TSTP Solution File: SWW470+6 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWW470+6 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n025.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 00:20:57 EDT 2023
% Result : Theorem 30.75s 30.99s
% Output : Proof 30.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.26 % Problem : SWW470+6 : TPTP v8.1.2. Released v5.3.0.
% 0.13/0.27 % Command : do_cvc5 %s %d
% 0.28/0.49 % Computer : n025.cluster.edu
% 0.28/0.49 % Model : x86_64 x86_64
% 0.28/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.28/0.49 % Memory : 8042.1875MB
% 0.28/0.49 % OS : Linux 3.10.0-693.el7.x86_64
% 0.28/0.49 % CPULimit : 300
% 0.28/0.49 % WCLimit : 300
% 0.28/0.49 % DateTime : Sun Aug 27 19:53:24 EDT 2023
% 0.28/0.49 % CPUTime :
% 0.35/0.76 %----Proving TF0_NAR, FOF, or CNF
% 30.75/30.99 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.l4JAdYOFLm/cvc5---1.0.5_17612.p...
% 30.75/30.99 ------- get file name : TPTP file name is SWW470+6
% 30.75/30.99 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_17612.smt2...
% 30.75/30.99 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 30.75/30.99 --- Run --no-e-matching --full-saturate-quant at 5...
% 30.75/30.99 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 30.75/30.99 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 30.75/30.99 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 30.75/30.99 % SZS status Theorem for SWW470+6
% 30.75/30.99 % SZS output start Proof for SWW470+6
% 30.75/30.99 (
% 30.75/30.99 (let ((_let_1 (tptp.hoare_1656922687triple tptp.x_a))) (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.bool))) (let ((_let_5 (tptp.fun _let_4 _let_4))) (let ((_let_6 (tptp.fun tptp.bool tptp.bool))) (let ((_let_7 (tptp.fun tptp.state _let_6))) (let ((_let_8 (tptp.fun _let_4 _let_7))) (let ((_let_9 (tptp.fun tptp.bool _let_6))) (let ((_let_10 (tptp.fun tptp.x_a _let_7))) (let ((_let_11 (tptp.fun tptp.x_a _let_4))) (let ((_let_12 (tptp.fun tptp.x_a _let_5))) (let ((_let_13 (tptp.hAPP _let_4 _let_11 (tptp.hAPP _let_12 (tptp.fun _let_4 _let_11) (tptp.combc tptp.x_a _let_4 _let_4) (tptp.hAPP _let_10 _let_12 (tptp.hAPP (tptp.fun _let_7 _let_5) (tptp.fun _let_10 _let_12) (tptp.combb _let_7 _let_5 tptp.x_a) (tptp.combs tptp.state tptp.bool tptp.bool)) (tptp.hAPP _let_11 _let_10 (tptp.hAPP _let_8 (tptp.fun _let_11 _let_10) (tptp.combb _let_4 _let_7 tptp.x_a) (tptp.hAPP _let_9 _let_8 (tptp.combb tptp.bool _let_6 tptp.state) tptp.fconj)) tptp.p))) (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_6 _let_5 (tptp.combb tptp.bool tptp.bool tptp.state) tptp.fNot) tptp.b)))) (let ((_let_14 (tptp.combk tptp.bool tptp.state))) (let ((_let_15 (tptp.hAPP tptp.bool _let_4 _let_14 tptp.fFalse))) (let ((_let_16 (tptp.combk _let_4 tptp.x_a))) (let ((_let_17 (tptp.hAPP _let_4 _let_11 _let_16 _let_15))) (let ((_let_18 (tptp.hoare_246368825triple tptp.x_a))) (let ((_let_19 (tptp.fun _let_11 _let_1))) (let ((_let_20 (tptp.fun tptp.com _let_19))) (let ((_let_21 (tptp.insert _let_1))) (let ((_let_22 (tptp.fun _let_2 _let_2))) (let ((_let_23 (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.hoare_279057269derivs tptp.x_a) tptp.g))) (let ((_let_24 (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_23 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 _let_22 _let_21 (tptp.hAPP _let_11 _let_1 (tptp.hAPP tptp.com _let_19 (tptp.hAPP _let_11 _let_20 _let_18 _let_17) tptp.c) _let_13)) _let_3))))) (let ((_let_25 (not _let_24))) (let ((_let_26 (tptp.hBOOL tptp.fFalse))) (let ((_let_27 (not _let_26))) (let ((_let_28 (forall ((X_b $$unsorted) (X_a $$unsorted) (P $$unsorted) (Q $$unsorted)) (= (tptp.hAPP X_b X_a (tptp.hAPP X_a (tptp.fun X_b X_a) (tptp.combk X_a X_b) P) Q) (tptp.ti X_a P))))) (let ((_let_29 (forall ((X_b $$unsorted) (Ga $$unsorted) (Ca $$unsorted) (Q_1 $$unsorted) (Pa $$unsorted)) (let ((_let_1 (tptp.hoare_1656922687triple X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun X_b (tptp.fun tptp.state tptp.bool)))) (let ((_let_4 (tptp.fun _let_3 _let_1))) (=> (forall ((Z_2 $$unsorted) (S_2 $$unsorted)) (let ((_let_1 (tptp.hoare_1656922687triple X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun tptp.state tptp.bool))) (let ((_let_4 (tptp.combk _let_3 X_b))) (let ((_let_5 (tptp.fun X_b _let_3))) (let ((_let_6 (tptp.fun tptp.state _let_3))) (let ((_let_7 (tptp.fun _let_5 _let_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP X_b _let_3 Pa Z_2) S_2)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.hoare_279057269derivs X_b) Ga) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 (tptp.fun _let_2 _let_2) (tptp.insert _let_1) (tptp.hAPP _let_5 _let_1 (tptp.hAPP tptp.com _let_7 (tptp.hAPP _let_5 (tptp.fun tptp.com _let_7) (tptp.hoare_246368825triple X_b) (tptp.hAPP _let_3 _let_5 _let_4 (tptp.hAPP tptp.state _let_3 (tptp.hAPP _let_6 _let_6 (tptp.combc tptp.state tptp.state tptp.bool) (tptp.fequal tptp.state)) S_2))) Ca) (tptp.hAPP _let_3 _let_5 _let_4 (tptp.hAPP X_b _let_3 Q_1 Z_2)))) (tptp.bot_bot _let_2))))))))))))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.hoare_279057269derivs X_b) Ga) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 (tptp.fun _let_2 _let_2) (tptp.insert _let_1) (tptp.hAPP _let_3 _let_1 (tptp.hAPP tptp.com _let_4 (tptp.hAPP _let_3 (tptp.fun tptp.com _let_4) (tptp.hoare_246368825triple X_b) Pa) Ca) Q_1)) (tptp.bot_bot _let_2)))))))))))) (let ((_let_30 (forall ((X_c $$unsorted) (X_a $$unsorted) (B_1_1 $$unsorted) (B_2_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a X_c B_1_1 B_2_1))) (= (tptp.ti X_c _let_1) _let_1))))) (let ((_let_31 (tptp.ti tptp.bool tptp.fFalse))) (let ((_let_32 (= _let_31 tptp.fFalse))) (let ((_let_33 (tptp.fun tptp.state _let_4))) (let ((_let_34 (tptp.fun tptp.com tptp.com))) (let ((_let_35 (tptp.fun tptp.state tptp.nat))) (let ((_let_36 (= tptp.fFalse _let_31))) (let ((_let_37 (tptp.ti _let_4 _let_15))) (let ((_let_38 (= _let_15 _let_37))) (let ((_let_39 (tptp.hAPP tptp.x_a _let_4 _let_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_30))) (let ((_let_40 (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool _let_39 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_31)))) (let ((_let_41 (= _let_37 _let_39))) (let ((_let_42 (= _let_31 (tptp.hAPP tptp.state tptp.bool _let_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_31)))) (let ((_let_43 (SYMM (ASSUME :args (_let_32))))) (let ((_let_44 (ASSUME :args (_let_27)))) (let ((_let_45 (forall ((X_c $$unsorted) (X_a $$unsorted) (B_1_1 $$unsorted) (B_2_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a X_c B_1_1 B_2_1))) (= _let_1 (tptp.ti X_c _let_1)))))) (let ((_let_46 (EQ_RESOLVE (ASSUME :args (_let_30)) (MACRO_SR_EQ_INTRO :args (_let_30 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_47 (not _let_40))) (let ((_let_48 (or _let_47 (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_23 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 _let_22 _let_21 (tptp.hAPP _let_11 _let_1 (tptp.hAPP tptp.com _let_19 (tptp.hAPP _let_11 _let_20 _let_18 (tptp.hAPP _let_4 _let_11 _let_16 (tptp.hAPP tptp.state _let_4 (tptp.hAPP _let_33 _let_33 (tptp.combc tptp.state tptp.state tptp.bool) (tptp.fequal tptp.state)) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_31))) tptp.c) (tptp.hAPP _let_4 _let_11 _let_16 (tptp.hAPP tptp.x_a _let_4 _let_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_30)))) _let_3)))))) (let ((_let_49 (forall ((Z_2 $$unsorted) (S_2 $$unsorted)) (let ((_let_1 (tptp.hoare_1656922687triple tptp.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 tptp.x_a _let_6))) (let ((_let_9 (tptp.fun tptp.x_a _let_3))) (let ((_let_10 (tptp.fun tptp.x_a _let_4))) (let ((_let_11 (tptp.combk _let_3 tptp.x_a))) (let ((_let_12 (tptp.fun tptp.state _let_3))) (let ((_let_13 (tptp.fun _let_9 _let_1))) (or (not (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP tptp.x_a _let_3 (tptp.hAPP _let_3 _let_9 _let_11 (tptp.hAPP tptp.bool _let_3 (tptp.combk tptp.bool tptp.state) tptp.fFalse)) Z_2) S_2))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.hoare_279057269derivs tptp.x_a) tptp.g) (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_13 (tptp.hAPP _let_9 (tptp.fun tptp.com _let_13) (tptp.hoare_246368825triple tptp.x_a) (tptp.hAPP _let_3 _let_9 _let_11 (tptp.hAPP tptp.state _let_3 (tptp.hAPP _let_12 _let_12 (tptp.combc tptp.state tptp.state tptp.bool) (tptp.fequal tptp.state)) S_2))) tptp.c) (tptp.hAPP _let_3 _let_9 _let_11 (tptp.hAPP tptp.x_a _let_3 (tptp.hAPP _let_3 _let_9 (tptp.hAPP _let_10 (tptp.fun _let_3 _let_9) (tptp.combc tptp.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 tptp.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 tptp.x_a) (tptp.hAPP (tptp.fun tptp.bool _let_5) _let_7 (tptp.combb tptp.bool _let_5 tptp.state) tptp.fconj)) tptp.p))) (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_5 _let_4 (tptp.combb tptp.bool tptp.bool tptp.state) tptp.fNot) tptp.b)) Z_2)))) (tptp.bot_bot _let_2))))))))))))))))))))) (let ((_let_50 (not _let_48))) (let ((_let_51 (not _let_49))) (let ((_let_52 (or _let_51 _let_24))) (let ((_let_53 (forall ((X_b $$unsorted) (Ga $$unsorted) (Ca $$unsorted) (Q_1 $$unsorted) (Pa $$unsorted)) (let ((_let_1 (tptp.hoare_1656922687triple X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun X_b (tptp.fun tptp.state tptp.bool)))) (let ((_let_4 (tptp.fun _let_3 _let_1))) (or (not (forall ((Z_2 $$unsorted) (S_2 $$unsorted)) (let ((_let_1 (tptp.hoare_1656922687triple X_b))) (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_b))) (let ((_let_5 (tptp.fun X_b _let_3))) (let ((_let_6 (tptp.fun tptp.state _let_3))) (let ((_let_7 (tptp.fun _let_5 _let_1))) (or (not (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP X_b _let_3 Pa Z_2) S_2))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.hoare_279057269derivs X_b) Ga) (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_b) (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_2))) Ca) (tptp.hAPP _let_3 _let_5 _let_4 (tptp.hAPP X_b _let_3 Q_1 Z_2)))) (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_b) Ga) (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_b) Pa) Ca) Q_1)) (tptp.bot_bot _let_2)))))))))))) (let ((_let_54 (EQ_RESOLVE (ASSUME :args (_let_29)) (MACRO_SR_EQ_INTRO :args (_let_29 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_55 (tptp.hoare_1656922687triple X_b))) (let ((_let_56 (tptp.fun _let_55 tptp.bool))) (let ((_let_57 (tptp.fun X_b _let_4))) (let ((_let_58 (tptp.fun _let_57 _let_55))) (let ((_let_59 (or))) (let ((_let_60 (_let_51))) (let ((_let_61 (_let_28))) (let ((_let_62 (ASSUME :args _let_61))) (let ((_let_63 (ASSUME :args (_let_42)))) (let ((_let_64 (ASSUME :args (_let_38)))) (let ((_let_65 (ASSUME :args (_let_41)))) (let ((_let_66 (ASSUME :args (_let_40)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_44 _let_43 _let_63 _let_64 _let_65 _let_66) :args (_let_27 _let_36 _let_38 _let_40 _let_41 _let_42)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_66)) (CONG (TRANS (CONG (REFL :args (tptp.state)) (REFL :args (tptp.bool)) (TRANS (SYMM _let_65) (SYMM _let_64)) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_31)) :args (APPLY_UF tptp.hAPP)) (SYMM _let_63) (SYMM _let_43)) :args (APPLY_UF tptp.hBOOL)) (FALSE_INTRO _let_44))) :args (_let_27 _let_36 _let_42 _let_38 _let_41 _let_40)) :args ((not (and _let_27 _let_36 _let_38 _let_40 _let_41 _let_42)) SB_LITERAL))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_27) _let_26))) (REFL :args ((not _let_36))) (REFL :args ((not _let_38))) (REFL :args (_let_47)) (REFL :args ((not _let_41))) (REFL :args ((not _let_42))) :args _let_59)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_62 :args (tptp.state tptp.bool tptp.fFalse SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_31 QUANTIFIERS_INST_CBQI_PROP)) :args _let_61))) _let_62 :args (_let_42 false _let_28)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_62 :args (tptp.x_a _let_4 _let_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_30 QUANTIFIERS_INST_CBQI_PROP)) :args _let_61))) _let_62 :args (_let_41 false _let_28)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_48 0)) (CONG (REFL :args (_let_48)) (MACRO_SR_PRED_INTRO :args ((= (not _let_47) _let_40))) :args _let_59)) :args ((or _let_40 _let_48))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_60)) :args _let_60)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_51) _let_49))) (REFL :args (_let_50)) :args _let_59)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_52)) :args ((or _let_24 _let_51 (not _let_52)))) (ASSUME :args (_let_25)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_54 :args (tptp.x_a tptp.g tptp.c _let_13 _let_17 QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP _let_56 tptp.bool (tptp.hAPP _let_56 (tptp.fun _let_56 tptp.bool) (tptp.hoare_279057269derivs X_b) Ga) (tptp.hAPP _let_56 _let_56 (tptp.hAPP _let_55 (tptp.fun _let_56 _let_56) (tptp.insert _let_55) (tptp.hAPP _let_57 _let_55 (tptp.hAPP tptp.com _let_58 (tptp.hAPP _let_57 (tptp.fun tptp.com _let_58) (tptp.hoare_246368825triple X_b) Pa) Ca) Q_1)) (tptp.bot_bot _let_56)))))) :args (_let_53))) _let_54 :args (_let_52 false _let_53)) :args (_let_51 true _let_24 false _let_52)) :args (_let_50 true _let_49)) :args (_let_40 true _let_48)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_46 :args (_let_4 tptp.bool _let_14 tptp.fFalse QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.hAPP X_a X_c B_1_1 B_2_1)))) :args (_let_45))) _let_46 :args (_let_38 false _let_45)) _let_44 _let_43 :args (false false _let_42 false _let_41 false _let_40 false _let_38 true _let_26 false _let_36)) :args ((forall ((X_b $$unsorted) (X_c $$unsorted)) (let ((_let_1 (tptp.big_comm_monoid_big X_b X_c))) (= (tptp.ti (tptp.fun (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun X_b (tptp.fun (tptp.fun (tptp.fun X_c X_b) (tptp.fun (tptp.fun X_c tptp.bool) X_b)) tptp.bool))) _let_1) _let_1))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.big_lattice_Sup_fin X_b))) (=> (tptp.lattice X_b) (= (tptp.ti (tptp.fun (tptp.fun X_b tptp.bool) X_b) _let_1) _let_1)))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.big_semilattice_big X_b))) (= (tptp.ti (tptp.fun (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun (tptp.fun (tptp.fun X_b tptp.bool) X_b) tptp.bool)) _let_1) _let_1))) (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.vname (tptp.fun _let_35 tptp.com)) tptp.ass) tptp.ass) (= (tptp.ti (tptp.fun tptp.loc_1 (tptp.fun _let_35 _let_34)) tptp.local) tptp.local) (= (tptp.ti tptp.com tptp.skip) tptp.skip) (= (tptp.ti (tptp.fun tptp.com _let_34) tptp.semi) tptp.semi) (= (tptp.ti (tptp.fun tptp.glb_1 tptp.vname) tptp.glb) tptp.glb) (= (tptp.ti (tptp.fun tptp.loc_1 tptp.vname) tptp.loc) tptp.loc) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.vname_case X_b))) (= (tptp.ti (tptp.fun (tptp.fun tptp.glb_1 X_b) (tptp.fun (tptp.fun tptp.loc_1 X_b) (tptp.fun tptp.vname X_b))) _let_1) _let_1))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.vname_rec X_b))) (= (tptp.ti (tptp.fun (tptp.fun tptp.glb_1 X_b) (tptp.fun (tptp.fun tptp.loc_1 X_b) (tptp.fun tptp.vname X_b))) _let_1) _let_1))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (let ((_let_1 (tptp.finite100568337ommute X_b X_c))) (= (tptp.ti (tptp.fun (tptp.fun X_b (tptp.fun X_c X_c)) tptp.bool) _let_1) _let_1))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (let ((_let_1 (tptp.finite_comp_fun_idem X_b X_c))) (= (tptp.ti (tptp.fun (tptp.fun X_b (tptp.fun X_c X_c)) tptp.bool) _let_1) _let_1))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.finite_finite_1 X_b))) (= (tptp.ti (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) _let_1) _let_1))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (let ((_let_1 (tptp.finite_fold X_b X_c))) (= (tptp.ti (tptp.fun (tptp.fun X_b (tptp.fun X_c X_c)) (tptp.fun X_c (tptp.fun (tptp.fun X_b tptp.bool) X_c))) _let_1) _let_1))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.finite_fold1 X_b))) (= (tptp.ti (tptp.fun (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun (tptp.fun X_b tptp.bool) X_b)) _let_1) _let_1))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.finite_fold1Set X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (= (tptp.ti (tptp.fun (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun _let_2 _let_2)) _let_1) _let_1)))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (let ((_let_1 (tptp.finite_fold_graph X_b X_c))) (= (tptp.ti (tptp.fun (tptp.fun X_b (tptp.fun X_c X_c)) (tptp.fun X_c (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool)))) _let_1) _let_1))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (let ((_let_1 (tptp.finite_fold_image X_b X_c))) (= (tptp.ti (tptp.fun (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun (tptp.fun X_c X_b) (tptp.fun X_b (tptp.fun (tptp.fun X_c tptp.bool) X_b)))) _let_1) _let_1))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (let ((_let_1 (tptp.finite1357897459simple X_b X_c))) (= (tptp.ti (tptp.fun (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun X_b (tptp.fun (tptp.fun X_c X_b) (tptp.fun (tptp.fun (tptp.fun X_c tptp.bool) X_b) tptp.bool)))) _let_1) _let_1))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (let ((_let_1 (tptp.finite908156982e_idem X_b X_c))) (= (tptp.ti (tptp.fun (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun X_b (tptp.fun (tptp.fun X_c X_b) (tptp.fun (tptp.fun (tptp.fun X_c tptp.bool) X_b) tptp.bool)))) _let_1) _let_1))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.finite_folding_one X_b))) (= (tptp.ti (tptp.fun (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun (tptp.fun (tptp.fun X_b tptp.bool) X_b) tptp.bool)) _let_1) _let_1))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.finite2073411215e_idem X_b))) (= (tptp.ti (tptp.fun (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun (tptp.fun (tptp.fun X_b tptp.bool) X_b) tptp.bool)) _let_1) _let_1))) (forall ((X_c $$unsorted)) (let ((_let_1 (tptp.minus_minus X_c))) (=> (tptp.minus X_c) (= (tptp.ti (tptp.fun X_c (tptp.fun X_c X_c)) _let_1) _let_1)))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.times_times X_b))) (=> (tptp.ab_semigroup_mult X_b) (= (tptp.ti (tptp.fun X_b (tptp.fun X_b X_b)) _let_1) _let_1)))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.the X_b))) (= (tptp.ti (tptp.fun (tptp.fun X_b tptp.bool) X_b) _let_1) _let_1))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.undefined X_a))) (= (tptp.ti X_a _let_1) _let_1))) (= (tptp.ti (tptp.fun tptp.com (tptp.hoare_1656922687triple tptp.state)) tptp.hoare_Mirabelle_MGT) tptp.hoare_Mirabelle_MGT) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.hoare_279057269derivs X_b))) (let ((_let_2 (tptp.fun (tptp.hoare_1656922687triple X_b) tptp.bool))) (= (tptp.ti (tptp.fun _let_2 (tptp.fun _let_2 tptp.bool)) _let_1) _let_1)))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.hoare_246368825triple X_b))) (let ((_let_2 (tptp.fun X_b (tptp.fun tptp.state tptp.bool)))) (= (tptp.ti (tptp.fun _let_2 (tptp.fun tptp.com (tptp.fun _let_2 (tptp.hoare_1656922687triple X_b)))) _let_1) _let_1)))) (forall ((X_c $$unsorted) (X_b $$unsorted)) (let ((_let_1 (tptp.hoare_1312322281e_case X_c X_b))) (let ((_let_2 (tptp.fun X_c (tptp.fun tptp.state tptp.bool)))) (= (tptp.ti (tptp.fun (tptp.fun _let_2 (tptp.fun tptp.com (tptp.fun _let_2 X_b))) (tptp.fun (tptp.hoare_1656922687triple X_c) X_b)) _let_1) _let_1)))) (forall ((X_c $$unsorted) (X_b $$unsorted)) (let ((_let_1 (tptp.hoare_1632998903le_rec X_c X_b))) (let ((_let_2 (tptp.fun X_c (tptp.fun tptp.state tptp.bool)))) (= (tptp.ti (tptp.fun (tptp.fun _let_2 (tptp.fun tptp.com (tptp.fun _let_2 X_b))) (tptp.fun (tptp.hoare_1656922687triple X_c) X_b)) _let_1) _let_1)))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.hoare_920331057_valid X_b))) (= (tptp.ti (tptp.fun tptp.nat (tptp.fun (tptp.hoare_1656922687triple X_b) tptp.bool)) _let_1) _let_1))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.semilattice_inf_inf X_a))) (=> (tptp.semilattice_inf X_a) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a X_a)) _let_1) _let_1)))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.semilattice_sup_sup X_b))) (=> (tptp.semilattice_sup X_b) (= (tptp.ti (tptp.fun X_b (tptp.fun X_b X_b)) _let_1) _let_1)))) (= (tptp.ti (tptp.fun tptp.com _let_33) tptp.evalc) tptp.evalc) (= (tptp.ti (tptp.fun tptp.com (tptp.fun tptp.state (tptp.fun tptp.nat _let_4))) tptp.evaln) tptp.evaln) (= (tptp.ti (tptp.fun tptp.state (tptp.fun tptp.loc_1 tptp.nat)) tptp.getlocs) tptp.getlocs) (= (tptp.ti (tptp.fun tptp.state (tptp.fun tptp.vname (tptp.fun tptp.nat tptp.state))) tptp.update) tptp.update) (forall ((X_b $$unsorted) (X_c $$unsorted)) (let ((_let_1 (tptp.fold_graph X_b X_c))) (= (tptp.ti (tptp.fun (tptp.fun X_b (tptp.fun X_c X_c)) (tptp.fun X_c (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool)))) _let_1) _let_1))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.bot_bot X_b))) (=> (tptp.bot X_b) (= (tptp.ti X_b _let_1) _let_1)))) (forall ((X_c $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_c))) (=> (tptp.ord X_c) (= (tptp.ti (tptp.fun X_c (tptp.fun X_c tptp.bool)) _let_1) _let_1)))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.partial_flat_lub X_b))) (= (tptp.ti (tptp.fun X_b (tptp.fun (tptp.fun X_b tptp.bool) X_b)) _let_1) _let_1))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.collect X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (= (tptp.ti (tptp.fun _let_2 _let_2) _let_1) _let_1)))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (let ((_let_1 (tptp.image X_b X_c))) (= (tptp.ti (tptp.fun (tptp.fun X_b X_c) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool))) _let_1) _let_1))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.insert X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (= (tptp.ti (tptp.fun X_b (tptp.fun _let_2 _let_2)) _let_1) _let_1)))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.the_elem X_b))) (= (tptp.ti (tptp.fun (tptp.fun X_b tptp.bool) X_b) _let_1) _let_1))) _let_32 (= (tptp.ti _let_6 tptp.fNot) tptp.fNot) (= (tptp.ti tptp.bool tptp.fTrue) tptp.fTrue) (= (tptp.ti _let_9 tptp.fconj) tptp.fconj) (= (tptp.ti _let_9 tptp.fdisj) tptp.fdisj) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.fequal X_a))) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a tptp.bool)) _let_1) _let_1))) (= (tptp.ti _let_9 tptp.fimplies) tptp.fimplies) (forall ((X_a $$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 $$unsorted)) (= (tptp.hAPP X_a X_c B_1_1 (tptp.ti X_a B_2_1)) (tptp.hAPP X_a X_c B_1_1 B_2_1))) _let_30 (forall ((B_1_1 $$unsorted)) (= (tptp.hBOOL (tptp.ti tptp.bool B_1_1)) (tptp.hBOOL B_1_1))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.member X_b))) (= (tptp.ti (tptp.fun X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool)) _let_1) _let_1))) (= (tptp.ti _let_2 tptp.g) tptp.g) (= (tptp.ti _let_11 tptp.p) tptp.p) (= (tptp.ti _let_4 tptp.b) tptp.b) (= (tptp.ti tptp.com tptp.c) tptp.c) (forall ((X_b $$unsorted) (Ga $$unsorted)) (let ((_let_1 (tptp.fun (tptp.hoare_1656922687triple X_b) tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.hoare_279057269derivs X_b) Ga) (tptp.bot_bot _let_1))))) (forall ((X_b $$unsorted) (Fun1_1 $$unsorted) (Com_1 $$unsorted) (Fun2_1 $$unsorted) (Fun1_2 $$unsorted) (Com $$unsorted) (Fun2_2 $$unsorted)) (let ((_let_1 (tptp.hoare_246368825triple X_b))) (let ((_let_2 (tptp.hoare_1656922687triple X_b))) (let ((_let_3 (tptp.fun X_b (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_1) 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) Fun2_2)) (and (= Fun1_1 Fun1_2) (= Com_1 Com) (= Fun2_1 Fun2_2))))))))) (forall ((X_b $$unsorted) (Ga $$unsorted) (G_1 $$unsorted) (Ts $$unsorted)) (let ((_let_1 (tptp.hoare_279057269derivs X_b))) (let ((_let_2 (tptp.fun (tptp.hoare_1656922687triple X_b) tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.hAPP _let_2 _let_3 _let_1 Ga))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 _let_3 _let_1 G_1) Ts)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_4 G_1)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_4 Ts))))))))) (forall ((X_b $$unsorted) (Ts $$unsorted) (Ga $$unsorted) (T_5 $$unsorted)) (let ((_let_1 (tptp.hoare_1656922687triple X_b))) (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_5))) (let ((_let_4 (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.hoare_279057269derivs X_b) Ga))) (=> (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_b $$unsorted) (Ga $$unsorted) (Pa $$unsorted) (Ca $$unsorted) (Q_1 $$unsorted) (C $$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 tptp.bool tptp.bool))) (let ((_let_5 (tptp.fun tptp.state _let_4))) (let ((_let_6 (tptp.fun tptp.state tptp.bool))) (let ((_let_7 (tptp.fun _let_6 _let_5))) (let ((_let_8 (tptp.fun X_b _let_5))) (let ((_let_9 (tptp.fun X_b _let_6))) (let ((_let_10 (tptp.fun tptp.bool _let_6))) (let ((_let_11 (tptp.fun X_b _let_10))) (let ((_let_12 (tptp.hoare_246368825triple X_b))) (let ((_let_13 (tptp.fun _let_9 _let_1))) (let ((_let_14 (tptp.fun tptp.com _let_13))) (let ((_let_15 (tptp.insert _let_1))) (let ((_let_16 (tptp.fun _let_2 _let_2))) (let ((_let_17 (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.hoare_279057269derivs X_b) Ga))) (=> (=> (tptp.hBOOL C) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_17 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 _let_16 _let_15 (tptp.hAPP _let_9 _let_1 (tptp.hAPP tptp.com _let_13 (tptp.hAPP _let_9 _let_14 _let_12 Pa) Ca) Q_1)) _let_3)))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_17 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 _let_16 _let_15 (tptp.hAPP _let_9 _let_1 (tptp.hAPP tptp.com _let_13 (tptp.hAPP _let_9 _let_14 _let_12 (tptp.hAPP tptp.bool _let_9 (tptp.hAPP _let_11 (tptp.fun tptp.bool _let_9) (tptp.combc X_b tptp.bool _let_6) (tptp.hAPP _let_8 _let_11 (tptp.hAPP (tptp.fun _let_5 _let_10) (tptp.fun _let_8 _let_11) (tptp.combb _let_5 _let_10 X_b) (tptp.combc 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_6 _let_5 X_b) (tptp.hAPP (tptp.fun tptp.bool _let_4) _let_7 (tptp.combb tptp.bool _let_4 tptp.state) tptp.fconj)) Pa))) C)) Ca) Q_1)) _let_3)))))))))))))))))))))) _let_29 (forall ((X_b $$unsorted) (Q_1 $$unsorted) (Ga $$unsorted) (Pa $$unsorted) (Ca $$unsorted) (Q_3 $$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.