.com _let_2 tptp.evalc C_1) S0_1) S1_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP tptp.state _let_1 _let_3 S1_2) S2_1)) (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP tptp.state _let_1 _let_3 S0_1) S2_1))))))))) (forall ((C1 $$unsorted) (S2 $$unsorted) (C0 $$unsorted) (S0 $$unsorted) (S1_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.state tptp.bool))) (let ((_let_2 (tptp.fun tptp.state _let_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP tptp.state _let_1 (tptp.hAPP tptp.com _let_2 tptp.evalc C0) S0) S1_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP tptp.state _let_1 (tptp.hAPP tptp.com _let_2 tptp.evalc C1) S1_1) S2)) (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP tptp.state _let_1 (tptp.hAPP tptp.com _let_2 tptp.evalc (tptp.hAPP tptp.com tptp.com (tptp.hAPP tptp.com (tptp.fun tptp.com tptp.com) tptp.semi C0) C1)) S0) S2))))))) (forall ((S_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.state tptp.bool))) (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP tptp.state _let_1 (tptp.hAPP tptp.com (tptp.fun tptp.state _let_1) tptp.evalc tptp.skip) S_2) S_2)))) (forall ((U $$unsorted) (C_2 $$unsorted) (S_2 $$unsorted) (T_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.state tptp.bool))) (let ((_let_2 (tptp.hAPP tptp.state _let_1 (tptp.hAPP tptp.com (tptp.fun tptp.state _let_1) tptp.evalc C_2) S_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool _let_2 T_4)) (=> (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool _let_2 U)) (= U T_4)))))) (forall ((C1 $$unsorted) (C2 $$unsorted) (S_2 $$unsorted) (T_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.state tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP tptp.state _let_1 (tptp.hAPP tptp.com (tptp.fun tptp.state _let_1) tptp.evalc (tptp.hAPP tptp.com tptp.com (tptp.hAPP tptp.com (tptp.fun tptp.com tptp.com) tptp.semi C1) C2)) S_2) T_4)) (not (forall ((S1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.state tptp.bool))) (let ((_let_2 (tptp.fun tptp.state _let_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP tptp.state _let_1 (tptp.hAPP tptp.com _let_2 tptp.evalc C1) S_2) S1)) (not (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP tptp.state _let_1 (tptp.hAPP tptp.com _let_2 tptp.evalc C2) S1) T_4))))))))))) (forall ((B_1 $$unsorted) (C_1 $$unsorted) (S_1 $$unsorted) (T_3 $$unsorted)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool B_1 S_1)))) (let ((_let_2 (tptp.fun tptp.state tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP tptp.state _let_2 (tptp.hAPP tptp.com (tptp.fun tptp.state _let_2) tptp.evalc (tptp.hAPP tptp.com tptp.com (tptp.hAPP _let_2 (tptp.fun tptp.com tptp.com) tptp.while B_1) C_1)) S_1) T_3)) (=> (=> (= T_3 S_1) _let_1) (not (=> _let_1 (forall ((S1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.state tptp.bool))) (let ((_let_2 (tptp.fun tptp.state _let_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP tptp.state _let_1 (tptp.hAPP tptp.com _let_2 tptp.evalc C_1) S_1) S1)) (not (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP tptp.state _let_1 (tptp.hAPP tptp.com _let_2 tptp.evalc (tptp.hAPP tptp.com tptp.com (tptp.hAPP _let_1 (tptp.fun tptp.com tptp.com) tptp.while B_1) C_1)) S1) T_3)))))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (and (tptp.order X_a) (tptp.order X_b)) (forall ((C_1 $$unsorted) (F $$unsorted) (B_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) C_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) B_1) A_3)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool _let_1 (tptp.hAPP X_a X_b F B_1))) (=> (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) Y_1) X_1)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) (tptp.hAPP X_a X_b F Y_1)) (tptp.hAPP X_a X_b F X_1))))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool _let_1 (tptp.hAPP X_a X_b F A_3)))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (and (tptp.order X_a) (tptp.ord X_b)) (forall ((C_1 $$unsorted) (F $$unsorted) (B_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_b X_a F B_1)) A_3)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) C_1) B_1)) (=> (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) Y_1) X_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP X_b X_a F Y_1)) (tptp.hAPP X_b X_a F X_1))))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_b X_a F C_1)) A_3)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((C_1 $$unsorted) (A_3 $$unsorted) (F $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (= (tptp.ti X_a A_3) (tptp.hAPP X_a X_a F B_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 C_1) B_1)) (=> (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 _let_1 Y_1) X_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a F Y_1)) (tptp.hAPP X_a X_a F X_1))))))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a F C_1)) A_3)))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (and (tptp.order X_b) (tptp.order X_a)) (forall ((C_1 $$unsorted) (A_3 $$unsorted) (F $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) A_3))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_b X_a F B_1))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) B_1) C_1)) (=> (forall ((X_1 $$unsorted) (Y_1 $$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_1) Y_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 X_b X_a F X_1)) (tptp.hAPP X_b X_a F Y_1))))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_b X_a F C_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((F $$unsorted) (C_1 $$unsorted) (B_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B_1) A_3)) (=> (= (tptp.hAPP X_a X_a F B_1) (tptp.ti X_a C_1)) (=> (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y_1) X_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a F Y_1)) (tptp.hAPP X_a X_a F X_1))))))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 C_1) (tptp.hAPP X_a X_a F A_3))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (and (tptp.ord X_b) (tptp.ord X_a)) (forall ((F $$unsorted) (C_1 $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) A_3) B_1)) (=> (= (tptp.hAPP X_a X_b F B_1) C_1) (=> (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X_1) Y_1)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) (tptp.hAPP X_a X_b F X_1)) (tptp.hAPP X_a X_b F Y_1))))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) (tptp.hAPP X_a X_b F A_3)) C_1)))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (and (tptp.order X_b) (tptp.order X_a)) (forall ((F $$unsorted) (C_1 $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) A_3) B_1)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 (tptp.hAPP X_a X_b F B_1)) C_1)) (=> (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X_1) Y_1)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) (tptp.hAPP X_a X_b F X_1)) (tptp.hAPP X_a X_b F Y_1))))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 (tptp.hAPP X_a X_b F A_3)) C_1)))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (and (tptp.ord X_b) (tptp.ord X_a)) (forall ((C_1 $$unsorted) (A_3 $$unsorted) (F $$unsorted) (B_1 $$unsorted)) (=> (= A_3 (tptp.hAPP X_b X_a F B_1)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) B_1) C_1)) (=> (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) X_1) Y_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP X_b X_a F X_1)) (tptp.hAPP X_b X_a F Y_1))))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) A_3) (tptp.hAPP X_b X_a F C_1))))))))) (forall ((X_a $$unsorted) (B $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 (tptp.semilattice_inf_inf _let_1) A_1) B))) (let ((_let_5 (tptp.finite_finite X_a))) (let ((_let_6 (tptp.fun _let_1 X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP (tptp.fun X_a _let_2) (tptp.fun _let_6 tptp.bool) (tptp.finite_folding_one X_a) F) Fa)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_5 A_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_5 B)) (=> (not (= _let_4 (tptp.bot_bot _let_1))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 F (tptp.hAPP _let_1 X_a Fa (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 (tptp.semilattice_sup_sup _let_1) A_1) B))) (tptp.hAPP _let_1 X_a Fa _let_4)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 F (tptp.hAPP _let_1 X_a Fa A_1)) (tptp.hAPP _let_1 X_a Fa B)))))))))))))) (forall ((X_a $$unsorted) (B $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.bot_bot _let_1))) (let ((_let_5 (tptp.finite_finite X_a))) (let ((_let_6 (tptp.fun _let_1 X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP (tptp.fun X_a _let_2) (tptp.fun _let_6 tptp.bool) (tptp.finite_folding_one X_a) F) Fa)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_5 A_1)) (=> (not (= (tptp.ti _let_1 A_1) _let_4)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_5 B)) (=> (not (= (tptp.ti _let_1 B) _let_4)) (=> (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 (tptp.semilattice_inf_inf _let_1) A_1) B) _let_4) (= (tptp.hAPP _let_1 X_a Fa (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 (tptp.semilattice_sup_sup _let_1) A_1) B)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 F (tptp.hAPP _let_1 X_a Fa A_1)) (tptp.hAPP _let_1 X_a Fa B)))))))))))))))) (forall ((X_a $$unsorted) (B $$unsorted) (C_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) C_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_inf_inf _let_1) A_1) B)))))))) (forall ((X_a $$unsorted) (C_1 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) C_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_inf_inf _let_1) A_1) B))) (not (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_1)) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B))))))))) (forall ((X_a $$unsorted) (B $$unsorted) (A_1 $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool A_1 X_2)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool B X_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_inf_inf _let_1) A_1) B) X_2)))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_inf_inf _let_1) A_1) B) X_2)) (not (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool A_1 X_2)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool B X_2)))))))) (forall ((X_a $$unsorted) (G_1 $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.finite_finite X_a))) (=> (or (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 Fa)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 G_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.semilattice_inf_inf _let_1) Fa) G_1))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (= (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_inf_inf _let_1) A_1) B) (tptp.bot_bot _let_1)) (forall ((X_1 $$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) A_1)) (forall ((Xa $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) Xa) B)) (not (= (tptp.ti X_a X_1) (tptp.ti X_a Xa)))))))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.bot_bot _let_1))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_inf_inf _let_1) A_1) _let_2) _let_2)))) (forall ((X_a $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.bot_bot _let_1))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_inf_inf _let_1) _let_2) B) _let_2)))) (forall ((X_a $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_inf_inf _let_1) A_1) A_1) (tptp.ti _let_1 A_1)))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _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.semilattice_inf_inf _let_1) A_1) B) (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_1))) (tptp.hAPP _let_1 _let_1 _let_3 B)))))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.semilattice_inf_inf _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 A_1) B) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 B) A_1)))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_inf_inf _let_1) A_1))) (let ((_let_3 (tptp.hAPP _let_1 _let_1 _let_2 