TSTP Solution File: SWW470+7 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWW470+7 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n003.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 91.43s 86.71s
% Output : Proof 91.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.33 % Problem : SWW470+7 : TPTP v8.1.2. Released v5.3.0.
% 0.13/0.34 % Command : do_cvc5 %s %d
% 0.35/0.55 % Computer : n003.cluster.edu
% 0.35/0.55 % Model : x86_64 x86_64
% 0.35/0.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.35/0.55 % Memory : 8042.1875MB
% 0.35/0.55 % OS : Linux 3.10.0-693.el7.x86_64
% 0.35/0.55 % CPULimit : 300
% 0.35/0.55 % WCLimit : 300
% 0.35/0.55 % DateTime : Sun Aug 27 18:49:25 EDT 2023
% 0.35/0.56 % CPUTime :
% 0.80/0.95 %----Proving TF0_NAR, FOF, or CNF
% 91.43/86.71 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.HCQYpqpkrw/cvc5---1.0.5_14661.p...
% 91.43/86.71 ------- get file name : TPTP file name is SWW470+7
% 91.43/86.71 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_14661.smt2...
% 91.43/86.71 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 91.43/86.71 --- Run --no-e-matching --full-saturate-quant at 5...
% 91.43/86.71 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 91.43/86.71 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 91.43/86.71 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 91.43/86.71 --- Run --trigger-sel=max --full-saturate-quant at 5...
% 91.43/86.71 --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 91.43/86.71 --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 91.43/86.71 --- Run --prenex-quant=none --full-saturate-quant at 5...
% 91.43/86.71 --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 5...
% 91.43/86.71 --- Run --relevant-triggers --full-saturate-quant at 5...
% 91.43/86.71 --- Run --finite-model-find --e-matching --sort-inference --uf-ss-fair at 5...
% 91.43/86.71 --- Run --pre-skolem-quant=on --full-saturate-quant at 10...
% 91.43/86.71 --- Run --cbqi-vo-exp --full-saturate-quant at 10...
% 91.43/86.71 % SZS status Theorem for SWW470+7
% 91.43/86.71 % SZS output start Proof for SWW470+7
% 91.43/86.71 (
% 91.43/86.71 (let ((_let_1 (tptp.hoare_2118899576triple 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_759811442triple 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_1301688828derivs 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 (tptp.one_one tptp.int))) (let ((_let_30 (tptp.zero_zero tptp.int))) (let ((_let_31 (tptp.fun tptp.int tptp.bool))) (let ((_let_32 (tptp.hAPP tptp.int _let_31 (tptp.ord_less_eq tptp.int) _let_30))) (let ((_let_33 (tptp.semiring_1_of_nat tptp.int))) (let ((_let_34 (tptp.hAPP tptp.nat tptp.int _let_33 (tptp.one_one tptp.nat)))) (let ((_let_35 (tptp.fun tptp.nat tptp.bool))) (let ((_let_36 (forall ((X_b $$unsorted) (Ga $$unsorted) (Ca $$unsorted) (Q_3 $$unsorted) (Pa $$unsorted)) (let ((_let_1 (tptp.hoare_2118899576triple X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun X_b (tptp.fun tptp.state tptp.bool)))) (let ((_let_4 (tptp.fun _let_3 _let_1))) (=> (forall ((Z_4 $$unsorted) (S_3 $$unsorted)) (let ((_let_1 (tptp.hoare_2118899576triple X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun tptp.state tptp.bool))) (let ((_let_4 (tptp.combk _let_3 X_b))) (let ((_let_5 (tptp.fun X_b _let_3))) (let ((_let_6 (tptp.fun tptp.state _let_3))) (let ((_let_7 (tptp.fun _let_5 _let_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP X_b _let_3 Pa Z_4) S_3)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.hoare_1301688828derivs X_b) Ga) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 (tptp.fun _let_2 _let_2) (tptp.insert _let_1) (tptp.hAPP _let_5 _let_1 (tptp.hAPP tptp.com _let_7 (tptp.hAPP _let_5 (tptp.fun tptp.com _let_7) (tptp.hoare_759811442triple X_b) (tptp.hAPP _let_3 _let_5 _let_4 (tptp.hAPP tptp.state _let_3 (tptp.hAPP _let_6 _let_6 (tptp.combc tptp.state tptp.state tptp.bool) (tptp.fequal tptp.state)) S_3))) Ca) (tptp.hAPP _let_3 _let_5 _let_4 (tptp.hAPP X_b _let_3 Q_3 Z_4)))) (tptp.bot_bot _let_2))))))))))))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.hoare_1301688828derivs X_b) Ga) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 (tptp.fun _let_2 _let_2) (tptp.insert _let_1) (tptp.hAPP _let_3 _let_1 (tptp.hAPP tptp.com _let_4 (tptp.hAPP _let_3 (tptp.fun tptp.com _let_4) (tptp.hoare_759811442triple X_b) Pa) Ca) Q_3)) (tptp.bot_bot _let_2)))))))))))) (let ((_let_37 (forall ((X_c $$unsorted) (X_a $$unsorted) (B_1_1 $$unsorted) (B_2_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a X_c B_1_1 B_2_1))) (= (tptp.ti X_c _let_1) _let_1))))) (let ((_let_38 (tptp.ti tptp.bool tptp.fFalse))) (let ((_let_39 (= _let_38 tptp.fFalse))) (let ((_let_40 (tptp.ord_gr1471790799AtMost tptp.nat))) (let ((_let_41 (= tptp.fFalse _let_38))) (let ((_let_42 (tptp.ti _let_4 _let_15))) (let ((_let_43 (= _let_15 _let_42))) (let ((_let_44 (tptp.hAPP tptp.x_a _let_4 _let_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_70))) (let ((_let_45 (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool _let_44 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_71)))) (let ((_let_46 (= _let_42 _let_44))) (let ((_let_47 (= _let_38 (tptp.hAPP tptp.state tptp.bool _let_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_71)))) (let ((_let_48 (SYMM (ASSUME :args (_let_39))))) (let ((_let_49 (ASSUME :args (_let_27)))) (let ((_let_50 (forall ((X_c $$unsorted) (X_a $$unsorted) (B_1_1 $$unsorted) (B_2_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a X_c B_1_1 B_2_1))) (= _let_1 (tptp.ti X_c _let_1)))))) (let ((_let_51 (EQ_RESOLVE (ASSUME :args (_let_37)) (MACRO_SR_EQ_INTRO :args (_let_37 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_52 (tptp.fun tptp.state _let_4))) (let ((_let_53 (not _let_45))) (let ((_let_54 (or _let_53 (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_23 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 _let_22 _let_21 (tptp.hAPP _let_11 _let_1 (tptp.hAPP tptp.com _let_19 (tptp.hAPP _let_11 _let_20 _let_18 (tptp.hAPP _let_4 _let_11 _let_16 (tptp.hAPP tptp.state _let_4 (tptp.hAPP _let_52 _let_52 (tptp.combc tptp.state tptp.state tptp.bool) (tptp.fequal tptp.state)) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_71))) tptp.c) (tptp.hAPP _let_4 _let_11 _let_16 (tptp.hAPP tptp.x_a _let_4 _let_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_70)))) _let_3)))))) (let ((_let_55 (forall ((Z_4 $$unsorted) (S_3 $$unsorted)) (let ((_let_1 (tptp.hoare_2118899576triple 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_4) S_3))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.hoare_1301688828derivs 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_759811442triple 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_3))) 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_4)))) (tptp.bot_bot _let_2))))))))))))))))))))) (let ((_let_56 (not _let_54))) (let ((_let_57 (not _let_55))) (let ((_let_58 (or _let_57 _let_24))) (let ((_let_59 (forall ((X_b $$unsorted) (Ga $$unsorted) (Ca $$unsorted) (Q_3 $$unsorted) (Pa $$unsorted)) (let ((_let_1 (tptp.hoare_2118899576triple 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_4 $$unsorted) (S_3 $$unsorted)) (let ((_let_1 (tptp.hoare_2118899576triple 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_4) S_3))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.hoare_1301688828derivs 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_759811442triple 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_3))) Ca) (tptp.hAPP _let_3 _let_5 _let_4 (tptp.hAPP X_b _let_3 Q_3 Z_4)))) (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_1301688828derivs 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_759811442triple X_b) Pa) Ca) Q_3)) (tptp.bot_bot _let_2)))))))))))) (let ((_let_60 (EQ_RESOLVE (ASSUME :args (_let_36)) (MACRO_SR_EQ_INTRO :args (_let_36 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_61 (tptp.hoare_2118899576triple X_b))) (let ((_let_62 (tptp.fun _let_61 tptp.bool))) (let ((_let_63 (tptp.fun X_b _let_4))) (let ((_let_64 (tptp.fun _let_63 _let_61))) (let ((_let_65 (or))) (let ((_let_66 (_let_57))) (let ((_let_67 (_let_28))) (let ((_let_68 (ASSUME :args _let_67))) (let ((_let_69 (ASSUME :args (_let_47)))) (let ((_let_70 (ASSUME :args (_let_43)))) (let ((_let_71 (ASSUME :args (_let_46)))) (let ((_let_72 (ASSUME :args (_let_45)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_49 _let_48 _let_69 _let_70 _let_71 _let_72) :args (_let_27 _let_41 _let_43 _let_45 _let_46 _let_47)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_72)) (CONG (TRANS (CONG (REFL :args (tptp.state)) (REFL :args (tptp.bool)) (TRANS (SYMM _let_71) (SYMM _let_70)) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_71)) :args (APPLY_UF tptp.hAPP)) (SYMM _let_69) (SYMM _let_48)) :args (APPLY_UF tptp.hBOOL)) (FALSE_INTRO _let_49))) :args (_let_27 _let_41 _let_47 _let_43 _let_46 _let_45)) :args ((not (and _let_27 _let_41 _let_43 _let_45 _let_46 _let_47)) SB_LITERAL))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_27) _let_26))) (REFL :args ((not _let_41))) (REFL :args ((not _let_43))) (REFL :args (_let_53)) (REFL :args ((not _let_46))) (REFL :args ((not _let_47))) :args _let_65)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_68 :args (tptp.state tptp.bool tptp.fFalse SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_71 QUANTIFIERS_INST_CBQI_PROP)) :args _let_67))) _let_68 :args (_let_47 false _let_28)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_68 :args (tptp.x_a _let_4 _let_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_70 QUANTIFIERS_INST_CBQI_PROP)) :args _let_67))) _let_68 :args (_let_46 false _let_28)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_54 0)) (CONG (REFL :args (_let_54)) (MACRO_SR_PRED_INTRO :args ((= (not _let_53) _let_45))) :args _let_65)) :args ((or _let_45 _let_54))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_66)) :args _let_66)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_57) _let_55))) (REFL :args (_let_56)) :args _let_65)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_58)) :args ((or _let_24 _let_57 (not _let_58)))) (ASSUME :args (_let_25)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_60 :args (tptp.x_a tptp.g tptp.c _let_13 _let_17 QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP _let_62 tptp.bool (tptp.hAPP _let_62 (tptp.fun _let_62 tptp.bool) (tptp.hoare_1301688828derivs X_b) Ga) (tptp.hAPP _let_62 _let_62 (tptp.hAPP _let_61 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(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 (tptp.fun tptp.state tptp.nat) tptp.com)) tptp.ass) tptp.ass) (= (tptp.ti tptp.com tptp.skip) tptp.skip) (= (tptp.ti (tptp.fun tptp.com (tptp.fun tptp.com tptp.com)) tptp.semi) tptp.semi) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.finite_card X_b))) (= (tptp.ti (tptp.fun (tptp.fun X_b tptp.bool) tptp.nat) _let_1) _let_1))) (forall ((X_b $$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.