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_b) Pa) Ca))) (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_b) Ga))) (=> (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_3)) _let_3))) (=> (forall ((Z_2 $$unsorted) (S_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.state tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP X_b _let_1 Q_3 Z_2) S_2)) (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP X_b _let_1 Q_1 Z_2) S_2))))) (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 ((X_b $$unsorted) (Pa $$unsorted) (Ga $$unsorted) (P_2 $$unsorted) (Ca $$unsorted) (Q_1 $$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.hoare_246368825triple X_b))) (let ((_let_5 (tptp.fun X_b (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_b) Ga))) (=> (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) Ca) Q_1)) _let_3))) (=> (forall ((Z_2 $$unsorted) (S_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.state tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP X_b _let_1 Pa Z_2) S_2)) (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP X_b _let_1 P_2 Z_2) S_2))))) (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 Pa) Ca) Q_1)) _let_3)))))))))))))))) (forall ((X_b $$unsorted) (Q_1 $$unsorted) (Pa $$unsorted) (Ga $$unsorted) (P_2 $$unsorted) (Ca $$unsorted) (Q_3 $$unsorted)) (let ((_let_1 (tptp.hoare_1656922687triple X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.bot_bot _let_2))) (let ((_let_4 (tptp.hoare_246368825triple X_b))) (let ((_let_5 (tptp.fun X_b (tptp.fun tptp.state tptp.bool)))) (let ((_let_6 (tptp.fun _let_5 _let_1))) (let ((_let_7 (tptp.fun tptp.com _let_6))) (let ((_let_8 (tptp.insert _let_1))) (let ((_let_9 (tptp.fun _let_2 _let_2))) (let ((_let_10 (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.hoare_279057269derivs X_b) Ga))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_10 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 _let_9 _let_8 (tptp.hAPP _let_5 _let_1 (tptp.hAPP tptp.com _let_6 (tptp.hAPP _let_5 _let_7 _let_4 P_2) Ca) Q_3)) _let_3))) (=> (forall ((Z_2 $$unsorted) (S_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP X_b (tptp.fun tptp.state tptp.bool) Pa Z_2) S_2)) (forall ((S_3 $$unsorted)) (=> (forall ((Z_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.state tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP X_b _let_1 P_2 Z_3) S_2)) (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP X_b _let_1 Q_3 Z_3) S_3))))) (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP X_b (tptp.fun tptp.state tptp.bool) Q_1 Z_2) S_3)))))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_10 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 _let_9 _let_8 (tptp.hAPP _let_5 _let_1 (tptp.hAPP tptp.com _let_6 (tptp.hAPP _let_5 _let_7 _let_4 Pa) Ca) Q_1)) _let_3)))))))))))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (Ba $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_3))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) Ba) A_1))) (=> (not (= (tptp.ti X_b A_3) (tptp.ti X_b Ba))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_1))))))) (forall ((X_b $$unsorted) (Ba $$unsorted) (A_3 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_3))) (=> (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B))) (= (tptp.ti X_b A_3) (tptp.ti X_b Ba))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) Ba) B))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_3) (tptp.bot_bot _let_1)))))) (forall ((X_b $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (tptp.hAPP _let_1 _let_1 (tptp.collect X_b) (tptp.hAPP X_b _let_1 (tptp.fequal X_b) A_3)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_3) (tptp.bot_bot _let_1))))) (forall ((X_b $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_b _let_1))) (= (tptp.hAPP _let_1 _let_1 (tptp.collect X_b) (tptp.hAPP X_b _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc X_b X_b tptp.bool) (tptp.fequal X_b)) A_3)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_3) (tptp.bot_bot _let_1)))))) (forall ((X_b $$unsorted) (Pa $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b 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_b _let_3))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (let ((_let_6 (tptp.hAPP _let_1 _let_1 (tptp.collect X_b) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_4 _let_5 (tptp.combs X_b 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_b) tptp.fconj) (tptp.hAPP X_b _let_1 (tptp.fequal X_b) A_3))) Pa)))) (let ((_let_7 (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa A_3)))) (and (=> _let_7 (= _let_6 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_5 (tptp.insert X_b) A_3) _let_2))) (=> (not _let_7) (= _let_6 _let_2))))))))))) (forall ((X_b $$unsorted) (Pa $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.bot_bot _let_1))) (let ((_let_3 (tptp.fun X_b _let_1))) (let ((_let_4 (tptp.fun tptp.bool tptp.bool))) (let ((_let_5 (tptp.fun X_b _let_4))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (let ((_let_7 (tptp.hAPP _let_1 _let_1 (tptp.collect X_b) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_5 _let_6 (tptp.combs X_b tptp.bool tptp.bool) (tptp.hAPP _let_1 _let_5 (tptp.hAPP (tptp.fun tptp.bool _let_4) (tptp.fun _let_1 _let_5) (tptp.combb tptp.bool _let_4 X_b) tptp.fconj) (tptp.hAPP X_b _let_1 (tptp.hAPP _let_3 _let_3 (tptp.combc X_b X_b tptp.bool) (tptp.fequal X_b)) A_3))) Pa)))) (let ((_let_8 (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa A_3)))) (and (=> _let_8 (= _let_7 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_6 (tptp.insert X_b) A_3) _let_2))) (=> (not _let_8) (= _let_7 _let_2)))))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F1 $$unsorted) (Fun1_1 $$unsorted) (Com_1 $$unsorted) (Fun2_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c (tptp.fun tptp.state tptp.bool)))) (let ((_let_2 (tptp.fun _let_1 X_b))) (let ((_let_3 (tptp.fun tptp.com _let_2))) (let ((_let_4 (tptp.hoare_1656922687triple X_c))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (= (tptp.hAPP _let_4 X_b (tptp.hAPP (tptp.fun _let_1 _let_3) (tptp.fun _let_4 X_b) (tptp.hoare_1632998903le_rec X_c X_b) F1) (tptp.hAPP _let_1 _let_4 (tptp.hAPP tptp.com _let_5 (tptp.hAPP _let_1 (tptp.fun tptp.com _let_5) (tptp.hoare_246368825triple X_c) Fun1_1) Com_1) Fun2_1)) (tptp.hAPP _let_1 X_b (tptp.hAPP tptp.com _let_2 (tptp.hAPP _let_1 _let_3 F1 Fun1_1) Com_1) Fun2_1)))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b 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_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_3) A_1)))))) (forall ((X_b $$unsorted) (Pa $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (= (tptp.hAPP _let_1 _let_1 (tptp.collect X_b) Pa) (tptp.bot_bot _let_1)) (forall ((X_2 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa X_2))))))) (forall ((X_b $$unsorted) (Ca $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) Ca) (tptp.bot_bot _let_1)))))) (forall ((X_b $$unsorted) (Pa $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (= (tptp.bot_bot _let_1) (tptp.hAPP _let_1 _let_1 (tptp.collect X_b) Pa)) (forall ((X_2 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa X_2))))))) (forall ((X_b $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (exists ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_2) A_1)))) (not (= (tptp.ti _let_1 A_1) (tptp.bot_bot _let_1)))))) (forall ((X_b $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (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.ti _let_1 A_1) (tptp.bot_bot _let_1))))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (tptp.bot_bot _let_1) (tptp.hAPP _let_1 _let_1 (tptp.collect X_b) (tptp.hAPP tptp.bool _let_1 (tptp.combk tptp.bool X_b) tptp.fFalse))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (A_1 $$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) A_3) A_1)) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_3) A_1) (tptp.ti _let_1 A_1))))) (forall ((X_b $$unsorted) (Ba $$unsorted) (A_3 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) 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_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) Ba) B))))))) (forall ((X_b $$unsorted) (B $$unsorted) (X_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_1))) (let ((_let_3 (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_1))) (=> (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_b $$unsorted) (Y_1 $$unsorted) (A_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) Y_1) A_1) X_1)) (or (= (tptp.ti X_b Y_1) (tptp.ti X_b X_1)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool A_1 X_1)))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (Ba $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_3))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) Ba) A_1))) (or (= (tptp.ti X_b A_3) (tptp.ti X_b Ba)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_1))))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.insert X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (let ((_let_4 (tptp.hAPP X_b _let_3 _let_1 X_1))) (let ((_let_5 (tptp.hAPP X_b _let_3 _let_1 Y_1))) (= (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_b $$unsorted) (X_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_1))) (let ((_let_3 (tptp.hAPP _let_1 _let_1 _let_2 A_1))) (= (tptp.hAPP _let_1 _let_1 _let_2 _let_3) _let_3))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (Pa $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_b _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_b _let_4))) (let ((_let_6 (tptp.collect X_b))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_3 (tptp.insert X_b) A_3) (tptp.hAPP _let_1 _let_1 _let_6 Pa)) (tptp.hAPP _let_1 _let_1 _let_6 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_5 _let_3 (tptp.combs X_b 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_b) tptp.fimplies) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_4 _let_3 (tptp.combb tptp.bool tptp.bool X_b) tptp.fNot) (tptp.hAPP X_b _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc X_b X_b tptp.bool) (tptp.fequal X_b)) A_3)))) Pa)))))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.fun X_b _let_1))) (let ((_let_4 (tptp.fun tptp.bool tptp.bool))) (let ((_let_5 (tptp.fun X_b _let_4))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_2 (tptp.insert X_b) A_3) B) (tptp.hAPP _let_1 _let_1 (tptp.collect X_b) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_5 _let_2 (tptp.combs X_b tptp.bool tptp.bool) (tptp.hAPP _let_1 _let_5 (tptp.hAPP (tptp.fun tptp.bool _let_4) (tptp.fun _let_1 _let_5) (tptp.combb tptp.bool _let_4 X_b) tptp.fdisj) (tptp.hAPP X_b _let_1 (tptp.hAPP _let_3 _let_3 (tptp.combc X_b X_b tptp.bool) (tptp.fequal X_b)) A_3))) (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_b (tptp.fun _let_1 tptp.bool)) _let_2 (tptp.combc X_b _let_1 tptp.bool) (tptp.member X_b)) B)))))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (B $$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) A_3) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_3) B))))) (forall ((X_b $$unsorted) (X_2 $$unsorted) (Xa $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.fun X_b _let_1))) (let ((_let_4 (tptp.fun tptp.bool tptp.bool))) (let ((_let_5 (tptp.fun X_b _let_4))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_2 (tptp.insert X_b) X_2) Xa) (tptp.hAPP _let_1 _let_1 (tptp.collect X_b) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_5 _let_2 (tptp.combs X_b tptp.bool tptp.bool) (tptp.hAPP _let_1 _let_5 (tptp.hAPP (tptp.fun tptp.bool _let_4) (tptp.fun _let_1 _let_5) (tptp.combb tptp.bool _let_4 X_b) tptp.fdisj) (tptp.hAPP X_b _let_1 (tptp.hAPP _let_3 _let_3 (tptp.combc X_b X_b tptp.bool) (tptp.fequal X_b)) X_2))) (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_b (tptp.fun _let_1 tptp.bool)) _let_2 (tptp.combc X_b _let_1 tptp.bool) (tptp.member X_b)) Xa)))))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.bot_bot _let_1))) (let ((_let_3 (tptp.insert X_b))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (=> (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_4 _let_3 A_3) _let_2) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_4 _let_3 Ba) _let_2)) (= (tptp.ti X_b A_3) (tptp.ti X_b Ba)))))))) (forall ((X_b $$unsorted) (Ba $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) Ba) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_3) (tptp.bot_bot _let_1)))) (= (tptp.ti X_b Ba) (tptp.ti X_b A_3))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (Ba $$unsorted) (Ca $$unsorted) (D_2 $$unsorted)) (let ((_let_1 (tptp.ti X_b Ca))) (let ((_let_2 (tptp.ti X_b Ba))) (let ((_let_3 (tptp.ti X_b D_2))) (let ((_let_4 (tptp.ti X_b A_3))) (let ((_let_5 (tptp.fun X_b tptp.bool))) (let ((_let_6 (tptp.bot_bot _let_5))) (let ((_let_7 (tptp.insert X_b))) (let ((_let_8 (tptp.fun _let_5 _let_5))) (= (= (tptp.hAPP _let_5 _let_5 (tptp.hAPP X_b _let_8 _let_7 A_3) (tptp.hAPP _let_5 _let_5 (tptp.hAPP X_b _let_8 _let_7 Ba) _let_6)) (tptp.hAPP _let_5 _let_5 (tptp.hAPP X_b _let_8 _let_7 Ca) (tptp.hAPP _let_5 _let_5 (tptp.hAPP X_b _let_8 _let_7 D_2) _let_6))) (or (and (= _let_4 _let_1) (= _let_2 _let_3)) (and (= _let_4 _let_3) (= _let_2 _let_1))))))))))))) (forall ((X_b $$unsorted) (Ba $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) Ba) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_3) (tptp.bot_bot _let_1)))) (= (tptp.ti X_b Ba) (tptp.ti X_b A_3))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (not (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_3) A_1) (tptp.bot_bot _let_1))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (not (= (tptp.bot_bot _let_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_3) A_1))))) (forall ((X_b $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (tptp.hAPP _let_1 X_b (tptp.the_elem X_b) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_1) (tptp.bot_bot _let_1))) (tptp.ti X_b X_1)))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F1 $$unsorted) (Fun1_1 $$unsorted) (Com_1 $$unsorted) (Fun2_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c (tptp.fun tptp.state tptp.bool)))) (let ((_let_2 (tptp.fun _let_1 X_b))) (let ((_let_3 (tptp.fun tptp.com _let_2))) (let ((_let_4 (tptp.hoare_1656922687triple X_c))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (= (tptp.hAPP _let_4 X_b (tptp.hAPP (tptp.fun _let_1 _let_3) (tptp.fun _let_4 X_b) (tptp.hoare_1312322281e_case X_c X_b) F1) (tptp.hAPP _let_1 _let_4 (tptp.hAPP tptp.com _let_5 (tptp.hAPP _let_1 (tptp.fun tptp.com _let_5) (tptp.hoare_246368825triple X_c) Fun1_1) Com_1) Fun2_1)) (tptp.hAPP _let_1 X_b (tptp.hAPP tptp.com _let_2 (tptp.hAPP _let_1 _let_3 F1 Fun1_1) Com_1) Fun2_1)))))))) (forall ((X_c $$unsorted) (X_b $$unsorted)) (=> (tptp.bot X_b) (forall ((X_1 $$unsorted)) (= (tptp.hAPP X_c X_b (tptp.bot_bot (tptp.fun X_c X_b)) X_1) (tptp.bot_bot X_b))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (tptp.bot X_c) (forall ((X_2 $$unsorted)) (= (tptp.hAPP X_b X_c (tptp.bot_bot (tptp.fun X_b X_c)) X_2) (tptp.bot_bot X_c))))) (forall ((X_b $$unsorted) (Ga $$unsorted) (Pa $$unsorted)) (let ((_let_1 (tptp.hoare_1656922687triple X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun X_b (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_b) Ga) (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_b) Pa) tptp.skip) Pa)) (tptp.bot_bot _let_2))))))))) (forall ((X_b $$unsorted) (D_2 $$unsorted) (R_1 $$unsorted) (Ga $$unsorted) (Pa $$unsorted) (Ca $$unsorted) (Q_1 $$unsorted)) (let ((_let_1 (tptp.hoare_1656922687triple X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.bot_bot _let_2))) (let ((_let_4 (tptp.hoare_246368825triple X_b))) (let ((_let_5 (tptp.fun X_b (tptp.fun tptp.state tptp.bool)))) (let ((_let_6 (tptp.fun _let_5 _let_1))) (let ((_let_7 (tptp.fun tptp.com _let_6))) (let ((_let_8 (tptp.hAPP _let_5 _let_7 _let_4 Pa))) (let ((_let_9 (tptp.insert _let_1))) (let ((_let_10 (tptp.fun _let_2 _let_2))) (let ((_let_11 (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.hoare_279057269derivs X_b) Ga))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_11 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 _let_10 _let_9 (tptp.hAPP _let_5 _let_1 (tptp.hAPP tptp.com _let_6 _let_8 Ca) Q_1)) _let_3))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_11 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 _let_10 _let_9 (tptp.hAPP _let_5 _let_1 (tptp.hAPP tptp.com _let_6 (tptp.hAPP _let_5 _let_7 _let_4 Q_1) D_2) R_1)) _let_3))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_11 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 _let_10 _let_9 (tptp.hAPP _let_5 _let_1 (tptp.hAPP tptp.com _let_6 _let_8 (tptp.hAPP tptp.com tptp.com (tptp.hAPP tptp.com (tptp.fun tptp.com tptp.com) tptp.semi Ca) D_2)) R_1)) _let_3))))))))))))))))) (forall ((X_b $$unsorted) (Y_1 $$unsorted)) (not (forall ((Fun1 $$unsorted) (Com_2 $$unsorted) (Fun2 $$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))) (not (= Y_1 (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_b) Fun1) Com_2) Fun2))))))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_1) A_1)) (not (forall ((B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (= (tptp.ti _let_1 A_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_1) B_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_1) B_2))))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_3) A_1)) (exists ((B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (and (= (tptp.ti _let_1 A_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_3) B_2)) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_3) B_2))))))))) (forall ((X_b $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (forall ((Y_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) Y_2) A_1))))) (= (tptp.ti _let_1 A_1) (tptp.bot_bot _let_1))))) (forall ((X_b $$unsorted) (Q_1 $$unsorted) (Ga $$unsorted) (Ca $$unsorted) (Pa $$unsorted)) (let ((_let_1 (tptp.hoare_1656922687triple X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun X_b (tptp.fun tptp.state tptp.bool)))) (let ((_let_4 (tptp.fun _let_3 _let_1))) (=> (forall ((Z_2 $$unsorted) (S_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP X_b (tptp.fun tptp.state tptp.bool) Pa Z_2) S_2)) (exists ((P_1 $$unsorted) (Q_2 $$unsorted)) (let ((_let_1 (tptp.hoare_1656922687triple X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun X_b (tptp.fun tptp.state tptp.bool)))) (let ((_let_4 (tptp.fun _let_3 _let_1))) (and (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.hoare_279057269derivs X_b) Ga) (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_b) P_1) Ca) Q_2)) (tptp.bot_bot _let_2)))) (forall ((S_3 $$unsorted)) (=> (forall ((Z_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.state tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP X_b _let_1 P_1 Z_3) S_2)) (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP X_b _let_1 Q_2 Z_3) S_3))))) (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP X_b (tptp.fun tptp.state tptp.bool) Q_1 Z_2) S_3)))))))))))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.hoare_279057269derivs X_b) Ga) (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_b) Pa) Ca) Q_1)) (tptp.bot_bot _let_2)))))))))) (forall ((Com1_2 $$unsorted) (Com2_2 $$unsorted)) (not (= (tptp.hAPP tptp.com tptp.com (tptp.hAPP tptp.com (tptp.fun tptp.com tptp.com) tptp.semi Com1_2) Com2_2) tptp.skip))) (forall ((Com1_2 $$unsorted) (Com2_2 $$unsorted)) (not (= tptp.skip (tptp.hAPP tptp.com tptp.com (tptp.hAPP tptp.com (tptp.fun tptp.com tptp.com) tptp.semi Com1_2) Com2_2)))) (forall ((X_b $$unsorted) (X_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_b _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.hAPP _let_1 X_b (tptp.the_elem X_b) X_3) (tptp.hAPP _let_1 X_b (tptp.the X_b) (tptp.hAPP _let_2 _let_1 (tptp.hAPP _let_3 (tptp.fun _let_2 _let_1) (tptp.combb _let_1 tptp.bool X_b) (tptp.hAPP _let_1 _let_3 (tptp.fequal _let_1) X_3)) (tptp.hAPP _let_1 _let_2 (tptp.hAPP (tptp.fun X_b (tptp.fun _let_1 _let_1)) (tptp.fun _let_1 _let_2) (tptp.combc X_b _let_1 _let_1) (tptp.insert X_b)) (tptp.bot_bot _let_1))))))))) (forall ((Com1_1 $$unsorted) (Com2_1 $$unsorted) (Com1 $$unsorted) (Com2 $$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_1) Com2_1) (tptp.hAPP tptp.com tptp.com (tptp.hAPP tptp.com _let_1 tptp.semi Com1) Com2)) (and (= Com1_1 Com1) (= Com2_1 Com2))))) (forall ((X_b $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (not (= (tptp.ti _let_1 A_1) (tptp.bot_bot _let_1))) (exists ((X_2 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (and (= (tptp.ti _let_1 A_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_2) B_2)) (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) B_2))))))))) (forall ((X_b $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.bot_bot _let_1))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool _let_2 X_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_2) _let_2)))))) (forall ((X_b $$unsorted) (Ga $$unsorted) (Pa $$unsorted) (X_3 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.hoare_1656922687triple X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun tptp.state tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.state))) (let ((_let_5 (tptp.fun tptp.state _let_4))) (let ((_let_6 (tptp.fun tptp.state tptp.state))) (let ((_let_7 (tptp.fun tptp.state tptp.bool))) (let ((_let_8 (tptp.fun _let_6 _let_7))) (let ((_let_9 (tptp.fun X_b _let_8))) (let ((_let_10 (tptp.fun X_b _let_7))) (let ((_let_11 (tptp.fun _let_10 _let_1))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.hoare_279057269derivs X_b) Ga) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 (tptp.fun _let_2 _let_2) (tptp.insert _let_1) (tptp.hAPP _let_10 _let_1 (tptp.hAPP tptp.com _let_11 (tptp.hAPP _let_10 (tptp.fun tptp.com _let_11) (tptp.hoare_246368825triple X_b) (tptp.hAPP _let_6 _let_10 (tptp.hAPP _let_9 (tptp.fun _let_6 _let_10) (tptp.combc X_b _let_6 _let_7) (tptp.hAPP _let_10 _let_9 (tptp.hAPP (tptp.fun _let_7 _let_8) (tptp.fun _let_10 _let_9) (tptp.combb _let_7 _let_8 X_b) (tptp.combb tptp.state tptp.bool tptp.state)) Pa)) (tptp.hAPP _let_3 _let_6 (tptp.hAPP _let_5 (tptp.fun _let_3 _let_6) (tptp.combs tptp.state tptp.nat tptp.state) (tptp.hAPP tptp.vname _let_5 (tptp.hAPP (tptp.fun tptp.state (tptp.fun tptp.vname _let_4)) (tptp.fun tptp.vname _let_5) (tptp.combc tptp.state tptp.vname _let_4) tptp.update) X_3)) A_3))) (tptp.hAPP _let_3 tptp.com (tptp.hAPP tptp.vname (tptp.fun _let_3 tptp.com) tptp.ass X_3) A_3)) Pa)) (tptp.bot_bot _let_2)))))))))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (Ca $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.bot_bot _let_1))) (let ((_let_3 (tptp.fun X_b X_c))) (let ((_let_4 (tptp.fun X_b tptp.bool))) (let ((_let_5 (tptp.hAPP _let_4 _let_1 (tptp.hAPP _let_3 (tptp.fun _let_4 _let_1) (tptp.image X_b X_c) (tptp.hAPP X_c _let_3 (tptp.combk X_c X_b) Ca)) A_1))) (let ((_let_6 (= (tptp.ti _let_4 A_1) (tptp.bot_bot _let_4)))) (and (=> _let_6 (= _let_5 _let_2)) (=> (not _let_6) (= _let_5 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_c (tptp.fun _let_1 _let_1) (tptp.insert X_c) Ca) _let_2))))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (Ca $$unsorted) (X_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b X_c))) (let ((_let_3 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_b (tptp.fun _let_3 tptp.bool) (tptp.member X_b) X_1) A_1)) (= (tptp.hAPP _let_3 _let_1 (tptp.hAPP _let_2 (tptp.fun _let_3 _let_1) (tptp.image X_b X_c) (tptp.hAPP X_c _let_2 (tptp.combk X_c X_b) Ca)) A_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_c (tptp.fun _let_1 _let_1) (tptp.insert X_c) Ca) (tptp.bot_bot _let_1)))))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (A_1 $$unsorted) (Ba $$unsorted) (F $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (=> (= (tptp.ti X_b Ba) (tptp.hAPP X_c X_b F X_1)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_c (tptp.fun _let_2 tptp.bool) (tptp.member X_c) 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) Ba) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun _let_2 _let_1) (tptp.image X_c X_b) F) A_1)))))))) (forall ((X_b $$unsorted) (Y_4 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_b X_b) (tptp.fun _let_1 _let_1) (tptp.image X_b X_b) (tptp.combi X_b)) Y_4) (tptp.ti _let_1 Y_4)))) (forall ((X_c $$unsorted) (X_b $$unsorted) (X_d $$unsorted) (F $$unsorted) (G $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_d X_b))) (let ((_let_2 (tptp.fun X_d X_c))) (let ((_let_3 (tptp.fun X_c X_b))) (let ((_let_4 (tptp.fun X_b tptp.bool))) (let ((_let_5 (tptp.fun X_d tptp.bool))) (let ((_let_6 (tptp.fun X_c tptp.bool))) (= (tptp.hAPP _let_6 _let_4 (tptp.hAPP _let_3 (tptp.fun _let_6 _let_4) (tptp.image X_c X_b) F) (tptp.hAPP _let_5 _let_6 (tptp.hAPP _let_2 (tptp.fun _let_5 _let_6) (tptp.image X_d X_c) G) A_1)) (tptp.hAPP _let_5 _let_4 (tptp.hAPP _let_1 (tptp.fun _let_5 _let_4) (tptp.image X_d X_b) (tptp.hAPP _let_2 _let_1 (tptp.hAPP _let_3 (tptp.fun _let_2 _let_1) (tptp.combb X_c X_b X_d) F) G)) A_1))))))))) (forall ((Vname $$unsorted) (Fun_1 $$unsorted) (Vname_1 $$unsorted) (Fun $$unsorted)) (let ((_let_1 (tptp.fun tptp.state tptp.nat))) (let ((_let_2 (tptp.fun _let_1 tptp.com))) (= (= (tptp.hAPP _let_1 tptp.com (tptp.hAPP tptp.vname _let_2 tptp.ass Vname) Fun_1) (tptp.hAPP _let_1 tptp.com (tptp.hAPP tptp.vname _let_2 tptp.ass Vname_1) Fun)) (and (= (tptp.ti tptp.vname Vname) (tptp.ti tptp.vname Vname_1)) (= Fun_1 Fun)))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (Ba $$unsorted) (F $$unsorted) (X_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_b (tptp.fun _let_2 tptp.bool) (tptp.member X_b) X_1) A_1)) (=> (= (tptp.ti X_c Ba) (tptp.hAPP X_b X_c F X_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_c (tptp.fun _let_1 tptp.bool) (tptp.member X_c) Ba) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun _let_2 _let_1) (tptp.image X_b X_c) F) A_1)))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (X_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_b (tptp.fun _let_2 tptp.bool) (tptp.member X_b) X_1) A_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_c (tptp.fun _let_1 tptp.bool) (tptp.member X_c) (tptp.hAPP X_b X_c F X_1)) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun _let_2 _let_1) (tptp.image X_b X_c) F) A_1))))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (Z_1 $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) Z_1) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun _let_2 _let_1) (tptp.image X_c X_b) F) A_1))) (exists ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_c (tptp.fun _let_1 tptp.bool) (tptp.member X_c) X_2) A_1)) (= (tptp.ti X_b Z_1) (tptp.hAPP X_c X_b F X_2))))))))) (forall ((Vname $$unsorted) (Fun_1 $$unsorted) (Com1 $$unsorted) (Com2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.state tptp.nat))) (not (= (tptp.hAPP _let_1 tptp.com (tptp.hAPP tptp.vname (tptp.fun _let_1 tptp.com) tptp.ass Vname) Fun_1) (tptp.hAPP tptp.com tptp.com (tptp.hAPP tptp.com (tptp.fun tptp.com tptp.com) tptp.semi Com1) Com2))))) (forall ((Com1 $$unsorted) (Com2 $$unsorted) (Vname $$unsorted) (Fun_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.state tptp.nat))) (not (= (tptp.hAPP tptp.com tptp.com (tptp.hAPP tptp.com (tptp.fun tptp.com tptp.com) tptp.semi Com1) Com2) (tptp.hAPP _let_1 tptp.com (tptp.hAPP tptp.vname (tptp.fun _let_1 tptp.com) tptp.ass Vname) Fun_1))))) (forall ((Vname_1 $$unsorted) (Fun $$unsorted)) (let ((_let_1 (tptp.fun tptp.state tptp.nat))) (not (= tptp.skip (tptp.hAPP _let_1 tptp.com (tptp.hAPP tptp.vname (tptp.fun _let_1 tptp.com) tptp.ass Vname_1) Fun))))) (forall ((Vname_1 $$unsorted) (Fun $$unsorted)) (let ((_let_1 (tptp.fun tptp.state tptp.nat))) (not (= (tptp.hAPP _let_1 tptp.com (tptp.hAPP tptp.vname (tptp.fun _let_1 tptp.com) tptp.ass Vname_1) Fun) tptp.skip)))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (= (= (tptp.hAPP _let_1 _let_2 (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun _let_1 _let_2) (tptp.image X_c X_b) F) A_1) (tptp.bot_bot _let_2)) (= (tptp.ti _let_1 A_1) (tptp.bot_bot _let_1)))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (= (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun _let_2 _let_1) (tptp.image X_c X_b) F) (tptp.bot_bot _let_2)) (tptp.bot_bot _let_1))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (= (= (tptp.bot_bot _let_2) (tptp.hAPP _let_1 _let_2 (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun _let_1 _let_2) (tptp.image X_c X_b) F) A_1)) (= (tptp.ti _let_1 A_1) (tptp.bot_bot _let_1)))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (F $$unsorted) (G $$unsorted)) (let ((_let_1 (tptp.fun X_b X_c))) (=> (forall ((X_2 $$unsorted)) (= (tptp.hAPP X_b X_c F X_2) (tptp.hAPP X_b X_c G X_2))) (= (tptp.ti _let_1 F) (tptp.ti _let_1 G))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_1 $$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.hBOOL (tptp.hAPP X_b tptp.bool A_1 X_1))))) (forall ((X_b $$unsorted) (Pa $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (tptp.hAPP _let_1 _let_1 (tptp.collect X_b) Pa) (tptp.ti _let_1 Pa)))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (X_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun _let_2 _let_1) (tptp.image X_b