B))) (= (tptp.hAPP _let_1 _let_1 _let_2 _let_3) _let_3))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.semilattice_inf_inf _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.hAPP _let_1 _let_3 _let_2 A_1))) (let ((_let_5 (tptp.hAPP _let_1 _let_3 _let_2 B))) (= (tptp.hAPP _let_1 _let_1 _let_4 (tptp.hAPP _let_1 _let_1 _let_5 C)) (tptp.hAPP _let_1 _let_1 _let_5 (tptp.hAPP _let_1 _let_1 _let_4 C))))))))) (forall ((X_a $$unsorted) (C_1 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) C_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.semilattice_inf_inf _let_1) A_1) B))) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.semilattice_inf_inf _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.hAPP _let_1 _let_3 _let_2 A_1))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 (tptp.hAPP _let_1 _let_1 _let_4 B)) C) (tptp.hAPP _let_1 _let_1 _let_4 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 B) C)))))))) (forall ((X_a $$unsorted) (C_1 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) C_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.semilattice_inf_inf _let_1) A_1) B))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_1)))))) (forall ((X_a $$unsorted) (C_1 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) C_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.semilattice_inf_inf _let_1) A_1) B))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B)))))) (forall ((X_a $$unsorted) (P_1 $$unsorted) (Q_1 $$unsorted)) (let ((_let_1 (tptp.collect X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (let ((_let_4 (tptp.fun tptp.bool tptp.bool))) (let ((_let_5 (tptp.fun X_a _let_4))) (= (tptp.hAPP _let_2 _let_2 _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_5 _let_3 (tptp.combs X_a tptp.bool tptp.bool) (tptp.hAPP _let_2 _let_5 (tptp.hAPP (tptp.fun tptp.bool _let_4) (tptp.fun _let_2 _let_5) (tptp.combb tptp.bool _let_4 X_a) tptp.fconj) P_1)) Q_1)) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_3 (tptp.semilattice_inf_inf _let_2) (tptp.hAPP _let_2 _let_2 _let_1 P_1)) (tptp.hAPP _let_2 _let_2 _let_1 Q_1))))))))) (forall ((X_a $$unsorted) (X_2 $$unsorted) (A_1 $$unsorted) (P_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_inf_inf _let_1) A_1) (tptp.hAPP _let_1 _let_1 (tptp.collect X_a) P_1)))) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool P_1 X_2))))))) (forall ((X_a $$unsorted) (R_1 $$unsorted) (S $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.semilattice_inf_inf _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.member X_a))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.hAPP (tptp.fun X_a _let_5) _let_3 (tptp.combc X_a _let_1 tptp.bool) _let_4))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 (tptp.hAPP _let_1 _let_1 _let_6 R_1)) (tptp.hAPP _let_1 _let_1 _let_6 S)) X_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a _let_5 _let_4 X_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 R_1) S))))))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_inf_inf _let_1) A_1) B) X_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool A_1 X_2))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_inf_inf _let_1) A_1) B) X_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool B X_2))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.semilattice_sup_sup _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.semilattice_inf_inf _let_1))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_4 A_1) B)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_4 B) C))) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_4 C) A_1)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_4 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_4 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 A_1) B)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 B) C))) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 C) A_1)))))))) (forall ((X_a $$unsorted) (B $$unsorted) (C $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.semilattice_sup_sup _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.semilattice_inf_inf _let_1))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_4 B) C)) A_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_4 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 B) A_1)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 C) A_1)))))))) (forall ((X_a $$unsorted) (B $$unsorted) (C $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.semilattice_inf_inf _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.semilattice_sup_sup _let_1))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_4 B) C)) A_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_4 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 B) A_1)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 C) A_1)))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP _let_1 _let_2 (tptp.semilattice_sup_sup _let_1) A_1))) (let ((_let_4 (tptp.semilattice_inf_inf _let_1))) (= (tptp.hAPP _let_1 _let_1 _let_3 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 _let_4 B) C)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 _let_4 (tptp.hAPP _let_1 _let_1 _let_3 B)) (tptp.hAPP _let_1 _let_1 _let_3 C)))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP _let_1 _let_2 (tptp.semilattice_inf_inf _let_1) A_1))) (let ((_let_4 (tptp.semilattice_sup_sup _let_1))) (= (tptp.hAPP _let_1 _let_1 _let_3 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 _let_4 B) C)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 _let_4 (tptp.hAPP _let_1 _let_1 _let_3 B)) (tptp.hAPP _let_1 _let_1 _let_3 C)))))))) (forall ((X_a $$unsorted) (B $$unsorted) (D_1 $$unsorted) (A_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.semilattice_inf_inf _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_1) C)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_5 _let_4 B) D_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_1) B)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 C) D_1))))))))))) (forall ((X_a $$unsorted) (B $$unsorted) (C $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) C))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_inf_inf _let_1) A_1) B)))))))) (forall ((X_a $$unsorted) (B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) B) A_1)) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_inf_inf _let_1) A_1) B) (tptp.ti _let_1 B))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) A_1) B)) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_inf_inf _let_1) A_1) B) (tptp.ti _let_1 A_1))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_inf_inf _let_1) A_1) B)) B)))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$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.semilattice_inf_inf _let_1) A_1) B)) A_1)))) (forall ((X_a $$unsorted) (B $$unsorted) (A_3 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.semilattice_inf_inf _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.hAPP X_a _let_3 (tptp.insert X_a) A_3))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) A_3) C)) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 (tptp.hAPP _let_1 _let_1 _let_4 B)) C) (tptp.hAPP _let_1 _let_1 _let_4 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 B) C))))))))) (forall ((X_a $$unsorted) (B $$unsorted) (A_3 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP _let_1 _let_2 (tptp.semilattice_inf_inf _let_1) A_1))) (let ((_let_4 (tptp.hAPP X_a _let_2 (tptp.insert X_a) A_3))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) A_3) A_1)) (= (tptp.hAPP _let_1 _let_1 _let_3 (tptp.hAPP _let_1 _let_1 _let_4 B)) (tptp.hAPP _let_1 _let_1 _let_4 (tptp.hAPP _let_1 _let_1 _let_3 B))))))))) (forall ((X_a $$unsorted) (B $$unsorted) (A_3 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.semilattice_inf_inf _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) A_3) C))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_3 (tptp.insert X_a) A_3) B)) C) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 B) C))))))) (forall ((X_a $$unsorted) (B $$unsorted) (A_3 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP _let_1 _let_2 (tptp.semilattice_inf_inf _let_1) A_1))) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) A_3) A_1))) (= (tptp.hAPP _let_1 _let_1 _let_3 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_2 (tptp.insert X_a) A_3) B)) (tptp.hAPP _let_1 _let_1 _let_3 B))))))) (forall ((X_a $$unsorted) (A_3 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.semilattice_inf_inf _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.hAPP X_a _let_3 (tptp.insert X_a) A_3))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 (tptp.hAPP _let_1 _let_1 _let_4 A_1)) (tptp.hAPP _let_1 _let_1 _let_4 B)) (tptp.hAPP _let_1 _let_1 _let_4 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 A_1) B)))))))) (forall ((X_a $$unsorted) (B $$unsorted) (A_3 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.semilattice_inf_inf _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 B) C))) (let ((_let_5 (tptp.hAPP X_a _let_3 (tptp.insert X_a) A_3))) (let ((_let_6 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 (tptp.hAPP _let_1 _let_1 _let_5 B)) C))) (let ((_let_7 (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) A_3) C)))) (and (=> _let_7 (= _let_6 (tptp.hAPP _let_1 _let_1 _let_5 _let_4))) (=> (not _let_7) (= _let_6 _let_4))))))))))) (forall ((X_a $$unsorted) (B $$unsorted) (A_3 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP _let_1 _let_2 (tptp.semilattice_inf_inf _let_1) A_1))) (let ((_let_4 (tptp.hAPP _let_1 _let_1 _let_3 B))) (let ((_let_5 (tptp.hAPP X_a _let_2 (tptp.insert X_a) A_3))) (let ((_let_6 (tptp.hAPP _let_1 _let_1 _let_3 (tptp.hAPP _let_1 _let_1 _let_5 B)))) (let ((_let_7 (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) A_3) A_1)))) (and (=> _let_7 (= _let_6 (tptp.hAPP _let_1 _let_1 _let_5 _let_4))) (=> (not _let_7) (= _let_6 _let_4))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.lattice X_a) (forall ((X $$unsorted) (Y $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.semilattice_inf_inf X_a) X) Y)) X))))) (forall ((X_a $$unsorted)) (=> (tptp.semilattice_inf 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.semilattice_inf_inf X_a) X) Y)) X))))) (forall ((X_a $$unsorted)) (=> (tptp.lattice X_a) (forall ((X $$unsorted) (Y $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.semilattice_inf_inf X_a) X) Y)) Y))))) (forall ((X_a $$unsorted)) (=> (tptp.semilattice_inf 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.semilattice_inf_inf X_a) X) Y)) Y))))) (forall ((X_a $$unsorted)) (=> (tptp.semilattice_inf X_a) (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X_2) Y_2)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.semilattice_inf_inf X_a) X_2) Y_2) (tptp.ti X_a X_2)))))) (forall ((X_a $$unsorted)) (=> (tptp.semilattice_inf X_a) (forall ((X_2 $$unsorted) (Y_2 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X_2))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.semilattice_inf_inf X_a) Y_2) Z))) (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 Y_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 Z)))))))) (forall ((X_a $$unsorted)) (=> (tptp.semilattice_inf X_a) (forall ((B_2 $$unsorted) (A_6 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_6) X)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.semilattice_inf_inf X_a) A_6) B_2)) X)))))))) (forall ((X_a $$unsorted)) (=> (tptp.semilattice_inf X_a) (forall ((A_6 $$unsorted) (B_2 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B_2) X)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.semilattice_inf_inf X_a) A_6) B_2)) X)))))))) (forall ((X_a $$unsorted)) (=> (tptp.semilattice_inf 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.semilattice_inf_inf X_a) X) Y) (tptp.ti X_a X)))))) (forall ((X_a $$unsorted)) (=> (tptp.semilattice_inf X_a) (forall ((Y $$unsorted) (X $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) Y) X)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.semilattice_inf_inf X_a) X) Y) (tptp.ti X_a Y)))))) (forall ((X_a $$unsorted)) (=> (tptp.semilattice_inf X_a) (forall ((B_2 $$unsorted) (X $$unsorted) (A_6 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_6)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.semilattice_inf_inf X_a) A_6) B_2))))))))) (forall ((X_a $$unsorted)) (=> (tptp.semilattice_inf X_a) (forall ((Z_1 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 Y)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 Z_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.semilattice_inf_inf X_a) Y) Z_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.semilattice_inf X_a) (forall ((B_2 $$unsorted) (D_2 $$unsorted) (A_6 $$unsorted) (C_2 $$unsorted)) (let ((_let_1 (tptp.semilattice_inf_inf 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_6) C_2)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 B_2) D_2)) (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_6) B_2)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 C_2) D_2)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.semilattice_inf X_a) (forall ((X $$unsorted) (A_6 $$unsorted) (B_2 $$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.semilattice_inf_inf X_a) A_6) B_2))) (not (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_6)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B_2)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.lattice X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.semilattice_inf_inf X_a) X) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.semilattice_sup_sup X_a) X) Y)) (tptp.ti X_a X)))))) (forall ((X_a $$unsorted)) (=> (tptp.lattice X_a) (forall ((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.semilattice_sup_sup X_a) X) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.semilattice_inf_inf X_a) X) Y)) (tptp.ti X_a X)))))) (forall ((X_a $$unsorted)) (=> (tptp.distrib_lattice X_a) (forall ((X $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.semilattice_inf_inf X_a) X))) (let ((_let_3 (tptp.semilattice_sup_sup X_a))) (= (tptp.hAPP X_a X_a _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 Y) Z_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 (tptp.hAPP X_a X_a _let_2 Y)) (tptp.hAPP X_a X_a _let_2 Z_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.distrib_lattice X_a) (forall ((X $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.semilattice_sup_sup X_a) X))) (let ((_let_3 (tptp.semilattice_inf_inf X_a))) (= (tptp.hAPP X_a X_a _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 Y) Z_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 (tptp.hAPP X_a X_a _let_2 Y)) (tptp.hAPP X_a X_a _let_2 Z_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.distrib_lattice X_a) (forall ((Y $$unsorted) (Z_1 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.semilattice_inf_inf X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.semilattice_sup_sup 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 Y) Z_1)) X) (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 Y) X)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Z_1) X))))))))) (forall ((X_a $$unsorted)) (=> (tptp.distrib_lattice X_a) (forall ((Y $$unsorted) (Z_1 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.semilattice_sup_sup X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.semilattice_inf_inf 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 Y) Z_1)) X) (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 Y) X)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Z_1) X))))))))) (forall ((X_a $$unsorted)) (=> (tptp.bounded_lattice_bot X_a) (forall ((X $$unsorted)) (let ((_let_1 (tptp.bot_bot X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.semilattice_inf_inf X_a) X) _let_1) _let_1))))) (forall ((X_a $$unsorted)) (=> (tptp.bounded_lattice_bot X_a) (forall ((X $$unsorted)) (let ((_let_1 (tptp.bot_bot X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.semilattice_inf_inf X_a) _let_1) X) _let_1))))) (forall ((X_a $$unsorted)) (=> (tptp.semilattice_inf X_a) (forall ((A_6 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.semilattice_inf_inf X_a) A_6) A_6) (tptp.ti X_a A_6))))) (forall ((X_a $$unsorted)) (=> (tptp.semilattice_inf X_a) (forall ((X $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.semilattice_inf_inf X_a) X) X) (tptp.ti X_a X))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.lattice X_b) (forall ((F $$unsorted) (G $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_b))) (= (tptp.hAPP X_a X_b (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_inf_inf _let_1) F) G) X_1) (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.semilattice_inf_inf X_b) (tptp.hAPP X_a X_b F X_1)) (tptp.hAPP X_a X_b G X_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.semilattice_inf X_a) (forall ((A_6 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.semilattice_inf_inf 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_6) B_2) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B_2) A_6))))))) (forall ((X_a $$unsorted)) (=> (tptp.lattice X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.semilattice_inf_inf X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 X) Y) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Y) X))))))) (forall ((X_a $$unsorted)) (=> (tptp.semilattice_inf X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.semilattice_inf_inf 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 $$unsorted)) (=> (tptp.semilattice_inf X_a) (forall ((A_6 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.semilattice_inf_inf X_a) A_6))) (let ((_let_2 (tptp.hAPP X_a X_a _let_1 B_2))) (= (tptp.hAPP X_a X_a _let_1 _let_2) _let_2)))))) (forall ((X_a $$unsorted)) (=> (tptp.lattice X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.semilattice_inf_inf 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 $$unsorted)) (=> (tptp.semilattice_inf X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.semilattice_inf_inf X_a) X))) (let ((_let_2 (tptp.hAPP X_a X_a _let_1 Y))) (= (tptp.hAPP X_a X_a _let_1 _let_2) _let_2)))))) (forall ((X_a $$unsorted)) (=> (tptp.semilattice_inf X_a) (forall ((B_2 $$unsorted) (A_6 $$unsorted) (C_2 $$unsorted)) (let ((_let_1 (tptp.semilattice_inf_inf X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 B_2))) (let ((_let_4 (tptp.hAPP X_a _let_2 _let_1 A_6))) (= (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a _let_4 C_2)) (tptp.hAPP X_a X_a _let_4 (tptp.hAPP X_a X_a _let_3 C_2)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.lattice X_a) (forall ((X $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.semilattice_inf_inf X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 X))) (let ((_let_4 (tptp.hAPP X_a _let_2 _let_1 Y))) (= (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a _let_4 Z_1)) (tptp.hAPP X_a X_a _let_4 (tptp.hAPP X_a X_a _let_3 Z_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.semilattice_inf X_a) (forall ((X $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.semilattice_inf_inf X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 X))) (let ((_let_4 (tptp.hAPP X_a _let_2 _let_1 Y))) (= (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a _let_4 Z_1)) (tptp.hAPP X_a X_a _let_4 (tptp.hAPP X_a X_a _let_3 Z_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.semilattice_inf X_a) (forall ((A_6 $$unsorted) (B_2 $$unsorted) (C_2 $$unsorted)) (let ((_let_1 (tptp.semilattice_inf_inf X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 A_6))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 B_2)) C_2) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B_2) C_2))))))))) (forall ((X_a $$unsorted)) (=> (tptp.lattice X_a) (forall ((X $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.semilattice_inf_inf X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 X))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 Y)) Z_1) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Y) Z_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.semilattice_inf X_a) (forall ((X $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.semilattice_inf_inf X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 X))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 Y)) Z_1) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Y) Z_1))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (tptp.lattice X_a) (forall ((F $$unsorted) (G $$unsorted) (X_2 $$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.semilattice_inf_inf _let_1) F) G) X_2) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.semilattice_inf_inf X_a) (tptp.hAPP X_b X_a F X_2)) (tptp.hAPP X_b X_a G X_2))))))) (forall ((X_a $$unsorted)) (=> (tptp.lattice X_a) (forall ((X $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.semilattice_sup_sup X_a) X))) (let ((_let_3 (tptp.semilattice_inf_inf 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.hAPP X_a X_a _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 Y) Z_1))) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 (tptp.hAPP X_a X_a _let_2 Y)) (tptp.hAPP X_a X_a _let_2 Z_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.lattice X_a) (forall ((X $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.semilattice_sup_sup X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 (tptp.semilattice_inf_inf X_a) X))) (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 _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 Y)) (tptp.hAPP X_a X_a _let_3 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 $$unsorted) (X_b $$unsorted) (F $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.hAPP (tptp.fun X_b X_a) (tptp.fun _let_2 _let_1) (tptp.image X_b X_a) F))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) (tptp.hAPP _let_2 _let_1 _let_3 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 (tptp.fun _let_2 _let_2) (tptp.semilattice_inf_inf _let_2) A_1) B))) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_inf_inf _let_1) (tptp.hAPP _let_2 _let_1 _let_3 A_1)) (tptp.hAPP _let_2 _let_1 _let_3 B)))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.semilattice_sup_sup _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.hAPP _let_1 _let_3 (tptp.semilattice_inf_inf _let_1) A_1))) (= (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 (tptp.hAPP _let_1 _let_1 _let_4 B)) C) (tptp.hAPP _let_1 _let_1 _let_4 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 B) C))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) C) A_1)))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (P_1 $$unsorted) (F $$unsorted) (G $$unsorted) (S $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.collect X_b))) (let ((_let_4 (tptp.hAPP _let_1 _let_2 (tptp.semilattice_inf_inf _let_1) S))) (let ((_let_5 (tptp.image X_b X_a))) (let ((_let_6 (tptp.fun X_a tptp.bool))) (let ((_let_7 (tptp.fun _let_1 _let_6))) (let ((_let_8 (tptp.fun X_b X_a))) (let ((_let_9 (tptp.fun X_a X_a))) (let ((_let_10 (tptp.fun X_a _let_9))) (let ((_let_11 (tptp.fun X_b _let_10))) (let ((_let_12 (tptp.fun X_b _let_9))) (= (tptp.hAPP _let_1 _let_6 (tptp.hAPP _let_8 _let_7 _let_5 (tptp.hAPP _let_8 _let_8 (tptp.hAPP _let_12 (tptp.fun _let_8 _let_8) (tptp.combs X_b X_a X_a) (tptp.hAPP _let_8 _let_12 (tptp.hAPP _let_11 (tptp.fun _let_8 _let_12) (tptp.combs X_b X_a _let_9) (tptp.hAPP _let_1 _let_11 (tptp.hAPP (tptp.fun tptp.bool _let_10) (tptp.fun _let_1 _let_11) (tptp.combb tptp.bool _let_10 X_b) (tptp.if X_a)) P_1)) F)) G)) S) (tptp.hAPP _let_6 _let_6 (tptp.hAPP _let_6 (tptp.fun _let_6 _let_6) (tptp.semilattice_sup_sup _let_6) (tptp.hAPP _let_1 _let_6 (tptp.hAPP _let_8 _let_7 _let_5 F) (tptp.hAPP _let_1 _let_1 _let_4 (tptp.hAPP _let_1 _let_1 _let_3 P_1)))) (tptp.hAPP _let_1 _let_6 (tptp.hAPP _let_8 _let_7 _let_5 