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_b $$unsorted)) (let ((_let_1 (tptp.minus_minus X_b))) (=> (tptp.minus X_b) (= (tptp.ti (tptp.fun X_b (tptp.fun X_b X_b)) _let_1) _let_1)))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.one_one X_b))) (=> (tptp.one X_b) (= (tptp.ti X_b _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (=> (tptp.ab_semigroup_add X_a) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a X_a)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (=> (tptp.cancel_semigroup_add X_a) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a X_a)) _let_1) _let_1)))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.times_times X_b))) (=> (tptp.power X_b) (= (tptp.ti (tptp.fun X_b (tptp.fun X_b X_b)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (=> (tptp.semiring X_a) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a X_a)) _let_1) _let_1)))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.times_times X_b))) (=> (tptp.ab_semigroup_mult X_b) (= (tptp.ti (tptp.fun X_b (tptp.fun X_b X_b)) _let_1) _let_1)))) (forall ((X_c $$unsorted)) (let ((_let_1 (tptp.uminus_uminus X_c))) (=> (tptp.uminus X_c) (= (tptp.ti (tptp.fun X_c X_c) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (=> (tptp.ordere216010020id_add X_a) (= (tptp.ti X_a _let_1) _let_1)))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.zero_zero X_b))) (=> (tptp.ab_group_add X_b) (= (tptp.ti 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))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.hoare_1301688828derivs X_b))) (let ((_let_2 (tptp.fun (tptp.hoare_2118899576triple X_b) tptp.bool))) (= (tptp.ti (tptp.fun _let_2 (tptp.fun _let_2 tptp.bool)) _let_1) _let_1)))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.hoare_759811442triple 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_2118899576triple X_b)))) _let_1) _let_1)))) (forall ((X_c $$unsorted) (X_b $$unsorted)) (let ((_let_1 (tptp.hoare_225284258e_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_2118899576triple X_c) X_b)) _let_1) _let_1)))) (forall ((X_c $$unsorted) (X_b $$unsorted)) (let ((_let_1 (tptp.hoare_1759541758le_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_2118899576triple X_c) X_b)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.if X_a))) (= (tptp.ti (tptp.fun tptp.bool (tptp.fun X_a (tptp.fun X_a X_a))) _let_1) _let_1))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat X_a))) (=> (tptp.semiring_1 X_a) (= (tptp.ti (tptp.fun tptp.nat X_a) _let_1) _let_1)))) (= (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 $$unsorted)) (let ((_let_1 (tptp.bot_bot X_b))) (=> (tptp.bot X_b) (= (tptp.ti X_b _let_1) _let_1)))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.max X_b))) (=> (tptp.ord X_b) (= (tptp.ti (tptp.fun (tptp.fun X_b (tptp.fun X_b tptp.bool)) (tptp.fun X_b (tptp.fun X_b X_b))) _let_1) _let_1)))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.min X_b))) (=> (tptp.ord X_b) (= (tptp.ti (tptp.fun (tptp.fun X_b (tptp.fun X_b tptp.bool)) (tptp.fun X_b (tptp.fun X_b X_b))) _let_1) _let_1)))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.ord_less X_b))) (=> (tptp.ord X_b) (= (tptp.ti (tptp.fun X_b (tptp.fun X_b tptp.bool)) _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.ord_max X_b))) (=> (tptp.ord X_b) (= (tptp.ti (tptp.fun X_b (tptp.fun X_b X_b)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.ord_min X_a))) (=> (tptp.ord X_a) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a X_a)) _let_1) _let_1)))) (forall ((X_b $$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 $$unsorted)) (let ((_let_1 (tptp.power_1 X_b))) (= (tptp.ti (tptp.fun X_b (tptp.fun (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun X_b (tptp.fun tptp.nat X_b)))) _let_1) _let_1))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.power_power X_b))) (=> (tptp.power X_b) (= (tptp.ti (tptp.fun X_b (tptp.fun tptp.nat X_b)) _let_1) _let_1)))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.ord_atLeastAtMost X_b))) (=> (tptp.order X_b) (= (tptp.ti (tptp.fun X_b (tptp.fun X_b (tptp.fun X_b tptp.bool))) _let_1) _let_1)))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.ord_greaterThan X_b))) (=> (tptp.ord X_b) (= (tptp.ti (tptp.fun X_b (tptp.fun X_b tptp.bool)) _let_1) _let_1)))) (= (tptp.ti (tptp.fun tptp.nat (tptp.fun tptp.nat _let_35)) _let_40) _let_40) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.ord_lessThan X_b))) (=> (tptp.ord X_b) (= (tptp.ti (tptp.fun X_b (tptp.fun X_b tptp.bool)) _let_1) _let_1)))) (forall ((X_b $$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))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.fEx X_a))) (= (tptp.ti (tptp.fun (tptp.fun X_a tptp.bool) tptp.bool) _let_1) _let_1))) _let_39 (= (tptp.ti _let_6 tptp.fNot) tptp.fNot) (= (tptp.ti tptp.bool tptp.fTrue) tptp.fTrue) (= (tptp.ti _let_9 tptp.fconj) tptp.fconj) (= (tptp.ti _let_9 tptp.fdisj) tptp.fdisj) (forall ((X_a $$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_37 (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_2118899576triple X_b) tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.hoare_1301688828derivs X_b) Ga) (tptp.bot_bot _let_1))))) (forall ((X_b $$unsorted) (Fun1_1 $$unsorted) (Com_1 $$unsorted) (Fun2_1 $$unsorted) (Fun1_2 $$unsorted) (Com_2 $$unsorted) (Fun2_2 $$unsorted)) (let ((_let_1 (tptp.hoare_759811442triple X_b))) (let ((_let_2 (tptp.hoare_2118899576triple X_b))) (let ((_let_3 (tptp.fun X_b (tptp.fun tptp.state tptp.bool)))) (let ((_let_4 (tptp.fun _let_3 _let_2))) (let ((_let_5 (tptp.fun tptp.com _let_4))) (= (= (tptp.hAPP _let_3 _let_2 (tptp.hAPP tptp.com _let_4 (tptp.hAPP _let_3 _let_5 _let_1 Fun1_1) Com_1) Fun2_1) (tptp.hAPP _let_3 _let_2 (tptp.hAPP tptp.com _let_4 (tptp.hAPP _let_3 _let_5 _let_1 Fun1_2) Com_2) Fun2_2)) (and (= Fun1_1 Fun1_2) (= Com_1 Com_2) (= Fun2_1 Fun2_2))))))))) (forall ((X_b $$unsorted) (Ga $$unsorted) (G_1 $$unsorted) (Ts $$unsorted)) (let ((_let_1 (tptp.hoare_1301688828derivs X_b))) (let ((_let_2 (tptp.fun (tptp.hoare_2118899576triple X_b) tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.hAPP _let_2 _let_3 _let_1 Ga))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 _let_3 _let_1 G_1) Ts)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_4 G_1)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_4 Ts))))))))) (forall ((X_b $$unsorted) (Ts $$unsorted) (Ga $$unsorted) (T_5 $$unsorted)) (let ((_let_1 (tptp.hoare_2118899576triple X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP _let_1 (tptp.fun _let_2 _let_2) (tptp.insert _let_1) T_5))) (let ((_let_4 (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.hoare_1301688828derivs X_b) Ga))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_4 (tptp.hAPP _let_2 _let_2 _let_3 (tptp.bot_bot _let_2)))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_4 Ts)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_4 (tptp.hAPP _let_2 _let_2 _let_3 Ts)))))))))) (forall ((X_b $$unsorted) (Ga $$unsorted) (Pa $$unsorted) (Ca $$unsorted) (Q_3 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.hoare_2118899576triple X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.bot_bot _let_2))) (let ((_let_4 (tptp.fun tptp.bool tptp.bool))) (let ((_let_5 (tptp.fun tptp.state _let_4))) (let ((_let_6 (tptp.fun tptp.state tptp.bool))) (let ((_let_7 (tptp.fun _let_6 _let_5))) (let ((_let_8 (tptp.fun X_b _let_5))) (let ((_let_9 (tptp.fun X_b _let_6))) (let ((_let_10 (tptp.fun tptp.bool _let_6))) (let ((_let_11 (tptp.fun X_b _let_10))) (let ((_let_12 (tptp.hoare_759811442triple X_b))) (let ((_let_13 (tptp.fun _let_9 _let_1))) (let ((_let_14 (tptp.fun tptp.com _let_13))) (let ((_let_15 (tptp.insert _let_1))) (let ((_let_16 (tptp.fun _let_2 _let_2))) (let ((_let_17 (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.hoare_1301688828derivs X_b) Ga))) (=> (=> (tptp.hBOOL C_1) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_17 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 _let_16 _let_15 (tptp.hAPP _let_9 _let_1 (tptp.hAPP tptp.com _let_13 (tptp.hAPP _let_9 _let_14 _let_12 Pa) Ca) Q_3)) _let_3)))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_17 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 _let_16 _let_15 (tptp.hAPP _let_9 _let_1 (tptp.hAPP tptp.com _let_13 (tptp.hAPP _let_9 _let_14 _let_12 (tptp.hAPP tptp.bool _let_9 (tptp.hAPP _let_11 (tptp.fun tptp.bool _let_9) (tptp.combc X_b tptp.bool _let_6) (tptp.hAPP _let_8 _let_11 (tptp.hAPP (tptp.fun _let_5 _let_10) (tptp.fun _let_8 _let_11) (tptp.combb _let_5 _let_10 X_b) (tptp.combc tptp.state tptp.bool tptp.bool)) (tptp.hAPP _let_9 _let_8 (tptp.hAPP _let_7 (tptp.fun _let_9 _let_8) (tptp.combb _let_6 _let_5 X_b) (tptp.hAPP (tptp.fun tptp.bool _let_4) _let_7 (tptp.combb tptp.bool _let_4 tptp.state) tptp.fconj)) Pa))) C_1)) Ca) Q_3)) _let_3)))))))))))))))))))))) _let_36 (forall ((X_b $$unsorted) (Q_3 $$unsorted) (Ga $$unsorted) (Pa $$unsorted) (Ca $$unsorted) (Q_5 $$unsorted)) (let ((_let_1 (tptp.hoare_2118899576triple X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.bot_bot _let_2))) (let ((_let_4 (tptp.fun X_b (tptp.fun tptp.state tptp.bool)))) (let ((_let_5 (tptp.fun _let_4 _let_1))) (let ((_let_6 (tptp.hAPP tptp.com _let_5 (tptp.hAPP _let_4 (tptp.fun tptp.com _let_5) (tptp.hoare_759811442triple X_b) Pa) Ca))) (let ((_let_7 (tptp.insert _let_1))) (let ((_let_8 (tptp.fun _let_2 _let_2))) (let ((_let_9 (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.hoare_1301688828derivs X_b) Ga))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_9 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 _let_8 _let_7 (tptp.hAPP _let_4 _let_1 _let_6 Q_5)) _let_3))) (=> (forall ((Z_4 $$unsorted) (S_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.state tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP X_b _let_1 Q_5 Z_4) S_3)) (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP X_b _let_1 Q_3 Z_4) S_3))))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_9 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 _let_8 _let_7 (tptp.hAPP _let_4 _let_1 _let_6 Q_3)) _let_3))))))))))))))) (forall ((X_b $$unsorted) (Pa $$unsorted) (Ga $$unsorted) (P_4 $$unsorted) (Ca $$unsorted) (Q_3 $$unsorted)) (let ((_let_1 (tptp.hoare_2118899576triple X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.bot_bot _let_2))) (let ((_let_4 (tptp.hoare_759811442triple X_b))) (let ((_let_5 (tptp.fun X_b (tptp.fun tptp.state tptp.bool)))) (let ((_let_6 (tptp.fun _let_5 _let_1))) (let ((_let_7 (tptp.fun tptp.com _let_6))) (let ((_let_8 (tptp.insert _let_1))) (let ((_let_9 (tptp.fun _let_2 _let_2))) (let ((_let_10 (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.hoare_1301688828derivs X_b) Ga))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_10 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 _let_9 _let_8 (tptp.hAPP _let_5 _let_1 (tptp.hAPP tptp.com _let_6 (tptp.hAPP _let_5 _let_7 _let_4 P_4) Ca) Q_3)) _let_3))) (=> (forall ((Z_4 $$unsorted) (S_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.state tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP X_b _let_1 Pa Z_4) S_3)) (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP X_b _let_1 P_4 Z_4) S_3))))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_10 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 _let_9 _let_8 (tptp.hAPP _let_5 _let_1 (tptp.hAPP tptp.com _let_6 (tptp.hAPP _let_5 _let_7 _let_4 Pa) Ca) Q_3)) _let_3)))))))))))))))) (forall ((X_b $$unsorted) (Q_3 $$unsorted) (Pa $$unsorted) (Ga $$unsorted) (P_4 $$unsorted) (Ca $$unsorted) (Q_5 $$unsorted)) (let ((_let_1 (tptp.hoare_2118899576triple X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.bot_bot _let_2))) (let ((_let_4 (tptp.hoare_759811442triple 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_1301688828derivs 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_4) Ca) Q_5)) _let_3))) (=> (forall ((Z_4 $$unsorted) (S_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP X_b (tptp.fun tptp.state tptp.bool) Pa Z_4) S_3)) (forall ((S_4 $$unsorted)) (=> (forall ((Z_5 $$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_4 Z_5) S_3)) (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP X_b _let_1 Q_5 Z_5) S_4))))) (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP X_b (tptp.fun tptp.state tptp.bool) Q_3 Z_4) S_4)))))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_10 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 _let_9 _let_8 (tptp.hAPP _let_5 _let_1 (tptp.hAPP tptp.com _let_6 (tptp.hAPP _let_5 _let_7 _let_4 Pa) Ca) Q_3)) _let_3)))))))))))))))) (forall ((X_b $$unsorted) (A_2 $$unsorted) (Ba $$unsorted) (A_3 $$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_2))) (=> (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_3))) (=> (not (= (tptp.ti X_b A_2) (tptp.ti X_b Ba))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_3))))))) (forall ((X_b $$unsorted) (Ba $$unsorted) (A_2 $$unsorted) (B_2 $$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_2))) (=> (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B_2))) (= (tptp.ti X_b A_2) (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_2))))))) (forall ((X_b $$unsorted) (A_2 $$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) A_2) (tptp.bot_bot _let_1)))))) (forall ((X_b $$unsorted) (A_2 $$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_2)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_2) (tptp.bot_bot _let_1))))) (forall ((X_b $$unsorted) (A_2 $$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_2)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_2) (tptp.bot_bot _let_1)))))) (forall ((X_b $$unsorted) (Pa $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.bot_bot _let_1))) (let ((_let_3 (tptp.fun tptp.bool tptp.bool))) (let ((_let_4 (tptp.fun X_b _let_3))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (let ((_let_6 (tptp.hAPP _let_1 _let_1 (tptp.collect X_b) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_4 _let_5 (tptp.combs X_b tptp.bool tptp.bool) (tptp.hAPP _let_1 _let_4 (tptp.hAPP (tptp.fun tptp.bool _let_3) (tptp.fun _let_1 _let_4) (tptp.combb tptp.bool _let_3 X_b) tptp.fconj) (tptp.hAPP X_b _let_1 (tptp.fequal X_b) A_2))) Pa)))) (let ((_let_7 (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa A_2)))) (and (=> _let_7 (= _let_6 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_5 (tptp.insert X_b) A_2) _let_2))) (=> (not _let_7) (= _let_6 _let_2))))))))))) (forall ((X_b $$unsorted) (Pa $$unsorted) (A_2 $$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_2))) Pa)))) (let ((_let_8 (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa A_2)))) (and (=> _let_8 (= _let_7 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_6 (tptp.insert X_b) A_2) _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_2118899576triple 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_1759541758le_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_759811442triple 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 $$unsorted) (A_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (= (tptp.ti _let_1 A_3) (tptp.bot_bot _let_1)) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_2) A_3)))))) (forall ((X_b $$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_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (exists ((X_2 $$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_3)))) (not (= (tptp.ti _let_1 A_3) (tptp.bot_bot _let_1)))))) (forall ((X_b $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_2) A_3))))) (= (tptp.ti _let_1 A_3) (tptp.bot_bot _let_1))))) (forall ((X_b $$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 $$unsorted) (A_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_2) A_3)) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_2) A_3) (tptp.ti _let_1 A_3))))) (forall ((X_b $$unsorted) (Ba $$unsorted) (A_2 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) Ba) B_2))))))) (forall ((X_b $$unsorted) (B_2 $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_1))) (let ((_let_3 (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_1))) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 A_3))) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 B_2))) (= (= (tptp.hAPP _let_1 _let_1 _let_2 A_3) (tptp.hAPP _let_1 _let_1 _let_2 B_2)) (= (tptp.ti _let_1 A_3) (tptp.ti _let_1 B_2))))))))) (forall ((X_b $$unsorted) (Y_2 $$unsorted) (A_3 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) Y_2) A_3) X_1)) (or (= (tptp.ti X_b Y_2) (tptp.ti X_b X_1)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool A_3 X_1)))))) (forall ((X_b $$unsorted) (A_2 $$unsorted) (Ba $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_2))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) Ba) A_3))) (or (= (tptp.ti X_b A_2) (tptp.ti X_b Ba)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_3))))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (Y_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.insert X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (let ((_let_4 (tptp.hAPP X_b _let_3 _let_1 X_1))) (let ((_let_5 (tptp.hAPP X_b _let_3 _let_1 Y_2))) (= (tptp.hAPP _let_2 _let_2 _let_4 (tptp.hAPP _let_2 _let_2 _let_5 A_3)) (tptp.hAPP _let_2 _let_2 _let_5 (tptp.hAPP _let_2 _let_2 _let_4 A_3))))))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$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_3))) (= (tptp.hAPP _let_1 _let_1 _let_2 _let_3) _let_3))))) (forall ((X_b $$unsorted) (A_2 $$unsorted) (Pa $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_b _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.fun tptp.bool tptp.bool))) (let ((_let_5 (tptp.fun X_b _let_4))) (let ((_let_6 (tptp.collect X_b))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_3 (tptp.insert X_b) A_2) (tptp.hAPP _let_1 _let_1 _let_6 Pa)) (tptp.hAPP _let_1 _let_1 _let_6 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_5 _let_3 (tptp.combs X_b tptp.bool tptp.bool) (tptp.hAPP _let_1 _let_5 (tptp.hAPP (tptp.fun tptp.bool _let_4) (tptp.fun _let_1 _let_5) (tptp.combb tptp.bool _let_4 X_b) tptp.fimplies) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_4 _let_3 (tptp.combb tptp.bool tptp.bool X_b) tptp.fNot) (tptp.hAPP X_b _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc X_b X_b tptp.bool) (tptp.fequal X_b)) A_2)))) Pa)))))))))) (forall ((X_b $$unsorted) (A_2 $$unsorted) (B_2 $$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_2) B_2) (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_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)) B_2)))))))))) (forall ((X_b $$unsorted) (A_2 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_2) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_2) B_2))))) (forall ((X_b $$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 $$unsorted) (A_2 $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.bot_bot _let_1))) (let ((_let_3 (tptp.insert X_b))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (=> (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_4 _let_3 A_2) _let_2) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_4 _let_3 Ba) _let_2)) (= (tptp.ti X_b A_2) (tptp.ti X_b Ba)))))))) (forall ((X_b $$unsorted) (Ba $$unsorted) (A_2 $$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) Ba) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_2) (tptp.bot_bot _let_1)))) (= (tptp.ti X_b Ba) (tptp.ti X_b A_2))))) (forall ((X_b $$unsorted) (A_2 $$unsorted) (Ba $$unsorted) (Ca $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.ti X_b Ca))) (let ((_let_2 (tptp.ti X_b Ba))) (let ((_let_3 (tptp.ti X_b D))) (let ((_let_4 (tptp.ti X_b A_2))) (let ((_let_5 (tptp.fun X_b tptp.bool))) (let ((_let_6 (tptp.bot_bot _let_5))) (let ((_let_7 (tptp.insert X_b))) (let ((_let_8 (tptp.fun _let_5 _let_5))) (= (= (tptp.hAPP _let_5 _let_5 (tptp.hAPP X_b _let_8 _let_7 A_2) (tptp.hAPP _let_5 _let_5 (tptp.hAPP X_b _let_8 _let_7 Ba) _let_6)) (tptp.hAPP _let_5 _let_5 (tptp.hAPP X_b _let_8 _let_7 Ca) (tptp.hAPP _let_5 _let_5 (tptp.hAPP X_b _let_8 _let_7 D) _let_6))) (or (and (= _let_4 _let_1) (= _let_2 _let_3)) (and (= _let_4 _let_3) (= _let_2 _let_1))))))))))))) (forall ((X_b $$unsorted) (Ba $$unsorted) (A_2 $$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) Ba) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_2) (tptp.bot_bot _let_1)))) (= (tptp.ti X_b Ba) (tptp.ti X_b A_2))))) (forall ((X_b $$unsorted) (A_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (not (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_2) A_3) (tptp.bot_bot _let_1))))) (forall ((X_b $$unsorted) (A_2 $$unsorted) (A_3 $$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_2) A_3))))) (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_2118899576triple 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_225284258e_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_759811442triple 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 $$unsorted)) (let ((_let_1 (tptp.hoare_2118899576triple X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun X_b (tptp.fun tptp.state tptp.bool)))) (let ((_let_4 (tptp.fun _let_3 _let_1))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.hoare_1301688828derivs X_b) Ga) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 (tptp.fun _let_2 _let_2) (tptp.insert _let_1) (tptp.hAPP _let_3 _let_1 (tptp.hAPP tptp.com _let_4 (tptp.hAPP _let_3 (tptp.fun tptp.com _let_4) (tptp.hoare_759811442triple X_b) Pa) tptp.skip) Pa)) (tptp.bot_bot _let_2))))))))) (forall ((X_b $$unsorted) (D $$unsorted) (R_1 $$unsorted) (Ga $$unsorted) (Pa $$unsorted) (Ca $$unsorted) (Q_3 $$unsorted)) (let ((_let_1 (tptp.hoare_2118899576triple X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.bot_bot _let_2))) (let ((_let_4 (tptp.hoare_759811442triple 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_1301688828derivs 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_3)) _let_3))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_11 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 _let_10 _let_9 (tptp.hAPP _let_5 _let_1 (tptp.hAPP tptp.com _let_6 (tptp.hAPP _let_5 _let_7 _let_4 Q_3) D) R_1)) _let_3))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_11 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 _let_10 _let_9 (tptp.hAPP _let_5 _let_1 (tptp.hAPP tptp.com _let_6 _let_8 (tptp.hAPP tptp.com tptp.com (tptp.hAPP tptp.com (tptp.fun tptp.com tptp.com) tptp.semi Ca) D)) R_1)) _let_3))))))))))))))))) (forall ((X_b $$unsorted) (Y_2 $$unsorted)) (not (forall ((Fun1 $$unsorted) (Com $$unsorted) (Fun2 $$unsorted)) (let ((_let_1 (tptp.hoare_2118899576triple X_b))) (let ((_let_2 (tptp.fun X_b (tptp.fun tptp.state tptp.bool)))) (let ((_let_3 (tptp.fun _let_2 _let_1))) (not (= Y_2 (tptp.hAPP _let_2 _let_1 (tptp.hAPP tptp.com _let_3 (tptp.hAPP _let_2 (tptp.fun tptp.com _let_3) (tptp.hoare_759811442triple X_b) Fun1) Com) Fun2))))))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$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) X_1) A_3)) (not (forall ((B_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (= (tptp.ti _let_1 A_3) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_1) B_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_1) B_3))))))))) (forall ((X_b $$unsorted) (A_2 $$unsorted) (A_3 $$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) A_2) A_3)) (exists ((B_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (and (= (tptp.ti _let_1 A_3) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_2) B_3)) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_2) B_3))))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (forall ((Y_1 $$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_1) A_3))))) (= (tptp.ti _let_1 A_3) (tptp.bot_bot _let_1))))) (forall ((X_b $$unsorted) (Q_3 $$unsorted) (Ga $$unsorted) (Ca $$unsorted) (Pa $$unsorted)) (let ((_let_1 (tptp.hoare_2118899576triple X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun X_b (tptp.fun tptp.state tptp.bool)))) (let ((_let_4 (tptp.fun _let_3 _let_1))) (=> (forall ((Z_4 $$unsorted) (S_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP X_b (tptp.fun tptp.state tptp.bool) Pa Z_4) S_3)) (exists ((P_3 $$unsorted) (Q_4 $$unsorted)) (let ((_let_1 (tptp.hoare_2118899576triple X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun X_b (tptp.fun tptp.state tptp.bool)))) (let ((_let_4 (tptp.fun _let_3 _let_1))) (and (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.hoare_1301688828derivs X_b) Ga) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 (tptp.fun _let_2 _let_2) (tptp.insert _let_1) (tptp.hAPP _let_3 _let_1 (tptp.hAPP tptp.com _let_4 (tptp.hAPP _let_3 (tptp.fun tptp.com _let_4) (tptp.hoare_759811442triple X_b) P_3) Ca) Q_4)) (tptp.bot_bot _let_2)))) (forall ((S_4 $$unsorted)) (=> (forall ((Z_5 $$unsorted)) (let ((_let_1 (tptp.fun tptp.state tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP X_b _let_1 P_3 Z_5) S_3)) (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP X_b _let_1 Q_4 Z_5) S_4))))) (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP X_b (tptp.fun tptp.state tptp.bool) Q_3 Z_4) S_4)))))))))))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.hoare_1301688828derivs X_b) Ga) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 (tptp.fun _let_2 _let_2) (tptp.insert _let_1) (tptp.hAPP _let_3 _let_1 (tptp.hAPP tptp.com _let_4 (tptp.hAPP _let_3 (tptp.fun tptp.com _let_4) (tptp.hoare_759811442triple X_b) Pa) Ca) Q_3)) (tptp.bot_bot _let_2)))))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (not (= (tptp.ti _let_1 A_3) (tptp.bot_bot _let_1))) (exists ((X_2 $$unsorted) (B_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (and (= (tptp.ti _let_1 A_3) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_2) B_3)) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_2) B_3))))))))) (forall ((Com1_2 $$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) (F $$unsorted) (A_2 $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) _let_2 (tptp.finite_fold1Set X_b) F) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_2 (tptp.insert X_b) A_2) (tptp.bot_bot _let_1))) Ba)) (= (tptp.ti X_b A_2) (tptp.ti X_b Ba)))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (F $$unsorted) (F_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun _let_2 tptp.bool) (tptp.finite_folding_one X_b) F) F_2)) (= (tptp.hAPP _let_1 X_b F_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_1) (tptp.bot_bot _let_1))) (tptp.ti X_b X_1)))))) (forall ((X_b $$unsorted) (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 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.hoare_2118899576triple 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_1301688828derivs 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_759811442triple 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_2))) (tptp.hAPP _let_3 tptp.com (tptp.hAPP tptp.vname (tptp.fun _let_3 tptp.com) tptp.ass X_3) A_2)) Pa)) (tptp.bot_bot _let_2)))))))))))))))) (forall ((X_b $$unsorted) (F $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (tptp.hAPP _let_1 X_b (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun _let_1 X_b) (tptp.finite_fold1 X_b) F) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_2) (tptp.bot_bot _let_1))) (tptp.ti X_b A_2)))) (forall ((X_b $$unsorted) (A_2 $$unsorted) (G $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (= G (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun _let_1 X_b) (tptp.finite_fold1 X_b) F)) (= (tptp.hAPP _let_1 X_b G (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_2) (tptp.bot_bot _let_1))) (tptp.ti X_b A_2))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (Ca $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.bot_bot _let_1))) (let ((_let_3 (tptp.fun X_b X_c))) (let ((_let_4 (tptp.fun X_b tptp.bool))) (let ((_let_5 (tptp.hAPP _let_4 _let_1 (tptp.hAPP _let_3 (tptp.fun _let_4 _let_1) (tptp.image X_b X_c) (tptp.hAPP X_c _let_3 (tptp.combk X_c X_b) Ca)) A_3))) (let ((_let_6 (= (tptp.ti _let_4 A_3) (tptp.bot_bot _let_4)))) (and (=> _let_6 (= _let_5 _let_2)) (=> (not _let_6) (= _let_5 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_c (tptp.fun _let_1 _let_1) (tptp.insert X_c) Ca) _let_2))))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (A_3 $$unsorted) (Ba $$unsorted) (F $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (=> (= (tptp.ti X_b Ba) (tptp.hAPP X_c X_b F X_1)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_c (tptp.fun _let_2 tptp.bool) (tptp.member X_c) X_1) A_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) Ba) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun _let_2 _let_1) (tptp.image X_c X_b) F) A_3)))))))) (forall ((X_b $$unsorted) (F $$unsorted) (A_3 $$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_3) (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_3)))))) (forall ((Vname_1 $$unsorted) (Fun_1 $$unsorted) (Vname $$unsorted) (Fun $$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_1) Fun_1) (tptp.hAPP _let_1 tptp.com (tptp.hAPP tptp.vname _let_2 tptp.ass Vname) Fun)) (and (= (tptp.ti tptp.vname Vname_1) (tptp.ti tptp.vname Vname)) (= Fun_1 Fun)))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (Ba $$unsorted) (F $$unsorted) (X_1 $$unsorted) (A_3 $$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_3)) (=> (= (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_3)))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_b (tptp.fun _let_2 tptp.bool) (tptp.member X_b) X_1) A_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_c (tptp.fun _let_1 tptp.bool) (tptp.member X_c) (tptp.hAPP X_b X_c F X_1)) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun _let_2 _let_1) (tptp.image X_b X_c) F) A_3))))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (Z_2 $$unsorted) (F $$unsorted) (A_3 $$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_2) (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_3))) (exists ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_c (tptp.fun _let_1 tptp.bool) (tptp.member X_c) X_2) A_3)) (= (tptp.ti X_b Z_2) (tptp.hAPP X_c X_b F X_2))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (X_d $$unsorted) (F $$unsorted) (G $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_d X_b))) (let ((_let_2 (tptp.fun X_d X_c))) (let ((_let_3 (tptp.fun X_c X_b))) (let ((_let_4 (tptp.fun X_b tptp.bool))) (let ((_let_5 (tptp.fun X_d tptp.bool))) (let ((_let_6 (tptp.fun X_c tptp.bool))) (= (tptp.hAPP _let_6 _let_4 (tptp.hAPP _let_3 (tptp.fun _let_6 _let_4) (tptp.image X_c X_b) F) (tptp.hAPP _let_5 _let_6 (tptp.hAPP _let_2 (tptp.fun _let_5 _let_6) (tptp.image X_d X_c) G) A_3)) (tptp.hAPP _let_5 _let_4 (tptp.hAPP _let_1 (tptp.fun _let_5 _let_4) (tptp.image X_d X_b) (tptp.hAPP _let_2 _let_1 (tptp.hAPP _let_3 (tptp.fun _let_2 _let_1) (tptp.combb X_c X_b X_d) F) G)) A_3))))))))) (forall ((X_b $$unsorted) (Y_4 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_b X_b) (tptp.fun _let_1 _let_1) (tptp.image X_b X_b) (tptp.combi X_b)) Y_4) (tptp.ti _let_1 Y_4)))) (forall ((Vname_1 $$unsorted) (Fun_1 $$unsorted) (Com1 $$unsorted) (Com2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.state tptp.nat))) (not (= (tptp.hAPP _let_1 tptp.com (tptp.hAPP tptp.vname (tptp.fun _let_1 tptp.com) tptp.ass Vname_1) Fun_1) (tptp.hAPP tptp.com tptp.com (tptp.hAPP tptp.com (tptp.fun tptp.com tptp.com) tptp.semi Com1) Com2))))) (forall ((Com1 $$unsorted) (Com2 $$unsorted) (Vname_1 $$unsorted) (Fun_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.state tptp.nat))) (not (= (tptp.hAPP tptp.com tptp.com (tptp.hAPP tptp.com (tptp.fun tptp.com tptp.com) tptp.semi Com1) Com2) (tptp.hAPP _let_1 tptp.com (tptp.hAPP tptp.vname (tptp.fun _let_1 tptp.com) tptp.ass Vname_1) Fun_1))))) (forall ((Vname $$unsorted) (Fun $$unsorted)) (let ((_let_1 (tptp.fun tptp.state tptp.nat))) (not (= tptp.skip (tptp.hAPP _let_1 tptp.com (tptp.hAPP tptp.vname (tptp.fun _let_1 tptp.com) tptp.ass Vname) Fun))))) (forall ((X_b $$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_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_1) A_3)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool A_3 X_1))))) (forall ((X_b $$unsorted) (Pa $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (tptp.hAPP _let_1 _let_1 (tptp.collect X_b) Pa) (tptp.ti _let_1 Pa)))) (forall ((Vname $$unsorted) (Fun $$unsorted)) (let ((_let_1 (tptp.fun tptp.state tptp.nat))) (not (= (tptp.hAPP _let_1 tptp.com (tptp.hAPP tptp.vname (tptp.fun _let_1 tptp.com) tptp.ass Vname) Fun) tptp.skip)))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (= (= (tptp.hAPP _let_1 _let_2 (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun _let_1 _let_2) (tptp.image X_c X_b) F) A_3) (tptp.bot_bot _let_2)) (= (tptp.ti _let_1 A_3) (tptp.bot_bot _let_1)))))) (forall ((X_c $$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 $$unsorted) (A_3 $$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_3)) (= (tptp.ti _let_1 A_3) (tptp.bot_bot _let_1)))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun _let_2 _let_1) (tptp.image X_b X_c) F) A_3))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_b (tptp.fun _let_2 tptp.bool) (tptp.member X_b) X_1) A_3)) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_c (tptp.fun _let_1 _let_1) (tptp.insert X_c) (tptp.hAPP X_b X_c F X_1)) _let_3) _let_3)))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (A_2 $$unsorted) (B_2 $$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_2) B_2)) (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_2)) (tptp.hAPP _let_2 _let_1 _let_3 B_2))))))) (forall ((X_b $$unsorted) (F $$unsorted) (A_3 $$unsorted) (X_1 $$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_3) X_1)) (not (= (tptp.ti _let_1 A_3) (tptp.bot_bot _let_1)))))) (forall ((X_b $$unsorted) (F $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (not (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun _let_1 _let_1) (tptp.finite_fold1Set X_b) F) (tptp.bot_bot _let_1)) X_1))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (Ca $$unsorted) (X_1 $$unsorted) (A_3 $$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_3)) (= (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_3) (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) (Ba $$unsorted) (F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) Ba) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun _let_2 _let_1) (tptp.image X_c X_b) F) A_3))) (not (forall ((X_2 $$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_3))))))))))) (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 $$unsorted) (A_2 $$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_2)) (tptp.ti X_b A_2))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (Y_2 $$unsorted) (Pa $$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_2)))))) (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_2) _let_8))))))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (G $$unsorted) (M_3 $$unsorted) (N_3 $$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_3) (tptp.ti _let_3 N_3)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_2) N_3)) (= (tptp.hAPP X_b X_c F X_2) (tptp.hAPP X_b X_c G X_2))))) (= (tptp.hAPP _let_3 _let_2 (tptp.hAPP _let_5 _let_4 _let_1 F) M_3) (tptp.hAPP _let_3 _let_2 (tptp.hAPP _let_5 _let_4 _let_1 G) N_3)))))))))) (forall ((X_b $$unsorted) (F $$unsorted) (A_2 $$unsorted) (A_3 $$unsorted) (X_1 $$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_2) A_3) 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_2) A_3))) (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_2) A_3)) X_1)))))))) (forall ((X_b $$unsorted) (Pa $$unsorted) (A_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa A_2)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa X_2)) (= (tptp.ti X_b X_2) (tptp.ti X_b A_2)))) (= (tptp.hAPP (tptp.fun X_b tptp.bool) X_b (tptp.the X_b) Pa) (tptp.ti X_b A_2))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (F $$unsorted) (F_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_b X_b))) (let ((_let_3 (tptp.fun _let_1 X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP (tptp.fun X_b _let_2) (tptp.fun _let_3 tptp.bool) (tptp.finite_folding_one X_b) F) F_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_1) A_3))) (=> (not (= (tptp.ti _let_1 A_3) (tptp.bot_bot _let_1))) (= (tptp.hAPP _let_1 X_b F_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_1) A_3)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_2 F X_1) (tptp.hAPP _let_1 X_b F_2 A_3))))))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (F $$unsorted) (F_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 X_b))) (let ((_let_3 (tptp.fun X_b (tptp.fun X_b X_b)))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_3 (tptp.fun _let_2 tptp.bool) (tptp.finite_folding_one X_b) F) F_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (= (tptp.hAPP _let_1 X_b F_2 A_3) (tptp.hAPP _let_1 X_b (tptp.hAPP _let_3 _let_2 (tptp.finite_fold1 X_b) F) A_3)))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (F $$unsorted) (F_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun _let_2 tptp.bool) (tptp.finite_folding_one X_b) F) F_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (=> (not (= (tptp.ti _let_1 A_3) (tptp.bot_bot _let_1))) (=> (forall ((X_2 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.insert X_b))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) F X_2) Y_1)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_3 _let_2 X_2) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_3 _let_2 Y_1) (tptp.bot_bot _let_1))))))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) (tptp.hAPP _let_1 X_b F_2 A_3)) A_3))))))))) (forall ((X_b $$unsorted) (Q_3 $$unsorted) (Pa $$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_3)))) (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_3))))))))))) (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_2 $$unsorted) (A_3 $$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_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) A_2) A_3))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (H $$unsorted) (F_2 $$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.finite_finite_1 X_b) F_2)) (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_2))))))) (forall ((X_b $$unsorted)) (=> (tptp.finite_finite X_b) (forall ((A_3 $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite_1 X_b) A_3))))) (forall ((X_b $$unsorted)) (=> (tptp.finite_finite X_b) (forall ((A_3 $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite_1 X_b) A_3))))) (forall ((X_b $$unsorted) (Pa $$unsorted) (Q_3 $$unsorted)) (let ((_let_1 (tptp.collect X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.finite_finite_1 X_b))) (let ((_let_4 (tptp.fun tptp.bool tptp.bool))) (let ((_let_5 (tptp.fun X_b _let_4))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 (tptp.hAPP _let_2 _let_2 _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_5 (tptp.fun _let_2 _let_2) (tptp.combs X_b tptp.bool tptp.bool) (tptp.hAPP _let_2 _let_5 (tptp.hAPP (tptp.fun tptp.bool _let_4) (tptp.fun _let_2 _let_5) (tptp.combb tptp.bool _let_4 X_b) tptp.fdisj) Pa)) Q_3)))) (and (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 (tptp.hAPP _let_2 _let_2 _let_1 Pa))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 (tptp.hAPP _let_2 _let_2 _let_1 Q_3))))))))))) (forall ((X_b $$unsorted) (A_2 $$unsorted) (A_3 $$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_2) A_3))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 A_3)))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (Z_2 $$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_2) (tptp.bot_bot _let_1)) Z_2)))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (Z_2 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (let ((_let_3 (tptp.fun _let_1 _let_2))) (=> (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.hAPP X_c _let_3 (tptp.hAPP (tptp.fun X_b (tptp.fun X_c X_c)) (tptp.fun X_c _let_3) (tptp.finite_fold_graph X_b X_c) F) Z_2) (tptp.bot_bot _let_1)) X_1)) (= (tptp.ti X_c X_1) (tptp.ti X_c Z_2))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (Z_2 $$unsorted) (Y_2 $$unsorted) (X_1 $$unsorted) (A_3 $$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_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_1) A_3))) (=> (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP _let_2 _let_3 _let_5 A_3) Y_2)) (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_3)) (tptp.hAPP X_c X_c (tptp.hAPP X_b _let_1 F X_1) Y_2))))))))))) (forall ((X_b $$unsorted) (F $$unsorted) (A_2 $$unsorted) (X_3 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) _let_2 (tptp.finite_fold1Set X_b) F) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_2 (tptp.insert X_b) A_2) X_3)) X_1)) (not (forall ((A_5 $$unsorted) (A_4 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.insert X_b))) (=> (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_2 _let_3 A_2) X_3) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_2 _let_3 A_5) A_4)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_2 (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun X_b _let_2) (tptp.finite_fold_graph X_b X_b) F) A_5) A_4) X_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_5) A_4))))))))))))) (forall ((X_b $$unsorted) (F $$unsorted) (A_3 $$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)) (=> (not (= (tptp.ti _let_1 A_3) (tptp.bot_bot _let_1))) (exists ((X1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun _let_1 _let_1) (tptp.finite_fold1Set X_b) F) A_3) X1)))))))) (forall ((X_b $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_2)) (or (= (tptp.ti _let_1 A_2) (tptp.bot_bot _let_1)) (exists ((A_4 $$unsorted) (A_5 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (and (= (tptp.ti _let_1 A_2) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_5) A_4)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_4))))))))) (forall ((X_b $$unsorted) (Pa $$unsorted) (F_2 $$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)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa (tptp.bot_bot _let_1))) (=> (forall ((X_2 $$unsorted) (F_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) F_3)) (=> (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_3))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa F_3)) (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_3)))))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa F_2))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (A_3 $$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_3))) (=> (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_3))) (exists ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b _let_1))) (let ((_let_3 (tptp.fun X_b X_c))) (let ((_let_4 (tptp.fun X_b tptp.bool))) (let ((_let_5 (tptp.member X_b))) (let ((_let_6 (tptp.fun _let_4 _let_4))) (let ((_let_7 (tptp.fun _let_4 tptp.bool))) (let ((_let_8 (tptp.fun tptp.bool tptp.bool))) (let ((_let_9 (tptp.fun X_b _let_8))) (and (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP X_b _let_7 _let_5 X_2) A_3)) (not (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.finite_finite_1 X_b) (tptp.hAPP _let_4 _let_4 (tptp.collect X_b) (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_9 _let_6 (tptp.combs X_b tptp.bool tptp.bool) (tptp.hAPP _let_4 _let_9 (tptp.hAPP (tptp.fun tptp.bool _let_8) (tptp.fun _let_4 _let_9) (tptp.combb tptp.bool _let_8 X_b) tptp.fconj) (tptp.hAPP _let_4 _let_4 (tptp.hAPP (tptp.fun X_b _let_7) _let_6 (tptp.combc X_b _let_4 tptp.bool) _let_5) A_3))) (tptp.hAPP X_c _let_4 (tptp.hAPP _let_2 (tptp.fun X_c _let_4) (tptp.combc X_b X_c tptp.bool) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun X_c _let_1) (tptp.fun _let_3 _let_2) (tptp.combb X_c _let_1 X_b) (tptp.fequal X_c)) F)) (tptp.hAPP X_b X_c F X_2))))))))))))))))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (Z_2 $$unsorted) (A_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite_1 X_b) A_3)) (exists ((X1 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun _let_2 _let_1))) (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP _let_2 _let_1 (tptp.hAPP X_c _let_3 (tptp.hAPP (tptp.fun X_b (tptp.fun X_c X_c)) (tptp.fun X_c _let_3) (tptp.finite_fold_graph X_b X_c) F) Z_2) A_3) X1)))))))) (forall ((X_b $$unsorted) (F $$unsorted) (A1 $$unsorted) (A2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun _let_1 _let_1) (tptp.finite_fold1Set X_b) F) A1) A2)) (exists ((A_5 $$unsorted) (A_4 $$unsorted) (X_2 $$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_5) A_4)) (= (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_5) A_4) 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_5) A_4)))))))))) (forall ((X_b $$unsorted) (Pa $$unsorted) (A_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa A_2)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa X_2)) (= (tptp.ti X_b X_2) (tptp.ti X_b A_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 $$unsorted) (A_2 $$unsorted) (Pa $$unsorted)) (=> (exists ((X_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa X_2)) (forall ((Y_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa Y_1)) (= (tptp.ti X_b Y_1) (tptp.ti X_b X_2)))))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa A_2)) (= (tptp.hAPP (tptp.fun X_b tptp.bool) X_b (tptp.the X_b) Pa) (tptp.ti X_b A_2))))) (forall ((X_b $$unsorted) (Pa $$unsorted)) (=> (exists ((X_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa X_2)) (forall ((Y_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa Y_1)) (= (tptp.ti X_b Y_1) (tptp.ti X_b X_2)))))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa (tptp.hAPP (tptp.fun X_b tptp.bool) X_b (tptp.the X_b) Pa))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (Z_2 $$unsorted) (A1 $$unsorted) (A2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (let ((_let_3 (tptp.fun _let_1 _let_2))) (= (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.hAPP X_c _let_3 (tptp.hAPP (tptp.fun X_b (tptp.fun X_c X_c)) (tptp.fun X_c _let_3) (tptp.finite_fold_graph X_b X_c) F) Z_2) A1) A2)) (or (and (= (tptp.ti _let_1 A1) (tptp.bot_bot _let_1)) (= (tptp.ti X_c A2) (tptp.ti X_c Z_2))) (exists ((X_2 $$unsorted) (A_4 $$unsorted) (Y_1 $$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_4)) (= (tptp.ti X_c A2) (tptp.hAPP X_c X_c (tptp.hAPP X_b _let_4 F X_2) Y_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_2) A_4))) (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_2) A_4) Y_1)))))))))))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (F $$unsorted) (F_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_b X_b))) (let ((_let_3 (tptp.fun _let_1 X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP (tptp.fun X_b _let_2) (tptp.fun _let_3 tptp.bool) (tptp.finite2073411215e_idem X_b) F) F_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (=> (not (= (tptp.ti _let_1 A_3) (tptp.bot_bot _let_1))) (= (tptp.hAPP _let_1 X_b F_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_1) A_3)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_2 F X_1) (tptp.hAPP _let_1 X_b F_2 A_3)))))))))) (forall ((X_b $$unsorted) (Pa $$unsorted) (F_2 $$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))) (=> (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_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) F_3)) (=> (not (= (tptp.ti _let_1 F_3) (tptp.bot_bot _let_1))) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_2) F_3))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa F_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_2) F_3))))))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa F_2)))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (F $$unsorted) (Z_2 $$unsorted) (G $$unsorted) (F_2 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b X_b))) (let ((_let_3 (tptp.fun _let_1 X_b))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.fun X_c X_b))) (let ((_let_6 (tptp.fun _let_5 _let_4))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_5 _let_4 (tptp.hAPP X_b _let_6 (tptp.hAPP (tptp.fun X_b _let_2) (tptp.fun X_b _let_6) (tptp.finite908156982e_idem X_b X_c) F) Z_2) G) F_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_c) A_3)) (= (tptp.hAPP _let_1 X_b F_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_c (tptp.fun _let_1 _let_1) (tptp.insert X_c) X_1) A_3)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_2 F (tptp.hAPP X_c X_b G X_1)) (tptp.hAPP _let_1 X_b F_2 A_3)))))))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (F $$unsorted) (F_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 X_b))) (let ((_let_3 (tptp.fun X_b (tptp.fun X_b X_b)))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_3 (tptp.fun _let_2 tptp.bool) (tptp.big_semilattice_big X_b) F) F_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (= (tptp.hAPP _let_1 X_b F_2 A_3) (tptp.hAPP _let_1 X_b (tptp.hAPP _let_3 _let_2 (tptp.finite_fold1 X_b) F) A_3)))))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (F $$unsorted) (F_2 $$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_3) (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_2 A_3))) (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_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 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) X_1) A_3)) (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_2 _let_4))))))))))))))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (F $$unsorted) (F_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.bot_bot _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.hAPP X_b _let_3 (tptp.insert X_b) X_1))) (let ((_let_5 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 (tptp.minus_minus _let_1) A_3) (tptp.hAPP _let_1 _let_1 _let_4 _let_2)))) (let ((_let_6 (tptp.fun X_b X_b))) (let ((_let_7 (tptp.hAPP _let_1 X_b F_2 (tptp.hAPP _let_1 _let_1 _let_4 A_3)))) (let ((_let_8 (= _let_5 _let_2))) (let ((_let_9 (tptp.fun _let_1 