X_c) F) A_1))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_b (tptp.fun _let_2 tptp.bool) (tptp.member X_b) X_1) A_1)) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_c (tptp.fun _let_1 _let_1) (tptp.insert X_c) (tptp.hAPP X_b X_c F X_1)) _let_3) _let_3)))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (A_3 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (let ((_let_3 (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun _let_2 _let_1) (tptp.image X_c X_b) F))) (= (tptp.hAPP _let_2 _let_1 _let_3 (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_c (tptp.fun _let_2 _let_2) (tptp.insert X_c) A_3) B)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) (tptp.hAPP X_c X_b F A_3)) (tptp.hAPP _let_2 _let_1 _let_3 B))))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (Ba $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) Ba) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun _let_2 _let_1) (tptp.image X_c X_b) F) A_1))) (not (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (=> (= (tptp.ti X_b Ba) (tptp.hAPP X_c X_b F X_2)) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_c (tptp.fun _let_1 tptp.bool) (tptp.member X_c) X_2) A_1))))))))))) (forall ((X_b $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (tptp.hAPP _let_1 X_b (tptp.the X_b) (tptp.hAPP X_b _let_1 (tptp.fequal X_b) X_1)) (tptp.ti X_b X_1)))) (forall ((X_b $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_b _let_1))) (= (tptp.hAPP _let_1 X_b (tptp.the X_b) (tptp.hAPP X_b _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc X_b X_b tptp.bool) (tptp.fequal X_b)) A_3)) (tptp.ti X_b A_3))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted) (Pa $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_b _let_1))) (let ((_let_3 (tptp.hAPP _let_2 _let_2 (tptp.combc X_b X_b tptp.bool) (tptp.fequal X_b)))) (let ((_let_4 (tptp.fun tptp.bool tptp.bool))) (let ((_let_5 (tptp.combb tptp.bool tptp.bool X_b))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (let ((_let_7 (tptp.fun X_b _let_4))) (let ((_let_8 (tptp.hAPP _let_1 X_b (tptp.the X_b) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_7 _let_6 (tptp.combs X_b 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_b) tptp.fconj) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_4 _let_6 _let_5 (tptp.hAPP tptp.bool _let_4 tptp.fimplies Pa)) (tptp.hAPP X_b _let_1 _let_3 X_1)))) (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 Pa))) (tptp.hAPP X_b _let_1 _let_3 Y_1)))))) (let ((_let_9 (tptp.hBOOL Pa))) (and (=> _let_9 (= (tptp.ti X_b X_1) _let_8)) (=> (not _let_9) (= (tptp.ti X_b Y_1) _let_8))))))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (G $$unsorted) (M_2 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.image X_b X_c))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (let ((_let_3 (tptp.fun X_b tptp.bool))) (let ((_let_4 (tptp.fun _let_3 _let_2))) (let ((_let_5 (tptp.fun X_b X_c))) (=> (= (tptp.ti _let_3 M_2) (tptp.ti _let_3 N)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_2) N)) (= (tptp.hAPP X_b X_c F X_2) (tptp.hAPP X_b X_c G X_2))))) (= (tptp.hAPP _let_3 _let_2 (tptp.hAPP _let_5 _let_4 _let_1 F) M_2) (tptp.hAPP _let_3 _let_2 (tptp.hAPP _let_5 _let_4 _let_1 G) N)))))))))) (forall ((X_b $$unsorted) (F $$unsorted) (A_3 $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) _let_2 (tptp.finite_fold1Set X_b) F) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_2 (tptp.insert X_b) A_3) (tptp.bot_bot _let_1))) Ba)) (= (tptp.ti X_b A_3) (tptp.ti X_b Ba)))))) (forall ((X_b $$unsorted) (Pa $$unsorted) (A_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa A_3)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa X_2)) (= (tptp.ti X_b X_2) (tptp.ti X_b A_3)))) (= (tptp.hAPP (tptp.fun X_b tptp.bool) X_b (tptp.the X_b) Pa) (tptp.ti X_b A_3))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun _let_2 tptp.bool) (tptp.finite_folding_one X_b) F) F_1)) (= (tptp.hAPP _let_1 X_b F_1 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_1) (tptp.bot_bot _let_1))) (tptp.ti X_b X_1)))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (Ga $$unsorted) (Pa $$unsorted) (Ca $$unsorted) (Q_1 $$unsorted) (X_3 $$unsorted) (S_5 $$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 tptp.com tptp.com))) (let ((_let_5 (tptp.fun tptp.state tptp.nat))) (let ((_let_6 (tptp.fun tptp.nat tptp.state))) (let ((_let_7 (tptp.fun tptp.state _let_6))) (let ((_let_8 (tptp.hAPP tptp.vname _let_7 (tptp.hAPP (tptp.fun tptp.state (tptp.fun tptp.vname _let_6)) (tptp.fun tptp.vname _let_7) (tptp.combc tptp.state tptp.vname _let_6) tptp.update) (tptp.hAPP tptp.loc_1 tptp.vname tptp.loc X_3)))) (let ((_let_9 (tptp.fun tptp.state tptp.state))) (let ((_let_10 (tptp.fun tptp.state tptp.bool))) (let ((_let_11 (tptp.fun _let_9 _let_10))) (let ((_let_12 (tptp.fun X_b _let_11))) (let ((_let_13 (tptp.fun X_b _let_10))) (let ((_let_14 (tptp.hAPP (tptp.fun _let_10 _let_11) (tptp.fun _let_13 _let_12) (tptp.combb _let_10 _let_11 X_b) (tptp.combb tptp.state tptp.bool tptp.state)))) (let ((_let_15 (tptp.combc X_b _let_9 _let_10))) (let ((_let_16 (tptp.fun _let_9 _let_13))) (let ((_let_17 (tptp.fun tptp.bool tptp.bool))) (let ((_let_18 (tptp.fun tptp.state _let_17))) (let ((_let_19 (tptp.fun _let_10 _let_10))) (let ((_let_20 (tptp.hoare_246368825triple X_b))) (let ((_let_21 (tptp.fun _let_13 _let_1))) (let ((_let_22 (tptp.fun tptp.com _let_21))) (let ((_let_23 (tptp.insert _let_1))) (let ((_let_24 (tptp.fun _let_2 _let_2))) (let ((_let_25 (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.hoare_279057269derivs X_b) Ga))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_25 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 _let_24 _let_23 (tptp.hAPP _let_13 _let_1 (tptp.hAPP tptp.com _let_21 (tptp.hAPP _let_13 _let_22 _let_20 Pa) Ca) (tptp.hAPP _let_9 _let_13 (tptp.hAPP _let_12 _let_16 _let_15 (tptp.hAPP _let_13 _let_12 _let_14 Q_1)) (tptp.hAPP tptp.nat _let_9 (tptp.hAPP _let_7 (tptp.fun tptp.nat _let_9) (tptp.combc tptp.state tptp.nat tptp.state) _let_8) (tptp.hAPP tptp.loc_1 tptp.nat (tptp.hAPP tptp.state (tptp.fun tptp.loc_1 tptp.nat) tptp.getlocs S_5) X_3))))) _let_3))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_25 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 _let_24 _let_23 (tptp.hAPP _let_13 _let_1 (tptp.hAPP tptp.com _let_21 (tptp.hAPP _let_13 _let_22 _let_20 (tptp.hAPP _let_13 _let_13 (tptp.hAPP _let_19 (tptp.fun _let_13 _let_13) (tptp.combb _let_10 _let_10 X_b) (tptp.hAPP _let_18 _let_19 (tptp.combs tptp.state tptp.bool tptp.bool) (tptp.hAPP _let_10 _let_18 (tptp.hAPP (tptp.fun tptp.bool _let_17) (tptp.fun _let_10 _let_18) (tptp.combb tptp.bool _let_17 tptp.state) tptp.fconj) (tptp.hAPP tptp.state _let_10 (tptp.fequal tptp.state) S_5)))) (tptp.hAPP _let_9 _let_13 (tptp.hAPP _let_12 _let_16 _let_15 (tptp.hAPP _let_13 _let_12 _let_14 Pa)) (tptp.hAPP _let_5 _let_9 (tptp.hAPP _let_7 (tptp.fun _let_5 _let_9) (tptp.combs tptp.state tptp.nat tptp.state) _let_8) A_3)))) (tptp.hAPP tptp.com tptp.com (tptp.hAPP _let_5 _let_4 (tptp.hAPP tptp.loc_1 (tptp.fun _let_5 _let_4) tptp.local X_3) A_3) Ca)) Q_1)) _let_3)))))))))))))))))))))))))))))) (forall ((Loc_2 $$unsorted) (Loc_3 $$unsorted)) (= (= (tptp.hAPP tptp.loc_1 tptp.vname tptp.loc Loc_2) (tptp.hAPP tptp.loc_1 tptp.vname tptp.loc Loc_3)) (= (tptp.ti tptp.loc_1 Loc_2) (tptp.ti tptp.loc_1 Loc_3)))) (forall ((Loc_2 $$unsorted) (Fun_1 $$unsorted) (Com_1 $$unsorted) (Loc_3 $$unsorted) (Fun $$unsorted) (Com $$unsorted)) (let ((_let_1 (tptp.fun tptp.com tptp.com))) (let ((_let_2 (tptp.fun tptp.state tptp.nat))) (let ((_let_3 (tptp.fun _let_2 _let_1))) (= (= (tptp.hAPP tptp.com tptp.com (tptp.hAPP _let_2 _let_1 (tptp.hAPP tptp.loc_1 _let_3 tptp.local Loc_2) Fun_1) Com_1) (tptp.hAPP tptp.com tptp.com (tptp.hAPP _let_2 _let_1 (tptp.hAPP tptp.loc_1 _let_3 tptp.local Loc_3) Fun) Com)) (and (= (tptp.ti tptp.loc_1 Loc_2) (tptp.ti tptp.loc_1 Loc_3)) (= Fun_1 Fun) (= Com_1 Com))))))) (forall ((Loc_2 $$unsorted) (Fun_1 $$unsorted) (Com_1 $$unsorted) (Com1 $$unsorted) (Com2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.com tptp.com))) (let ((_let_2 (tptp.fun tptp.state tptp.nat))) (not (= (tptp.hAPP tptp.com tptp.com (tptp.hAPP _let_2 _let_1 (tptp.hAPP tptp.loc_1 (tptp.fun _let_2 _let_1) tptp.local Loc_2) Fun_1) Com_1) (tptp.hAPP tptp.com tptp.com (tptp.hAPP tptp.com _let_1 tptp.semi Com1) Com2)))))) (forall ((Com1 $$unsorted) (Com2 $$unsorted) (Loc_2 $$unsorted) (Fun_1 $$unsorted) (Com_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.com tptp.com))) (let ((_let_2 (tptp.fun tptp.state tptp.nat))) (not (= (tptp.hAPP tptp.com tptp.com (tptp.hAPP tptp.com _let_1 tptp.semi Com1) Com2) (tptp.hAPP tptp.com tptp.com (tptp.hAPP _let_2 _let_1 (tptp.hAPP tptp.loc_1 (tptp.fun _let_2 _let_1) tptp.local Loc_2) Fun_1) Com_1)))))) (forall ((Loc_3 $$unsorted) (Fun $$unsorted) (Com $$unsorted) (Vname $$unsorted) (Fun_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.state tptp.nat))) (let ((_let_2 (tptp.fun tptp.com tptp.com))) (not (= (tptp.hAPP tptp.com tptp.com (tptp.hAPP _let_1 _let_2 (tptp.hAPP tptp.loc_1 (tptp.fun _let_1 _let_2) tptp.local Loc_3) Fun) Com) (tptp.hAPP _let_1 tptp.com (tptp.hAPP tptp.vname (tptp.fun _let_1 tptp.com) tptp.ass Vname) Fun_1)))))) (forall ((Vname $$unsorted) (Fun_1 $$unsorted) (Loc_3 $$unsorted) (Fun $$unsorted) (Com $$unsorted)) (let ((_let_1 (tptp.fun tptp.com tptp.com))) (let ((_let_2 (tptp.fun tptp.state tptp.nat))) (not (= (tptp.hAPP _let_2 tptp.com (tptp.hAPP tptp.vname (tptp.fun _let_2 tptp.com) tptp.ass Vname) Fun_1) (tptp.hAPP tptp.com tptp.com (tptp.hAPP _let_2 _let_1 (tptp.hAPP tptp.loc_1 (tptp.fun _let_2 _let_1) tptp.local Loc_3) Fun) Com)))))) (forall ((Loc_3 $$unsorted) (Fun $$unsorted) (Com $$unsorted)) (let ((_let_1 (tptp.fun tptp.com tptp.com))) (let ((_let_2 (tptp.fun tptp.state tptp.nat))) (not (= (tptp.hAPP tptp.com tptp.com (tptp.hAPP _let_2 _let_1 (tptp.hAPP tptp.loc_1 (tptp.fun _let_2 _let_1) tptp.local Loc_3) Fun) Com) tptp.skip))))) (forall ((Loc_3 $$unsorted) (Fun $$unsorted) (Com $$unsorted)) (let ((_let_1 (tptp.fun tptp.com tptp.com))) (let ((_let_2 (tptp.fun tptp.state tptp.nat))) (not (= tptp.skip (tptp.hAPP tptp.com tptp.com (tptp.hAPP _let_2 _let_1 (tptp.hAPP tptp.loc_1 (tptp.fun _let_2 _let_1) tptp.local Loc_3) Fun) Com)))))) (forall ((X_b $$unsorted) (F $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (not (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun _let_1 _let_1) (tptp.finite_fold1Set X_b) F) (tptp.bot_bot _let_1)) X_1))))) (forall ((X_b $$unsorted) (F $$unsorted) (A_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun _let_1 _let_1) (tptp.finite_fold1Set X_b) F) A_1) X_1)) (not (= (tptp.ti _let_1 A_1) (tptp.bot_bot _let_1)))))) (forall ((X_b $$unsorted) (Pa $$unsorted) (A_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa A_3)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa X_2)) (= (tptp.ti X_b X_2) (tptp.ti X_b A_3)))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa (tptp.hAPP (tptp.fun X_b tptp.bool) X_b (tptp.the X_b) Pa)))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (Pa $$unsorted)) (=> (exists ((X_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa X_2)) (forall ((Y_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa Y_2)) (= (tptp.ti X_b Y_2) (tptp.ti X_b X_2)))))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa A_3)) (= (tptp.hAPP (tptp.fun X_b tptp.bool) X_b (tptp.the X_b) Pa) (tptp.ti X_b A_3))))) (forall ((X_b $$unsorted) (Pa $$unsorted)) (=> (exists ((X_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa X_2)) (forall ((Y_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa Y_2)) (= (tptp.ti X_b Y_2) (tptp.ti X_b X_2)))))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa (tptp.hAPP (tptp.fun X_b tptp.bool) X_b (tptp.the X_b) Pa))))) (forall ((X_b $$unsorted) (F1 $$unsorted) (F2 $$unsorted) (Loc_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.vname X_b))) (let ((_let_2 (tptp.fun tptp.loc_1 X_b))) (= (tptp.hAPP tptp.vname X_b (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun tptp.glb_1 X_b) (tptp.fun _let_2 _let_1) (tptp.vname_rec X_b) F1) F2) (tptp.hAPP tptp.loc_1 tptp.vname tptp.loc Loc_2)) (tptp.hAPP tptp.loc_1 X_b F2 Loc_2))))) (forall ((X_b $$unsorted) (F1 $$unsorted) (F2 $$unsorted) (Loc_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.vname X_b))) (let ((_let_2 (tptp.fun tptp.loc_1 X_b))) (= (tptp.hAPP tptp.vname X_b (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun tptp.glb_1 X_b) (tptp.fun _let_2 _let_1) (tptp.vname_case X_b) F1) F2) (tptp.hAPP tptp.loc_1 tptp.vname tptp.loc Loc_2)) (tptp.hAPP tptp.loc_1 X_b F2 Loc_2))))) (forall ((Ca $$unsorted) (S0_1 $$unsorted) (Y_4 $$unsorted) (A_3 $$unsorted) (S1_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.loc_1 tptp.vname tptp.loc Y_4))) (let ((_let_2 (tptp.fun tptp.nat tptp.state))) (let ((_let_3 (tptp.fun tptp.vname _let_2))) (let ((_let_4 (tptp.fun tptp.com tptp.com))) (let ((_let_5 (tptp.fun tptp.state tptp.nat))) (let ((_let_6 (tptp.fun tptp.state tptp.bool))) (let ((_let_7 (tptp.fun tptp.state _let_6))) (=> (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP tptp.state _let_6 (tptp.hAPP tptp.com _let_7 tptp.evalc Ca) (tptp.hAPP tptp.nat tptp.state (tptp.hAPP tptp.vname _let_2 (tptp.hAPP tptp.state _let_3 tptp.update S0_1) _let_1) (tptp.hAPP tptp.state tptp.nat A_3 S0_1))) S1_2)) (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP tptp.state _let_6 (tptp.hAPP tptp.com _let_7 tptp.evalc (tptp.hAPP tptp.com tptp.com (tptp.hAPP _let_5 _let_4 (tptp.hAPP tptp.loc_1 (tptp.fun _let_5 _let_4) tptp.local Y_4) A_3) Ca)) S0_1) (tptp.hAPP tptp.nat tptp.state (tptp.hAPP tptp.vname _let_2 (tptp.hAPP tptp.state _let_3 tptp.update S1_2) _let_1) (tptp.hAPP tptp.loc_1 tptp.nat (tptp.hAPP tptp.state (tptp.fun tptp.loc_1 tptp.nat) tptp.getlocs S0_1) Y_4))))))))))))) (forall ((Ca $$unsorted) (S0_1 $$unsorted) (Y_4 $$unsorted) (A_3 $$unsorted) (N_3 $$unsorted) (S1_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.loc_1 tptp.vname tptp.loc Y_4))) (let ((_let_2 (tptp.fun tptp.nat tptp.state))) (let ((_let_3 (tptp.fun tptp.vname _let_2))) (let ((_let_4 (tptp.fun tptp.com tptp.com))) (let ((_let_5 (tptp.fun tptp.state tptp.nat))) (let ((_let_6 (tptp.fun tptp.state tptp.bool))) (let ((_let_7 (tptp.fun tptp.nat _let_6))) (let ((_let_8 (tptp.fun tptp.state _let_7))) (=> (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP tptp.nat _let_6 (tptp.hAPP tptp.state _let_7 (tptp.hAPP tptp.com _let_8 tptp.evaln Ca) (tptp.hAPP tptp.nat tptp.state (tptp.hAPP tptp.vname _let_2 (tptp.hAPP tptp.state _let_3 tptp.update S0_1) _let_1) (tptp.hAPP tptp.state tptp.nat A_3 S0_1))) N_3) S1_2)) (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP tptp.nat _let_6 (tptp.hAPP tptp.state _let_7 (tptp.hAPP tptp.com _let_8 tptp.evaln (tptp.hAPP tptp.com tptp.com (tptp.hAPP _let_5 _let_4 (tptp.hAPP tptp.loc_1 (tptp.fun _let_5 _let_4) tptp.local Y_4) A_3) Ca)) S0_1) N_3) (tptp.hAPP tptp.nat tptp.state (tptp.hAPP tptp.vname _let_2 (tptp.hAPP tptp.state _let_3 tptp.update S1_2) _let_1) (tptp.hAPP tptp.loc_1 tptp.nat (tptp.hAPP tptp.state (tptp.fun tptp.loc_1 tptp.nat) tptp.getlocs S0_1) Y_4)))))))))))))) (forall ((X_b $$unsorted) (F $$unsorted) (A_3 $$unsorted) (A_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.fun X_b (tptp.fun X_b X_b)))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_2 (tptp.hAPP _let_3 (tptp.fun X_b _let_2) (tptp.finite_fold_graph X_b X_b) F) A_3) A_1) X_1)) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_3) A_1))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_3 _let_2 (tptp.finite_fold1Set X_b) F) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_2 (tptp.insert X_b) A_3) A_1)) X_1)))))))) (forall ((C1 $$unsorted) (S2 $$unsorted) (C0 $$unsorted) (S0 $$unsorted) (N_2 $$unsorted) (S1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.state tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (let ((_let_3 (tptp.fun tptp.state _let_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.state _let_2 (tptp.hAPP tptp.com _let_3 tptp.evaln C0) S0) N_2) S1)) (=> (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.state _let_2 (tptp.hAPP tptp.com _let_3 tptp.evaln C1) S1) N_2) S2)) (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.state _let_2 (tptp.hAPP tptp.com _let_3 tptp.evaln (tptp.hAPP tptp.com tptp.com (tptp.hAPP tptp.com (tptp.fun tptp.com tptp.com) tptp.semi C0) C1)) S0) N_2) S2)))))))) (forall ((S_1 $$unsorted) (N_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.state tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.state _let_2 (tptp.hAPP tptp.com (tptp.fun tptp.state _let_2) tptp.evaln tptp.skip) S_1) N_2) S_1))))) (forall ((S_1 $$unsorted) (N_2 $$unsorted) (T_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.state tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.state _let_2 (tptp.hAPP tptp.com (tptp.fun tptp.state _let_2) tptp.evaln tptp.skip) S_1) N_2) T_4)) (= T_4 S_1))))) (forall ((C1 $$unsorted) (S2 $$unsorted) (C0 $$unsorted) (S0 $$unsorted) (S1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.state tptp.bool))) (let ((_let_2 (tptp.fun tptp.state _let_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP tptp.state _let_1 (tptp.hAPP tptp.com _let_2 tptp.evalc C0) S0) S1)) (=> (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP tptp.state _let_1 (tptp.hAPP tptp.com _let_2 tptp.evalc C1) S1) S2)) (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP tptp.state _let_1 (tptp.hAPP tptp.com _let_2 tptp.evalc (tptp.hAPP tptp.com tptp.com (tptp.hAPP tptp.com (tptp.fun tptp.com tptp.com) tptp.semi C0) C1)) S0) S2))))))) (forall ((S_1 $$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_1) S_1)))) (forall ((S_1 $$unsorted) (T_4 $$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_1) T_4)) (= T_4 S_1)))) (forall ((X_3 $$unsorted) (A_3 $$unsorted) (S_4 $$unsorted) (N_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.state))) (let ((_let_2 (tptp.fun tptp.state tptp.nat))) (let ((_let_3 (tptp.fun tptp.state tptp.bool))) (let ((_let_4 (tptp.fun tptp.nat _let_3))) (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP tptp.nat _let_3 (tptp.hAPP tptp.state _let_4 (tptp.hAPP tptp.com (tptp.fun tptp.state _let_4) tptp.evaln (tptp.hAPP _let_2 tptp.com (tptp.hAPP tptp.vname (tptp.fun _let_2 tptp.com) tptp.ass X_3) A_3)) S_4) N_3) (tptp.hAPP tptp.nat tptp.state (tptp.hAPP tptp.vname _let_1 (tptp.hAPP tptp.state (tptp.fun tptp.vname _let_1) tptp.update S_4) X_3) (tptp.hAPP tptp.state tptp.nat A_3 S_4))))))))) (forall ((X_3 $$unsorted) (A_3 $$unsorted) (S_4 $$unsorted) (N_3 $$unsorted) (T_5 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.state))) (let ((_let_2 (tptp.fun tptp.state tptp.nat))) (let ((_let_3 (tptp.fun tptp.state tptp.bool))) (let ((_let_4 (tptp.fun tptp.nat _let_3))) (=> (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP tptp.nat _let_3 (tptp.hAPP tptp.state _let_4 (tptp.hAPP tptp.com (tptp.fun tptp.state _let_4) tptp.evaln (tptp.hAPP _let_2 tptp.com (tptp.hAPP tptp.vname (tptp.fun _let_2 tptp.com) tptp.ass X_3) A_3)) S_4) N_3) T_5)) (= T_5 (tptp.hAPP tptp.nat tptp.state (tptp.hAPP tptp.vname _let_1 (tptp.hAPP tptp.state (tptp.fun tptp.vname _let_1) tptp.update S_4) X_3) (tptp.hAPP tptp.state tptp.nat A_3 S_4))))))))) (forall ((X_3 $$unsorted) (A_3 $$unsorted) (S_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.state))) (let ((_let_2 (tptp.fun tptp.state tptp.nat))) (let ((_let_3 (tptp.fun tptp.state tptp.bool))) (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP tptp.state _let_3 (tptp.hAPP tptp.com (tptp.fun tptp.state _let_3) tptp.evalc (tptp.hAPP _let_2 tptp.com (tptp.hAPP tptp.vname (tptp.fun _let_2 tptp.com) tptp.ass X_3) A_3)) S_4) (tptp.hAPP tptp.nat tptp.state (tptp.hAPP tptp.vname _let_1 (tptp.hAPP tptp.state (tptp.fun tptp.vname _let_1) tptp.update S_4) X_3) (tptp.hAPP tptp.state tptp.nat A_3 S_4)))))))) (forall ((X_3 $$unsorted) (A_3 $$unsorted) (S_4 $$unsorted) (T_5 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.state))) (let ((_let_2 (tptp.fun tptp.state tptp.nat))) (let ((_let_3 (tptp.fun tptp.state tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP tptp.state _let_3 (tptp.hAPP tptp.com (tptp.fun tptp.state _let_3) tptp.evalc (tptp.hAPP _let_2 tptp.com (tptp.hAPP tptp.vname (tptp.fun _let_2 tptp.com) tptp.ass X_3) A_3)) S_4) T_5)) (= T_5 (tptp.hAPP tptp.nat tptp.state (tptp.hAPP tptp.vname _let_1 (tptp.hAPP tptp.state (tptp.fun tptp.vname _let_1) tptp.update S_4) X_3) (tptp.hAPP tptp.state tptp.nat A_3 S_4)))))))) (forall ((Ca $$unsorted) (S_4 $$unsorted) (T_5 $$unsorted)) (let ((_let_1 (tptp.fun tptp.state tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP tptp.state _let_1 (tptp.hAPP tptp.com (tptp.fun tptp.state _let_1) tptp.evalc Ca) S_4) T_5)) (exists ((N_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.state tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.state _let_2 (tptp.hAPP tptp.com (tptp.fun tptp.state _let_2) tptp.evaln Ca) S_4) N_1) T_5)))))))) (forall ((U_1 $$unsorted) (C_1 $$unsorted) (S_1 $$unsorted) (T_4 $$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_1) S_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool _let_2 T_4)) (=> (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool _let_2 U_1)) (= U_1 T_4)))))) (forall ((C_1 $$unsorted) (S_1 $$unsorted) (N_2 $$unsorted) (T_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.state tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.state _let_2 (tptp.hAPP tptp.com (tptp.fun tptp.state _let_2) tptp.evaln C_1) S_1) N_2) T_4)) (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 C_1) S_1) T_4)))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (Z_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (let ((_let_3 (tptp.fun _let_1 _let_2))) (=> (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.hAPP X_c _let_3 (tptp.hAPP (tptp.fun X_b (tptp.fun X_c X_c)) (tptp.fun X_c _let_3) (tptp.finite_fold_graph X_b X_c) F) Z_1) (tptp.bot_bot _let_1)) X_1)) (= (tptp.ti X_c X_1) (tptp.ti X_c Z_1))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (let ((_let_3 (tptp.fun _let_1 _let_2))) (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.hAPP X_c _let_3 (tptp.hAPP (tptp.fun X_b (tptp.fun X_c X_c)) (tptp.fun X_c _let_3) (tptp.finite_fold_graph X_b X_c) F) Z_1) (tptp.bot_bot _let_1)) Z_1)))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (Z_1 $$unsorted) (Y_1 $$unsorted) (X_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c X_c))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun X_c tptp.bool))) (let ((_let_4 (tptp.fun _let_2 _let_3))) (let ((_let_5 (tptp.hAPP X_c _let_4 (tptp.hAPP (tptp.fun X_b _let_1) (tptp.fun X_c _let_4) (tptp.finite_fold_graph X_b X_c) F) Z_1))) (=> (not (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_b (tptp.fun _let_2 tptp.bool) (tptp.member X_b) X_1) A_1))) (=> (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP _let_2 _let_3 _let_5 A_1) Y_1)) (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP _let_2 _let_3 _let_5 (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_b (tptp.fun _let_2 _let_2) (tptp.insert X_b) X_1) A_1)) (tptp.hAPP X_c X_c (tptp.hAPP X_b _let_1 F X_1) Y_1))))))))))) (forall ((Y_4 $$unsorted) (A_3 $$unsorted) (Ca $$unsorted) (S_4 $$unsorted) (T_5 $$unsorted)) (let ((_let_1 (tptp.fun tptp.com tptp.com))) (let ((_let_2 (tptp.fun tptp.state tptp.nat))) (let ((_let_3 (tptp.fun tptp.state tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP tptp.state _let_3 (tptp.hAPP tptp.com (tptp.fun tptp.state _let_3) tptp.evalc (tptp.hAPP tptp.com tptp.com (tptp.hAPP _let_2 _let_1 (tptp.hAPP tptp.loc_1 (tptp.fun _let_2 _let_1) tptp.local Y_4) A_3) Ca)) S_4) T_5)) (not (forall ((S1_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.loc_1 tptp.vname tptp.loc Y_4))) (let ((_let_2 (tptp.fun tptp.nat tptp.state))) (let ((_let_3 (tptp.fun tptp.vname _let_2))) (let ((_let_4 (tptp.fun tptp.state tptp.bool))) (=> (= T_5 (tptp.hAPP tptp.nat tptp.state (tptp.hAPP tptp.vname _let_2 (tptp.hAPP tptp.state _let_3 tptp.update S1_1) _let_1) (tptp.hAPP tptp.loc_1 tptp.nat (tptp.hAPP tptp.state (tptp.fun tptp.loc_1 tptp.nat) tptp.getlocs S_4) Y_4))) (not (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP tptp.state _let_4 (tptp.hAPP tptp.com (tptp.fun tptp.state _let_4) tptp.evalc Ca) (tptp.hAPP tptp.nat tptp.state (tptp.hAPP tptp.vname _let_2 (tptp.hAPP tptp.state _let_3 tptp.update S_4) _let_1) (tptp.hAPP tptp.state tptp.nat A_3 S_4))) S1_1))))))))))))))) (forall ((Y_4 $$unsorted) (A_3 $$unsorted) (Ca $$unsorted) (S_4 $$unsorted) (N_3 $$unsorted) (T_5 $$unsorted)) (let ((_let_1 (tptp.fun tptp.com tptp.com))) (let ((_let_2 (tptp.fun tptp.state tptp.nat))) (let ((_let_3 (tptp.fun tptp.state tptp.bool))) (let ((_let_4 (tptp.fun tptp.nat _let_3))) (=> (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP tptp.nat _let_3 (tptp.hAPP tptp.state _let_4 (tptp.hAPP tptp.com (tptp.fun tptp.state _let_4) tptp.evaln (tptp.hAPP tptp.com tptp.com (tptp.hAPP _let_2 _let_1 (tptp.hAPP tptp.loc_1 (tptp.fun _let_2 _let_1) tptp.local Y_4) A_3) Ca)) S_4) N_3) T_5)) (not (forall ((S1_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.loc_1 tptp.vname tptp.loc Y_4))) (let ((_let_2 (tptp.fun tptp.nat tptp.state))) (let ((_let_3 (tptp.fun tptp.vname _let_2))) (let ((_let_4 (tptp.fun tptp.state tptp.bool))) (let ((_let_5 (tptp.fun tptp.nat _let_4))) (=> (= T_5 (tptp.hAPP tptp.nat tptp.state (tptp.hAPP tptp.vname _let_2 (tptp.hAPP tptp.state _let_3 tptp.update S1_1) _let_1) (tptp.hAPP tptp.loc_1 tptp.nat (tptp.hAPP tptp.state (tptp.fun tptp.loc_1 tptp.nat) tptp.getlocs S_4) Y_4))) (not (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP tptp.nat _let_4 (tptp.hAPP tptp.state _let_5 (tptp.hAPP tptp.com (tptp.fun tptp.state _let_5) tptp.evaln Ca) (tptp.hAPP tptp.nat tptp.state (tptp.hAPP tptp.vname _let_2 (tptp.hAPP tptp.state _let_3 tptp.update S_4) _let_1) (tptp.hAPP tptp.state tptp.nat A_3 S_4))) N_3) S1_1))))))))))))))))) (forall ((C1 $$unsorted) (C2 $$unsorted) (S_1 $$unsorted) (T_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.state tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP tptp.state _let_1 (tptp.hAPP tptp.com (tptp.fun tptp.state _let_1) tptp.evalc (tptp.hAPP tptp.com tptp.com (tptp.hAPP tptp.com (tptp.fun tptp.com tptp.com) tptp.semi C1) C2)) S_1) T_4)) (not (forall ((S1_1 $$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 C1) S_1) S1_1)) (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_1) T_4))))))))))) (forall ((C1 $$unsorted) (C2 $$unsorted) (S_1 $$unsorted) (N_2 $$unsorted) (T_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.state tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.state _let_2 (tptp.hAPP tptp.com (tptp.fun tptp.state _let_2) tptp.evaln (tptp.hAPP tptp.com tptp.com (tptp.hAPP tptp.com (tptp.fun tptp.com tptp.com) tptp.semi C1) C2)) S_1) N_2) T_4)) (not (forall ((S1_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.state tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (let ((_let_3 (tptp.fun tptp.state _let_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.state _let_2 (tptp.hAPP tptp.com _let_3 tptp.evaln C1) S_1) N_2) S1_1)) (not (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.state _let_2 (tptp.hAPP tptp.com _let_3 tptp.evaln C2) S1_1) N_2) T_4))))))))))))) (forall ((X_b $$unsorted) (F $$unsorted) (A_3 $$unsorted) (X_3 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) _let_2 (tptp.finite_fold1Set X_b) F) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_2 (tptp.insert X_b) A_3) X_3)) X_1)) (not (forall ((A_4 $$unsorted) (A_5 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.insert X_b))) (=> (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_2 _let_3 