G) (tptp.hAPP _let_1 _let_1 _let_4 (tptp.hAPP _let_1 _let_1 _let_3 (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun tptp.bool tptp.bool) _let_2 (tptp.combb tptp.bool tptp.bool X_b) tptp.fNot) P_1))))))))))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (P_1 $$unsorted) (F $$unsorted) (G $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.collect X_a))) (let ((_let_4 (tptp.dom X_a X_b))) (let ((_let_5 (tptp.option X_b))) (let ((_let_6 (tptp.fun X_a _let_5))) (let ((_let_7 (tptp.semilattice_inf_inf _let_1))) (let ((_let_8 (tptp.fun _let_5 _let_5))) (let ((_let_9 (tptp.fun _let_5 _let_8))) (let ((_let_10 (tptp.fun X_a _let_9))) (let ((_let_11 (tptp.fun X_a _let_8))) (= (tptp.hAPP _let_6 _let_1 _let_4 (tptp.hAPP _let_6 _let_6 (tptp.hAPP _let_11 (tptp.fun _let_6 _let_6) (tptp.combs X_a _let_5 _let_5) (tptp.hAPP _let_6 _let_11 (tptp.hAPP _let_10 (tptp.fun _let_6 _let_11) (tptp.combs X_a _let_5 _let_8) (tptp.hAPP _let_1 _let_10 (tptp.hAPP (tptp.fun tptp.bool _let_9) (tptp.fun _let_1 _let_10) (tptp.combb tptp.bool _let_9 X_a) (tptp.if _let_5)) P_1)) F)) G)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.semilattice_sup_sup _let_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 _let_7 (tptp.hAPP _let_6 _let_1 _let_4 F)) (tptp.hAPP _let_1 _let_1 _let_3 P_1))) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 _let_7 (tptp.hAPP _let_6 _let_1 _let_4 G)) (tptp.hAPP _let_1 _let_1 _let_3 (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun tptp.bool tptp.bool) _let_2 (tptp.combb tptp.bool tptp.bool X_a) tptp.fNot) P_1))))))))))))))))) (forall ((X_a $$unsorted) (Q_1 $$unsorted) (P_1 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.collect X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.semilattice_inf_inf _let_2))) (let ((_let_4 (tptp.fun _let_2 _let_2))) (let ((_let_5 (tptp.ord_less_eq _let_2))) (let ((_let_6 (tptp.fun _let_2 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 _let_6 _let_5 A_1) B)) (=> (forall ((X_1 $$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) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool P_1 X_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool Q_1 X_1)))))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 _let_6 _let_5 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_4 _let_3 A_1) (tptp.hAPP _let_2 _let_2 _let_1 P_1))) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_4 _let_3 B) (tptp.hAPP _let_2 _let_2 _let_1 Q_1))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.lattice X_a) (forall ((X $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.semilattice_sup_sup X_a) X))) (let ((_let_3 (tptp.semilattice_inf_inf X_a))) (=> (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (Z_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.semilattice_inf_inf X_a) X_1))) (let ((_let_3 (tptp.semilattice_sup_sup X_a))) (= (tptp.hAPP X_a X_a _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 Y_1) Z_2)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 (tptp.hAPP X_a X_a _let_2 Y_1)) (tptp.hAPP X_a X_a _let_2 Z_2))))))) (= (tptp.hAPP X_a X_a _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 Y) Z_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 (tptp.hAPP X_a X_a _let_2 Y)) (tptp.hAPP X_a X_a _let_2 Z_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.lattice X_a) (forall ((X $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.semilattice_inf_inf X_a) X))) (let ((_let_3 (tptp.semilattice_sup_sup X_a))) (=> (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (Z_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.semilattice_sup_sup X_a) X_1))) (let ((_let_3 (tptp.semilattice_inf_inf X_a))) (= (tptp.hAPP X_a X_a _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 Y_1) Z_2)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 (tptp.hAPP X_a X_a _let_2 Y_1)) (tptp.hAPP X_a X_a _let_2 Z_2))))))) (= (tptp.hAPP X_a X_a _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 Y) Z_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 (tptp.hAPP X_a X_a _let_2 Y)) (tptp.hAPP X_a X_a _let_2 Z_1)))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (B $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Z $$unsorted) (G $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.finite_finite X_b))) (let ((_let_5 (tptp.fun _let_1 X_a))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (let ((_let_7 (tptp.fun X_b X_a))) (let ((_let_8 (tptp.fun _let_7 _let_6))) (=> (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP _let_7 _let_6 (tptp.hAPP X_a _let_8 (tptp.hAPP (tptp.fun X_a _let_2) (tptp.fun X_a _let_8) (tptp.finite1357897459simple X_a X_b) F) Z) G) Fa)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_4 A_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_4 B)) (=> (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 (tptp.semilattice_inf_inf _let_1) A_1) B) (tptp.bot_bot _let_1)) (= (tptp.hAPP _let_1 X_a Fa (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 (tptp.semilattice_sup_sup _let_1) A_1) B)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 F (tptp.hAPP _let_1 X_a Fa A_1)) (tptp.hAPP _let_1 X_a Fa B)))))))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (B $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Z $$unsorted) (G $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.finite_finite X_b))) (let ((_let_5 (tptp.fun _let_1 X_a))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (let ((_let_7 (tptp.fun X_b X_a))) (let ((_let_8 (tptp.fun _let_7 _let_6))) (=> (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP _let_7 _let_6 (tptp.hAPP X_a _let_8 (tptp.hAPP (tptp.fun X_a _let_2) (tptp.fun X_a _let_8) (tptp.finite1357897459simple X_a X_b) F) Z) G) Fa)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_4 A_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_4 B)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 F (tptp.hAPP _let_1 X_a Fa (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 (tptp.semilattice_sup_sup _let_1) A_1) B))) (tptp.hAPP _let_1 X_a Fa (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 (tptp.semilattice_inf_inf _let_1) A_1) B))) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 F (tptp.hAPP _let_1 X_a Fa A_1)) (tptp.hAPP _let_1 X_a Fa B))))))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F $$unsorted) (Z $$unsorted) (G $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 X_a))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.fun X_b X_a))) (let ((_let_5 (tptp.fun _let_4 _let_3))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_4 _let_3 (tptp.hAPP X_a _let_5 (tptp.hAPP (tptp.fun X_a (tptp.fun X_a X_a)) (tptp.fun X_a _let_5) (tptp.finite1357897459simple X_a X_b) F) Z) G) Fa)) (= (tptp.hAPP _let_1 X_a Fa (tptp.bot_bot _let_1)) (tptp.ti X_a Z))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (X_2 $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Z $$unsorted) (G $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.fun _let_1 X_a))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.fun X_b X_a))) (let ((_let_6 (tptp.fun _let_5 _let_4))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_5 _let_4 (tptp.hAPP X_a _let_6 (tptp.hAPP (tptp.fun X_a _let_2) (tptp.fun X_a _let_6) (tptp.finite1357897459simple X_a X_b) F) Z) G) Fa)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) A_1)) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_2) A_1))) (= (tptp.hAPP _let_1 X_a Fa (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_2) A_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 F (tptp.hAPP X_b X_a G X_2)) (tptp.hAPP _let_1 X_a Fa A_1))))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (B $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Z $$unsorted) (G $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.finite_finite X_b))) (let ((_let_4 (tptp.fun _let_1 X_a))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (let ((_let_6 (tptp.fun X_b X_a))) (let ((_let_7 (tptp.fun _let_6 _let_5))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP _let_6 _let_5 (tptp.hAPP X_a _let_7 (tptp.hAPP (tptp.fun X_a _let_2) (tptp.fun X_a _let_7) (tptp.finite1357897459simple X_a X_b) F) Z) G) Fa)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 A_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 B)) (=> (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_inf_inf _let_1) A_1) B))) (= (tptp.hAPP X_b X_a G X_1) (tptp.ti X_a Z))))) (= (tptp.hAPP _let_1 X_a Fa (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_sup_sup _let_1) A_1) B)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 F (tptp.hAPP _let_1 X_a Fa A_1)) (tptp.hAPP _let_1 X_a Fa B))))))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Z $$unsorted) (G $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 X_a))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.fun X_b X_a))) (let ((_let_5 (tptp.fun _let_4 _let_3))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_4 _let_3 (tptp.hAPP X_a _let_5 (tptp.hAPP (tptp.fun X_a (tptp.fun X_a X_a)) (tptp.fun X_a _let_5) (tptp.finite1357897459simple X_a X_b) F) Z) G) Fa)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) A_1)) (=> (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_1) A_1)) (= (tptp.hAPP X_b X_a G X_1) (tptp.ti X_a Z))))) (= (tptp.hAPP _let_1 X_a Fa A_1) (tptp.ti X_a Z))))))))))) (forall ((X_a $$unsorted) (X_2 $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.bot_bot _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 (tptp.minus_minus _let_1) A_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_3 (tptp.insert X_a) X_2) _let_2)))) (let ((_let_5 (tptp.fun X_a X_a))) (let ((_let_6 (tptp.hAPP _let_1 X_a Fa A_1))) (let ((_let_7 (= _let_4 _let_2))) (let ((_let_8 (tptp.fun _let_1 X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_8 tptp.bool (tptp.hAPP (tptp.fun X_a _let_5) (tptp.fun _let_8 tptp.bool) (tptp.finite_folding_one X_a) F) Fa)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_a) A_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) A_1)) (and (=> _let_7 (= _let_6 (tptp.ti X_a X_2))) (=> (not _let_7) (= _let_6 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_5 F X_2) (tptp.hAPP _let_1 X_a Fa _let_4))))))))))))))))) (forall ((X_a $$unsorted) (X_2 $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.bot_bot _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.hAPP X_a _let_3 (tptp.insert X_a) X_2))) (let ((_let_5 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 (tptp.minus_minus _let_1) A_1) (tptp.hAPP _let_1 _let_1 _let_4 _let_2)))) (let ((_let_6 (tptp.fun X_a X_a))) (let ((_let_7 (tptp.hAPP _let_1 X_a Fa (tptp.hAPP _let_1 _let_1 _let_4 A_1)))) (let ((_let_8 (= _let_5 _let_2))) (let ((_let_9 (tptp.fun _let_1 X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_9 tptp.bool (tptp.hAPP (tptp.fun X_a _let_6) (tptp.fun _let_9 tptp.bool) (tptp.finite_folding_one X_a) F) Fa)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_a) A_1)) (and (=> _let_8 (= _let_7 (tptp.ti X_a X_2))) (=> (not _let_8) (= _let_7 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_6 F X_2) (tptp.hAPP _let_1 X_a Fa _let_5))))))))))))))))) (forall ((X_a $$unsorted) (B $$unsorted) (C_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) C_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_1)) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) A_1) B)))))))) (forall ((X_a $$unsorted) (C_1 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) C_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) A_1) B))) (not (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B)))))))) (forall ((X_a $$unsorted) (B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.finite_finite X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_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_1) B))))))) (forall ((X_a $$unsorted) (C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP _let_1 _let_2 (tptp.semilattice_inf_inf _let_1) C))) (let ((_let_4 (tptp.minus_minus _let_1))) (= (tptp.hAPP _let_1 _let_1 _let_3 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 _let_4 A_1) B)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 _let_4 (tptp.hAPP _let_1 _let_1 _let_3 A_1)) (tptp.hAPP _let_1 _let_1 _let_3 B)))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted) (C $$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_3 (tptp.semilattice_inf_inf _let_1) A_1))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 (tptp.hAPP _let_1 _let_1 _let_4 B)) C) (tptp.hAPP _let_1 _let_1 _let_4 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 B) C)))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.semilattice_inf_inf _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.minus_minus _let_1))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_4 A_1) B)) C) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_4 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 A_1) C)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 B) C)))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (C $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.semilattice_inf_inf _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.hAPP _let_1 _let_3 (tptp.minus_minus _let_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 A_1) C)))) (= (tptp.hAPP _let_1 _let_1 _let_4 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 B) C)) (tptp.hAPP _let_1 _let_1 _let_4 B))))))) (forall ((X_a $$unsorted) (A_3 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP X_a _let_2 (tptp.insert X_a) A_3))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) A_3) A_1)) (= (tptp.hAPP _let_1 _let_1 _let_3 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.minus_minus _let_1) A_1) (tptp.hAPP _let_1 _let_1 _let_3 (tptp.bot_bot _let_1)))) (tptp.ti _let_1 A_1))))))) (forall ((X_a $$unsorted) (X_2 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP X_a _let_2 (tptp.insert X_a) X_2))) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) A_1))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.minus_minus _let_1) (tptp.hAPP _let_1 _let_1 _let_3 A_1)) (tptp.hAPP _let_1 _let_1 _let_3 (tptp.bot_bot _let_1))) (tptp.ti _let_1 A_1))))))) (forall ((X_a $$unsorted) (A_3 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP X_a _let_2 (tptp.insert X_a) A_3))) (= (tptp.hAPP _let_1 _let_1 _let_3 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.minus_minus _let_1) A_1) (tptp.hAPP _let_1 _let_1 _let_3 (tptp.bot_bot _let_1)))) (tptp.hAPP _let_1 _let_1 _let_3 A_1)))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (A_3 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP X_a _let_2 (tptp.insert X_a) A_3))) (let ((_let_4 (tptp.minus_minus _let_1))) (let ((_let_5 (tptp.hAPP _let_1 _let_2 _let_4 A_1))) (= (tptp.hAPP _let_1 _let_1 _let_5 (tptp.hAPP _let_1 _let_1 _let_3 B)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 _let_4 (tptp.hAPP _let_1 _let_1 _let_5 (tptp.hAPP _let_1 _let_1 _let_3 (tptp.bot_bot _let_1)))) B)))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (A_3 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP X_a _let_2 (tptp.insert X_a) A_3))) (let ((_let_4 (tptp.minus_minus _let_1))) (let ((_let_5 (tptp.hAPP _let_1 _let_2 _let_4 A_1))) (= (tptp.hAPP _let_1 _let_1 _let_5 (tptp.hAPP _let_1 _let_1 _let_3 B)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 _let_4 (tptp.hAPP _let_1 _let_1 _let_5 B)) (tptp.hAPP _let_1 _let_1 _let_3 (tptp.bot_bot _let_1)))))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (A_3 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP _let_1 _let_2 (tptp.minus_minus _let_1) A_1))) (let ((_let_4 (tptp.finite_finite X_a))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_4 (tptp.hAPP _let_1 _let_1 _let_3 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_2 (tptp.insert X_a) A_3) B)))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_4 (tptp.hAPP _let_1 _let_1 _let_3 B))))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.semilattice_inf_inf _let_1) A_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.minus_minus _let_1) B) A_1)) (tptp.bot_bot _let_1))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (=> (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.semilattice_inf_inf _let_1) A_1) B) (tptp.bot_bot _let_1)) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.minus_minus _let_1) A_1) B) (tptp.ti _let_1 A_1)))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (F $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP (tptp.fun X_b X_a) (tptp.fun _let_1 _let_2) (tptp.image X_b X_a) F))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 (tptp.fun _let_2 _let_2) (tptp.minus_minus _let_2) (tptp.hAPP _let_1 _let_2 _let_3 A_1)) (tptp.hAPP _let_1 _let_2 _let_3 B))) (tptp.hAPP _let_1 _let_2 _let_3 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) A_1) B)))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) A_1) B)) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.semilattice_sup_sup _let_1) A_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.minus_minus _let_1) B) A_1)) (tptp.ti _let_1 B)))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.ord_less_eq _let_1))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_4 _let_3 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.minus_minus _let_1) A_1) B)) C)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_4 _let_3 A_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.semilattice_sup_sup _let_1) B) C))))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP _let_1 _let_2 (tptp.minus_minus _let_1) A_1))) (= (tptp.hAPP _let_1 _let_1 _let_3 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.semilattice_inf_inf _let_1) B) C)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.semilattice_sup_sup _let_1) (tptp.hAPP _let_1 _let_1 _let_3 B)) (tptp.hAPP _let_1 _let_1 _let_3 C))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP _let_1 _let_2 (tptp.minus_minus _let_1) A_1))) (= (tptp.hAPP _let_1 _let_1 _let_3 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.semilattice_sup_sup _let_1) B) C)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.semilattice_inf_inf _let_1) (tptp.hAPP _let_1 _let_1 _let_3 B)) (tptp.hAPP _let_1 _let_1 _let_3 C))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.semilattice_sup_sup _let_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.minus_minus _let_1) A_1) B)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.semilattice_inf_inf _let_1) A_1) B)) (tptp.ti _let_1 A_1))))) (forall ((X_a $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) A_1) A_1) (tptp.bot_bot _let_1)))) (forall ((X_a $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) A_1) (tptp.bot_bot _let_1)) (tptp.ti _let_1 A_1)))) (forall ((X_a $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.bot_bot _let_1))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) _let_2) A_1) _let_2)))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.finite_finite X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 B)) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 (tptp.fun _let_2 _let_2) (tptp.minus_minus _let_2) A_1) B))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 A_1))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (X_2 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.minus_minus _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) B)) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_3 (tptp.insert X_a) X_2) A_1)) B) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 A_1) B))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (X_2 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.minus_minus _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 A_1) B))) (let ((_let_5 (tptp.hAPP X_a _let_3 (tptp.insert X_a) X_2))) (let ((_let_6 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 (tptp.hAPP _let_1 _let_1 _let_5 A_1)) B))) (let ((_let_7 (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) B)))) (and (=> _let_7 (= _let_6 _let_4)) (=> (not _let_7) (= _let_6 (tptp.hAPP _let_1 _let_1 _let_5 _let_4)))))))))))) (forall ((X_a $$unsorted) (C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.minus_minus _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.ord_less_eq _let_1))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_5 _let_4 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_5 _let_4 B) C)) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 B) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 C) A_1)) (tptp.ti _let_1 A_1)))))))))) (forall ((X_a $$unsorted) (D_1 $$unsorted) (B $$unsorted) (A_1 $$unsorted) (C $$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_1) C)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_5 _let_4 D_1) B)) (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_1) B)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 C) D_1))))))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) A_1) B)) A_1)))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _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_1) B) (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_1))) (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))))))))))) (forall ((X_a $$unsorted) (C_1 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) C_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_1) B))) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_1)) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B)))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.minus_minus _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 A_1) B))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 _let_4) B) _let_4)))))) (forall ((X_a $$unsorted) (C_1 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) C_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) A_1) B))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_1)))))) (forall ((X_a $$unsorted) (C_1 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) C_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) A_1) B))) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.minus_minus _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.semilattice_sup_sup _let_1))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_4 A_1) B)) C) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_4 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 A_1) C)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 B) C)))))))) (forall ((X_a $$unsorted) (B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.semilattice_sup_sup _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 (tptp.minus_minus _let_1) B) A_1)) A_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 B) A_1)))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP _let_1 _let_2 (tptp.semilattice_sup_sup _let_1) A_1))) (= (tptp.hAPP _let_1 _let_1 _let_3 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.minus_minus _let_1) B) A_1)) (tptp.hAPP _let_1 _let_1 _let_3 B)))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.minus X_b) (forall ((A_1 $$unsorted) (B $$unsorted) (X_1 $$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_1) B) X_1) (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_1 X_1)) (tptp.hAPP X_a X_b B X_1))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (tptp.minus X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b X_a))) (= (tptp.hAPP X_b X_a (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) A_1) B) X_2) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.minus_minus X_a) (tptp.hAPP X_b X_a A_1 X_2)) (tptp.hAPP X_b X_a B X_2))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (X_2 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.ord_less_eq _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.hAPP _let_1 _let_3 _let_2 A_1))) (let ((_let_5 (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a _let_3 (tptp.member X_a) X_2) A_1)))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (let ((_let_7 (tptp.hAPP X_a _let_6 (tptp.insert X_a) X_2))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_4 (tptp.hAPP _let_1 _let_1 _let_7 B))) (and (=> _let_5 (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_6 (tptp.minus_minus _let_1) A_1) (tptp.hAPP _let_1 _let_1 _let_7 (tptp.bot_bot _let_1)))) B))) (=> (not _let_5) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_4 B))))))))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (X_2 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP X_a _let_2 (tptp.insert X_a) X_2))) (let ((_let_4 (tptp.ord_less_eq _let_1))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_5 _let_4 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.minus_minus _let_1) A_1) (tptp.hAPP _let_1 _let_1 _let_3 (tptp.bot_bot _let_1)))) B)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a _let_5 (tptp.member X_a) X_2) A_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_5 _let_4 A_1) (tptp.hAPP _let_1 _let_1 _let_3 B))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (X_2 $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Z $$unsorted) (G $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.fun X_a X_a))) (let ((_let_4 (tptp.fun _let_1 X_a))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (let ((_let_6 (tptp.fun X_b X_a))) (let ((_let_7 (tptp.fun _let_6 _let_5))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP _let_6 _let_5 (tptp.hAPP X_a _let_7 (tptp.hAPP (tptp.fun X_a _let_3) (tptp.fun X_a _let_7) (tptp.finite1357897459simple X_a X_b) F) Z) G) Fa)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) A_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_2) A_1)) (= (tptp.hAPP _let_1 X_a Fa A_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 F (tptp.hAPP X_b X_a G X_2)) (tptp.hAPP _let_1 X_a Fa (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.minus_minus _let_1) A_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_2 (tptp.insert X_b) X_2) (tptp.bot_bot _let_1))))))))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (X_2 $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Z $$unsorted) (G $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP X_b _let_2 (tptp.insert X_b) X_2))) (let ((_let_4 (tptp.fun X_a X_a))) (let ((_let_5 (tptp.fun _let_1 X_a))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (let ((_let_7 (tptp.fun X_b X_a))) (let ((_let_8 (tptp.fun _let_7 _let_6))) (=> (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP _let_7 _let_6 (tptp.hAPP X_a _let_8 (tptp.hAPP (tptp.fun X_a _let_4) (tptp.fun X_a _let_8) (tptp.finite1357897459simple X_a X_b) F) Z) G) Fa)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) A_1)) (= (tptp.hAPP _let_1 X_a Fa (tptp.hAPP _let_1 _let_1 _let_3 A_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 F (tptp.hAPP X_b X_a G X_2)) (tptp.hAPP _let_1 X_a Fa (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.minus_minus _let_1) A_1) (tptp.hAPP _let_1 _let_1 _let_3 (tptp.bot_bot _let_1))))))))))))))))) (forall ((X_a $$unsorted) (P_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_a) A_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool P_1 A_1)) (=> (forall ((A_5 $$unsorted) (A_4 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_a) A_4)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) A_5) A_4)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool P_1 A_4)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool P_1 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.minus_minus _let_1) A_4) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_2 (tptp.insert X_a) A_5) (tptp.bot_bot _let_1))))))))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool P_1 (tptp.bot_bot _let_1)))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (F $$unsorted) (G $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.dom X_a X_b))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.option X_b))) (let ((_let_4 (tptp.fun X_a _let_3))) (let ((_let_5 (tptp.hAPP _let_4 _let_2 _let_1 G))) (let ((_let_6 (tptp.fun _let_2 _let_2))) (let ((_let_7 (tptp.hAPP (tptp.fun X_a (tptp.fun _let_2 tptp.bool)) _let_6 (tptp.combc X_a _let_2 tptp.bool) (tptp.member X_a)))) (let ((_let_8 (tptp.collect X_a))) (let ((_let_9 (tptp.minus_minus _let_2))) (let ((_let_10 (tptp.fun _let_2 _let_4))) (= (tptp.hAPP _let_4 _let_2 _let_1 (tptp.hAPP _let_2 _let_4 (tptp.hAPP _let_4 _let_10 (tptp.hAPP _let_4 (tptp.fun _let_4 _let_10) (tptp.override_on X_a _let_3) F) G) A_1)) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_6 (tptp.semilattice_sup_sup _let_2) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_6 _let_9 (tptp.hAPP _let_4 _let_2 _let_1 F)) (tptp.hAPP _let_2 _let_2 _let_8 (tptp.hAPP _let_2 _let_2 _let_7 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_6 _let_9 A_1) _let_5))))) (tptp.hAPP _let_2 _let_2 _let_8 (tptp.hAPP _let_2 _let_2 _let_7 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_6 (tptp.semilattice_inf_inf _let_2) A_1) _let_5)))))))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (F $$unsorted) (G $$unsorted)) (let ((_let_1 (tptp.fun X_a X_b))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.fun _let_2 _let_1))) (= (tptp.hAPP _let_2 _let_1 (tptp.hAPP _let_1 _let_3 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_3) (tptp.override_on X_a X_b) F) G) (tptp.bot_bot _let_2)) (tptp.ti _let_1 F)))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ab_group_add X_a) (forall ((A_3 $$unsorted) (B_1 $$unsorted) (C_1 $$unsorted) (D $$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 A_3) B_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 C_1) D)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_3) B_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 C_1) D))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ab_group_add X_a) (forall ((A_3 $$unsorted) (B_1 $$unsorted) (C_1 $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.minus_minus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (=> (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_3) B_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 C_1) D)) (= (= (tptp.ti X_a A_3) (tptp.ti X_a B_1)) (= (tptp.ti X_a C_1) (tptp.ti X_a D))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F $$unsorted) (G $$unsorted) (A_3 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_b))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.fun _let_2 _let_1))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a (tptp.fun _let_2 tptp.bool) (tptp.member X_a) A_3) A_1)) (= (tptp.hAPP X_a X_b (tptp.hAPP _let_2 _let_1 (tptp.hAPP _let_1 _let_3 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_3) (tptp.override_on X_a X_b) F) G) A_1) A_3) (tptp.hAPP X_a X_b G A_3))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F $$unsorted) (G $$unsorted) (A_3 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_b))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.fun _let_2 _let_1))) (=> (not (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a (tptp.fun _let_2 tptp.bool) (tptp.member X_a) A_3) A_1))) (= (tptp.hAPP X_a X_b (tptp.hAPP _let_2 _let_1 (tptp.hAPP _let_1 _let_3 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_3) (tptp.override_on X_a X_b) F) G) A_1) A_3) (tptp.hAPP X_a X_b F A_3))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F $$unsorted) (G $$unsorted) (A_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_b))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.fun _let_2 _let_1))) (let ((_let_4 (tptp.hAPP X_a X_b (tptp.hAPP _let_2 _let_1 (tptp.hAPP _let_1 _let_3 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_3) (tptp.override_on X_a X_b) F) G) A_1) X_1))) (let ((_let_5 (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a (tptp.fun _let_2 tptp.bool) (tptp.member X_a) X_1) A_1)))) (and (=> _let_5 (= _let_4 (tptp.hAPP X_a X_b G X_1))) (=> (not _let_5) (= _let_4 (tptp.hAPP X_a X_b F X_1)))))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a _let_2 (tptp.insert X_a) B_1) (tptp.bot_bot _let_1)))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.hAPP _let_1 X_a (tptp.hAPP X_a (tptp.fun _let_1 X_a) (tptp.partial_flat_lub X_a) B_1) A_1))) (let ((_let_6 (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_4 (tptp.ord_less_eq _let_1) A_1) _let_3)))) (and (=> _let_6 (= _let_5 (tptp.ti X_a B_1))) (=> (not _let_6) (= _let_5 (tptp.hAPP _let_1 X_a (tptp.the_1 X_a) (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_a _let_4) _let_2 (tptp.combc X_a _let_1 tptp.bool) (tptp.member X_a)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.minus_minus _let_1) A_1) _let_3))))))))))))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun X_a _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.fun X_a _let_3))) (let ((_let_5 (tptp.fun _let_1 _let_3))) (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.finite_comp_fun_idem X_a _let_1) (tptp.hAPP _let_2 _let_4 (tptp.hAPP _let_5 (tptp.fun _let_2 _let_4) (tptp.combb _let_1 _let_3 X_a) (tptp.hAPP _let_5 _let_5 (tptp.combc _let_1 _let_1 _let_1) (tptp.minus_minus _let_1))) (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_4 (tptp.fun _let_1 _let_2) (tptp.combc X_a _let_1 _let_1) (tptp.insert X_a)) (tptp.bot_bot _let_1))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_2 $$unsorted) (Z $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun X_b X_b))) (let ((_let_2 (tptp.hAPP X_a _let_1 F X_2))) (let ((_let_3 (tptp.hAPP X_b X_b _let_2 Z))) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_a _let_1) tptp.bool (tptp.finite_comp_fun_idem X_a X_b) F)) (= (tptp.hAPP X_b X_b _let_2 _let_3) _let_3)))))) (forall ((X_a $$unsorted)) (=> (tptp.semilattice_inf X_a) (tptp.hBOOL (tptp.hAPP (tptp.fun X_a (tptp.fun X_a X_a)) tptp.bool (tptp.finite_comp_fun_idem X_a X_a) (tptp.semilattice_inf_inf X_a))))) (forall ((X_a $$unsorted)) (=> (tptp.semilattice_sup X_a) (tptp.hBOOL (tptp.hAPP (tptp.fun X_a (tptp.fun X_a X_a)) tptp.bool (tptp.finite_comp_fun_idem X_a X_a) (tptp.semilattice_sup_sup X_a))))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (tptp.hBOOL (tptp.hAPP (tptp.fun X_a (tptp.fun _let_1 _let_1)) tptp.bool (tptp.finite_comp_fun_idem X_a _let_1) (tptp.insert X_a))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F $$unsorted) (Y_2 $$unsorted) (X_2 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.image X_a X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.fun _let_3 _let_2))) (let ((_let_5 (tptp.fun X_a X_b))) (let ((_let_6 (tptp.hAPP _let_5 _let_4 _let_1 F))) (let ((_let_7 (tptp.fun X_b _let_5))) (let ((_let_8 (tptp.hAPP _let_3 _let_2 (tptp.hAPP _let_5 _let_4 _let_1 (tptp.hAPP X_b _let_5 (tptp.hAPP X_a _let_7 (tptp.hAPP _let_5 (tptp.fun X_a _let_7) (tptp.fun_upd X_a X_b) F) X_2) Y_2)) A_1))) (let ((_let_9 (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_a (tptp.fun _let_3 tptp.bool) (tptp.member X_a) X_2) A_1)))) (let ((_let_10 (tptp.fun _let_3 _let_3))) (and (=> _let_9 (= _let_8 (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_b (tptp.fun _let_2 _let_2) (tptp.insert X_b) Y_2) (tptp.hAPP _let_3 _let_2 _let_6 (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_3 _let_10 (tptp.minus_minus _let_3) A_1) (tptp.hAPP _let_3 _let_3 (tptp.hAPP X_a _let_10 (tptp.insert X_a) X_2) (tptp.bot_bot _let_3))))))) (=> (not _let_9) (= _let_8 (tptp.hAPP _let_3 _let_2 _let_6 A_1))))))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F $$unsorted) (Z $$unsorted) (Y_2 $$unsorted) (X_2 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.fun _let_3 _let_2))) (let ((_let_5 (tptp.hAPP X_b _let_4 (tptp.hAPP (tptp.fun X_a _let_1) (tptp.fun X_b _let_4) (tptp.fold_graph X_a X_b) F) Z))) (let ((_let_6 (tptp.fun _let_3 _let_3))) (=> (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_1)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP _let_3 _let_2 _let_5 (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_3 _let_6 (tptp.minus_minus _let_3) A_1) (tptp.hAPP _let_3 _let_3 (tptp.hAPP X_a _let_6 (tptp.insert X_a) X_2) (tptp.bot_bot _let_3)))) Y_2)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP _let_3 _let_2 _let_5 A_1) (tptp.hAPP X_b X_b (tptp.hAPP X_a _let_1 F X_2) Y_2)))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_b))) (let ((_let_2 (tptp.fun X_b _let_1))) (= (tptp.hAPP X_b _let_1 (tptp.hAPP X_a _let_2 (tptp.hAPP _let_1 (tptp.fun X_a _let_2) (tptp.fun_upd X_a X_b) F) X_2) (tptp.hAPP X_a X_b F X_2)) (tptp.ti _let_1 F))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (M $$unsorted) (Y_2 $$unsorted) (X_2 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.option X_b))) (let ((_let_2 (tptp.image X_a _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (let ((_let_5 (tptp.fun _let_4 _let_3))) (let ((_let_6 (tptp.fun X_a _let_1))) (let ((_let_7 (tptp.fun _let_1 _let_6))) (=> (not (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP X_a (tptp.fun _let_4 tptp.bool) (tptp.member X_a) X_2) A_1))) (= (tptp.hAPP _let_4 _let_3 (tptp.hAPP _let_6 _let_5 _let_2 (tptp.hAPP _let_1 _let_6 (tptp.hAPP X_a _let_7 (tptp.hAPP _let_6 (tptp.fun X_a _let_7) (tptp.fun_upd X_a _let_1) M) X_2) (tptp.hAPP X_b _let_1 (tptp.some X_b) Y_2))) A_1) (tptp.hAPP _let_4 _let_3 (tptp.hAPP _let_6 _let_5 _let_2 M) A_1))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (M $$unsorted) (A_3 $$unsorted) (X_2 $$unsorted) (N $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.some X_b))) (let ((_let_2 (tptp.option X_b))) (let ((_let_3 (tptp.fun_upd X_a _let_2))) (let ((_let_4 (tptp.fun X_a _let_2))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (let ((_let_6 (tptp.fun X_a _let_5))) (=> (= (tptp.hAPP _let_2 _let_4 (tptp.hAPP X_a _let_5 (tptp.hAPP _let_4 _let_6 _let_3 M) A_3) (tptp.hAPP X_b _let_2 _let_1 X_2)) (tptp.hAPP _let_2 _let_4 (tptp.hAPP X_a _let_5 (tptp.hAPP _let_4 _let_6 _let_3 N) A_3) (tptp.hAPP X_b _let_2 _let_1 Y_2))) (= (tptp.ti X_b X_2) (tptp.ti X_b Y_2)))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (T_3 $$unsorted) (K $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.option X_a))) (let ((_let_2 (tptp.fun X_b _let_1))) (let ((_let_3 (tptp.hAPP X_a _let_1 (tptp.some X_a) X_2))) (let ((_let_4 (tptp.fun _let_1 _let_2))) (=> (= (tptp.hAPP X_b _let_1 T_3 K) _let_3) (= (tptp.hAPP _let_1 _let_2 (tptp.hAPP X_b _let_4 (tptp.hAPP _let_2 (tptp.fun X_b _let_4) (tptp.fun_upd X_b _let_1) T_3) K) _let_3) (tptp.ti _let_2 T_3)))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (M $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted) (X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.some X_a))) (let ((_let_2 (tptp.option X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 Y_2))) (let ((_let_4 (= (tptp.ti X_b X_2) (tptp.ti X_b A_3)))) (let ((_let_5 (tptp.fun X_b _let_2))) (let ((_let_6 (tptp.fun _let_2 _let_5))) (= (= (tptp.hAPP X_b _let_2 (tptp.hAPP _let_2 _let_5 (tptp.hAPP X_b _let_6 (tptp.hAPP _let_5 (tptp.fun X_b _let_6) (tptp.fun_upd X_b _let_2) M) A_3) (tptp.hAPP X_a _let_2 _let_1 B_1)) X_2) _let_3) (or (and _let_4 (= (tptp.ti X_a B_1) (tptp.ti X_a Y_2))) (and (not _let_4) (= (tptp.hAPP X_b _let_2 M X_2) _let_3))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun _let_1 _let_2))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.hAPP X_b _let_3 (tptp.hAPP (tptp.fun X_a (tptp.fun X_b X_b)) (tptp.fun X_b _let_3) (tptp.fold_graph X_a X_b) F) Z) (tptp.bot_bot _let_1)) Z)))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F $$unsorted) (X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_b))) (let ((_let_2 (tptp.fun X_b _let_1))) (= (= (tptp.hAPP X_b _let_1 (tptp.hAPP X_a _let_2 (tptp.hAPP _let_1 (tptp.fun X_a _let_2) (tptp.fun_upd X_a X_b) F) X_2) Y_2) (tptp.ti _let_1 F)) (= (tptp.hAPP X_a X_b F X_2) (tptp.ti X_b Y_2)))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F $$unsorted) (X_2 $$unsorted) (Y_2 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.fun_upd X_a X_b))) (let ((_let_2 (tptp.fun X_a X_b))) (let ((_let_3 (tptp.fun X_b _let_2))) (let ((_let_4 (tptp.fun X_a _let_3))) (let ((_let_5 (tptp.hAPP X_a _let_3 (tptp.hAPP _let_2 _let_4 _let_1 F) X_2))) (= (tptp.hAPP X_b _let_2 (tptp.hAPP X_a _let_3 (tptp.hAPP _let_2 _let_4 _let_1 (tptp.hAPP X_b _let_2 _let_5 Y_2)) X_2) Z) (tptp.hAPP X_b _let_2 _let_5 Z)))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F $$unsorted) (X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b X_a))) (let ((_let_2 (tptp.fun X_a _let_1))) (= (tptp.hAPP X_b X_a (tptp.hAPP X_a _let_1 (tptp.hAPP X_b _let_2 (tptp.hAPP _let_1 (tptp.fun X_b _let_2) (tptp.fun_upd X_b X_a) F) X_2) Y_2) X_2) (tptp.ti X_a Y_2))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F $$unsorted) (Y_2 $$unsorted) (Z $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_b))) (let ((_let_2 (tptp.fun X_b _let_1))) (let ((_let_3 (tptp.hAPP X_a X_b (tptp.hAPP X_b _let_1 (tptp.hAPP X_a _let_2 (tptp.hAPP _let_1 (tptp.fun X_a _let_2) (tptp.fun_upd X_a X_b) F) X_2) Y_2) Z))) (let ((_let_4 (= (tptp.ti X_a Z) (tptp.ti X_a X_2)))) (and (=> _let_4 (= _let_3 (tptp.ti X_b Y_2))) (=> (not _let_4) (= _let_3 (tptp.hAPP X_a X_b F Z))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (M $$unsorted) (B_1 $$unsorted) (D $$unsorted) (A_3 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.fun_upd X_a X_b))) (let ((_let_2 (tptp.fun X_a X_b))) (let ((_let_3 (tptp.fun X_b _let_2))) (let ((_let_4 (tptp.fun X_a _let_3))) (let ((_let_5 (tptp.hAPP _let_2 _let_4 _let_1 M))) (=> (not (= (tptp.ti X_a A_3) (tptp.ti X_a C_1))) (= (tptp.hAPP X_b _let_2 (tptp.hAPP X_a _let_3 (tptp.hAPP _let_2 _let_4 _let_1 (tptp.hAPP X_b _let_2 (tptp.hAPP X_a _let_3 _let_5 A_3) B_1)) C_1) D) (tptp.hAPP X_b _let_2 (tptp.hAPP X_a _let_3 (tptp.hAPP _let_2 _let_4 _let_1 (tptp.hAPP X_b _let_2 (tptp.hAPP X_a _let_3 _let_5 C_1) D)) A_3) B_1))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F $$unsorted) (Y_2 $$unsorted) (Z $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_b))) (let ((_let_2 (tptp.fun X_b _let_1))) (=> (not (= (tptp.ti X_a Z) (tptp.ti X_a X_2))) (= (tptp.hAPP X_a X_b (tptp.hAPP X_b _let_1 (tptp.hAPP X_a _let_2 (tptp.hAPP _let_1 (tptp.fun X_a _let_2) (tptp.fun_upd X_a X_b) F) X_2) Y_2) Z) (tptp.hAPP X_a X_b F Z)))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F $$unsorted) (X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b X_a))) (let ((_let_2 (tptp.fun X_a _let_1))) (=> (= (tptp.hAPP X_b X_a F X_2) (tptp.ti X_a Y_2)) (= (tptp.hAPP X_a _let_1 (tptp.hAPP X_b _let_2 (tptp.hAPP _let_1 (tptp.fun X_b _let_2) (tptp.fun_upd X_b X_a) F) X_2) Y_2) (tptp.ti _let_1 F)))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F $$unsorted) (B_1 $$unsorted) (A_3 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_b))) (let ((_let_2 (tptp.fun X_b _let_1))) (let ((_let_3 (tptp.hAPP X_a X_b (tptp.hAPP X_b _let_1 (tptp.hAPP X_a _let_2 (tptp.hAPP _let_1 (tptp.fun X_a _let_2) (tptp.fun_upd X_a X_b) F) A_3) B_1) X_1))) (let ((_let_4 (= (tptp.ti X_a X_1) (tptp.ti X_a A_3)))) (and (=> _let_4 (= _let_3 (tptp.ti X_b B_1))) (=> (not _let_4) (= _let_3 (tptp.hAPP X_a X_b F X_1))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (F $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.minus_minus _let_2))) (let ((_let_4 (tptp.fun _let_2 _let_2))) (let ((_let_5 (tptp.fun X_a X_b))) (let ((_let_6 (tptp.hAPP _let_5 (tptp.fun _let_2 _let_1) (tptp.image X_a X_b) F))) (let ((_let_7 (tptp.hAPP _let_5 (tptp.fun _let_2 tptp.bool) (tptp.inj_on X_a X_b) F))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_7 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_4 (tptp.semilattice_sup_sup _let_2) A_1) B))) (and (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_7 A_1)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_7 B)) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_inf_inf _let_1) (tptp.hAPP _let_2 _let_1 _let_6 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_4 _let_3 A_1) B))) (tptp.hAPP _let_2 _let_1 _let_6 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_4 _let_3 B) A_1))) (tptp.bot_bot _let_1)))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (F $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (= (= (tptp.hAPP (tptp.fun X_a (tptp.option X_b)) _let_1 (tptp.dom X_a X_b) F) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.insert X_a) X_2) (tptp.bot_bot _let_1))) (exists ((V $$unsorted)) (let ((_let_1 (tptp.option X_b))) (let ((_let_2 (tptp.fun X_a _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_2))) (= (tptp.ti _let_2 F) (tptp.hAPP _let_1 _let_2 (tptp.hAPP X_a _let_3 (tptp.hAPP _let_2 (tptp.fun X_a _let_3) (tptp.fun_upd X_a _let_1) (tptp.hAPP _let_1 _let_2 (tptp.combk _let_1 X_a) (tptp.none X_b))) X_2) (tptp.hAPP X_b _let_1 (tptp.some X_b) V)))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun _let_1 tptp.bool) (tptp.inj_on X_a X_b) F) (tptp.bot_bot _let_1))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_2 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.none X_b))) (let ((_let_2 (tptp.option X_b))) (let ((_let_3 (tptp.fun X_a _let_2))) (let ((_let_4 (tptp.fun _let_2 _let_3))) (= (tptp.hAPP X_a _let_2 (tptp.hAPP _let_2 _let_3 (tptp.hAPP X_a _let_4 (tptp.hAPP _let_3 (tptp.fun X_a _let_4) (tptp.fun_upd X_a _let_2) (tptp.hAPP _let_2 _let_3 (tptp.combk _let_2 X_a) _let_1)) X_2) _let_1) X_1) _let_1)))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (T_3 $$unsorted) (K $$unsorted) (X_2 $$unsorted)) (not (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.option X_b))) (let ((_let_2 (tptp.fun X_a _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_2))) (= (tptp.hAPP X_a _let_1 (tptp.hAPP _let_1 _let_2 (tptp.hAPP X_a _let_3 (tptp.hAPP _let_2 (tptp.fun X_a _let_3) (tptp.fun_upd X_a _let_1) T_3) K) (tptp.hAPP X_b _let_1 (tptp.some X_b) X_2)) X_1) (tptp.none X_b)))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_2 $$unsorted) (Y_2 $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_b))) (let ((_let_2 (tptp.fun X_b _let_1))) (let ((_let_3 (tptp.inj_on X_a X_b))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (let ((_let_6 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP _let_1 _let_5 _let_3 F) A_1)) (=> (not (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP X_b (tptp.fun _let_6 tptp.bool) (tptp.member X_b) Y_2) (tptp.hAPP _let_4 _let_6 (tptp.hAPP _let_1 (tptp.fun _let_4 _let_6) (tptp.image X_a X_b) F) A_1)))) (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP _let_1 _let_5 _let_3 (tptp.hAPP X_b _let_1 (tptp.hAPP X_a _let_2 (tptp.hAPP _let_1 (tptp.fun X_a _let_2) (tptp.fun_upd X_a X_b) F) X_2) Y_2)) A_1))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (B $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun _let_1 tptp.bool) (tptp.inj_on X_a X_b) F))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) A_1) B))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (B $$unsorted) (A_1 $$unsorted) (F $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.fun X_a X_b))) (let ((_let_4 (tptp.hAPP _let_3 (tptp.fun _let_2 _let_1) (tptp.image X_a X_b) F))) (let ((_let_5 (tptp.ord_less_eq _let_2))) (let ((_let_6 (tptp.fun _let_2 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_3 _let_6 (tptp.inj_on X_a X_b) F) C)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 _let_6 _let_5 A_1) C)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 _let_6 _let_5 B) C)) (= (tptp.hAPP _let_2 _let_1 _let_4 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 (tptp.fun _let_2 _let_2) (tptp.minus_minus _let_2) A_1) B)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) (tptp.hAPP _let_2 _let_1 _let_4 A_1)) (tptp.hAPP _let_2 _let_1 _let_4 B))))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (B $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun _let_1 tptp.bool) (tptp.inj_on