A_3) X_3) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_2 _let_3 A_4) A_5)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_2 (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun X_b _let_2) (tptp.finite_fold_graph X_b X_b) F) A_4) A_5) X_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_4) A_5))))))))))))) (forall ((Ca $$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 Ca) (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)) Ca) (tptp.hAPP tptp.com _let_1 tptp.evalc Ca))))))) (forall ((C_1 $$unsorted) (S_1 $$unsorted) (T_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.state tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP tptp.state _let_1 (tptp.hAPP tptp.com (tptp.fun tptp.state _let_1) tptp.evalc C_1) S_1) T_4)) (exists ((N_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.state tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.state _let_2 (tptp.hAPP tptp.com (tptp.fun tptp.state _let_2) tptp.evaln C_1) S_1) N_1) T_4)))))))) (forall ((X_b $$unsorted) (F $$unsorted) (A1 $$unsorted) (A2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun _let_1 _let_1) (tptp.finite_fold1Set X_b) F) A1) A2)) (exists ((A_4 $$unsorted) (A_5 $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (and (= (tptp.ti _let_1 A1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_2 (tptp.insert X_b) A_4) A_5)) (= (tptp.ti X_b A2) (tptp.ti X_b X_2)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_2 (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun X_b _let_2) (tptp.finite_fold_graph X_b X_b) F) A_4) A_5) X_2)) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_4) A_5)))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (Z_1 $$unsorted) (A1 $$unsorted) (A2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (let ((_let_3 (tptp.fun _let_1 _let_2))) (= (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.hAPP X_c _let_3 (tptp.hAPP (tptp.fun X_b (tptp.fun X_c X_c)) (tptp.fun X_c _let_3) (tptp.finite_fold_graph X_b X_c) F) Z_1) A1) A2)) (or (and (= (tptp.ti _let_1 A1) (tptp.bot_bot _let_1)) (= (tptp.ti X_c A2) (tptp.ti X_c Z_1))) (exists ((X_2 $$unsorted) (A_5 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun _let_2 _let_1))) (let ((_let_4 (tptp.fun X_c X_c))) (and (= (tptp.ti _let_2 A1) (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_b (tptp.fun _let_2 _let_2) (tptp.insert X_b) X_2) A_5)) (= (tptp.ti X_c A2) (tptp.hAPP X_c X_c (tptp.hAPP X_b _let_4 F X_2) Y_2)) (not (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_5))) (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP _let_2 _let_1 (tptp.hAPP X_c _let_3 (tptp.hAPP (tptp.fun X_b _let_4) (tptp.fun X_c _let_3) (tptp.finite_fold_graph X_b X_c) F) Z_1) A_5) Y_2)))))))))))))) (forall ((C2 $$unsorted) (S2 $$unsorted) (N2 $$unsorted) (T2 $$unsorted) (C1 $$unsorted) (S1 $$unsorted) (N1 $$unsorted) (T1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.state tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (let ((_let_3 (tptp.fun tptp.state _let_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.state _let_2 (tptp.hAPP tptp.com _let_3 tptp.evaln C1) S1) N1) T1)) (=> (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.state _let_2 (tptp.hAPP tptp.com _let_3 tptp.evaln C2) S2) N2) T2)) (exists ((N_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.state tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (let ((_let_3 (tptp.fun tptp.state _let_2))) (and (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.state _let_2 (tptp.hAPP tptp.com _let_3 tptp.evaln C1) S1) N_1) T1)) (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.state _let_2 (tptp.hAPP tptp.com _let_3 tptp.evaln C2) S2) N_1) T2))))))))))))) (forall ((X_b $$unsorted) (F1 $$unsorted) (F2 $$unsorted) (Glb_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.vname X_b))) (let ((_let_2 (tptp.fun tptp.loc_1 X_b))) (= (tptp.hAPP tptp.vname X_b (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun tptp.glb_1 X_b) (tptp.fun _let_2 _let_1) (tptp.vname_rec X_b) F1) F2) (tptp.hAPP tptp.glb_1 tptp.vname tptp.glb Glb_3)) (tptp.hAPP tptp.glb_1 X_b F1 Glb_3))))) (forall ((X_b $$unsorted) (F1 $$unsorted) (F2 $$unsorted) (Glb_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.vname X_b))) (let ((_let_2 (tptp.fun tptp.loc_1 X_b))) (= (tptp.hAPP tptp.vname X_b (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun tptp.glb_1 X_b) (tptp.fun _let_2 _let_1) (tptp.vname_case X_b) F1) F2) (tptp.hAPP tptp.glb_1 tptp.vname tptp.glb Glb_3)) (tptp.hAPP tptp.glb_1 X_b F1 Glb_3))))) (forall ((X_b $$unsorted) (N_3 $$unsorted) (Pa $$unsorted) (Ca $$unsorted) (Q_1 $$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))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.nat (tptp.fun _let_1 tptp.bool) (tptp.hoare_920331057_valid X_b) N_3) (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_b) Pa) Ca) Q_1))) (forall ((Z_2 $$unsorted) (S_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP X_b (tptp.fun tptp.state tptp.bool) Pa Z_2) S_2)) (forall ((S_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.state tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.state _let_2 (tptp.hAPP tptp.com (tptp.fun tptp.state _let_2) tptp.evaln Ca) S_2) N_3) S_3)) (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP X_b _let_1 Q_1 Z_2) S_3))))))))))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_1 $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_b X_b))) (let ((_let_3 (tptp.fun _let_1 X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP (tptp.fun X_b _let_2) (tptp.fun _let_3 tptp.bool) (tptp.finite_folding_one X_b) F) F_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 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_1) A_1))) (=> (not (= (tptp.ti _let_1 A_1) (tptp.bot_bot _let_1))) (= (tptp.hAPP _let_1 X_b F_1 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_1) A_1)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_2 F X_1) (tptp.hAPP _let_1 X_b F_1 A_1))))))))))) (forall ((X_b $$unsorted) (Q_1 $$unsorted) (Pa $$unsorted)) (let ((_let_1 (tptp.fun tptp.bool tptp.bool))) (let ((_let_2 (tptp.fun X_b _let_1))) (let ((_let_3 (tptp.fun X_b tptp.bool))) (let ((_let_4 (tptp.collect X_b))) (let ((_let_5 (tptp.finite_finite_1 X_b))) (=> (or (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool _let_5 (tptp.hAPP _let_3 _let_3 _let_4 Pa))) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool _let_5 (tptp.hAPP _let_3 _let_3 _let_4 Q_1)))) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool _let_5 (tptp.hAPP _let_3 _let_3 _let_4 (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_2 (tptp.fun _let_3 _let_3) (tptp.combs X_b tptp.bool tptp.bool) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun tptp.bool _let_1) (tptp.fun _let_3 _let_2) (tptp.combb tptp.bool _let_1 X_b) tptp.fconj) Pa)) Q_1))))))))))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) (tptp.bot_bot _let_1))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.finite_finite_1 X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_3) A_1))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (H $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_b) F_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_c) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun _let_2 _let_1) (tptp.image X_b X_c) H) F_1))))))) (forall ((X_b $$unsorted) (Pa $$unsorted) (Q_1 $$unsorted)) (let ((_let_1 (tptp.collect X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.finite_finite_1 X_b))) (let ((_let_4 (tptp.fun tptp.bool tptp.bool))) (let ((_let_5 (tptp.fun X_b _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_b 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_b) tptp.fdisj) Pa)) Q_1)))) (and (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 (tptp.hAPP _let_2 _let_2 _let_1 Pa))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 (tptp.hAPP _let_2 _let_2 _let_1 Q_1))))))))))) (forall ((Glb_3 $$unsorted) (Glb_2 $$unsorted)) (= (= (tptp.hAPP tptp.glb_1 tptp.vname tptp.glb Glb_3) (tptp.hAPP tptp.glb_1 tptp.vname tptp.glb Glb_2)) (= (tptp.ti tptp.glb_1 Glb_3) (tptp.ti tptp.glb_1 Glb_2)))) (forall ((X_b $$unsorted)) (=> (tptp.finite_finite X_b) (forall ((A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite_1 X_b) A_1))))) (forall ((X_b $$unsorted)) (=> (tptp.finite_finite X_b) (forall ((A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite_1 X_b) A_1))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.finite_finite_1 X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_b (tptp.fun _let_2 _let_2) (tptp.insert X_b) A_3) A_1))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 A_1)))))) (forall ((Loc_1 $$unsorted) (Glb_1 $$unsorted)) (not (= (tptp.hAPP tptp.loc_1 tptp.vname tptp.loc Loc_1) (tptp.hAPP tptp.glb_1 tptp.vname tptp.glb Glb_1)))) (forall ((Glb_1 $$unsorted) (Loc_1 $$unsorted)) (not (= (tptp.hAPP tptp.glb_1 tptp.vname tptp.glb Glb_1) (tptp.hAPP tptp.loc_1 tptp.vname tptp.loc Loc_1)))) (forall ((X_b $$unsorted) (A_1 $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun _let_2 tptp.bool) (tptp.finite_folding_one X_b) F) F_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_1)) (=> (not (= (tptp.ti _let_1 A_1) (tptp.bot_bot _let_1))) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.insert X_b))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) F X_2) Y_2)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_3 _let_2 X_2) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_3 _let_2 Y_2) (tptp.bot_bot _let_1))))))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) (tptp.hAPP _let_1 X_b F_1 A_1)) A_1))))))))) (forall ((X_b $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_1)) (=> (not (= (tptp.ti _let_1 A_1) (tptp.bot_bot _let_1))) (exists ((X1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun _let_1 _let_1) (tptp.finite_fold1Set X_b) F) A_1) X1)))))))) (forall ((X_b $$unsorted) (Pa $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) F_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa (tptp.bot_bot _let_1))) (=> (forall ((X_2 $$unsorted) (F_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) F_2)) (=> (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) F_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa F_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_2) F_2)))))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa F_1))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (or (= (tptp.ti _let_1 A_3) (tptp.bot_bot _let_1)) (exists ((A_5 $$unsorted) (A_4 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (and (= (tptp.ti _let_1 A_3) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_4) A_5)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_5))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (not (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_b) A_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_c) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun _let_2 _let_1) (tptp.image X_b X_c) F) A_1))) (exists ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b _let_1))) (let ((_let_3 (tptp.fun X_b X_c))) (let ((_let_4 (tptp.fun X_b tptp.bool))) (let ((_let_5 (tptp.member X_b))) (let ((_let_6 (tptp.fun _let_4 _let_4))) (let ((_let_7 (tptp.fun _let_4 tptp.bool))) (let ((_let_8 (tptp.fun tptp.bool tptp.bool))) (let ((_let_9 (tptp.fun X_b _let_8))) (and (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP X_b _let_7 _let_5 X_2) A_1)) (not (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.finite_finite_1 X_b) (tptp.hAPP _let_4 _let_4 (tptp.collect X_b) (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_9 _let_6 (tptp.combs X_b tptp.bool tptp.bool) (tptp.hAPP _let_4 _let_9 (tptp.hAPP (tptp.fun tptp.bool _let_8) (tptp.fun _let_4 _let_9) (tptp.combb tptp.bool _let_8 X_b) tptp.fconj) (tptp.hAPP _let_4 _let_4 (tptp.hAPP (tptp.fun X_b _let_7) _let_6 (tptp.combc X_b _let_4 tptp.bool) _let_5) A_1))) (tptp.hAPP X_c _let_4 (tptp.hAPP _let_2 (tptp.fun X_c _let_4) (tptp.combc X_b X_c tptp.bool) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun X_c _let_1) (tptp.fun _let_3 _let_2) (tptp.combb X_c _let_1 X_b) (tptp.fequal X_c)) F)) (tptp.hAPP X_b X_c F X_2))))))))))))))))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (Z_1 $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite_1 X_b) A_1)) (exists ((X1 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun _let_2 _let_1))) (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP _let_2 _let_1 (tptp.hAPP X_c _let_3 (tptp.hAPP (tptp.fun X_b (tptp.fun X_c X_c)) (tptp.fun X_c _let_3) (tptp.finite_fold_graph X_b X_c) F) Z_1) A_1) X1)))))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_1 $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_b X_b))) (let ((_let_3 (tptp.fun _let_1 X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP (tptp.fun X_b _let_2) (tptp.fun _let_3 tptp.bool) (tptp.finite2073411215e_idem X_b) F) F_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_1)) (=> (not (= (tptp.ti _let_1 A_1) (tptp.bot_bot _let_1))) (= (tptp.hAPP _let_1 X_b F_1 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_1) A_1)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_2 F X_1) (tptp.hAPP _let_1 X_b F_1 A_1)))))))))) (forall ((X_b $$unsorted) (Pa $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) F_1)) (=> (not (= (tptp.ti _let_1 F_1) (tptp.bot_bot _let_1))) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_2) (tptp.bot_bot _let_1)))))) (=> (forall ((X_2 $$unsorted) (F_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) F_2)) (=> (not (= (tptp.ti _let_1 F_2) (tptp.bot_bot _let_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) F_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa F_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_2) F_2))))))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa F_1)))))))) (forall ((Y $$unsorted)) (=> (forall ((Glb $$unsorted)) (not (= (tptp.ti tptp.vname Y) (tptp.hAPP tptp.glb_1 tptp.vname tptp.glb Glb)))) (not (forall ((Loc $$unsorted)) (not (= (tptp.ti tptp.vname Y) (tptp.hAPP tptp.loc_1 tptp.vname tptp.loc Loc))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (X_1 $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Z_1 $$unsorted) (G $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b X_b))) (let ((_let_3 (tptp.fun _let_1 X_b))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.fun X_c X_b))) (let ((_let_6 (tptp.fun _let_5 _let_4))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_5 _let_4 (tptp.hAPP X_b _let_6 (tptp.hAPP (tptp.fun X_b _let_2) (tptp.fun X_b _let_6) (tptp.finite908156982e_idem X_b X_c) F) Z_1) G) F_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_c) A_1)) (= (tptp.hAPP _let_1 X_b F_1 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_c (tptp.fun _let_1 _let_1) (tptp.insert X_c) X_1) A_1)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_2 F (tptp.hAPP X_c X_b G X_1)) (tptp.hAPP _let_1 X_b F_1 A_1)))))))))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_1 $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b 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_b _let_3 (tptp.insert X_b) X_1) _let_2)))) (let ((_let_5 (tptp.fun X_b X_b))) (let ((_let_6 (tptp.hAPP _let_1 X_b F_1 A_1))) (let ((_let_7 (= _let_4 _let_2))) (let ((_let_8 (tptp.fun _let_1 X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_8 tptp.bool (tptp.hAPP (tptp.fun X_b _let_5) (tptp.fun _let_8 tptp.bool) (tptp.finite_folding_one X_b) F) F_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_1) A_1)) (and (=> _let_7 (= _let_6 (tptp.ti X_b X_1))) (=> (not _let_7) (= _let_6 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_5 F X_1) (tptp.hAPP _let_1 X_b F_1 _let_4))))))))))))))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_1 $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.bot_bot _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.hAPP X_b _let_3 (tptp.insert X_b) X_1))) (let ((_let_5 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 (tptp.minus_minus _let_1) A_1) (tptp.hAPP _let_1 _let_1 _let_4 _let_2)))) (let ((_let_6 (tptp.fun X_b X_b))) (let ((_let_7 (tptp.hAPP _let_1 X_b F_1 (tptp.hAPP _let_1 _let_1 _let_4 A_1)))) (let ((_let_8 (= _let_5 _let_2))) (let ((_let_9 (tptp.fun _let_1 X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_9 tptp.bool (tptp.hAPP (tptp.fun X_b _let_6) (tptp.fun _let_9 tptp.bool) (tptp.finite_folding_one X_b) F) F_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_1)) (and (=> _let_8 (= _let_7 (tptp.ti X_b X_1))) (=> (not _let_8) (= _let_7 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_6 F X_1) (tptp.hAPP _let_1 X_b F_1 _let_5))))))))))))))))) (forall ((X_b $$unsorted) (Ca $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) Ca))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) A_1) B))) (not (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B)))))))) (forall ((X_b $$unsorted) (B $$unsorted) (Ca $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) Ca))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_1)) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) A_1) B)))))))) (forall ((X_b $$unsorted) (B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.finite_finite_1 X_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.minus_minus _let_1) A_1) B))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (X_1 $$unsorted) (F $$unsorted) (Z_1 $$unsorted) (G $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b X_b))) (let ((_let_2 (tptp.fun (tptp.fun X_c tptp.bool) X_b))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.fun X_c X_b))) (let ((_let_5 (tptp.fun _let_4 _let_3))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_4 _let_3 (tptp.hAPP X_b _let_5 (tptp.hAPP (tptp.fun X_b _let_1) (tptp.fun X_b _let_5) (tptp.finite908156982e_idem X_b X_c) F) Z_1) G) F_1)) (= (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 F X_1) X_1) (tptp.ti X_b X_1))))))))) (forall ((X_b $$unsorted) (Ca $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) Ca))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) A_1) B))) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B))))))) (forall ((X_b $$unsorted) (Ca $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) Ca))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) A_1) B))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_1)))))) (forall ((X_b $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b 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_b $$unsorted) (Ca $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) Ca))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) A_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_b $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP (tptp.fun X_b (tptp.fun _let_1 tptp.bool)) _let_2 (tptp.combc X_b _let_1 tptp.bool) (tptp.member X_b)))) (let ((_let_4 (tptp.fun tptp.bool tptp.bool))) (let ((_let_5 (tptp.fun X_b _let_4))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.minus_minus _let_1) A_1) B) (tptp.hAPP _let_1 _let_1 (tptp.collect X_b) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_5 _let_2 (tptp.combs X_b tptp.bool tptp.bool) (tptp.hAPP _let_1 _let_5 (tptp.hAPP (tptp.fun tptp.bool _let_4) (tptp.fun _let_1 _let_5) (tptp.combb tptp.bool _let_4 X_b) tptp.fconj) (tptp.hAPP _let_1 _let_1 _let_3 A_1))) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_4 _let_2 (tptp.combb tptp.bool tptp.bool X_b) tptp.fNot) (tptp.hAPP _let_1 _let_1 _let_3 B))))))))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b X_b))) (let ((_let_2 (tptp.fun (tptp.fun X_b tptp.bool) X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP (tptp.fun X_b _let_1) (tptp.fun _let_2 tptp.bool) (tptp.finite2073411215e_idem X_b) F) F_1)) (= (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 F X_1) X_1) (tptp.ti X_b X_1)))))) (forall ((X_b $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) A_1) A_1) (tptp.bot_bot _let_1)))) (forall ((X_b $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) A_1) (tptp.bot_bot _let_1)) (tptp.ti _let_1 A_1)))) (forall ((X_b $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.bot_bot _let_1))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) _let_2) A_1) _let_2)))) (forall ((X_b $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.finite_finite_1 X_b))) (let ((_let_2 (tptp.fun X_b 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_b $$unsorted) (A_1 $$unsorted) (X_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b 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_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_1) B)) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_3 (tptp.insert X_b) X_1) A_1)) B) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 A_1) B))))))) (forall ((X_b $$unsorted) (A_1 $$unsorted) (X_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b 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_b _let_3 (tptp.insert X_b) X_1))) (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_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_1) 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_b $$unsorted) (A_3 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP X_b _let_2 (tptp.insert X_b) A_3))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_3) A_1)) (= (tptp.hAPP _let_1 _let_1 _let_3 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.minus_minus _let_1) A_1) (tptp.hAPP _let_1 _let_1 _let_3 (tptp.bot_bot _let_1)))) (tptp.ti _let_1 A_1))))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_1 $$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_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))) (= (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_b $$unsorted) (A_3 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP X_b _let_2 (tptp.insert X_b) A_3))) (= (tptp.hAPP _let_1 _let_1 _let_3 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.minus_minus _let_1) A_1) (tptp.hAPP _let_1 _let_1 _let_3 (tptp.bot_bot _let_1)))) (tptp.hAPP _let_1 _let_1 _let_3 A_1)))))) (forall ((X_b $$unsorted) (A_1 $$unsorted) (A_3 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP X_b _let_2 (tptp.insert X_b) A_3))) (let ((_let_4 (tptp.minus_minus _let_1))) (let ((_let_5 (tptp.hAPP _let_1 _let_2 _let_4 A_1))) (= (tptp.hAPP _let_1 _let_1 _let_5 (tptp.hAPP _let_1 _let_1 _let_3 B)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 _let_4 (tptp.hAPP _let_1 _let_1 _let_5 (tptp.hAPP _let_1 _let_1 _let_3 (tptp.bot_bot _let_1)))) B)))))))) (forall ((X_b $$unsorted) (A_1 $$unsorted) (A_3 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP X_b _let_2 (tptp.insert X_b) A_3))) (let ((_let_4 (tptp.minus_minus _let_1))) (let ((_let_5 (tptp.hAPP _let_1 _let_2 _let_4 A_1))) (= (tptp.hAPP _let_1 _let_1 _let_5 (tptp.hAPP _let_1 _let_1 _let_3 B)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 _let_4 (tptp.hAPP _let_1 _let_1 _let_5 B)) (tptp.hAPP _let_1 _let_1 _let_3 (tptp.bot_bot _let_1)))))))))) (forall ((X_b $$unsorted) (A_1 $$unsorted) (A_3 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP _let_1 _let_2 (tptp.minus_minus _let_1) A_1))) (let ((_let_4 (tptp.finite_finite_1 X_b))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_4 (tptp.hAPP _let_1 _let_1 _let_3 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_2 (tptp.insert X_b) A_3) B)))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_4 (tptp.hAPP _let_1 _let_1 _let_3 B))))))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_1 $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP _let_1 X_b F_1 A_1))) (let ((_let_3 (tptp.fun X_b X_b))) (let ((_let_4 (tptp.fun _let_1 X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP (tptp.fun X_b _let_3) (tptp.fun _let_4 tptp.bool) (tptp.finite2073411215e_idem X_b) F) F_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_1) A_1)) (= (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_3 F X_1) _let_2) _let_2))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (X_1 $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Z_1 $$unsorted) (G $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.hAPP _let_1 X_b F_1 A_1))) (let ((_let_3 (tptp.fun X_b X_b))) (let ((_let_4 (tptp.fun _let_1 X_b))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (let ((_let_6 (tptp.fun X_c X_b))) (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_b _let_7 (tptp.hAPP (tptp.fun X_b _let_3) (tptp.fun X_b _let_7) (tptp.finite908156982e_idem X_b X_c) F) Z_1) G) F_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_c) A_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_c (tptp.fun _let_1 tptp.bool) (tptp.member X_c) X_1) A_1)) (= (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_3 F (tptp.hAPP X_c X_b G X_1)) _let_2) _let_2)))))))))))) (forall ((X_b $$unsorted) (N $$unsorted) (H $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_b X_b))) (let ((_let_3 (tptp.fun _let_1 X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP (tptp.fun X_b _let_2) (tptp.fun _let_3 tptp.bool) (tptp.finite2073411215e_idem X_b) F) F_1)) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b X_b))) (= (tptp.hAPP X_b X_b H (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 F X_2) Y_2)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 F (tptp.hAPP X_b X_b H X_2)) (tptp.hAPP X_b X_b H Y_2))))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) N)) (=> (not (= (tptp.ti _let_1 N) (tptp.bot_bot _let_1))) (= (tptp.hAPP X_b X_b H (tptp.hAPP _let_1 X_b F_1 N)) (tptp.hAPP _let_1 X_b F_1 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_2 (tptp.fun _let_1 _let_1) (tptp.image X_b X_b) H) N))))))))))) (forall ((X_b $$unsorted) (Pa $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa A_1)) (=> (forall ((A_4 $$unsorted) (A_5 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_5)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_4) A_5)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa A_5)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.minus_minus _let_1) A_5) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_2 (tptp.insert X_b) A_4) (tptp.bot_bot _let_1))))))))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa (tptp.bot_bot _let_1)))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (X_1 $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Z_1 $$unsorted) (G $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.fun X_b X_b))) (let ((_let_4 (tptp.fun _let_1 X_b))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (let ((_let_6 (tptp.fun X_c X_b))) (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_b _let_7 (tptp.hAPP (tptp.fun X_b _let_3) (tptp.fun X_b _let_7) (tptp.finite1357897459simple X_b X_c) F) Z_1) G) F_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_c) A_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_c (tptp.fun _let_1 tptp.bool) (tptp.member X_c) X_1) A_1)) (= (tptp.hAPP _let_1 X_b F_1 A_1) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_3 F (tptp.hAPP X_c X_b G X_1)) (tptp.hAPP _let_1 X_b F_1 (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_c _let_2 (tptp.insert X_c) X_1) (tptp.bot_bot _let_1))))))))))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (X_1 $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Z_1 $$unsorted) (G $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP X_c _let_2 (tptp.insert X_c) X_1))) (let ((_let_4 (tptp.fun X_b X_b))) (let ((_let_5 (tptp.fun _let_1 X_b))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (let ((_let_7 (tptp.fun X_c X_b))) (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_b _let_8 (tptp.hAPP (tptp.fun X_b _let_4) (tptp.fun X_b _let_8) (tptp.finite1357897459simple X_b X_c) F) Z_1) G) F_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_c) A_1)) (= (tptp.hAPP _let_1 X_b F_1 (tptp.hAPP _let_1 _let_1 _let_3 A_1)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_4 F (tptp.hAPP X_c X_b G X_1)) (tptp.hAPP _let_1 X_b F_1 (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_b $$unsorted) (X_c $$unsorted)) (=> (tptp.minus X_c) (forall ((A_1 $$unsorted) (B $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b X_c))) (= (tptp.hAPP X_b X_c (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) A_1) B) X_2) (tptp.hAPP X_c X_c (tptp.hAPP X_c (tptp.fun X_c X_c) (tptp.minus_minus X_c) (tptp.hAPP X_b X_c A_1 X_2)) (tptp.hAPP X_b X_c B X_2))))))) (forall ((X_c $$unsorted) (X_b $$unsorted)) (=> (tptp.minus X_b) (forall ((A_1 $$unsorted) (B $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c X_b))) (= (tptp.hAPP X_c 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_c X_b A_1 X_1)) (tptp.hAPP X_c X_b B X_1))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (Z_1 $$unsorted) (G $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun _let_1 X_b))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.fun X_c X_b))) (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_b _let_5 (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun X_b _let_5) (tptp.finite1357897459simple X_b X_c) F) Z_1) G) F_1)) (= (tptp.hAPP _let_1 X_b F_1 (tptp.bot_bot _let_1)) (tptp.ti X_b Z_1))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (X_1 $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Z_1 $$unsorted) (G $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b X_b))) (let ((_let_3 (tptp.fun _let_1 X_b))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.fun X_c X_b))) (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_b _let_6 (tptp.hAPP (tptp.fun X_b _let_2) (tptp.fun X_b _let_6) (tptp.finite1357897459simple X_b X_c) F) Z_1) G) F_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_c) A_1)) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_c (tptp.fun _let_1 tptp.bool) (tptp.member X_c) X_1) A_1))) (= (tptp.hAPP _let_1 X_b F_1 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_c (tptp.fun _let_1 _let_1) (tptp.insert X_c) X_1) A_1)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_2 F (tptp.hAPP X_c X_b G X_1)) (tptp.hAPP _let_1 X_b F_1 A_1))))))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Z_1 $$unsorted) (G $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun _let_1 X_b))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.fun X_c X_b))) (let ((_let_5 (tptp.fun _let_4 _let_3))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_4 _let_3 (tptp.hAPP X_b _let_5 (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun X_b _let_5) (tptp.finite1357897459simple X_b X_c) F) Z_1) G) F_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_c) A_1)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_c (tptp.fun _let_1 tptp.bool) (tptp.member X_c) X_2) A_1)) (= (tptp.hAPP X_c X_b G X_2) (tptp.ti X_b Z_1))))) (= (tptp.hAPP _let_1 X_b F_1 A_1) (tptp.ti X_b Z_1))))))))))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_b _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.fun X_b _let_3))) (let ((_let_5 (tptp.fun _let_1 _let_3))) (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.finite_comp_fun_idem X_b _let_1) (tptp.hAPP _let_2 _let_4 (tptp.hAPP _let_5 (tptp.fun _let_2 _let_4) (tptp.combb _let_1 _let_3 X_b) (tptp.hAPP _let_5 _let_5 (tptp.combc _let_1 _let_1 _let_1) (tptp.minus_minus _let_1))) (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_4 (tptp.fun _let_1 _let_2) (tptp.combc X_b _let_1 _let_1) (tptp.insert X_b)) (tptp.bot_bot _let_1))))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (A_3 $$unsorted) (Z_1 $$unsorted) (A_1 $$unsorted) (Y_1 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (let ((_let_3 (tptp.fun _let_1 _let_2))) (let ((_let_4 (tptp.fun X_b (tptp.fun X_c X_c)))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.finite100568337ommute X_b X_c) F)) (=> (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.hAPP X_c _let_3 (tptp.hAPP _let_4 (tptp.fun X_c _let_3) (tptp.finite_fold_graph X_b X_c) F) Z_1) A_1) Y_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) A_1)) (exists ((Y_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.fun X_c tptp.bool))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.fun X_c X_c))) (and (= (tptp.ti X_c Y_1) (tptp.hAPP X_c X_c (tptp.hAPP X_b _let_5 F A_3) Y_3)) (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP _let_1 _let_3 (tptp.hAPP X_c _let_4 (tptp.hAPP (tptp.fun X_b _let_5) (tptp.fun X_c _let_4) (tptp.finite_fold_graph X_b X_c) F) Z_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.minus_minus _let_1) A_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_2 (tptp.insert X_b) A_3) (tptp.bot_bot _let_1)))) Y_3))))))))))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (Z_1 $$unsorted) (Y_1 $$unsorted) (X_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c X_c))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (let ((_let_3 (tptp.fun X_b tptp.bool))) (let ((_let_4 (tptp.fun _let_3 _let_2))) (let ((_let_5 (tptp.hAPP X_c _let_4 (tptp.hAPP (tptp.fun X_b _let_1) (tptp.fun X_c _let_4) (tptp.fold_graph X_b X_c) F) Z_1))) (let ((_let_6 (tptp.fun _let_3 _let_3))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_b (tptp.fun _let_3 tptp.bool) (tptp.member X_b) X_1) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_c 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_b _let_6 (tptp.insert X_b) X_1) (tptp.bot_bot _let_3)))) Y_1)) (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP _let_3 _let_2 _let_5 A_1) (tptp.hAPP X_c X_c (tptp.hAPP X_b _let_1 F X_1) Y_1)))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.ab_semigroup_mult X_b) (forall ((A_3 $$unsorted) (Ba $$unsorted) (A_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.insert X_b))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun X_b _let_3) (tptp.finite_fold_graph X_b X_b) (tptp.times_times X_b)))) (let ((_let_5 (tptp.member X_b))) (let ((_let_6 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_3 _let_4 Ba) A_1) X_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_6 _let_5 A_3) A_1)) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_6 _let_5 Ba) A_1))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_3 _let_4 A_3) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_3 _let_2 Ba) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 (tptp.minus_minus _let_1) A_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_3 _let_2 A_3) (tptp.bot_bot _let_1))))) X_1)))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ab_sem1668676832m_mult X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_2))) (let ((_let_2 (tptp.hAPP X_a X_a _let_1 B_1))) (= (tptp.hAPP X_a X_a _let_1 _let_2) _let_2)))))) (forall ((X_a $$unsorted)) (=> (tptp.ab_sem1668676832m_mult X_a) (forall ((X $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) X) X) (tptp.ti X_a X))))) (forall ((X_a $$unsorted)) (=> (tptp.ab_sem1668676832m_mult X_a) (forall ((A_2 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_2) A_2) (tptp.ti X_a A_2))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted) (Z_1 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun X_c X_c))) (let ((_let_2 (tptp.hAPP X_b _let_1 F X_1))) (let ((_let_3 (tptp.hAPP X_b _let_1 F Y_1))) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b _let_1) tptp.bool (tptp.finite100568337ommute X_b X_c) F)) (= (tptp.hAPP X_c X_c _let_2 (tptp.hAPP X_c X_c _let_3 Z_1)) (tptp.hAPP X_c X_c _let_3 (tptp.hAPP X_c X_c _let_2 Z_1)))))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (X_1 $$unsorted) (Z_1 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun X_c X_c))) (let ((_let_2 (tptp.hAPP X_b _let_1 F X_1))) (let ((_let_3 (tptp.hAPP X_c X_c _let_2 Z_1))) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b _let_1) tptp.bool (tptp.finite_comp_fun_idem X_b X_c) F)) (= (tptp.hAPP X_c X_c _let_2 _let_3) _let_3)))))) (forall ((X_b $$unsorted)) (=> (tptp.ab_semigroup_mult X_b) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) tptp.bool (tptp.finite100568337ommute X_b X_b) (tptp.times_times X_b))))) (forall ((X_b $$unsorted)) (=> (tptp.ab_sem1668676832m_mult X_b) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) tptp.bool (tptp.finite_comp_fun_idem X_b X_b) (tptp.times_times X_b))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (let ((_let_3 (tptp.fun _let_1 _let_2))) (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.hAPP X_c _let_3 (tptp.hAPP (tptp.fun X_b (tptp.fun X_c X_c)) (tptp.fun X_c _let_3) (tptp.fold_graph X_b X_c) F) Z_1) (tptp.bot_bot _let_1)) Z_1)))))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b (tptp.fun _let_1 _let_1)) tptp.bool (tptp.finite_comp_fun_idem X_b _let_1) (tptp.insert X_b))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (Y_1 $$unsorted) (Z_1 $$unsorted) (A_1 $$unsorted) (X_1 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun _let_2 _let_1))) (let ((_let_4 (tptp.fun X_b (tptp.fun X_c X_c)))) (let ((_let_5 (tptp.hAPP _let_2 _let_1 (tptp.hAPP X_c _let_3 (tptp.hAPP _let_4 (tptp.fun X_c _let_3) (tptp.finite_fold_graph X_b X_c) F) Z_1) A_1))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.finite100568337ommute X_b X_c) F)) (=> (tptp.hBOOL (tptp.hAPP X_c tptp.bool _let_5 X_1)) (=> (tptp.hBOOL (tptp.hAPP X_c tptp.bool _let_5 Y_1)) (= (tptp.ti X_c Y_1) (tptp.ti X_c X_1))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.ab_semigroup_mult X_b) (forall ((Z_1 $$unsorted) (Ba $$unsorted) (A_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.times_times X_b))) (let ((_let_2 (tptp.fun X_b X_b))) (let ((_let_3 (tptp.fun X_b tptp.bool))) (let ((_let_4 (tptp.fun _let_3 _let_3))) (let ((_let_5 (tptp.hAPP (tptp.fun X_b _let_2) (tptp.fun X_b _let_4) (tptp.finite_fold_graph X_b X_b) _let_1))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP _let_3 _let_3 (tptp.hAPP X_b _let_4 _let_5 Ba) A_1) Y_1)) (=> (not (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_b (tptp.fun _let_3 tptp.bool) (tptp.member X_b) Ba) A_1))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP _let_3 _let_3 (tptp.hAPP X_b _let_4 _let_5 Z_1) (tptp.hAPP _let_3 _let_3 (tptp.hAPP X_b _let_4 (tptp.insert X_b) Ba) A_1)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_2 _let_1 Z_1) Y_1))))))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (Z_1 $$unsorted) (X_1 $$unsorted) (A_1 $$unsorted) (V $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (let ((_let_3 (tptp.fun _let_1 _let_2))) (let ((_let_4 (tptp.fun X_b (tptp.fun X_c X_c)))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.finite100568337ommute X_b X_c) F)) (=> (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.hAPP X_c _let_3 (tptp.hAPP _let_4 (tptp.fun X_c _let_3) (tptp.finite_fold_graph X_b X_c) F) Z_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_1) A_1)) V)) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_1) A_1))) (not (forall ((Y_2 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun _let_2 _let_1))) (let ((_let_4 (tptp.fun X_c X_c))) (=> (= (tptp.ti X_c V) (tptp.hAPP X_c X_c (tptp.hAPP X_b _let_4 F X_1) Y_2)) (not (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP _let_2 _let_1 (tptp.hAPP X_c _let_3 (tptp.hAPP (tptp.fun X_b _let_4) (tptp.fun X_c _let_3) (tptp.finite_fold_graph X_b X_c) F) Z_1) A_1) Y_2)))))))))))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (Z_1 $$unsorted) (X_1 $$unsorted) (A_1 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.fun _let_1 X_c))) (let ((_let_4 (tptp.fun X_c X_c))) (let ((_let_5 (tptp.fun X_b _let_4))) (let ((_let_6 (tptp.hAPP X_c _let_3 (tptp.hAPP _let_5 (tptp.fun X_c _let_3) (tptp.finite_fold X_b X_c) F) Z_1))) (=> (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.finite100568337ommute X_b X_c) F)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_1) A_1)) (= (tptp.hAPP _let_1 X_c _let_6 A_1) (tptp.hAPP X_c X_c (tptp.hAPP X_b _let_4 F X_1) (tptp.hAPP _let_1 X_c _let_6 (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_1) (tptp.bot_bot _let_1)))))))))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (Z_1 $$unsorted) (X_1 $$unsorted) (A_1 $$unsorted) (F $$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_1))) (let ((_let_4 (tptp.fun _let_1 X_c))) (let ((_let_5 (tptp.fun X_c X_c))) (let ((_let_6 (tptp.fun X_b _let_5))) (let ((_let_7 (tptp.hAPP X_c _let_4 (tptp.hAPP _let_6 (tptp.fun X_c _let_4) (tptp.finite_fold X_b X_c) F) Z_1))) (=> (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.finite100568337ommute X_b X_c) F)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_1)) (= (tptp.hAPP _let_1 X_c _let_7 (tptp.hAPP _let_1 _let_1 _let_3 A_1)) (tptp.hAPP X_c X_c (tptp.hAPP X_b _let_5 F X_1) (tptp.hAPP _let_1 X_c _let_7 (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_b $$unsorted)) (=> (tptp.ab_semigroup_mult X_b) (forall ((X_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.times_times X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun X_b X_b))) (let ((_let_4 (tptp.hAPP (tptp.fun X_b _let_3) (tptp.fun _let_2 X_b) (tptp.finite_fold1 X_b) _let_1))) (=> (not (= (tptp.ti _let_2 A_1) (tptp.bot_bot _let_2))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_b) A_1)) (=> (not (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_b (tptp.fun _let_2 tptp.bool) (tptp.member X_b) X_1) A_1))) (= (tptp.hAPP _let_2 X_b _let_4 (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_b (tptp.fun _let_2 _let_2) (tptp.insert X_b) X_1) A_1)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_3 _let_1 X_1) (tptp.hAPP _let_2 X_b _let_4 A_1))))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.ab_sem1668676832m_mult X_b) (forall ((X_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.times_times X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun X_b X_b))) (let ((_let_4 (tptp.hAPP (tptp.fun X_b _let_3) (tptp.fun _let_2 X_b) (tptp.finite_fold1 X_b) _let_1))) (=> (not (= (tptp.ti _let_2 A_1) (tptp.bot_bot _let_2))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_b) A_1)) (= (tptp.hAPP _let_2 X_b _let_4 (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_b (tptp.fun _let_2 _let_2) (tptp.insert X_b) X_1) A_1)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_3 _let_1 X_1) (tptp.hAPP _let_2 X_b _let_4 A_1)))))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun _let_1 X_b))) (= (tptp.hAPP _let_1 X_b (tptp.hAPP X_b _let_2 (tptp.hAPP (tptp.fun X_c (tptp.fun X_b X_b)) (tptp.fun X_b _let_2) (tptp.finite_fold X_c X_b) F) Z_1) (tptp.bot_bot _let_1)) (tptp.ti X_b Z_1))))) (forall ((X_b $$unsorted)) (=> (tptp.ab_sem1668676832m_mult X_b) (forall ((A_3 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.times_times X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun _let_2 X_b))) (let ((_let_4 (tptp.fun X_b (tptp.fun X_b X_b)))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_b) A_1)) (= (tptp.hAPP _let_2 X_b (tptp.hAPP _let_4 _let_3 (tptp.finite_fold1 X_b) _let_1) (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_b (tptp.fun _let_2 _let_2) (tptp.insert X_b) A_3) A_1)) (tptp.hAPP _let_2 X_b (tptp.hAPP X_b _let_3 (tptp.hAPP _let_4 (tptp.fun X_b _let_3) (tptp.finite_fold X_b X_b) _let_1) A_3) A_1)))))))))) (forall ((X_b $$unsorted)) (=> (tptp.ab_semigroup_mult X_b) (forall ((A_3 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.times_times X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun _let_2 X_b))) (let ((_let_4 (tptp.fun X_b (tptp.fun X_b X_b)))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_b) A_1)) (=> (not (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_b (tptp.fun _let_2 tptp.bool) (tptp.member X_b) A_3) A_1))) (= (tptp.hAPP _let_2 X_b (tptp.hAPP _let_4 _let_3 (tptp.finite_fold1 X_b) _let_1) (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_b (tptp.fun _let_2 _let_2) (tptp.insert X_b) A_3) A_1)) (tptp.hAPP _let_2 X_b (tptp.hAPP X_b _let_3 (tptp.hAPP _let_4 (tptp.fun X_b _let_3) (tptp.finite_fold X_b X_b) _let_1) A_3) A_1))))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (X_1 $$unsorted) (Z_1 $$unsorted) (A_1 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun X_c X_c))) (let ((_let_2 (tptp.hAPP X_b _let_1 F X_1))) (let ((_let_3 (tptp.fun X_b tptp.bool))) (let ((_let_4 (tptp.fun _let_3 X_c))) (let ((_let_5 (tptp.fun X_b _let_1))) (let ((_let_6 (tptp.hAPP _let_5 (tptp.fun X_c _let_4) (tptp.finite_fold X_b X_c) F))) (=> (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.finite100568337ommute X_b X_c) F)) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.finite_finite_1 X_b) A_1)) (= (tptp.hAPP X_c X_c _let_2 (tptp.hAPP _let_3 X_c (tptp.hAPP X_c _let_4 _let_6 Z_1) A_1)) (tptp.hAPP _let_3 X_c (tptp.hAPP X_c _let_4 _let_6 (tptp.hAPP X_c X_c _let_2 Z_1)) A_1))))))))))) (forall ((X_b $$unsorted) (F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (tptp.hAPP _let_1 X_b (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun _let_1 X_b) (tptp.finite_fold1 X_b) F) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_3) (tptp.bot_bot _let_1))) (tptp.ti X_b A_3)))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (G $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (= G (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun _let_1 X_b) (tptp.finite_fold1 X_b) F)) (= (tptp.hAPP _let_1 X_b G (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_3) (tptp.bot_bot _let_1))) (tptp.ti X_b A_3))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (Z_1 $$unsorted) (A_1 $$unsorted) (Y_1 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 X_c))) (let ((_let_3 (tptp.fun X_b (tptp.fun X_c X_c)))) (let ((_let_4 (tptp.fun X_c tptp.bool))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.finite100568337ommute X_b X_c) F)) (=> (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP _let_1 _let_4 (tptp.hAPP X_c _let_5 (tptp.hAPP _let_3 (tptp.fun X_c _let_5) (tptp.finite_fold_graph X_b X_c) F) Z_1) A_1) Y_1)) (= (tptp.hAPP _let_1 X_c (tptp.hAPP X_c _let_2 (tptp.hAPP _let_3 (tptp.fun X_c _let_2) (tptp.finite_fold X_b X_c) F) Z_1) A_1) (tptp.ti X_c Y_1)))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (Z_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (let ((_let_3 (tptp.fun _let_2 _let_1))) (let ((_let_4 (tptp.fun X_c (tptp.fun X_b X_b)))) (let ((_let_5 (tptp.fun _let_2 X_b))) (= (tptp.hAPP _let_2 X_b (tptp.hAPP X_b _let_5 (tptp.hAPP _let_4 (tptp.fun X_b _let_5) (tptp.finite_fold X_c X_b) F) Z_1) A_1) (tptp.hAPP _let_1 X_b (tptp.the X_b) (tptp.hAPP _let_2 _let_1 (tptp.hAPP X_b _let_3 (tptp.hAPP _let_4 (tptp.fun X_b _let_3) (tptp.finite_fold_graph X_c X_b) F) Z_1) A_1))))))))) (forall ((X_b $$unsorted) (A_1 $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 X_b))) (let ((_let_3 (tptp.fun X_b (tptp.fun X_b X_b)))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_3 (tptp.fun _let_2 tptp.bool) (tptp.finite_folding_one X_b) F) F_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_1)) (= (tptp.hAPP _let_1 X_b F_1 A_1) (tptp.hAPP _let_1 X_b (tptp.hAPP _let_3 _let_2 (tptp.finite_fold1 X_b) F) A_1)))))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (Z_1 $$unsorted) (X_1 $$unsorted) (A_1 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun X_c X_c))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun _let_2 X_c))) (let ((_let_4 (tptp.fun X_b _let_1))) (let ((_let_5 (tptp.hAPP _let_4 (tptp.fun X_c _let_3) (tptp.finite_fold X_b X_c) F))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.finite100568337ommute X_b X_c) F)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_b) A_1)) (=> (not (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_b (tptp.fun _let_2 tptp.bool) (tptp.member X_b) X_1) A_1))) (= (tptp.hAPP _let_2 X_c (tptp.hAPP X_c _let_3 _let_5 Z_1) (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_b (tptp.fun _let_2 _let_2) (tptp.insert X_b) X_1) A_1)) (tptp.hAPP _let_2 X_c (tptp.hAPP X_c _let_3 _let_5 (tptp.hAPP X_c X_c (tptp.hAPP X_b _let_1 F X_1) Z_1)) A_1))))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (Z_1 $$unsorted) (X_1 $$unsorted) (A_1 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 X_c))) (let ((_let_3 (tptp.fun X_c X_c))) (let ((_let_4 (tptp.fun X_b _let_3))) (let ((_let_5 (tptp.hAPP X_c _let_2 (tptp.hAPP _let_4 (tptp.fun X_c _let_2) (tptp.finite_fold X_b X_c) F) Z_1))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.finite100568337ommute X_b X_c) F)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 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_1) A_1))) (= (tptp.hAPP _let_1 X_c _let_5 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_1) A_1)) (tptp.hAPP X_c X_c (tptp.hAPP X_b _let_3 F X_1) (tptp.hAPP _let_1 X_c _let_5 A_1)))))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (Z_1 $$unsorted) (X_1 $$unsorted) (A_1 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun X_c X_c))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun _let_2 X_c))) (let ((_let_4 (tptp.fun X_b _let_1))) (let ((_let_5 (tptp.hAPP _let_4 (tptp.fun X_c _let_3) (tptp.finite_fold X_b X_c) F))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.finite_comp_fun_idem X_b X_c) F)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_b) A_1)) (= (tptp.hAPP _let_2 X_c (tptp.hAPP X_c _let_3 _let_5 Z_1) (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_b (tptp.fun _let_2 _let_2) (tptp.insert X_b) X_1) A_1)) (tptp.hAPP _let_2 X_c (tptp.hAPP X_c _let_3 _let_5 (tptp.hAPP X_c X_c (tptp.hAPP X_b _let_1 F X_1) Z_1)) A_1)))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (Z_1 $$unsorted) (X_1 $$unsorted) (A_1 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 X_c))) (let ((_let_3 (tptp.fun X_c X_c))) (let ((_let_4 (tptp.fun X_b _let_3))) (let ((_let_5 (tptp.hAPP X_c _let_2 (tptp.hAPP _let_4 (tptp.fun X_c _let_2) (tptp.finite_fold X_b X_c) F) Z_1))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.finite_comp_fun_idem X_b X_c) F)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_1)) (= (tptp.hAPP _let_1 X_c _let_5 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_1) A_1)) (tptp.hAPP X_c X_c (tptp.hAPP X_b _let_3 F X_1) (tptp.hAPP _let_1 X_c _let_5 A_1))))))))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_1 $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 X_b))) (let ((_let_3 (tptp.fun X_b (tptp.fun X_b X_b)))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_3 (tptp.fun _let_2 tptp.bool) (tptp.finite_folding_one X_b) F) F_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_1)) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_1) A_1))) (= (tptp.hAPP _let_1 X_b F_1 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_1) A_1)) (tptp.hAPP _let_1 X_b (tptp.hAPP X_b _let_2 (tptp.hAPP _let_3 (tptp.fun X_b _let_2) (tptp.finite_fold X_b X_b) F) X_1) A_1))))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (A_1 $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 X_b))) (let ((_let_3 (tptp.fun X_b (tptp.fun X_b X_b)))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_3 (tptp.fun _let_2 tptp.bool) (tptp.finite2073411215e_idem X_b) F) F_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_1)) (= (tptp.hAPP _let_1 X_b F_1 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_3) A_1)) (tptp.hAPP _let_1 X_b (tptp.hAPP X_b _let_2 (tptp.hAPP _let_3 (tptp.fun X_b _let_2) (tptp.finite_fold X_b X_b) F) A_3) A_1)))))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (Z_1 $$unsorted) (A_1 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 X_c))) (let ((_let_3 (tptp.fun X_b (tptp.fun X_c X_c)))) (let ((_let_4 (tptp.fun X_c tptp.bool))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.finite100568337ommute X_b X_c) F)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_1)) (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP _let_1 _let_4 (tptp.hAPP X_c _let_5 (tptp.hAPP _let_3 (tptp.fun X_c _let_5) (tptp.finite_fold_graph X_b X_c) F) Z_1) A_1) (tptp.hAPP _let_1 X_c (tptp.hAPP X_c _let_2 (tptp.hAPP _let_3 (tptp.fun X_c _let_2) (tptp.finite_fold X_b X_c) F) Z_1) A_1))))))))))) (forall ((X_b $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_b (tptp.fun X_b X_b)))) (= (tptp.hAPP _let_1 X_b (tptp.hAPP _let_2 (tptp.fun _let_1 X_b) (tptp.finite_fold1 X_b) F) A_1) (tptp.hAPP _let_1 X_b (tptp.the X_b) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_2 (tptp.fun _let_1 _let_1) (tptp.finite_fold1Set X_b) F) A_1)))))) (forall ((X_b $$unsorted) (B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_b _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.fun X_b _let_3))) (let ((_let_5 (tptp.minus_minus _let_1))) (let ((_let_6 (tptp.fun _let_1 _let_3))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_1)) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_5 B) A_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 (tptp.hAPP _let_4 _let_6 (tptp.finite_fold X_b _let_1) (tptp.hAPP _let_2 _let_4 (tptp.hAPP _let_6 (tptp.fun _let_2 _let_4) (tptp.combb _let_1 _let_3 X_b) (tptp.hAPP _let_6 _let_6 (tptp.combc _let_1 _let_1 _let_1) _let_5)) (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_4 (tptp.fun _let_1 _let_2) (tptp.combc X_b _let_1 _let_1) (tptp.insert X_b)) (tptp.bot_bot _let_1)))) B) A_1)))))))))) (forall ((X_b $$unsorted)) (=> (tptp.ab_sem1668676832m_mult X_b) (forall ((N $$unsorted) (H $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_b X_b))) (let ((_let_3 (tptp.hAPP (tptp.fun X_b _let_2) (tptp.fun _let_1 X_b) (tptp.finite_fold1 X_b) (tptp.times_times X_b)))) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.times_times X_b))) (let ((_let_2 (tptp.fun X_b X_b))) (= (tptp.hAPP X_b X_b H (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_2 _let_1 X_2) Y_2)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_2 _let_1 (tptp.hAPP X_b X_b H X_2)) (tptp.hAPP X_b X_b H Y_2)))))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) N)) (=> (not (= (tptp.ti _let_1 N) (tptp.bot_bot _let_1))) (= (tptp.hAPP X_b X_b H (tptp.hAPP _let_1 X_b _let_3 N)) (tptp.hAPP _let_1 X_b _let_3 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_2 (tptp.fun _let_1 _let_1) (tptp.image X_b X_b) H) N)))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.ab_semigroup_mult X_b) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_1)) (=> (not (= (tptp.ti _let_1 A_1) (tptp.bot_bot _let_1))) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.insert X_b))) (let ((_let_3 (tptp.fun _let_1 _let_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_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.times_times X_b) X_2) Y_2)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_3 _let_2 X_2) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_3 _let_2 Y_2) (tptp.bot_bot _let_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 _let_1 X_b (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun _let_1 X_b) (tptp.finite_fold1 X_b) (tptp.times_times X_b)) A_1)) A_1))))))))) (forall ((X_b $$unsorted) (A_1 $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 X_b))) (let ((_let_3 (tptp.fun X_b (tptp.fun X_b X_b)))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_3 (tptp.fun _let_2 tptp.bool) (tptp.big_semilattice_big X_b) F) F_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_1)) (= (tptp.hAPP _let_1 X_b F_1 A_1) (tptp.hAPP _let_1 X_b (tptp.hAPP _let_3 _let_2 (tptp.finite_fold1 X_b) F) A_1)))))))) (forall ((X_b $$unsorted)) (=> (tptp.ab_sem1668676832m_mult X_b) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.times_times X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun X_b X_b))) (let ((_let_4 (tptp.hAPP (tptp.fun X_b _let_3) (tptp.fun _let_2 X_b) (tptp.finite_fold1 X_b) _let_1))) (let ((_let_5 (tptp.bot_bot _let_2))) (let ((_let_6 (tptp.finite_finite_1 X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_6 A_1)) (=> (not (= (tptp.ti _let_2 A_1) _let_5)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_6 B)) (=> (not (= (tptp.ti _let_2 B) _let_5)) (= (tptp.hAPP _let_2 X_b _let_4 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 (tptp.fun _let_2 _let_2) (tptp.semilattice_sup_sup _let_2) A_1) B)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_3 _let_1 (tptp.hAPP _let_2 X_b _let_4 A_1)) (tptp.hAPP _let_2 X_b _let_4 B)))))))))))))))) (forall ((X_b $$unsorted) (B $$unsorted) (A_1 $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP _let_1 X_b F_1 A_1))) (let ((_let_3 (tptp.fun X_b X_b))) (let ((_let_4 (tptp.fun _let_1 X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP (tptp.fun X_b _let_3) (tptp.fun _let_4 tptp.bool) (tptp.finite2073411215e_idem X_b) F) F_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) 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_b X_b (tptp.hAPP X_b _let_3 F (tptp.hAPP _let_1 X_b F_1 B)) _let_2) _let_2)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((X $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X) X))))) (forall ((X_b $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.ord_less_eq _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 B) A_1)) (= (tptp.ti _let_1 A_1) (tptp.ti _let_1 B)))))))) (forall ((X_b $$unsorted) (Ca $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP X_b _let_2 (tptp.member X_b) Ca))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_1) B)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 A_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 B)))))))) (forall ((X_b $$unsorted) (A_1 $$unsorted) (Ca $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) Ca))) (=> (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_1))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_sup_sup _let_1) A_1) B))))))) (forall ((X_b $$unsorted) (Ca $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) Ca))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_sup_sup _let_1) A_1) B))) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_1))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B))))))) (forall ((X_b $$unsorted) (A_1 $$unsorted) (B $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (=> (not (tptp.hBOOL (tptp.hAPP X_b tptp.bool B X_1))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool A_1 X_1))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_sup_sup _let_1) A_1) B) X_1))))) (forall ((X_b $$unsorted) (A_1 $$unsorted) (B $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_sup_sup _let_1) A_1) B) X_1)) (=> (not (tptp.hBOOL (tptp.hAPP X_b tptp.bool A_1 X_1))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool B X_1)))))) (forall ((X_b $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) (tptp.bot_bot _let_1)) A_1)))) (forall ((X_b $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun _let_1 _let_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_1)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 _let_1) (tptp.hAPP _let_2 _let_2 (tptp.collect _let_1) (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_3 _let_3 (tptp.combc _let_1 _let_1 tptp.bool) (tptp.ord_less_eq _let_1)) A_1))))))))) (forall ((X_b $$unsorted)) (=> (tptp.semilattice_sup X_b) (forall ((Ba $$unsorted) (A_3 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.semilattice_sup_sup X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun _let_2 X_b))) (let ((_let_4 (tptp.fun X_b X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_b) A_1)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_b (tptp.fun _let_2 tptp.bool) (tptp.member X_b) A_3) A_1)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 (tptp.ord_less_eq X_b) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_4 _let_1 A_3) Ba)) (tptp.hAPP _let_2 X_b (tptp.hAPP X_b _let_3 (tptp.hAPP (tptp.fun X_b _let_4) (tptp.fun X_b _let_3) (tptp.finite_fold X_b X_b) _let_1) Ba) A_1)))))))))))) (forall ((X_b $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.bot_bot _let_1))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) A_1) _let_2)) (= (tptp.ti _let_1 A_1) _let_2))))) (forall ((X_b $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.finite_finite_1 X_b))) (let ((_let_2 (tptp.fun X_b 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_b $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.finite_finite_1 X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) A_1) B)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 B)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 A_1))))))) (forall ((X_b $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b 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_b $$unsorted) (B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.semilattice_sup_sup _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 (tptp.minus_minus _let_1) B) A_1)) A_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 B) A_1)))))) (forall ((X_b $$unsorted) (A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.minus_minus _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.semilattice_sup_sup _let_1))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_4 A_1) B)) C) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_4 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 A_1) C)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 B) C)))))))) (forall ((X_b $$unsorted) (B $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (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_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_3) B))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b 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_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_1) A_1)) B)) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_3 (tptp.member X_b) X_1) B)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 A_1) B)))))))) (forall ((X_b $$unsorted) (B $$unsorted) (X_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b 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_b _let_2 (tptp.member X_b) X_1) A_1))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_1) B))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 B)))))))) (forall ((X_b $$unsorted) (Ba $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b 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_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) Ba) B))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) 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)) (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))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (B $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) B) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun _let_2 _let_1) (tptp.image X_c X_b) F) A_1))) (exists ((AA $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_c 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_c X_b) (tptp.fun _let_2 _let_1) (tptp.image X_c X_b) F) AA)))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun _let_2 _let_1) (tptp.image X_b X_c) F))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) A_1) B)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) (tptp.hAPP _let_2 _let_1 _let_3 A_1)) (tptp.hAPP _let_2 _let_1 _let_3 B)))))))) (forall ((X_b $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (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) (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_b $$unsorted) (D $$unsorted) (B $$unsorted) (A_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.minus_minus _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.ord_less_eq _let_1))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_5 _let_4 A_1) C)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_5 _let_4 D) B)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_5 _let_4 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 A_1) B)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 C) D))))))))))) (forall ((X_b $$unsorted) (C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.minus_minus _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.ord_less_eq _let_1))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_5 _let_4 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_5 _let_4 B) C)) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 B) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 C) A_1)) (tptp.ti _let_1 A_1)))))))))) (forall ((X_b $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b 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_b $$unsorted) (A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.fun X_b 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 $$unsorted)) (=> (tptp.semilattice_sup X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.semilattice_sup_sup X_a) A_2) B_1)) X)) (not (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_2) X)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B_1) X))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.semilattice_sup X_a) (forall ((B_1 $$unsorted) (D_1 $$unsorted) (A_2 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.semilattice_sup_sup X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less_eq X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 A_2) C_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 B_1) D_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_2) B_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 C_1) D_1)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.semilattice_sup X_a) (forall ((Z $$unsorted) (Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Z) X)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.semilattice_sup_sup X_a) Y) Z)) X))))))))) (forall ((X_a $$unsorted)) (=> (tptp.semilattice_sup X_a) (forall ((B_1 $$unsorted) (A_2 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_2) X)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B_1) X)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.semilattice_sup_sup X_a) A_2) B_1)) X))))))))) (forall ((X_a $$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_2 $$unsorted) (X $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.semilattice_sup_sup X_a) A_2) B_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.semilattice_sup X_a) (forall ((B_1 $$unsorted) (X $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.semilattice_sup_sup X_a) A_2) B_1)))))))) (forall ((X_c $$unsorted) (X_b $$unsorted)) (=> (tptp.lattice X_b) (forall ((F $$unsorted) (G $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c X_b))) (= (tptp.hAPP X_c 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_c X_b F X_1)) (tptp.hAPP X_c X_b G X_1))))))) (forall ((X_b $$unsorted)) (=> (tptp.semilattice_sup X_b) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.semilattice_sup_sup X_b) X_1) Y_1)) Z_1)) (and (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 X_1) Z_1)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 Y_1) Z_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.semilattice_sup X_a) (forall ((X $$unsorted) (Y $$unsorted) (Z $$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) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Y) Z))))))))) (forall ((X_a $$unsorted)) (=> (tptp.lattice X_a) (forall ((X $$unsorted) (Y $$unsorted) (Z $$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) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Y) Z))))))))) (forall ((X_a $$unsorted)) (=> (tptp.semilattice_sup X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (C_1 $$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 A_2))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 B_1)) C_1) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B_1) C_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.semilattice_sup X_a) (forall ((X $$unsorted) (Y $$unsorted) (Z $$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)) (tptp.hAPP X_a X_a _let_4 (tptp.hAPP X_a X_a _let_3 Z)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.lattice X_a) (forall ((X $$unsorted) (Y $$unsorted) (Z $$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)) (tptp.hAPP X_a X_a _let_4 (tptp.hAPP X_a X_a _let_3 Z)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.semilattice_sup X_a) (forall ((B_1 $$unsorted) (A_2 $$unsorted) (C_1 $$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 B_1))) (let ((_let_4 (tptp.hAPP X_a _let_2 _let_1 A_2))) (= (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a _let_4 C_1)) (tptp.hAPP X_a X_a _let_4 (tptp.hAPP X_a X_a _let_3 C_1)))))))))) (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 $$unsorted)) (=> (tptp.semilattice_sup X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.semilattice_sup_sup X_a) A_2))) (let ((_let_2 (tptp.hAPP X_a X_a _let_1 B_1))) (= (tptp.hAPP X_a X_a _let_1 _let_2) _let_2)))))) (forall ((X_b $$unsorted)) (=> (tptp.semilattice_sup X_b) (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.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.semilattice_sup_sup X_b) X_1) Y_1) (tptp.ti X_b Y_1)))))) (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 $$unsorted)) (=> (tptp.semilattice_sup X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.semilattice_sup_sup X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_2) B_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B_1) A_2))))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (tptp.lattice X_c) (forall ((F $$unsorted) (G $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b X_c))) (= (tptp.hAPP X_b X_c (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_c X_c (tptp.hAPP X_c (tptp.fun X_c X_c) (tptp.semilattice_sup_sup X_c) (tptp.hAPP X_b X_c F X_2)) (tptp.hAPP X_b X_c G X_2))))))) (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 $$unsorted)) (=> (tptp.semilattice_sup X_a) (forall ((A_2 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.semilattice_sup_sup X_a) A_2) A_2) (tptp.ti X_a A_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_b $$unsorted)) (=> (tptp.bounded_lattice_bot X_b) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.bot_bot X_b))) (= (= (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.semilattice_sup_sup X_b) X_1) Y_1) _let_1) (and (= (tptp.ti X_b X_1) _let_1) (= (tptp.ti X_b Y_1) _let_1))))))) (forall ((X_a $$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 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.semilattice_sup_sup X_a) (tptp.bot_bot X_a)) X) (tptp.ti X_a X))))) (forall ((X_b $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_sup_sup _let_1) (tptp.bot_bot _let_1)) B) (tptp.ti _let_1 B)))) (forall ((X_b $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_sup_sup _let_1) A_1) (tptp.bot_bot _let_1)) (tptp.ti _let_1 A_1)))) (forall ((X_b $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b 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_b $$unsorted) (F_1 $$unsorted) (Ga $$unsorted)) (let ((_let_1 (tptp.finite_finite_1 X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 (tptp.fun _let_2 _let_2) (tptp.semilattice_sup_sup _let_2) F_1) Ga))) (and (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 F_1)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 Ga))))))) (forall ((X_b $$unsorted) (Ga $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.finite_finite_1 X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 F_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 Ga)) (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) F_1) Ga)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X) Y))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X)))))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (tptp.ord X_c) (forall ((X_1 $$unsorted) (F $$unsorted) (G $$unsorted)) (let ((_let_1 (tptp.fun X_b X_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) F) G)) (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less_eq X_c) (tptp.hAPP X_b X_c F X_1)) (tptp.hAPP X_b X_c G X_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((Z $$unsorted) (Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 Z))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 X)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((Y $$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 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 X))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 Y)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) Z)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 Z)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((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 $$unsorted)) (=> (tptp.order X_a) (forall ((C_1 $$unsorted) (B_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B_1) A_2)) (=> (= (tptp.ti X_a B_1) (tptp.ti X_a C_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 C_1) A_2))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ord X_a) (forall ((C_1 $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) A_2))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B_1)) (=> (= B_1 C_1) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 C_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((C_1 $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) C_1))) (=> (= (tptp.ti X_a A_2) (tptp.ti X_a B_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_2)))))))) (forall ((X_a $$unsorted)) (=> (tptp.ord X_a) (forall ((C_1 $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (= A_2 B_1) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B_1) C_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_2) C_1))))))))) (forall ((X_b $$unsorted)) (=> (tptp.order X_b) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 Y_1) X_1)) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 X_1) Y_1)) (= (tptp.ti X_b X_1) (tptp.ti X_b Y_1))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (tptp.ord X_c) (forall ((X_1 $$unsorted) (F $$unsorted) (G $$unsorted)) (let ((_let_1 (tptp.fun X_b X_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) F) G)) (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less_eq X_c) (tptp.hAPP X_b X_c F X_1)) (tptp.hAPP X_b X_c G X_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (=> (= X Y) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X) Y)))))) (forall ((X_b $$unsorted)) (=> (tptp.order X_b) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (= (= (tptp.ti X_b X_1) (tptp.ti X_b Y_1)) (and (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 X_1) Y_1)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 Y_1) X_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (or (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X) Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X)))))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (tptp.ord X_c) (forall ((F $$unsorted) (G $$unsorted)) (let ((_let_1 (tptp.fun X_b X_c))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) F) G)) (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less_eq X_c) (tptp.hAPP X_b X_c F X_2)) (tptp.hAPP X_b X_c G X_2))))))))) (forall ((X_b $$unsorted) (Pa $$unsorted) (Q_1 $$unsorted)) (let ((_let_1 (tptp.collect X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (let ((_let_4 (tptp.fun tptp.bool tptp.bool))) (let ((_let_5 (tptp.fun X_b _let_4))) (= (tptp.hAPP _let_2 _let_2 _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_5 _let_3 (tptp.combs X_b tptp.bool tptp.bool) (tptp.hAPP _let_2 _let_5 (tptp.hAPP (tptp.fun tptp.bool _let_4) (tptp.fun _let_2 _let_5) (tptp.combb tptp.bool _let_4 X_b) tptp.fdisj) Pa)) Q_1)) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_3 (tptp.semilattice_sup_sup _let_2) (tptp.hAPP _let_2 _let_2 _let_1 Pa)) (tptp.hAPP _let_2 _let_2 _let_1 Q_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.lattice X_a) (forall ((X $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.semilattice_sup_sup X_a) X) X) (tptp.ti X_a X))))) (forall ((X_b $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.ord_less_eq _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (=> (= (tptp.ti _let_1 A_1) (tptp.ti _let_1 B)) (not (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 A_1) B)) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 B) A_1)))))))))) (forall ((X_b $$unsorted) (B $$unsorted) (D $$unsorted) (A_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.semilattice_sup_sup _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.ord_less_eq _let_1))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_5 _let_4 A_1) C)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_5 _let_4 B) D)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_5 _let_4 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 A_1) B)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 C) D))))))))))) (forall ((X_b $$unsorted) (B $$unsorted) (A_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.ord_less_eq _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 A_1) C)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 B) C)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_sup_sup _let_1) A_1) B)) C)))))))) (forall ((X_b $$unsorted) (C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.ord_less_eq _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.hAPP _let_1 _let_3 _let_2 A_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_4 B)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 B) C)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_4 C))))))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP X_b _let_2 (tptp.member X_b) X_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_1) B)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 A_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 B)))))))) (forall ((X_b $$unsorted) (B $$unsorted) (X_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP X_b _let_2 (tptp.member X_b) X_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 A_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_1) B)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 B)))))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP X_b _let_2 (tptp.member X_b) X_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_1) B)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 A_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 B)))))))) (forall ((X_b $$unsorted) (B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (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) 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_b $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) A_1) B)) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_sup_sup _let_1) A_1) B) (tptp.ti _let_1 B))))) (forall ((X_b $$unsorted) (A_1 $$unsorted) (Ca $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) Ca))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_sup_sup _let_1) A_1) B))))))) (forall ((X_b $$unsorted) (B $$unsorted) (Ca $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) Ca))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_sup_sup _let_1) A_1) B))))))) (forall ((X_b $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b 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_b $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (= (tptp.ti _let_1 A_1) (tptp.ti _let_1 B)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) A_1) B))))) (forall ((X_b $$unsorted) (Pa $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (= (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_2) (tptp.hAPP _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_b tptp.bool Pa X_2))))) (and (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_2) A_1)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa X_2))))) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_2) B)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa X_2)))))))) (forall ((X_b $$unsorted) (Pa $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (= (exists ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_2) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_sup_sup _let_1) A_1) B))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa X_2))))) (or (exists ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_2) A_1)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa X_2))))) (exists ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_2) B)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa X_2)))))))) (forall ((X_b $$unsorted) (A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.semilattice_sup_sup _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.hAPP _let_1 _let_3 _let_2 A_1))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 (tptp.hAPP _let_1 _let_1 _let_4 B)) C) (tptp.hAPP _let_1 _let_1 _let_4 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 B) C)))))))) (forall ((X_b $$unsorted) (Ca $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) Ca))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_sup_sup _let_1) A_1) B))) (or (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B))))))) (forall ((X_b $$unsorted) (A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.semilattice_sup_sup _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.hAPP _let_1 _let_3 _let_2 A_1))) (let ((_let_5 (tptp.hAPP _let_1 _let_3 _let_2 B))) (= (tptp.hAPP _let_1 _let_1 _let_4 (tptp.hAPP _let_1 _let_1 _let_5 C)) (tptp.hAPP _let_1 _let_1 _let_5 (tptp.hAPP _let_1 _let_1 _let_4 C))))))))) (forall ((X_b $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b 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_b $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.ord_less_eq _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (= (tptp.ti _let_1 A_1) (tptp.ti _let_1 B)) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 A_1) B)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 B) A_1)))))))) (forall ((X_b $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (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) 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_b $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.semilattice_sup_sup _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 A_1) B) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 B) A_1)))))) (forall ((X_b $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP (tptp.fun X_b (tptp.fun _let_1 tptp.bool)) _let_2 (tptp.combc X_b _let_1 tptp.bool) (tptp.member X_b)))) (let ((_let_4 (tptp.fun tptp.bool tptp.bool))) (let ((_let_5 (tptp.fun X_b _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_b) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_5 _let_2 (tptp.combs X_b 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_b) tptp.fdisj) (tptp.hAPP _let_1 _let_1 _let_3 A_1))) (tptp.hAPP _let_1 _let_1 _let_3 B)))))))))) (forall ((X_b $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b 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_b $$unsorted) (B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) B) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_sup_sup _let_1) A_1) B))))) (forall ((X_b $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (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) 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 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (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) A_1) A_1)))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (Pa $$unsorted) (Q_1 $$unsorted)) (let ((_let_1 (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) Pa) Q_1)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa X_1)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool Q_1 X_1)))))) (forall ((X_b $$unsorted) (Q_1 $$unsorted) (Pa $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa X_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) Pa) Q_1)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool Q_1 X_1)))))) (forall ((X_b $$unsorted) (A_1 $$unsorted) (B $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool B X_1)) (tptp.hBOOL (tptp.hAPP X_b 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_1))))) (forall ((X_b $$unsorted) (B $$unsorted) (A_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool A_1 X_1)) (tptp.hBOOL (tptp.hAPP X_b 