X_a X_b) F))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_inf_inf _let_1) A_1) B)))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (B $$unsorted) (A_1 $$unsorted) (F $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.fun X_a X_b))) (let ((_let_4 (tptp.hAPP _let_3 (tptp.fun _let_2 _let_1) (tptp.image X_a X_b) F))) (let ((_let_5 (tptp.ord_less_eq _let_2))) (let ((_let_6 (tptp.fun _let_2 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_3 _let_6 (tptp.inj_on X_a X_b) F) C)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 _let_6 _let_5 A_1) C)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 _let_6 _let_5 B) C)) (= (tptp.hAPP _let_2 _let_1 _let_4 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 (tptp.fun _let_2 _let_2) (tptp.semilattice_inf_inf _let_2) A_1) B)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_inf_inf _let_1) (tptp.hAPP _let_2 _let_1 _let_4 A_1)) (tptp.hAPP _let_2 _let_1 _let_4 B))))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (F $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun X_a X_b))) (let ((_let_4 (tptp.hAPP _let_3 (tptp.fun _let_1 _let_2) (tptp.image X_a X_b) F))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_3 (tptp.fun _let_1 tptp.bool) (tptp.inj_on X_a X_b) F) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_sup_sup _let_1) A_1) B))) (= (= (tptp.hAPP _let_1 _let_2 _let_4 A_1) (tptp.hAPP _let_1 _let_2 _let_4 B)) (= (tptp.ti _let_1 A_1) (tptp.ti _let_1 B))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_2 $$unsorted) (Y_2 $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.member X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP (tptp.fun X_a X_b) _let_3 (tptp.inj_on X_a X_b) F) A_1)) (=> (= (tptp.hAPP X_a X_b F X_2) (tptp.hAPP X_a X_b F Y_2)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a _let_3 _let_1 X_2) A_1)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a _let_3 _let_1 Y_2) A_1)) (= (tptp.ti X_a X_2) (tptp.ti X_a Y_2)))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (Y_2 $$unsorted) (X_2 $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.member X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP (tptp.fun X_a X_b) _let_3 (tptp.inj_on X_a X_b) F) A_1)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a _let_3 _let_1 X_2) A_1)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a _let_3 _let_1 Y_2) A_1)) (= (= (tptp.hAPP X_a X_b F X_2) (tptp.hAPP X_a X_b F Y_2)) (= (tptp.ti X_a X_2) (tptp.ti X_a Y_2)))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_2 $$unsorted) (Y_2 $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.member X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP (tptp.fun X_a X_b) _let_3 (tptp.inj_on X_a X_b) F) A_1)) (=> (not (= (tptp.ti X_a X_2) (tptp.ti X_a Y_2))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a _let_3 _let_1 X_2) A_1)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a _let_3 _let_1 Y_2) A_1)) (not (= (tptp.hAPP X_a X_b F X_2) (tptp.hAPP X_a X_b F Y_2))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun _let_1 tptp.bool) (tptp.inj_on X_a X_b) F) A_1)) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_1) A_1)) (forall ((Xa $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) Xa) A_1)) (=> (= (tptp.hAPP X_a X_b F X_1) (tptp.hAPP X_a X_b F Xa)) (= (tptp.ti X_a X_1) (tptp.ti X_a Xa)))))))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP (tptp.fun X_a X_a) (tptp.fun _let_1 tptp.bool) (tptp.inj_on X_a X_a) (tptp.combi X_a)) A_1)))) (forall ((X_a $$unsorted) (X_b $$unsorted) (A_1 $$unsorted) (F $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP (tptp.fun X_a X_b) _let_2 (tptp.inj_on X_a X_b) F))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 B)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_1) B)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 A_1)))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.option X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP (tptp.fun X_a _let_1) (tptp.fun _let_2 tptp.bool) (tptp.inj_on X_a _let_1) (tptp.some X_a)) A_1))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.option X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun X_a _let_2))) (let ((_let_4 (tptp.fun X_a _let_1))) (let ((_let_5 (tptp.fun X_a tptp.bool))) (= (tptp.hAPP _let_4 _let_5 (tptp.dom X_a X_b) M) (tptp.hAPP _let_5 _let_5 (tptp.collect X_a) (tptp.hAPP _let_5 _let_5 (tptp.hAPP (tptp.fun tptp.bool tptp.bool) (tptp.fun _let_5 _let_5) (tptp.combb tptp.bool tptp.bool X_a) tptp.fNot) (tptp.hAPP _let_1 _let_5 (tptp.hAPP _let_3 (tptp.fun _let_1 _let_5) (tptp.combc X_a _let_1 tptp.bool) (tptp.hAPP _let_4 _let_3 (tptp.hAPP (tptp.fun _let_1 _let_2) (tptp.fun _let_4 _let_3) (tptp.combb _let_1 _let_2 X_a) (tptp.fequal _let_1)) M)) (tptp.none X_b))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (A_3 $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.option X_b))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a (tptp.fun _let_2 tptp.bool) (tptp.member X_a) A_3) (tptp.hAPP (tptp.fun X_a _let_1) _let_2 (tptp.dom X_a X_b) M))) (not (= (tptp.hAPP X_a _let_1 M A_3) (tptp.none X_b))))))) (forall ((X_a $$unsorted) (X_2 $$unsorted)) (= (not (= (tptp.ti (tptp.option X_a) X_2) (tptp.none X_a))) (exists ((Y_1 $$unsorted)) (let ((_let_1 (tptp.option X_a))) (= (tptp.ti _let_1 X_2) (tptp.hAPP X_a _let_1 (tptp.some X_a) Y_1)))))) (forall ((X_a $$unsorted) (X_2 $$unsorted)) (= (forall ((Y_1 $$unsorted)) (let ((_let_1 (tptp.option X_a))) (not (= (tptp.ti _let_1 X_2) (tptp.hAPP X_a _let_1 (tptp.some X_a) Y_1))))) (= (tptp.ti (tptp.option X_a) X_2) (tptp.none X_a)))) (forall ((X_a $$unsorted) (A_2 $$unsorted)) (not (= (tptp.hAPP X_a (tptp.option X_a) (tptp.some X_a) A_2) (tptp.none X_a)))) (forall ((X_a $$unsorted) (A_2 $$unsorted)) (not (= (tptp.none X_a) (tptp.hAPP X_a (tptp.option X_a) (tptp.some X_a) A_2)))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F1 $$unsorted) (F2 $$unsorted)) (let ((_let_1 (tptp.option X_b))) (let ((_let_2 (tptp.fun _let_1 X_a))) (let ((_let_3 (tptp.fun X_b X_a))) (= (tptp.hAPP _let_1 X_a (tptp.hAPP _let_3 _let_2 (tptp.hAPP X_a (tptp.fun _let_3 _let_2) (tptp.option_rec X_a X_b) F1) F2) (tptp.none X_b)) (tptp.ti X_a F1)))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (= (= (tptp.hAPP (tptp.fun X_a (tptp.option X_b)) _let_1 (tptp.dom X_a X_b) F) (tptp.bot_bot _let_1)) (forall ((X_1 $$unsorted)) (= (tptp.hAPP X_a (tptp.option X_b) F X_1) (tptp.none X_b)))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_b X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.finite_finite X_a) (tptp.hAPP _let_1 _let_3 (tptp.hAPP _let_2 (tptp.fun _let_1 _let_3) (tptp.image X_b X_a) F) A_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_1 tptp.bool) (tptp.inj_on X_b X_a) F) A_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) A_1)))))))) (tptp.bounded_lattice tptp.bool) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.bounded_lattice T_1) (tptp.bounded_lattice (tptp.fun T_2 T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.bounded_lattice T_1) (tptp.bounded_lattice_bot (tptp.fun T_2 T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.lattice T_1) (tptp.semilattice_sup (tptp.fun T_2 T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.lattice T_1) (tptp.semilattice_inf (tptp.fun T_2 T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.distrib_lattice T_1) (tptp.distrib_lattice (tptp.fun T_2 T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.preorder T_1) (tptp.preorder (tptp.fun T_2 T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (and (tptp.finite_finite_1 T_1) (tptp.finite_finite_1 T_2)) (tptp.finite_finite_1 (tptp.fun T_2 T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.lattice T_1) (tptp.lattice (tptp.fun T_2 T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.order T_1) (tptp.order (tptp.fun T_2 T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.ord T_1) (tptp.ord (tptp.fun T_2 T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.bot T_1) (tptp.bot (tptp.fun T_2 T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.minus T_1) (tptp.minus (tptp.fun T_2 T_1)))) (tptp.bounded_lattice_bot tptp.bool) (tptp.semilattice_sup tptp.bool) (tptp.semilattice_inf tptp.bool) (tptp.distrib_lattice tptp.bool) (tptp.preorder tptp.bool) (tptp.finite_finite_1 tptp.bool) (tptp.lattice tptp.bool) (tptp.order tptp.bool) (tptp.ord tptp.bool) (tptp.bot tptp.bool) (tptp.minus tptp.bool) (forall ((T_1 $$unsorted)) (=> (tptp.finite_finite_1 T_1) (tptp.finite_finite_1 (tptp.option 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) (X $$unsorted) (P $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.fun X_a tptp.bool) tptp.bool (tptp.fAll X_a) P))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool P X)))) (forall ((P $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool tptp.fNot P))) (not (tptp.hBOOL P)))) (forall ((P $$unsorted)) (or (tptp.hBOOL P) (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool tptp.fNot P)))) (forall ((X_a $$unsorted) (X_c $$unsorted) (X_b $$unsorted) (P $$unsorted) (Q $$unsorted) (R $$unsorted)) (let ((_let_1 (tptp.fun X_a X_c))) (let ((_let_2 (tptp.fun X_a X_b))) (= (tptp.hAPP X_a X_c (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun _let_2 _let_1) (tptp.combb X_b X_c X_a) P) Q) R) (tptp.hAPP X_b X_c P (tptp.hAPP X_a X_b Q R)))))) (forall ((X_a $$unsorted) (X_c $$unsorted) (X_b $$unsorted) (P $$unsorted) (Q $$unsorted) (R $$unsorted)) (let ((_let_1 (tptp.fun X_b X_c))) (let ((_let_2 (tptp.fun X_a X_c))) (= (tptp.hAPP X_a X_c (tptp.hAPP X_b _let_2 (tptp.hAPP (tptp.fun X_a _let_1) (tptp.fun X_b _let_2) (tptp.combc X_a X_b X_c) P) Q) R) (tptp.hAPP X_b X_c (tptp.hAPP X_a _let_1 P R) Q))))) (forall ((X_a $$unsorted) (P $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.combi X_a) P) (tptp.ti X_a P))) (forall ((X_b $$unsorted) (X_a $$unsorted) (P $$unsorted) (Q $$unsorted)) (= (tptp.hAPP X_b X_a (tptp.hAPP X_a (tptp.fun X_b X_a) (tptp.combk X_a X_b) P) Q) (tptp.ti X_a P))) (forall ((X_a $$unsorted) (X_c $$unsorted) (X_b $$unsorted) (P $$unsorted) (Q $$unsorted) (R $$unsorted)) (let ((_let_1 (tptp.fun X_b X_c))) (let ((_let_2 (tptp.fun X_a X_c))) (let ((_let_3 (tptp.fun X_a X_b))) (= (tptp.hAPP X_a X_c (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun X_a _let_1) (tptp.fun _let_3 _let_2) (tptp.combs X_a X_b X_c) P) Q) R) (tptp.hAPP X_b X_c (tptp.hAPP X_a _let_1 P R) (tptp.hAPP X_a X_b Q R))))))) (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 $$unsorted)) (or (not (= (tptp.ti X_a X) (tptp.ti X_a Y))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.fequal X_a) X) Y)))) (forall ((Q $$unsorted) (P $$unsorted)) (or (tptp.hBOOL P) (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fimplies P) Q)))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL Q)) (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fimplies P) Q)))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fimplies P) Q))) (not (tptp.hBOOL P)) (tptp.hBOOL Q))) _let_25 _let_24 (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite _let_1) tptp.fa)) (not (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 _let_18 (tptp.member _let_1) _let_4) tptp.fa))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 _let_18 (tptp.ord_less_eq _let_2) tptp.fa) (tptp.hAPP _let_6 _let_2 (tptp.hAPP _let_10 _let_15 _let_14 (tptp.hAPP _let_11 _let_10 _let_13 (tptp.hAPP _let_8 _let_11 (tptp.hAPP (tptp.fun _let_7 tptp.com) (tptp.fun _let_8 _let_11) (tptp.combb _let_7 tptp.com tptp.pname) (tptp.the tptp.com)) tptp.body))) _let_9))) _let_23 (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_19 tptp.fa)) _let_21 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 27.21/27.40 )
% 27.21/27.40 % SZS output end Proof for SWW474+6
% 27.21/27.40 % cvc5---1.0.5 exiting
% 27.21/27.40 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------