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_1))))) (forall ((X_b $$unsorted) (R_1 $$unsorted) (S $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.ord_less_eq _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.hAPP (tptp.fun X_b _let_3) (tptp.fun _let_1 _let_1) (tptp.combc X_b _let_1 tptp.bool) (tptp.member X_b)))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 (tptp.hAPP _let_1 _let_1 _let_4 R_1)) (tptp.hAPP _let_1 _let_1 _let_4 S))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 R_1) S)))))))) (forall ((X_b $$unsorted) (R_1 $$unsorted) (S $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.semilattice_sup_sup _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.member X_b))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.hAPP (tptp.fun X_b _let_5) _let_3 (tptp.combc X_b _let_1 tptp.bool) _let_4))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 (tptp.hAPP _let_1 _let_1 _let_6 R_1)) (tptp.hAPP _let_1 _let_1 _let_6 S)) X_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_5 _let_4 X_2) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 R_1) S))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.bot X_a) (forall ((A_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.bot_bot X_a)) A_2))))) (forall ((X_b $$unsorted)) (=> (tptp.bot X_b) (forall ((A_3 $$unsorted)) (let ((_let_1 (tptp.bot_bot X_b))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) A_3) _let_1)) (= (tptp.ti X_b A_3) _let_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.bot X_a) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.bot_bot X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) A_2) _let_1)) (= (tptp.ti X_a A_2) _let_1)))))) (forall ((X_c $$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_c tptp.bool))) (let ((_let_3 (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun _let_2 _let_1) (tptp.image X_c X_b) 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_b $$unsorted) (A_1 $$unsorted) (A_3 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b 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_b _let_2 (tptp.insert X_b) 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_b $$unsorted) (A_3 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.fun X_b 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_b _let_3 (tptp.insert X_b) 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_b $$unsorted) (Ts $$unsorted) (Ga $$unsorted) (Ts_1 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.hoare_1656922687triple X_b) tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP _let_1 _let_2 (tptp.hoare_279057269derivs X_b) Ga))) (=> (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_b $$unsorted) (Ts $$unsorted) (Ga $$unsorted)) (let ((_let_1 (tptp.fun (tptp.hoare_1656922687triple X_b) tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) Ts) Ga)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.hoare_279057269derivs X_b) Ga) Ts)))))) (forall ((X_b $$unsorted)) (=> (tptp.semilattice_sup X_b) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) tptp.bool (tptp.finite_comp_fun_idem X_b X_b) (tptp.semilattice_sup_sup X_b))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_b _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_3 (tptp.insert X_b) A_3) B) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 (tptp.semilattice_sup_sup _let_1) (tptp.hAPP _let_1 _let_1 (tptp.collect X_b) (tptp.hAPP X_b _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc X_b X_b tptp.bool) (tptp.fequal X_b)) A_3))) B)))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (A_1 $$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) 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_b $$unsorted)) (=> (tptp.semilattice_sup X_b) (forall ((Ba $$unsorted) (A_3 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.semilattice_sup_sup X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun _let_2 X_b))) (let ((_let_4 (tptp.fun X_b X_b))) (let ((_let_5 (tptp.hAPP X_b _let_3 (tptp.hAPP (tptp.fun X_b _let_4) (tptp.fun X_b _let_3) (tptp.finite_fold X_b X_b) _let_1) Ba))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_b) A_1)) (= (tptp.hAPP _let_2 X_b _let_5 (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_b (tptp.fun _let_2 _let_2) (tptp.insert X_b) A_3) A_1)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_4 _let_1 A_3) (tptp.hAPP _let_2 X_b _let_5 A_1)))))))))))) (forall ((X_b $$unsorted) (B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_1)) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.semilattice_sup_sup _let_1) A_1) B) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.hAPP (tptp.fun X_b _let_2) (tptp.fun _let_1 _let_2) (tptp.finite_fold X_b _let_1) (tptp.insert X_b)) B) A_1)))))) (forall ((X_b $$unsorted) (A_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.bot_bot _let_1))) (let ((_let_3 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_1) _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)))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (B $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_b) A_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) B) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun _let_2 _let_1) (tptp.image X_b X_c) F) A_1))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_c) B))))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (F $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun _let_1 _let_2) (tptp.image X_c 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) (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_c $$unsorted) (X_b $$unsorted) (B $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Z_1 $$unsorted) (G $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b X_b))) (let ((_let_3 (tptp.finite_finite_1 X_c))) (let ((_let_4 (tptp.fun _let_1 X_b))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (let ((_let_6 (tptp.fun X_c X_b))) (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_b _let_7 (tptp.hAPP (tptp.fun X_b _let_2) (tptp.fun X_b _let_7) (tptp.finite908156982e_idem X_b X_c) F) Z_1) G) F_1)) (=> (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_b F_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.hAPP X_b X_b (tptp.hAPP X_b _let_2 F (tptp.hAPP _let_1 X_b F_1 A_1)) (tptp.hAPP _let_1 X_b F_1 B)))))))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (B $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Z_1 $$unsorted) (G $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.hAPP _let_1 X_b F_1 A_1))) (let ((_let_3 (tptp.fun X_b X_b))) (let ((_let_4 (tptp.fun _let_1 X_b))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (let ((_let_6 (tptp.fun X_c X_b))) (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_b _let_7 (tptp.hAPP (tptp.fun X_b _let_3) (tptp.fun X_b _let_7) (tptp.finite908156982e_idem X_b X_c) F) Z_1) G) F_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_c) 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_b X_b (tptp.hAPP X_b _let_3 F (tptp.hAPP _let_1 X_b F_1 B)) _let_2) _let_2)))))))))))) (forall ((X_b $$unsorted) (A_1 $$unsorted) (X_1 $$unsorted) (B $$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_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 (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_b _let_5 (tptp.member X_b) X_1) 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 $$unsorted) (A_1 $$unsorted) (X_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b 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_b _let_3 (tptp.member X_b) X_1) A_1)))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (let ((_let_7 (tptp.hAPP X_b _let_6 (tptp.insert X_b) X_1))) (= (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_b $$unsorted) (B $$unsorted) (A_1 $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_b X_b))) (let ((_let_3 (tptp.bot_bot _let_1))) (let ((_let_4 (tptp.finite_finite_1 X_b))) (let ((_let_5 (tptp.fun _let_1 X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP (tptp.fun X_b _let_2) (tptp.fun _let_5 tptp.bool) (tptp.finite2073411215e_idem X_b) F) F_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_4 A_1)) (=> (not (= (tptp.ti _let_1 A_1) _let_3)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_4 B)) (=> (not (= (tptp.ti _let_1 B) _let_3)) (= (tptp.hAPP _let_1 X_b F_1 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_sup_sup _let_1) A_1) B)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_2 F (tptp.hAPP _let_1 X_b F_1 A_1)) (tptp.hAPP _let_1 X_b F_1 B)))))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.semilattice_sup X_b) (forall ((Ca $$unsorted) (Ba $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.semilattice_sup_sup X_b))) (let ((_let_2 (tptp.fun X_b X_b))) (let ((_let_3 (tptp.fun X_b tptp.bool))) (let ((_let_4 (tptp.fun _let_3 X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.finite_finite_1 X_b) A_1)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_2) A_1)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less_eq X_b) X_2) Ba))))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_3 (tptp.ord_less_eq X_b) (tptp.hAPP _let_3 X_b (tptp.hAPP X_b _let_4 (tptp.hAPP (tptp.fun X_b _let_2) (tptp.fun X_b _let_4) (tptp.finite_fold X_b X_b) _let_1) Ca) A_1)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_2 _let_1 Ba) Ca)))))))))))) (forall ((X_b $$unsorted) (Pa $$unsorted) (A_1 $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) F_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_1) A_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa (tptp.bot_bot _let_1))) (=> (forall ((A_4 $$unsorted) (F_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_4))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) F_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_1)) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 F_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa F_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_4) F_2)))))))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa F_1)))))))) (forall ((X_b $$unsorted) (B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B)))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) A_1) B))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) B)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) B) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun _let_2 _let_1) (tptp.image X_c X_b) F) A_1))) (exists ((C_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_c 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_2) A_1)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_c) C_2)) (= (tptp.ti _let_1 B) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun _let_2 _let_1) (tptp.image X_c X_b) F) C_2))))))))))) (forall ((M_1 $$unsorted) (C_1 $$unsorted) (S_1 $$unsorted) (N_2 $$unsorted) (T_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.state tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (let ((_let_3 (tptp.hAPP tptp.state _let_2 (tptp.hAPP tptp.com (tptp.fun tptp.state _let_2) tptp.evaln C_1) S_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP tptp.nat _let_1 _let_3 N_2) T_4)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N_2) M_1)) (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP tptp.nat _let_1 _let_3 M_1) T_4)))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_b (tptp.fun _let_2 tptp.bool) (tptp.member X_b) X_2) A_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_c (tptp.fun _let_1 tptp.bool) (tptp.member X_c) (tptp.hAPP X_b X_c F X_2)) B)))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun _let_2 _let_1) (tptp.image X_b X_c) F) A_1)) B)))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (tptp.ord X_c) (forall ((F $$unsorted) (G $$unsorted)) (let ((_let_1 (tptp.fun X_b X_c))) (=> (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less_eq X_c) (tptp.hAPP X_b X_c F X_2)) (tptp.hAPP X_b X_c G X_2)))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) F) G))))))) (forall ((K $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 tptp.nat) (tptp.hAPP _let_1 _let_1 (tptp.collect tptp.nat) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc tptp.nat tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat)) K))))))) (forall ((X_b $$unsorted)) (=> (tptp.ordered_ab_group_add X_b) (forall ((A_3 $$unsorted) (Ba $$unsorted) (Ca $$unsorted) (D_2 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.minus_minus X_b))) (let ((_let_4 (tptp.fun X_b X_b))) (=> (= (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_4 _let_3 A_3) Ba) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_4 _let_3 Ca) D_2)) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 A_3) Ba)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 Ca) D_2))))))))))) (forall ((X_b $$unsorted) (A_1 $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_2 (tptp.insert X_b) Ba) (tptp.bot_bot _let_1)))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.hAPP _let_1 X_b (tptp.hAPP X_b (tptp.fun _let_1 X_b) (tptp.partial_flat_lub X_b) Ba) A_1))) (let ((_let_6 (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_4 (tptp.ord_less_eq _let_1) A_1) _let_3)))) (and (=> _let_6 (= _let_5 (tptp.ti X_b Ba))) (=> (not _let_6) (= _let_5 (tptp.hAPP _let_1 X_b (tptp.the X_b) (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_b _let_4) _let_2 (tptp.combc X_b _let_1 tptp.bool) (tptp.member X_b)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.minus_minus _let_1) A_1) _let_3))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ab_semigroup_mult X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 A_2))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 B_1)) C_1) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B_1) C_1))))))))) (forall ((X_b $$unsorted)) (=> (tptp.ab_group_add X_b) (forall ((A_3 $$unsorted) (Ba $$unsorted) (Ca $$unsorted) (D_2 $$unsorted)) (let ((_let_1 (tptp.minus_minus X_b))) (let ((_let_2 (tptp.fun X_b X_b))) (=> (= (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_2 _let_1 A_3) Ba) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_2 _let_1 Ca) D_2)) (= (= (tptp.ti X_b A_3) (tptp.ti X_b Ba)) (= (tptp.ti X_b Ca) (tptp.ti X_b D_2))))))))) (forall ((N $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat tptp.bool) tptp.bool (tptp.finite_finite_1 tptp.nat) N)) (exists ((M $$unsorted)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.nat (tptp.fun _let_1 tptp.bool) (tptp.member tptp.nat) X_2) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) X_2) M)))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.bot_bot _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.fun X_b _let_3))) (let ((_let_5 (tptp.fun X_b X_c))) (let ((_let_6 (tptp.fun X_b _let_1))) (let ((_let_7 (tptp.fun X_b tptp.bool))) (let ((_let_8 (tptp.fun _let_7 _let_1))) (let ((_let_9 (tptp.fun _let_1 _let_8))) (=> (tptp.hBOOL (tptp.hAPP _let_7 tptp.bool (tptp.finite_finite_1 X_b) A_1)) (= (tptp.hAPP _let_7 _let_1 (tptp.hAPP _let_5 _let_8 (tptp.image X_b X_c) F) A_1) (tptp.hAPP _let_7 _let_1 (tptp.hAPP _let_1 _let_8 (tptp.hAPP _let_6 _let_9 (tptp.hAPP (tptp.fun _let_1 _let_3) (tptp.fun _let_6 _let_9) (tptp.finite_fold_image _let_1 X_b) (tptp.semilattice_sup_sup _let_1)) (tptp.hAPP _let_1 _let_6 (tptp.hAPP _let_4 (tptp.fun _let_1 _let_6) (tptp.combc X_b _let_1 _let_1) (tptp.hAPP _let_5 _let_4 (tptp.hAPP (tptp.fun X_c _let_3) (tptp.fun _let_5 _let_4) (tptp.combb X_c _let_3 X_b) (tptp.insert X_c)) F)) _let_2)) _let_2) A_1))))))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (G $$unsorted)) (let ((_let_1 (tptp.fun X_b X_b))) (let ((_let_2 (tptp.fun X_c _let_1))) (let ((_let_3 (tptp.fun X_c X_b))) (let ((_let_4 (tptp.fun X_b _let_1))) (let ((_let_5 (tptp.fun X_b (tptp.fun (tptp.fun X_c tptp.bool) X_b)))) (= (tptp.hAPP _let_3 _let_5 (tptp.hAPP _let_4 (tptp.fun _let_3 _let_5) (tptp.finite_fold_image X_b X_c) F) G) (tptp.hAPP _let_2 _let_5 (tptp.finite_fold X_c X_b) (tptp.hAPP _let_3 _let_2 (tptp.hAPP _let_4 (tptp.fun _let_3 _let_2) (tptp.combb X_b _let_1 X_c) F) G))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (G $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun _let_1 X_b))) (let ((_let_3 (tptp.fun X_b _let_2))) (let ((_let_4 (tptp.fun X_c X_b))) (= (tptp.hAPP _let_1 X_b (tptp.hAPP X_b _let_2 (tptp.hAPP _let_4 _let_3 (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun _let_4 _let_3) (tptp.finite_fold_image X_b X_c) F) G) Z_1) (tptp.bot_bot _let_1)) (tptp.ti X_b Z_1))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Z_1 $$unsorted) (G $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun _let_1 X_b))) (let ((_let_3 (tptp.fun X_b _let_2))) (let ((_let_4 (tptp.fun X_c X_b))) (let ((_let_5 (tptp.fun X_b (tptp.fun X_b X_b)))) (let ((_let_6 (tptp.fun _let_2 tptp.bool))) (let ((_let_7 (tptp.fun _let_4 _let_6))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_4 _let_6 (tptp.hAPP X_b _let_7 (tptp.hAPP _let_5 (tptp.fun X_b _let_7) (tptp.finite1357897459simple X_b X_c) F) Z_1) G) F_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_c) A_1)) (= (tptp.hAPP _let_1 X_b F_1 A_1) (tptp.hAPP _let_1 X_b (tptp.hAPP X_b _let_2 (tptp.hAPP _let_4 _let_3 (tptp.hAPP _let_5 (tptp.fun _let_4 _let_3) (tptp.finite_fold_image X_b X_c) F) G) Z_1) A_1)))))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (tptp.ab_semigroup_mult X_c) (forall ((G $$unsorted) (Z_1 $$unsorted) (A_3 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.times_times X_c))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun _let_2 X_c))) (let ((_let_4 (tptp.fun X_c _let_3))) (let ((_let_5 (tptp.fun X_b X_c))) (let ((_let_6 (tptp.fun X_c X_c))) (let ((_let_7 (tptp.hAPP X_c _let_3 (tptp.hAPP _let_5 _let_4 (tptp.hAPP (tptp.fun X_c _let_6) (tptp.fun _let_5 _let_4) (tptp.finite_fold_image X_c X_b) _let_1) G) Z_1))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_b) A_1)) (=> (not (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_b (tptp.fun _let_2 tptp.bool) (tptp.member X_b) A_3) A_1))) (= (tptp.hAPP _let_2 X_c _let_7 (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_b (tptp.fun _let_2 _let_2) (tptp.insert X_b) A_3) A_1)) (tptp.hAPP X_c X_c (tptp.hAPP X_c _let_6 _let_1 (tptp.hAPP X_b X_c G A_3)) (tptp.hAPP _let_2 X_c _let_7 A_1))))))))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (tptp.ab_semigroup_mult X_c) (forall ((Z_1 $$unsorted) (G $$unsorted) (H $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 X_c))) (let ((_let_3 (tptp.fun X_c _let_2))) (let ((_let_4 (tptp.fun X_b X_c))) (let ((_let_5 (tptp.hAPP (tptp.fun X_c (tptp.fun X_c X_c)) (tptp.fun _let_4 _let_3) (tptp.finite_fold_image X_c X_b) (tptp.times_times X_c)))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_1)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_2) A_1)) (= (tptp.hAPP X_b X_c G X_2) (tptp.hAPP X_b X_c H X_2))))) (= (tptp.hAPP _let_1 X_c (tptp.hAPP X_c _let_2 (tptp.hAPP _let_4 _let_3 _let_5 G) Z_1) A_1) (tptp.hAPP _let_1 X_c (tptp.hAPP X_c _let_2 (tptp.hAPP _let_4 _let_3 _let_5 H) Z_1) A_1)))))))))))) (forall ((U $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (let ((_let_3 (tptp.fun tptp.nat tptp.nat))) (=> (forall ((N_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N_1) (tptp.hAPP tptp.nat tptp.nat F N_1)))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 tptp.nat) (tptp.hAPP _let_1 _let_1 (tptp.collect tptp.nat) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc tptp.nat tptp.nat tptp.bool) (tptp.hAPP _let_3 _let_2 (tptp.hAPP _let_2 (tptp.fun _let_3 _let_2) (tptp.combb tptp.nat _let_1 tptp.nat) (tptp.ord_less_eq tptp.nat)) F)) U))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (X_d $$unsorted)) (=> (tptp.comm_monoid_mult X_d) (forall ((E $$unsorted) (G $$unsorted) (F $$unsorted) (H $$unsorted) (K $$unsorted) (T_3 $$unsorted) (S $$unsorted)) (let ((_let_1 (tptp.times_times X_d))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (let ((_let_3 (tptp.fun _let_2 X_d))) (let ((_let_4 (tptp.fun X_d _let_3))) (let ((_let_5 (tptp.fun X_c X_d))) (let ((_let_6 (tptp.fun X_d (tptp.fun X_d X_d)))) (let ((_let_7 (tptp.fun X_b tptp.bool))) (let ((_let_8 (tptp.fun _let_7 X_d))) (let ((_let_9 (tptp.fun X_d _let_8))) (let ((_let_10 (tptp.fun X_b X_d))) (=> (tptp.hBOOL (tptp.hAPP _let_7 tptp.bool (tptp.finite_finite_1 X_b) S)) (=> (forall ((Y_2 $$unsorted)) (let ((_let_1 (tptp.hAPP X_c X_b K Y_2))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun X_c tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_c (tptp.fun _let_3 tptp.bool) (tptp.member X_c) Y_2) T_3)) (and (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_b (tptp.fun _let_2 tptp.bool) (tptp.member X_b) _let_1) S)) (= (tptp.hAPP X_b X_c H _let_1) (tptp.ti X_c Y_2)))))))) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.hAPP X_b X_c H X_2))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (let ((_let_3 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_b (tptp.fun _let_3 tptp.bool) (tptp.member X_b) X_2) S)) (and (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_c (tptp.fun _let_2 tptp.bool) (tptp.member X_c) _let_1) T_3)) (= (tptp.hAPP X_c X_b K _let_1) (tptp.ti X_b X_2)) (= (tptp.hAPP X_c X_d G _let_1) (tptp.hAPP X_b X_d F X_2)))))))) (= (tptp.hAPP _let_7 X_d (tptp.hAPP X_d _let_8 (tptp.hAPP _let_10 _let_9 (tptp.hAPP _let_6 (tptp.fun _let_10 _let_9) (tptp.finite_fold_image X_d X_b) _let_1) F) E) S) (tptp.hAPP _let_2 X_d (tptp.hAPP X_d _let_3 (tptp.hAPP _let_5 _let_4 (tptp.hAPP _let_6 (tptp.fun _let_5 _let_4) (tptp.finite_fold_image X_d X_c) _let_1) G) E) T_3)))))))))))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted)) (=> (tptp.comm_monoid_mult X_b) (forall ((H $$unsorted) (G $$unsorted) (S $$unsorted) (R_1 $$unsorted) (E $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun _let_1 X_b))) (let ((_let_3 (tptp.fun X_b _let_2))) (let ((_let_4 (tptp.fun X_c X_b))) (let ((_let_5 (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun _let_4 _let_3) (tptp.finite_fold_image X_b X_c) (tptp.times_times X_b)))) (let ((_let_6 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_6 R_1 E) E)) (=> (forall ((X1 $$unsorted) (Y1 $$unsorted) (X2 $$unsorted) (Y2 $$unsorted)) (let ((_let_1 (tptp.times_times X_b))) (let ((_let_2 (tptp.fun X_b X_b))) (let ((_let_3 (tptp.fun X_b tptp.bool))) (=> (and (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_3 R_1 X1) X2)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_3 R_1 Y1) Y2))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_3 R_1 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_2 _let_1 X1) Y1)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_2 _let_1 X2) Y2)))))))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_c) S)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_c (tptp.fun _let_1 tptp.bool) (tptp.member X_c) X_2) S)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) R_1 (tptp.hAPP X_c X_b H X_2)) (tptp.hAPP X_c X_b G X_2)))))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_6 R_1 (tptp.hAPP _let_1 X_b (tptp.hAPP X_b _let_2 (tptp.hAPP _let_4 _let_3 _let_5 H) E) S)) (tptp.hAPP _let_1 X_b (tptp.hAPP X_b _let_2 (tptp.hAPP _let_4 _let_3 _let_5 G) E) S)))))))))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (G $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Z_1 $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun _let_1 X_b))) (let ((_let_3 (tptp.fun X_c X_b))) (let ((_let_4 (tptp.hAPP _let_1 X_b (tptp.hAPP _let_3 _let_2 F_1 G) A_1))) (let ((_let_5 (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_c) A_1)))) (let ((_let_6 (tptp.fun X_b _let_2))) (let ((_let_7 (tptp.fun X_b (tptp.fun X_b X_b)))) (let ((_let_8 (tptp.fun _let_3 _let_2))) (let ((_let_9 (tptp.fun _let_8 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_8 tptp.bool (tptp.hAPP X_b _let_9 (tptp.hAPP _let_7 (tptp.fun X_b _let_9) (tptp.big_comm_monoid_big X_b X_c) F) Z_1) F_1)) (and (=> _let_5 (= _let_4 (tptp.hAPP _let_1 X_b (tptp.hAPP X_b _let_2 (tptp.hAPP _let_3 _let_6 (tptp.hAPP _let_7 (tptp.fun _let_3 _let_6) (tptp.finite_fold_image X_b X_c) F) G) Z_1) A_1))) (=> (not _let_5) (= _let_4 (tptp.ti X_b Z_1))))))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.lattice X_b) (forall ((X_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.bot_bot _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 (tptp.minus_minus _let_1) A_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_3 (tptp.insert X_b) X_1) _let_2)))) (let ((_let_5 (tptp.big_lattice_Sup_fin X_b))) (let ((_let_6 (tptp.hAPP _let_1 X_b _let_5 A_1))) (let ((_let_7 (= _let_4 _let_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_1) A_1)) (and (=> _let_7 (= _let_6 (tptp.ti X_b X_1))) (=> (not _let_7) (= _let_6 (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.semilattice_sup_sup X_b) X_1) (tptp.hAPP _let_1 X_b _let_5 _let_4))))))))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.lattice X_b) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (tptp.hAPP _let_1 X_b (tptp.big_lattice_Sup_fin X_b) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_1) (tptp.bot_bot _let_1))) (tptp.ti X_b X_1)))))) (forall ((X_b $$unsorted)) (=> (tptp.lattice X_b) (forall ((X_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP _let_1 X_b (tptp.big_lattice_Sup_fin X_b) A_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_1) A_1)) (= (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.semilattice_sup_sup X_b) X_1) _let_2) _let_2)))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (G $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Z_1 $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun _let_1 X_b))) (let ((_let_3 (tptp.fun X_c X_b))) (let ((_let_4 (tptp.fun _let_3 _let_2))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP X_b _let_5 (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun X_b _let_5) (tptp.big_comm_monoid_big X_b X_c) F) Z_1) F_1)) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_c) A_1))) (= (tptp.hAPP _let_1 X_b (tptp.hAPP _let_3 _let_2 F_1 G) A_1) (tptp.ti X_b Z_1)))))))))) (forall ((X_b $$unsorted)) (=> (tptp.lattice X_b) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_1)) (= (tptp.hAPP _let_1 X_b (tptp.big_lattice_Sup_fin X_b) A_1) (tptp.hAPP _let_1 X_b (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun _let_1 X_b) (tptp.finite_fold1 X_b) (tptp.semilattice_sup_sup X_b)) A_1))))))) (forall ((X_b $$unsorted)) (=> (tptp.lattice X_b) (forall ((X_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.big_lattice_Sup_fin X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_b) A_1)) (=> (not (= (tptp.ti _let_2 A_1) (tptp.bot_bot _let_2))) (= (tptp.hAPP _let_2 X_b _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_b (tptp.fun _let_2 _let_2) (tptp.insert X_b) X_1) A_1)) (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.semilattice_sup_sup X_b) X_1) (tptp.hAPP _let_2 X_b _let_1 A_1)))))))))) (forall ((X_b $$unsorted)) (=> (tptp.lattice X_b) (forall ((X_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.big_lattice_Sup_fin X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_b) A_1)) (=> (not (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_b (tptp.fun _let_2 tptp.bool) (tptp.member X_b) X_1) A_1))) (=> (not (= (tptp.ti _let_2 A_1) (tptp.bot_bot _let_2))) (= (tptp.hAPP _let_2 X_b _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_b (tptp.fun _let_2 _let_2) (tptp.insert X_b) X_1) A_1)) (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.semilattice_sup_sup X_b) X_1) (tptp.hAPP _let_2 X_b _let_1 A_1))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.lattice X_b) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.big_lattice_Sup_fin X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.hAPP _let_2 X_b _let_1 A_1))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_b) A_1)) (=> (not (= (tptp.ti _let_2 B) (tptp.bot_bot _let_2))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) B) A_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 _let_2 X_b _let_1 B)) _let_3) _let_3)))))))))) (forall ((X_b $$unsorted)) (=> (tptp.lattice X_b) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.big_lattice_Sup_fin X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.bot_bot _let_2))) (let ((_let_4 (tptp.finite_finite_1 X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_4 A_1)) (=> (not (= (tptp.ti _let_2 A_1) _let_3)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_4 B)) (=> (not (= (tptp.ti _let_2 B) _let_3)) (= (tptp.hAPP _let_2 X_b _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 (tptp.fun _let_2 _let_2) (tptp.semilattice_sup_sup _let_2) A_1) B)) (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.semilattice_sup_sup X_b) (tptp.hAPP _let_2 X_b _let_1 A_1)) (tptp.hAPP _let_2 X_b _let_1 B)))))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.lattice X_b) (forall ((A_3 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_1)) (= (tptp.hAPP _let_1 X_b (tptp.big_lattice_Sup_fin X_b) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_3) A_1)) (tptp.hAPP _let_1 X_b (tptp.hAPP X_b _let_2 (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun X_b _let_2) (tptp.finite_fold X_b X_b) (tptp.semilattice_sup_sup X_b)) A_3) A_1)))))))) (forall ((X_b $$unsorted)) (=> (tptp.lattice X_b) (forall ((X_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_1)) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_1) A_1))) (= (tptp.hAPP _let_1 X_b (tptp.big_lattice_Sup_fin X_b) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_1) A_1)) (tptp.hAPP _let_1 X_b (tptp.hAPP X_b _let_2 (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun X_b _let_2) (tptp.finite_fold X_b X_b) (tptp.semilattice_sup_sup X_b)) X_1) A_1))))))))) (forall ((X_b $$unsorted)) (=> (tptp.lattice X_b) (forall ((X_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 _let_1 _let_1))) (let ((_let_4 (tptp.hAPP X_b _let_3 (tptp.insert X_b) X_1))) (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.big_lattice_Sup_fin X_b))) (let ((_let_7 (tptp.hAPP _let_1 X_b _let_6 (tptp.hAPP _let_1 _let_1 _let_4 A_1)))) (let ((_let_8 (= _let_5 _let_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_1)) (and (=> _let_8 (= _let_7 (tptp.ti X_b X_1))) (=> (not _let_8) (= _let_7 (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.semilattice_sup_sup X_b) X_1) (tptp.hAPP _let_1 X_b _let_6 _let_5))))))))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.lattice X_b) (forall ((N $$unsorted) (H $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.big_lattice_Sup_fin X_b))) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.semilattice_sup_sup X_b))) (let ((_let_2 (tptp.fun X_b X_b))) (= (tptp.hAPP X_b X_b H (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_2 _let_1 X_2) Y_2)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_2 _let_1 (tptp.hAPP X_b X_b H X_2)) (tptp.hAPP X_b X_b H Y_2)))))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) N)) (=> (not (= (tptp.ti _let_1 N) (tptp.bot_bot _let_1))) (= (tptp.hAPP X_b X_b H (tptp.hAPP _let_1 X_b _let_2 N)) (tptp.hAPP _let_1 X_b _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_b X_b) (tptp.fun _let_1 _let_1) (tptp.image X_b X_b) H) N))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.lattice X_b) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_1)) (=> (not (= (tptp.ti _let_1 A_1) (tptp.bot_bot _let_1))) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.insert X_b))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.semilattice_sup_sup X_b) X_2) Y_2)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_3 _let_2 X_2) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_3 _let_2 Y_2) (tptp.bot_bot _let_1))))))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) (tptp.hAPP _let_1 X_b (tptp.big_lattice_Sup_fin X_b) A_1)) A_1))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (H $$unsorted) (G $$unsorted) (A_1 $$unsorted) (B $$unsorted) (F $$unsorted) (Z_1 $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun _let_1 X_b))) (let ((_let_3 (tptp.fun X_c X_b))) (let ((_let_4 (tptp.fun _let_3 _let_2))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP X_b _let_5 (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun X_b _let_5) (tptp.big_comm_monoid_big X_b X_c) F) Z_1) F_1)) (=> (= (tptp.ti _let_1 A_1) (tptp.ti _let_1 B)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_c (tptp.fun _let_1 tptp.bool) (tptp.member X_c) X_2) B)) (= (tptp.hAPP X_c X_b H X_2) (tptp.hAPP X_c X_b G X_2))))) (= (tptp.hAPP _let_1 X_b (tptp.hAPP _let_3 _let_2 F_1 H) A_1) (tptp.hAPP _let_1 X_b (tptp.hAPP _let_3 _let_2 F_1 G) B))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.lattice X_b) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.big_lattice_Sup_fin X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (let ((_let_4 (tptp.bot_bot _let_2))) (let ((_let_5 (tptp.finite_finite_1 X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_5 A_1)) (=> (not (= (tptp.ti _let_2 A_1) _let_4)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_5 B)) (=> (not (= (tptp.ti _let_2 B) _let_4)) (=> (= (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_3 (tptp.semilattice_inf_inf _let_2) A_1) B) _let_4) (= (tptp.hAPP _let_2 X_b _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_3 (tptp.semilattice_sup_sup _let_2) A_1) B)) (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.semilattice_sup_sup X_b) (tptp.hAPP _let_2 X_b _let_1 A_1)) (tptp.hAPP _let_2 X_b _let_1 B)))))))))))))))) (forall ((X_b $$unsorted) (B $$unsorted) (A_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool A_1 X_1)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool B X_1)) (tptp.hBOOL (tptp.hAPP X_b 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_1)))))) (forall ((X_b $$unsorted) (A_1 $$unsorted) (B $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_b 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_1)) (not (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool A_1 X_1)) (not (tptp.hBOOL (tptp.hAPP X_b tptp.bool B X_1)))))))) (forall ((X_b $$unsorted) (B $$unsorted) (Ca $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) Ca))) (=> (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_b $$unsorted) (Ca $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) Ca))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.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_b $$unsorted) (Ga $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.finite_finite_1 X_b))) (=> (or (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 F_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 Ga))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_inf_inf _let_1) F_1) Ga))))))) (forall ((X_a $$unsorted)) (=> (tptp.semilattice_inf X_a) (forall ((X $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.semilattice_inf_inf X_a) A_2) B_1))) (not (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_2)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.semilattice_inf X_a) (forall ((B_1 $$unsorted) (D_1 $$unsorted) (A_2 $$unsorted) (C_1 $$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_2) C_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 B_1) D_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_2) B_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 C_1) D_1)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.semilattice_inf X_a) (forall ((Z $$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)) (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))))))))) (forall ((X_a $$unsorted)) (=> (tptp.semilattice_inf X_a) (forall ((B_1 $$unsorted) (X $$unsorted) (A_2 $$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 A_2)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.semilattice_inf_inf X_a) A_2) B_1))))))))) (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 ((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 $$unsorted)) (=> (tptp.semilattice_inf X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B_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_inf_inf X_a) A_2) B_1)) X)))))))) (forall ((X_a $$unsorted)) (=> (tptp.semilattice_inf X_a) (forall ((B_1 $$unsorted) (A_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 A_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_2) B_1)) X)))))))) (forall ((X_b $$unsorted)) (=> (tptp.semilattice_inf X_b) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) X_1))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool _let_1 (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.semilattice_inf_inf X_b) Y_1) Z_1))) (and (tptp.hBOOL (tptp.hAPP X_b tptp.bool _let_1 Y_1)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool _let_1 Z_1)))))))) (forall ((X_b $$unsorted)) (=> (tptp.semilattice_inf X_b) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) X_1) Y_1)) (= (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.semilattice_inf_inf X_b) X_1) Y_1) (tptp.ti X_b X_1)))))) (forall ((X_a $$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 $$unsorted)) (=> (tptp.lattice X_a) (forall ((X $$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)) X))))) (forall ((X_a $$unsorted)) (=> (tptp.lattice X_a) (forall ((X $$unsorted) (Y $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.semilattice_inf_inf X_a) X) Y)) X))))) (forall ((X_b $$unsorted) (B $$unsorted) (D $$unsorted) (A_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.fun X_b 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)) (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))))))))))) (forall ((X_b $$unsorted) (B $$unsorted) (C $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b 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_b $$unsorted) (B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) B) A_1)) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_inf_inf _let_1) A_1) B) (tptp.ti _let_1 B))))) (forall ((X_b $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (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) 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_b $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_inf_inf _let_1) A_1) B)) B)))) (forall ((X_b $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (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) (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 $$unsorted)) (=> (tptp.lattice X_a) (forall ((X $$unsorted) (Y $$unsorted) (Z $$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))) (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)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.lattice X_a) (forall ((X $$unsorted) (Y $$unsorted) (Z $$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))) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Y) Z)))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (F $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (let ((_let_3 (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun _let_2 _let_1) (tptp.image X_c X_b) F))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) (tptp.hAPP _let_2 _let_1 _let_3 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 (tptp.fun _let_2 _let_2) (tptp.semilattice_inf_inf _let_2) A_1) B))) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_inf_inf _let_1) (tptp.hAPP _let_2 _let_1 _let_3 A_1)) (tptp.hAPP _let_2 _let_1 _let_3 B)))))))) (forall ((X_b $$unsorted) (A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.semilattice_sup_sup _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.hAPP _let_1 _let_3 (tptp.semilattice_inf_inf _let_1) A_1))) (= (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 (tptp.hAPP _let_1 _let_1 _let_4 B)) C) (tptp.hAPP _let_1 _let_1 _let_4 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 B) C))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) C) A_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.lattice X_a) (forall ((X $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.semilattice_inf_inf X_a) X) X) (tptp.ti X_a X))))) (forall ((X_b $$unsorted)) (=> (tptp.semilattice_inf X_b) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) tptp.bool (tptp.finite_comp_fun_idem X_b X_b) (tptp.semilattice_inf_inf X_b))))) (forall ((X_b $$unsorted) (B $$unsorted) (A_3 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.fun X_b 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_b _let_3 (tptp.insert X_b) A_3))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) 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_b $$unsorted) (B $$unsorted) (A_3 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b 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_b _let_2 (tptp.insert X_b) A_3))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) 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_b $$unsorted) (B $$unsorted) (A_3 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.fun X_b 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_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) 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_b _let_3 (tptp.insert X_b) A_3) B)) C) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 B) C))))))) (forall ((X_b $$unsorted) (B $$unsorted) (A_3 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b 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_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_3) A_1))) (= (tptp.hAPP _let_1 _let_1 _let_3 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_2 (tptp.insert X_b) A_3) B)) (tptp.hAPP _let_1 _let_1 _let_3 B))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b 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_b _let_3 (tptp.insert X_b) 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_b $$unsorted) (B $$unsorted) (A_3 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.fun X_b 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_b _let_3 (tptp.insert X_b) 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_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) 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_b $$unsorted) (B $$unsorted) (A_3 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b 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_b _let_2 (tptp.insert X_b) 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_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) 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_b $$unsorted) (R_1 $$unsorted) (S $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b 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_b))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.hAPP (tptp.fun X_b _let_5) _let_3 (tptp.combc X_b _let_1 tptp.bool) _let_4))) (= (tptp.hBOOL (tptp.hAPP X_b 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_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_5 _let_4 X_2) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 R_1) S))))))))))) (forall ((X_b $$unsorted) (A_1 $$unsorted) (B $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_b 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_1)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool A_1 X_1))))) (forall ((X_b $$unsorted) (A_1 $$unsorted) (B $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_b 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_1)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool B X_1))))) (forall ((X_b $$unsorted) (Pa $$unsorted) (Q_1 $$unsorted)) (let ((_let_1 (tptp.collect X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (let ((_let_4 (tptp.fun tptp.bool tptp.bool))) (let ((_let_5 (tptp.fun X_b _let_4))) (= (tptp.hAPP _let_2 _let_2 _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_5 _let_3 (tptp.combs X_b tptp.bool tptp.bool) (tptp.hAPP _let_2 _let_5 (tptp.hAPP (tptp.fun tptp.bool _let_4) (tptp.fun _let_2 _let_5) (tptp.combb tptp.bool _let_4 X_b) tptp.fconj) Pa)) Q_1)) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_3 (tptp.semilattice_inf_inf _let_2) (tptp.hAPP _let_2 _let_2 _let_1 Pa)) (tptp.hAPP _let_2 _let_2 _let_1 Q_1))))))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_1 $$unsorted) (Pa $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_1))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_inf_inf _let_1) A_1) (tptp.hAPP _let_1 _let_1 (tptp.collect X_b) Pa)))) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_1)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa X_1))))))) (forall ((X_b $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_inf_inf _let_1) A_1) A_1) (tptp.ti _let_1 A_1)))) (forall ((X_b $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP (tptp.fun X_b (tptp.fun _let_1 tptp.bool)) _let_2 (tptp.combc X_b _let_1 tptp.bool) (tptp.member X_b)))) (let ((_let_4 (tptp.fun tptp.bool tptp.bool))) (let ((_let_5 (tptp.fun X_b _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_b) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_5 _let_2 (tptp.combs X_b 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_b) tptp.fconj) (tptp.hAPP _let_1 _let_1 _let_3 A_1))) (tptp.hAPP _let_1 _let_1 _let_3 B)))))))))) (forall ((X_b $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.semilattice_inf_inf _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 A_1) B) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 B) A_1)))))) (forall ((X_b $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b 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_b $$unsorted) (A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.fun X_b 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_b $$unsorted) (Ca $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) Ca))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.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_b $$unsorted) (A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.fun X_b 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_b $$unsorted) (Ca $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) Ca))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_inf_inf _let_1) A_1) B))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_1)))))) (forall ((X_b $$unsorted) (Ca $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) Ca))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_inf_inf _let_1) A_1) B))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B)))))) (forall ((X_b $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_inf_inf _let_1) A_1) B) (tptp.bot_bot _let_1)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_2) A_1)) (forall ((Xa $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) Xa) B)) (not (= (tptp.ti X_b X_2) (tptp.ti X_b Xa)))))))))))) (forall ((X_b $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.bot_bot _let_1))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_inf_inf _let_1) A_1) _let_2) _let_2)))) (forall ((X_b $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.bot_bot _let_1))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_inf_inf _let_1) _let_2) B) _let_2)))) (forall ((X_a $$unsorted)) (=> (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.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.semilattice_inf X_a) (forall ((A_2 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.semilattice_inf_inf X_a) A_2) A_2) (tptp.ti X_a A_2))))) (forall ((X_a $$unsorted)) (=> (tptp.semilattice_inf X_a) (forall ((X $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.semilattice_inf_inf X_a) X) X) (tptp.ti X_a X))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (tptp.lattice X_c) (forall ((F $$unsorted) (G $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b X_c))) (= (tptp.hAPP X_b X_c (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_c X_c (tptp.hAPP X_c (tptp.fun X_c X_c) (tptp.semilattice_inf_inf X_c) (tptp.hAPP X_b X_c F X_2)) (tptp.hAPP X_b X_c G X_2))))))) (forall ((X_a $$unsorted)) (=> (tptp.semilattice_inf X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.semilattice_inf_inf X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_2) B_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B_1) A_2))))))) (forall ((X_a $$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_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.semilattice_inf_inf X_a) A_2))) (let ((_let_2 (tptp.hAPP X_a X_a _let_1 B_1))) (= (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 $$unsorted)) (=> (tptp.semilattice_inf X_a) (forall ((B_1 $$unsorted) (A_2 $$unsorted) (C_1 $$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 B_1))) (let ((_let_4 (tptp.hAPP X_a _let_2 _let_1 A_2))) (= (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a _let_4 C_1)) (tptp.hAPP X_a X_a _let_4 (tptp.hAPP X_a X_a _let_3 C_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.lattice X_a) (forall ((X $$unsorted) (Y $$unsorted) (Z $$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)) (tptp.hAPP X_a X_a _let_4 (tptp.hAPP X_a X_a _let_3 Z)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.semilattice_inf X_a) (forall ((X $$unsorted) (Y $$unsorted) (Z $$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)) (tptp.hAPP X_a X_a _let_4 (tptp.hAPP X_a X_a _let_3 Z)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.semilattice_inf X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (C_1 $$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 A_2))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 B_1)) C_1) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B_1) C_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.lattice X_a) (forall ((X $$unsorted) (Y $$unsorted) (Z $$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) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Y) Z))))))))) (forall ((X_a $$unsorted)) (=> (tptp.semilattice_inf X_a) (forall ((X $$unsorted) (Y $$unsorted) (Z $$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) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Y) Z))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted)) (=> (tptp.lattice X_b) (forall ((F $$unsorted) (G $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c X_b))) (= (tptp.hAPP X_c X_b (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.semilattice_inf_inf _let_1) F) G) X_1) (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.semilattice_inf_inf X_b) (tptp.hAPP X_c X_b F X_1)) (tptp.hAPP X_c X_b G X_1))))))) (forall ((X_b $$unsorted) (A_1 $$unsorted) (C $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.semilattice_inf_inf _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.hAPP _let_1 _let_3 (tptp.minus_minus _let_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 A_1) C)))) (= (tptp.hAPP _let_1 _let_1 _let_4 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 B) C)) (tptp.hAPP _let_1 _let_1 _let_4 B))))))) (forall ((X_b $$unsorted) (A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.semilattice_inf_inf _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.minus_minus _let_1))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_4 A_1) B)) C) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_4 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 A_1) C)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 B) C)))))))) (forall ((X_b $$unsorted) (A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.minus_minus _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.hAPP _let_1 _let_3 (tptp.semilattice_inf_inf _let_1) A_1))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 (tptp.hAPP _let_1 _let_1 _let_4 B)) C) (tptp.hAPP _let_1 _let_1 _let_4 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 B) C)))))))) (forall ((X_b $$unsorted) (C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP _let_1 _let_2 (tptp.semilattice_inf_inf _let_1) C))) (let ((_let_4 (tptp.minus_minus _let_1))) (= (tptp.hAPP _let_1 _let_1 _let_3 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 _let_4 A_1) B)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 _let_4 (tptp.hAPP _let_1 _let_1 _let_3 A_1)) (tptp.hAPP _let_1 _let_1 _let_3 B)))))))) (forall ((X_b $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b 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_b $$unsorted) (A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.fun X_b 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_b $$unsorted) (A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.fun X_b 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_b $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (=> (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.semilattice_inf_inf _let_1) A_1) B) (tptp.bot_bot _let_1)) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.minus_minus _let_1) A_1) B) (tptp.ti _let_1 A_1)))))) (forall ((X_b $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b 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_b $$unsorted) (A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.fun X_b 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_b $$unsorted) (A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.fun X_b 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_b $$unsorted) (B $$unsorted) (C $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b 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_b $$unsorted) (B $$unsorted) (C $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b 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_b $$unsorted) (A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.fun X_b 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)))))))) (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.preorder T_1) (tptp.preorder (tptp.fun T_2 T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (and (tptp.finite_finite T_1) (tptp.finite_finite T_2)) (tptp.finite_finite (tptp.fun T_2 T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.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.semilattice_sup tptp.nat) (tptp.semilattice_inf tptp.nat) (tptp.ab_semigroup_mult tptp.nat) (tptp.comm_monoid_mult tptp.nat) (tptp.preorder tptp.nat) (tptp.linorder tptp.nat) (tptp.lattice tptp.nat) (tptp.order tptp.nat) (tptp.ord tptp.nat) (tptp.bot tptp.nat) (tptp.minus tptp.nat) (tptp.bounded_lattice_bot tptp.bool) (tptp.semilattice_sup tptp.bool) (tptp.semilattice_inf tptp.bool) (tptp.preorder tptp.bool) (tptp.finite_finite tptp.bool) (tptp.lattice tptp.bool) (tptp.order tptp.bool) (tptp.ord tptp.bool) (tptp.bot tptp.bool) (tptp.minus tptp.bool) (forall ((T $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.ti T A))) (= (tptp.ti T _let_1) _let_1))) (forall ((P $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool tptp.fNot P))) (not (tptp.hBOOL P)))) (forall ((P $$unsorted)) (or (tptp.hBOOL P) (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool tptp.fNot P)))) (forall ((X_a $$unsorted) (X_c $$unsorted) (X_b $$unsorted) (P $$unsorted) (Q $$unsorted) (R $$unsorted)) (let ((_let_1 (tptp.fun X_a X_c))) (let ((_let_2 (tptp.fun X_a X_b))) (= (tptp.hAPP X_a X_c (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun _let_2 _let_1) (tptp.combb X_b X_c X_a) P) Q) R) (tptp.hAPP X_b X_c P (tptp.hAPP X_a X_b Q R)))))) (forall ((X_a $$unsorted) (X_c $$unsorted) (X_b $$unsorted) (P $$unsorted) (Q $$unsorted) (R $$unsorted)) (let ((_let_1 (tptp.fun X_b X_c))) (let ((_let_2 (tptp.fun X_a X_c))) (= (tptp.hAPP X_a X_c (tptp.hAPP X_b _let_2 (tptp.hAPP (tptp.fun X_a _let_1) (tptp.fun X_b _let_2) (tptp.combc X_a X_b X_c) P) Q) R) (tptp.hAPP X_b X_c (tptp.hAPP X_a _let_1 P R) Q))))) (forall ((X_a $$unsorted) (P $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.combi X_a) P) (tptp.ti X_a P))) _let_28 (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))) _let_27 (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 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 30.75/31.00 )
% 30.75/31.00 % SZS output end Proof for SWW470+6
% 30.75/31.00 % cvc5---1.0.5 exiting
% 30.75/31.00 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------