X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_9 tptp.bool (tptp.hAPP (tptp.fun X_b _let_6) (tptp.fun _let_9 tptp.bool) (tptp.finite_folding_one X_b) F) F_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (and (=> _let_8 (= _let_7 (tptp.ti X_b X_1))) (=> (not _let_8) (= _let_7 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_6 F X_1) (tptp.hAPP _let_1 X_b F_2 _let_5))))))))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.ab_semigroup_mult X_b) (forall ((X_1 $$unsorted) (A_3 $$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_3) (tptp.bot_bot _let_2))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (=> (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_3))) (= (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_3)) (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_3))))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.ab_sem1668676832m_mult X_b) (forall ((X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.times_times X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun X_b X_b))) (let ((_let_4 (tptp.hAPP (tptp.fun X_b _let_3) (tptp.fun _let_2 X_b) (tptp.finite_fold1 X_b) _let_1))) (=> (not (= (tptp.ti _let_2 A_3) (tptp.bot_bot _let_2))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (= (tptp.hAPP _let_2 X_b _let_4 (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_b (tptp.fun _let_2 _let_2) (tptp.insert X_b) X_1) A_3)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_3 _let_1 X_1) (tptp.hAPP _let_2 X_b _let_4 A_3)))))))))))) (forall ((X_b $$unsorted) (B_2 $$unsorted) (Ca $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) Ca))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_3)) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B_2))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) A_3) B_2)))))))) (forall ((X_b $$unsorted) (Ca $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) Ca))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) A_3) B_2))) (not (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B_2)))))))) (forall ((X_b $$unsorted) (B_2 $$unsorted) (A_3 $$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_3)) (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_3) B_2))))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (F $$unsorted) (F_2 $$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_2)) (= (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 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP (tptp.fun X_b (tptp.fun _let_1 tptp.bool)) _let_2 (tptp.combc X_b _let_1 tptp.bool) (tptp.member X_b)))) (let ((_let_4 (tptp.fun tptp.bool tptp.bool))) (let ((_let_5 (tptp.fun X_b _let_4))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.minus_minus _let_1) A_3) B_2) (tptp.hAPP _let_1 _let_1 (tptp.collect X_b) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_5 _let_2 (tptp.combs X_b tptp.bool tptp.bool) (tptp.hAPP _let_1 _let_5 (tptp.hAPP (tptp.fun tptp.bool _let_4) (tptp.fun _let_1 _let_5) (tptp.combb tptp.bool _let_4 X_b) tptp.fconj) (tptp.hAPP _let_1 _let_1 _let_3 A_3))) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_4 _let_2 (tptp.combb tptp.bool tptp.bool X_b) tptp.fNot) (tptp.hAPP _let_1 _let_1 _let_3 B_2))))))))))) (forall ((X_b $$unsorted) (Ca $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) Ca))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) A_3) B_2))) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_3)) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B_2)))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_2 $$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_3) B_2))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 _let_4) B_2) _let_4)))))) (forall ((X_b $$unsorted) (Ca $$unsorted) (A_3 $$unsorted) (B_2 $$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) 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_3) B_2))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_3)))))) (forall ((X_b $$unsorted) (Ca $$unsorted) (A_3 $$unsorted) (B_2 $$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) 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_3) B_2))) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B_2))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (X_1 $$unsorted) (F $$unsorted) (Z_2 $$unsorted) (G $$unsorted) (F_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b X_b))) (let ((_let_2 (tptp.fun (tptp.fun X_c tptp.bool) X_b))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.fun X_c X_b))) (let ((_let_5 (tptp.fun _let_4 _let_3))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_4 _let_3 (tptp.hAPP X_b _let_5 (tptp.hAPP (tptp.fun X_b _let_1) (tptp.fun X_b _let_5) (tptp.finite908156982e_idem X_b X_c) F) Z_2) G) F_2)) (= (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 F X_1) X_1) (tptp.ti X_b X_1))))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.bot_bot _let_1))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) _let_2) A_3) _let_2)))) (forall ((X_b $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) A_3) (tptp.bot_bot _let_1)) (tptp.ti _let_1 A_3)))) (forall ((X_b $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) A_3) A_3) (tptp.bot_bot _let_1)))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_2 $$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_2)) (= (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_3) B_2))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 A_3))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (X_1 $$unsorted) (B_2 $$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_3) B_2))) (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_3)) B_2))) (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_2)))) (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) (X_1 $$unsorted) (B_2 $$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_2)) (= (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_3)) B_2) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 A_3) B_2))))))) (forall ((X_b $$unsorted)) (=> (tptp.ab_semigroup_mult X_b) (forall ((A_2 $$unsorted) (Ba $$unsorted) (A_3 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.insert X_b))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun X_b _let_3) (tptp.finite_fold_graph X_b X_b) (tptp.times_times X_b)))) (let ((_let_5 (tptp.member X_b))) (let ((_let_6 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_3 _let_4 Ba) A_3) X_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_6 _let_5 A_2) A_3)) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_6 _let_5 Ba) A_3))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_3 _let_4 A_2) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_3 _let_2 Ba) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 (tptp.minus_minus _let_1) A_3) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_3 _let_2 A_2) (tptp.bot_bot _let_1))))) X_1)))))))))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (A_2 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP X_b _let_2 (tptp.insert X_b) A_2))) (let ((_let_4 (tptp.minus_minus _let_1))) (let ((_let_5 (tptp.hAPP _let_1 _let_2 _let_4 A_3))) (= (tptp.hAPP _let_1 _let_1 _let_5 (tptp.hAPP _let_1 _let_1 _let_3 B_2)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 _let_4 (tptp.hAPP _let_1 _let_1 _let_5 B_2)) (tptp.hAPP _let_1 _let_1 _let_3 (tptp.bot_bot _let_1)))))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (A_2 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP X_b _let_2 (tptp.insert X_b) A_2))) (let ((_let_4 (tptp.minus_minus _let_1))) (let ((_let_5 (tptp.hAPP _let_1 _let_2 _let_4 A_3))) (= (tptp.hAPP _let_1 _let_1 _let_5 (tptp.hAPP _let_1 _let_1 _let_3 B_2)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 _let_4 (tptp.hAPP _let_1 _let_1 _let_5 (tptp.hAPP _let_1 _let_1 _let_3 (tptp.bot_bot _let_1)))) B_2)))))))) (forall ((X_b $$unsorted) (A_2 $$unsorted) (A_3 $$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_2))) (= (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_3) (tptp.hAPP _let_1 _let_1 _let_3 (tptp.bot_bot _let_1)))) (tptp.hAPP _let_1 _let_1 _let_3 A_3)))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP X_b _let_2 (tptp.insert X_b) X_1))) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_1) A_3))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.minus_minus _let_1) (tptp.hAPP _let_1 _let_1 _let_3 A_3)) (tptp.hAPP _let_1 _let_1 _let_3 (tptp.bot_bot _let_1))) (tptp.ti _let_1 A_3))))))) (forall ((X_b $$unsorted) (A_2 $$unsorted) (A_3 $$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_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_2) 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_3) (tptp.hAPP _let_1 _let_1 _let_3 (tptp.bot_bot _let_1)))) (tptp.ti _let_1 A_3))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (A_2 $$unsorted) (B_2 $$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_3))) (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_2) B_2)))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_4 (tptp.hAPP _let_1 _let_1 _let_3 B_2))))))))) (forall ((X_b $$unsorted)) (=> (tptp.ab_semigroup_mult X_b) (forall ((Z_2 $$unsorted) (Ba $$unsorted) (A_3 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.times_times X_b))) (let ((_let_2 (tptp.fun X_b X_b))) (let ((_let_3 (tptp.fun X_b tptp.bool))) (let ((_let_4 (tptp.fun _let_3 _let_3))) (let ((_let_5 (tptp.hAPP (tptp.fun X_b _let_2) (tptp.fun X_b _let_4) (tptp.finite_fold_graph X_b X_b) _let_1))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP _let_3 _let_3 (tptp.hAPP X_b _let_4 _let_5 Ba) A_3) Y_2)) (=> (not (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_b (tptp.fun _let_3 tptp.bool) (tptp.member X_b) Ba) A_3))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP _let_3 _let_3 (tptp.hAPP X_b _let_4 _let_5 Z_2) (tptp.hAPP _let_3 _let_3 (tptp.hAPP X_b _let_4 (tptp.insert X_b) Ba) A_3)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_2 _let_1 Z_2) Y_2))))))))))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (F $$unsorted) (F_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP _let_1 X_b F_2 A_3))) (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_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 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) X_1) A_3)) (= (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 $$unsorted) (A_3 $$unsorted) (F $$unsorted) (Z_2 $$unsorted) (G $$unsorted) (F_2 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.hAPP _let_1 X_b F_2 A_3))) (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_2) G) F_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_c) A_3)) (=> (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_3)) (= (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 $$unsorted)) (=> (tptp.ab_sem1668676832m_mult X_b) (forall ((N_3 $$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_1 $$unsorted)) (let ((_let_1 (tptp.times_times X_b))) (let ((_let_2 (tptp.fun X_b X_b))) (= (tptp.hAPP X_b X_b H (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_2 _let_1 X_2) Y_1)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_2 _let_1 (tptp.hAPP X_b X_b H X_2)) (tptp.hAPP X_b X_b H Y_1)))))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) N_3)) (=> (not (= (tptp.ti _let_1 N_3) (tptp.bot_bot _let_1))) (= (tptp.hAPP X_b X_b H (tptp.hAPP _let_1 X_b _let_3 N_3)) (tptp.hAPP _let_1 X_b _let_3 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_2 (tptp.fun _let_1 _let_1) (tptp.image X_b X_b) H) N_3)))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.ab_semigroup_mult X_b) (forall ((A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (=> (not (= (tptp.ti _let_1 A_3) (tptp.bot_bot _let_1))) (=> (forall ((X_2 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.insert X_b))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.times_times X_b) X_2) Y_1)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_3 _let_2 X_2) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_3 _let_2 Y_1) (tptp.bot_bot _let_1))))))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) (tptp.hAPP _let_1 X_b (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun _let_1 X_b) (tptp.finite_fold1 X_b) (tptp.times_times X_b)) A_3)) A_3))))))))) (forall ((X_b $$unsorted) (N_3 $$unsorted) (H $$unsorted) (F $$unsorted) (F_2 $$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_2)) (=> (forall ((X_2 $$unsorted) (Y_1 $$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_1)) (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_1))))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) N_3)) (=> (not (= (tptp.ti _let_1 N_3) (tptp.bot_bot _let_1))) (= (tptp.hAPP X_b X_b H (tptp.hAPP _let_1 X_b F_2 N_3)) (tptp.hAPP _let_1 X_b F_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_2 (tptp.fun _let_1 _let_1) (tptp.image X_b X_b) H) N_3))))))))))) (forall ((X_b $$unsorted) (Pa $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa A_3)) (=> (forall ((A_5 $$unsorted) (A_4 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_4)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_5) A_4)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa A_4)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.minus_minus _let_1) A_4) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_2 (tptp.insert X_b) A_5) (tptp.bot_bot _let_1))))))))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa (tptp.bot_bot _let_1)))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (F $$unsorted) (Z_2 $$unsorted) (G $$unsorted) (F_2 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP X_c _let_2 (tptp.insert X_c) X_1))) (let ((_let_4 (tptp.fun X_b X_b))) (let ((_let_5 (tptp.fun _let_1 X_b))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (let ((_let_7 (tptp.fun X_c X_b))) (let ((_let_8 (tptp.fun _let_7 _let_6))) (=> (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP _let_7 _let_6 (tptp.hAPP X_b _let_8 (tptp.hAPP (tptp.fun X_b _let_4) (tptp.fun X_b _let_8) (tptp.finite1357897459simple X_b X_c) F) Z_2) G) F_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_c) A_3)) (= (tptp.hAPP _let_1 X_b F_2 (tptp.hAPP _let_1 _let_1 _let_3 A_3)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_4 F (tptp.hAPP X_c X_b G X_1)) (tptp.hAPP _let_1 X_b F_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.minus_minus _let_1) A_3) (tptp.hAPP _let_1 _let_1 _let_3 (tptp.bot_bot _let_1))))))))))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (F $$unsorted) (Z_2 $$unsorted) (G $$unsorted) (F_2 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.fun X_b X_b))) (let ((_let_4 (tptp.fun _let_1 X_b))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (let ((_let_6 (tptp.fun X_c X_b))) (let ((_let_7 (tptp.fun _let_6 _let_5))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP _let_6 _let_5 (tptp.hAPP X_b _let_7 (tptp.hAPP (tptp.fun X_b _let_3) (tptp.fun X_b _let_7) (tptp.finite1357897459simple X_b X_c) F) Z_2) G) F_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_c) A_3)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_c (tptp.fun _let_1 tptp.bool) (tptp.member X_c) X_1) A_3)) (= (tptp.hAPP _let_1 X_b F_2 A_3) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_3 F (tptp.hAPP X_c X_b G X_1)) (tptp.hAPP _let_1 X_b F_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.minus_minus _let_1) A_3) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_c _let_2 (tptp.insert X_c) X_1) (tptp.bot_bot _let_1))))))))))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted)) (=> (tptp.minus X_b) (forall ((A_3 $$unsorted) (B_2 $$unsorted) (X_1 $$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_3) B_2) 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_3 X_1)) (tptp.hAPP X_c X_b B_2 X_1))))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (tptp.minus X_c) (forall ((A_3 $$unsorted) (B_2 $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b X_c))) (= (tptp.hAPP X_b X_c (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) A_3) B_2) X_2) (tptp.hAPP X_c X_c (tptp.hAPP X_c (tptp.fun X_c X_c) (tptp.minus_minus X_c) (tptp.hAPP X_b X_c A_3 X_2)) (tptp.hAPP X_b X_c B_2 X_2))))))) (forall ((X_b $$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) (X_1 $$unsorted) (Z_2 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun X_c X_c))) (let ((_let_2 (tptp.hAPP X_b _let_1 F X_1))) (let ((_let_3 (tptp.hAPP X_c X_c _let_2 Z_2))) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b _let_1) tptp.bool (tptp.finite_comp_fun_idem X_b X_c) F)) (= (tptp.hAPP X_c X_c _let_2 _let_3) _let_3)))))) (forall ((X_b $$unsorted)) (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 $$unsorted)) (=> (tptp.ab_sem1668676832m_mult X_b) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) tptp.bool (tptp.finite_comp_fun_idem X_b X_b) (tptp.times_times X_b))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (Z_2 $$unsorted) (G $$unsorted) (F_2 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun _let_1 X_b))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.fun X_c X_b))) (let ((_let_5 (tptp.fun _let_4 _let_3))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_4 _let_3 (tptp.hAPP X_b _let_5 (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun X_b _let_5) (tptp.finite1357897459simple X_b X_c) F) Z_2) G) F_2)) (= (tptp.hAPP _let_1 X_b F_2 (tptp.bot_bot _let_1)) (tptp.ti X_b Z_2))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ab_sem1668676832m_mult X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1) A_1) (tptp.ti X_a A_1))))) (forall ((X_a $$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_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1))) (let ((_let_2 (tptp.hAPP X_a X_a _let_1 B))) (= (tptp.hAPP X_a X_a _let_1 _let_2) _let_2)))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (F $$unsorted) (Z_2 $$unsorted) (G $$unsorted) (F_2 $$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_2) G) F_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_c) A_3)) (=> (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_3))) (= (tptp.hAPP _let_1 X_b F_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_c (tptp.fun _let_1 _let_1) (tptp.insert X_c) X_1) A_3)) (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_2 A_3))))))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (A_3 $$unsorted) (F $$unsorted) (Z_2 $$unsorted) (G $$unsorted) (F_2 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun _let_1 X_b))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.fun X_c X_b))) (let ((_let_5 (tptp.fun _let_4 _let_3))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_4 _let_3 (tptp.hAPP X_b _let_5 (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun X_b _let_5) (tptp.finite1357897459simple X_b X_c) F) Z_2) G) F_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_c) A_3)) (=> (forall ((X_2 $$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_3)) (= (tptp.hAPP X_c X_b G X_2) (tptp.ti X_b Z_2))))) (= (tptp.hAPP _let_1 X_b F_2 A_3) (tptp.ti X_b Z_2))))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (A_2 $$unsorted) (Z_2 $$unsorted) (A_3 $$unsorted) (Y_2 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (let ((_let_3 (tptp.fun _let_1 _let_2))) (let ((_let_4 (tptp.fun X_b (tptp.fun X_c X_c)))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.finite100568337ommute X_b X_c) F)) (=> (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.hAPP X_c _let_3 (tptp.hAPP _let_4 (tptp.fun X_c _let_3) (tptp.finite_fold_graph X_b X_c) F) Z_2) A_3) Y_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_2) A_3)) (exists ((Y_3 $$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_2) (tptp.hAPP X_c X_c (tptp.hAPP X_b _let_5 F A_2) 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_2) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.minus_minus _let_1) A_3) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_2 (tptp.insert X_b) A_2) (tptp.bot_bot _let_1)))) Y_3))))))))))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (Z_2 $$unsorted) (Y_2 $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_c X_c))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (let ((_let_3 (tptp.fun X_b tptp.bool))) (let ((_let_4 (tptp.fun _let_3 _let_2))) (let ((_let_5 (tptp.hAPP X_c _let_4 (tptp.hAPP (tptp.fun X_b _let_1) (tptp.fun X_c _let_4) (tptp.fold_graph X_b X_c) F) Z_2))) (let ((_let_6 (tptp.fun _let_3 _let_3))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_b (tptp.fun _let_3 tptp.bool) (tptp.member X_b) X_1) A_3)) (=> (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP _let_3 _let_2 _let_5 (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_3 _let_6 (tptp.minus_minus _let_3) A_3) (tptp.hAPP _let_3 _let_3 (tptp.hAPP X_b _let_6 (tptp.insert X_b) X_1) (tptp.bot_bot _let_3)))) Y_2)) (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP _let_3 _let_2 _let_5 A_3) (tptp.hAPP X_c X_c (tptp.hAPP X_b _let_1 F X_1) Y_2)))))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (tptp.ab_group_add X_c) (forall ((F $$unsorted) (A_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun _let_1 X_c) (tptp.big_co1399186613setsum X_b X_c) F))) (let ((_let_3 (tptp.hAPP _let_1 X_c _let_2 A_3))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.hAPP _let_1 X_c _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_4 (tptp.minus_minus _let_1) A_3) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_4 (tptp.insert X_b) A_2) (tptp.bot_bot _let_1)))))) (let ((_let_6 (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_2) A_3)))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (and (=> _let_6 (= _let_5 (tptp.hAPP X_c X_c (tptp.hAPP X_c (tptp.fun X_c X_c) (tptp.minus_minus X_c) _let_3) (tptp.hAPP X_b X_c F A_2)))) (=> (not _let_6) (= _let_5 _let_3))))))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (tptp.ring X_c) (forall ((F $$unsorted) (A_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun _let_1 X_c) (tptp.big_co1399186613setsum X_b X_c) F))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_2) A_3)) (= (tptp.hAPP _let_1 X_c _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 (tptp.minus_minus _let_1) A_3) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_3 (tptp.insert X_b) A_2) (tptp.bot_bot _let_1)))) (tptp.hAPP X_c X_c (tptp.hAPP X_c (tptp.fun X_c X_c) (tptp.minus_minus X_c) (tptp.hAPP _let_1 X_c _let_2 A_3)) (tptp.hAPP X_b X_c F A_2))))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (tptp.comm_monoid_mult X_c) (forall ((G $$unsorted) (X_1 $$unsorted) (A_3 $$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.hAPP (tptp.fun X_b X_c) (tptp.fun _let_1 X_c) (tptp.big_co302546470etprod X_b X_c) G))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (= (tptp.hAPP _let_1 X_c _let_4 (tptp.hAPP _let_1 _let_1 _let_3 A_3)) (tptp.hAPP X_c X_c (tptp.hAPP X_c (tptp.fun X_c X_c) (tptp.times_times X_c) (tptp.hAPP X_b X_c G X_1)) (tptp.hAPP _let_1 X_c _let_4 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.minus_minus _let_1) A_3) (tptp.hAPP _let_1 _let_1 _let_3 (tptp.bot_bot _let_1)))))))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (tptp.comm_monoid_mult X_c) (forall ((G $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun _let_1 X_c) (tptp.big_co302546470etprod X_b X_c) G))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_1) A_3)) (= (tptp.hAPP _let_1 X_c _let_3 A_3) (tptp.hAPP X_c X_c (tptp.hAPP X_c (tptp.fun X_c X_c) (tptp.times_times X_c) (tptp.hAPP X_b X_c G X_1)) (tptp.hAPP _let_1 X_c _let_3 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.minus_minus _let_1) A_3) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_2 (tptp.insert X_b) X_1) (tptp.bot_bot _let_1)))))))))))))) (forall ((X_b $$unsorted) (B_2 $$unsorted) (A_3 $$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 _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_3)) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_5 B_2) A_3) (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_2) A_3)))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (X_1 $$unsorted) (Z_2 $$unsorted) (A_3 $$unsorted) (F $$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_3)) (= (tptp.hAPP X_c X_c _let_2 (tptp.hAPP _let_3 X_c (tptp.hAPP X_c _let_4 _let_6 Z_2) A_3)) (tptp.hAPP _let_3 X_c (tptp.hAPP X_c _let_4 _let_6 (tptp.hAPP X_c X_c _let_2 Z_2)) A_3))))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (X_1 $$unsorted) (Y_2 $$unsorted) (Z_2 $$unsorted) (F $$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_2))) (=> (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_2)) (tptp.hAPP X_c X_c _let_3 (tptp.hAPP X_c X_c _let_2 Z_2)))))))) (forall ((X_c $$unsorted) (X_d $$unsorted) (X_b $$unsorted)) (=> (tptp.comm_monoid_add X_b) (forall ((F $$unsorted) (B_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_c X_b))) (let ((_let_2 (tptp.fun X_d _let_1))) (let ((_let_3 (tptp.fun X_d X_b))) (let ((_let_4 (tptp.fun X_c _let_3))) (let ((_let_5 (tptp.big_co1399186613setsum X_c X_b))) (let ((_let_6 (tptp.fun X_c tptp.bool))) (let ((_let_7 (tptp.fun _let_6 X_b))) (let ((_let_8 (tptp.fun X_d _let_7))) (let ((_let_9 (tptp.big_co1399186613setsum X_d X_b))) (let ((_let_10 (tptp.fun X_d tptp.bool))) (let ((_let_11 (tptp.fun _let_10 X_b))) (let ((_let_12 (tptp.fun X_c _let_11))) (= (tptp.hAPP _let_6 X_b (tptp.hAPP _let_1 _let_7 _let_5 (tptp.hAPP _let_10 _let_1 (tptp.hAPP _let_12 (tptp.fun _let_10 _let_1) (tptp.combc X_c _let_10 X_b) (tptp.hAPP _let_4 _let_12 (tptp.hAPP (tptp.fun _let_3 _let_11) (tptp.fun _let_4 _let_12) (tptp.combb _let_3 _let_11 X_c) _let_9) F)) B_2)) A_3) (tptp.hAPP _let_10 X_b (tptp.hAPP _let_3 _let_11 _let_9 (tptp.hAPP _let_6 _let_3 (tptp.hAPP _let_8 (tptp.fun _let_6 _let_3) (tptp.combc X_d _let_6 X_b) (tptp.hAPP _let_2 _let_8 (tptp.hAPP (tptp.fun _let_1 _let_7) (tptp.fun _let_2 _let_8) (tptp.combb _let_1 _let_7 X_d) _let_5) (tptp.hAPP _let_4 _let_2 (tptp.combc X_c X_d X_b) F))) A_3)) B_2))))))))))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (Z_2 $$unsorted) (A_3 $$unsorted) (Y_2 $$unsorted) (F $$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_2) A_3) Y_2)) (= (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_2) A_3) (tptp.ti X_c Y_2)))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (Z_2 $$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_2) (tptp.bot_bot _let_1)) (tptp.ti X_b Z_2))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (Z_2 $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (F $$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_3)) (=> (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_3))) (= (tptp.hAPP _let_2 X_c (tptp.hAPP X_c _let_3 _let_5 Z_2) (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_b (tptp.fun _let_2 _let_2) (tptp.insert X_b) X_1) A_3)) (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_2)) A_3))))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (Z_2 $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (F $$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_2))) (=> (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_3)) (=> (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_3))) (= (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_3)) (tptp.hAPP X_c X_c (tptp.hAPP X_b _let_3 F X_1) (tptp.hAPP _let_1 X_c _let_5 A_3)))))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (Z_2 $$unsorted) (A_3 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 X_c))) (let ((_let_3 (tptp.fun X_b (tptp.fun X_c X_c)))) (let ((_let_4 (tptp.fun X_c tptp.bool))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.finite100568337ommute X_b X_c) F)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP _let_1 _let_4 (tptp.hAPP X_c _let_5 (tptp.hAPP _let_3 (tptp.fun X_c _let_5) (tptp.finite_fold_graph X_b X_c) F) Z_2) A_3) (tptp.hAPP _let_1 X_c (tptp.hAPP X_c _let_2 (tptp.hAPP _let_3 (tptp.fun X_c _let_2) (tptp.finite_fold X_b X_c) F) Z_2) A_3))))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted)) (=> (tptp.comm_monoid_mult X_b) (forall ((F $$unsorted) (G $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.big_co302546470etprod X_c X_b))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (let ((_let_3 (tptp.fun _let_2 X_b))) (let ((_let_4 (tptp.fun X_c X_b))) (let ((_let_5 (tptp.times_times X_b))) (let ((_let_6 (tptp.fun X_b X_b))) (let ((_let_7 (tptp.fun X_c _let_6))) (= (tptp.hAPP _let_2 X_b (tptp.hAPP _let_4 _let_3 _let_1 (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_7 (tptp.fun _let_4 _let_4) (tptp.combs X_c X_b X_b) (tptp.hAPP _let_4 _let_7 (tptp.hAPP (tptp.fun X_b _let_6) (tptp.fun _let_4 _let_7) (tptp.combb X_b _let_6 X_c) _let_5) F)) G)) A_3) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_6 _let_5 (tptp.hAPP _let_2 X_b (tptp.hAPP _let_4 _let_3 _let_1 F) A_3)) (tptp.hAPP _let_2 X_b (tptp.hAPP _let_4 _let_3 _let_1 G) A_3))))))))))))) (forall ((X_c $$unsorted) (X_d $$unsorted) (X_b $$unsorted)) (=> (tptp.semiring_0 X_b) (forall ((F $$unsorted) (A_3 $$unsorted) (G $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.times_times X_b))) (let ((_let_2 (tptp.fun X_b X_b))) (let ((_let_3 (tptp.fun X_c _let_2))) (let ((_let_4 (tptp.fun X_c X_b))) (let ((_let_5 (tptp.fun X_d X_b))) (let ((_let_6 (tptp.fun _let_5 _let_5))) (let ((_let_7 (tptp.fun X_c _let_6))) (let ((_let_8 (tptp.fun X_c _let_5))) (let ((_let_9 (tptp.big_co1399186613setsum X_d X_b))) (let ((_let_10 (tptp.fun X_d tptp.bool))) (let ((_let_11 (tptp.fun _let_10 X_b))) (let ((_let_12 (tptp.fun X_c _let_11))) (let ((_let_13 (tptp.big_co1399186613setsum X_c X_b))) (let ((_let_14 (tptp.fun X_c tptp.bool))) (let ((_let_15 (tptp.fun _let_14 X_b))) (= (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_2 _let_1 (tptp.hAPP _let_14 X_b (tptp.hAPP _let_4 _let_15 _let_13 F) A_3)) (tptp.hAPP _let_10 X_b (tptp.hAPP _let_5 _let_11 _let_9 G) B_2)) (tptp.hAPP _let_14 X_b (tptp.hAPP _let_4 _let_15 _let_13 (tptp.hAPP _let_10 _let_4 (tptp.hAPP _let_12 (tptp.fun _let_10 _let_4) (tptp.combc X_c _let_10 X_b) (tptp.hAPP _let_8 _let_12 (tptp.hAPP (tptp.fun _let_5 _let_11) (tptp.fun _let_8 _let_12) (tptp.combb _let_5 _let_11 X_c) _let_9) (tptp.hAPP _let_5 _let_8 (tptp.hAPP _let_7 (tptp.fun _let_5 _let_8) (tptp.combc X_c _let_5 _let_5) (tptp.hAPP _let_3 _let_7 (tptp.hAPP (tptp.fun _let_2 _let_6) (tptp.fun _let_3 _let_7) (tptp.combb _let_2 _let_6 X_c) (tptp.combb X_b X_b X_d)) (tptp.hAPP _let_4 _let_3 (tptp.hAPP (tptp.fun X_b _let_2) (tptp.fun _let_4 _let_3) (tptp.combb X_b _let_2 X_c) _let_1) F))) G))) B_2)) A_3)))))))))))))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted)) (=> (tptp.semiring_0 X_b) (forall ((F $$unsorted) (A_3 $$unsorted) (R_2 $$unsorted)) (let ((_let_1 (tptp.times_times X_b))) (let ((_let_2 (tptp.fun X_b X_b))) (let ((_let_3 (tptp.fun X_c _let_2))) (let ((_let_4 (tptp.fun X_c X_b))) (let ((_let_5 (tptp.big_co1399186613setsum X_c X_b))) (let ((_let_6 (tptp.fun X_c tptp.bool))) (let ((_let_7 (tptp.fun _let_6 X_b))) (= (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_2 _let_1 (tptp.hAPP _let_6 X_b (tptp.hAPP _let_4 _let_7 _let_5 F) A_3)) R_2) (tptp.hAPP _let_6 X_b (tptp.hAPP _let_4 _let_7 _let_5 (tptp.hAPP X_b _let_4 (tptp.hAPP _let_3 (tptp.fun X_b _let_4) (tptp.combc X_c X_b X_b) (tptp.hAPP _let_4 _let_3 (tptp.hAPP (tptp.fun X_b _let_2) (tptp.fun _let_4 _let_3) (tptp.combb X_b _let_2 X_c) _let_1) F)) R_2)) A_3)))))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted)) (=> (tptp.semiring_0 X_b) (forall ((R_2 $$unsorted) (F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b X_b))) (let ((_let_2 (tptp.hAPP X_b _let_1 (tptp.times_times X_b) R_2))) (let ((_let_3 (tptp.fun X_c X_b))) (let ((_let_4 (tptp.big_co1399186613setsum X_c X_b))) (let ((_let_5 (tptp.fun X_c tptp.bool))) (let ((_let_6 (tptp.fun _let_5 X_b))) (= (tptp.hAPP X_b X_b _let_2 (tptp.hAPP _let_5 X_b (tptp.hAPP _let_3 _let_6 _let_4 F) A_3)) (tptp.hAPP _let_5 X_b (tptp.hAPP _let_3 _let_6 _let_4 (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_1 (tptp.fun _let_3 _let_3) (tptp.combb X_b X_b X_c) _let_2) F)) A_3))))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted)) (=> (tptp.ab_group_add X_b) (forall ((F $$unsorted) (G $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.big_co1399186613setsum X_c X_b))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (let ((_let_3 (tptp.fun _let_2 X_b))) (let ((_let_4 (tptp.fun X_c X_b))) (let ((_let_5 (tptp.minus_minus X_b))) (let ((_let_6 (tptp.fun X_b X_b))) (let ((_let_7 (tptp.fun X_c _let_6))) (= (tptp.hAPP _let_2 X_b (tptp.hAPP _let_4 _let_3 _let_1 (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_7 (tptp.fun _let_4 _let_4) (tptp.combs X_c X_b X_b) (tptp.hAPP _let_4 _let_7 (tptp.hAPP (tptp.fun X_b _let_6) (tptp.fun _let_4 _let_7) (tptp.combb X_b _let_6 X_c) _let_5) F)) G)) A_3) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_6 _let_5 (tptp.hAPP _let_2 X_b (tptp.hAPP _let_4 _let_3 _let_1 F) A_3)) (tptp.hAPP _let_2 X_b (tptp.hAPP _let_4 _let_3 _let_1 G) A_3))))))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (Z_2 $$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_2) (tptp.bot_bot _let_1)) Z_2)))))) (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) (X_c $$unsorted) (Y_2 $$unsorted) (Z_2 $$unsorted) (A_3 $$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_2) A_3))) (=> (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_2)) (= (tptp.ti X_c Y_2) (tptp.ti X_c X_1))))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (tptp.comm_monoid_mult X_c) (forall ((G $$unsorted) (H $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.big_co302546470etprod X_b X_c))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun _let_2 X_c))) (let ((_let_4 (tptp.fun X_b X_c))) (let ((_let_5 (tptp.times_times X_c))) (let ((_let_6 (tptp.fun X_c X_c))) (let ((_let_7 (tptp.fun X_b _let_6))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (= (tptp.hAPP _let_2 X_c (tptp.hAPP _let_4 _let_3 _let_1 (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_7 (tptp.fun _let_4 _let_4) (tptp.combs X_b X_c X_c) (tptp.hAPP _let_4 _let_7 (tptp.hAPP (tptp.fun X_c _let_6) (tptp.fun _let_4 _let_7) (tptp.combb X_c _let_6 X_b) _let_5) G)) H)) A_3) (tptp.hAPP X_c X_c (tptp.hAPP X_c _let_6 _let_5 (tptp.hAPP _let_2 X_c (tptp.hAPP _let_4 _let_3 _let_1 G) A_3)) (tptp.hAPP _let_2 X_c (tptp.hAPP _let_4 _let_3 _let_1 H) A_3)))))))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (Z_2 $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.fun _let_1 X_c))) (let ((_let_4 (tptp.fun X_c X_c))) (let ((_let_5 (tptp.fun X_b _let_4))) (let ((_let_6 (tptp.hAPP X_c _let_3 (tptp.hAPP _let_5 (tptp.fun X_c _let_3) (tptp.finite_fold X_b X_c) F) Z_2))) (=> (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.finite100568337ommute X_b X_c) F)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_1) A_3)) (= (tptp.hAPP _let_1 X_c _let_6 A_3) (tptp.hAPP X_c X_c (tptp.hAPP X_b _let_4 F X_1) (tptp.hAPP _let_1 X_c _let_6 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.minus_minus _let_1) A_3) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_2 (tptp.insert X_b) X_1) (tptp.bot_bot _let_1)))))))))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (Z_2 $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP X_b _let_2 (tptp.insert X_b) X_1))) (let ((_let_4 (tptp.fun _let_1 X_c))) (let ((_let_5 (tptp.fun X_c X_c))) (let ((_let_6 (tptp.fun X_b _let_5))) (let ((_let_7 (tptp.hAPP X_c _let_4 (tptp.hAPP _let_6 (tptp.fun X_c _let_4) (tptp.finite_fold X_b X_c) F) Z_2))) (=> (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.finite100568337ommute X_b X_c) F)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (= (tptp.hAPP _let_1 X_c _let_7 (tptp.hAPP _let_1 _let_1 _let_3 A_3)) (tptp.hAPP X_c X_c (tptp.hAPP X_b _let_5 F X_1) (tptp.hAPP _let_1 X_c _let_7 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.minus_minus _let_1) A_3) (tptp.hAPP _let_1 _let_1 _let_3 (tptp.bot_bot _let_1)))))))))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (tptp.comm_monoid_mult X_c) (forall ((F $$unsorted) (A_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun _let_1 X_c) (tptp.big_co302546470etprod X_b X_c) F))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_2) A_3))) (= (tptp.hAPP _let_1 X_c _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_2) A_3)) (tptp.hAPP X_c X_c (tptp.hAPP X_c (tptp.fun X_c X_c) (tptp.times_times X_c) (tptp.hAPP X_b X_c F A_2)) (tptp.hAPP _let_1 X_c _let_2 A_3)))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (tptp.comm_monoid_mult X_c) (forall ((G $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun _let_1 X_c) (tptp.big_co302546470etprod X_b X_c) G))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_1) A_3))) (= (tptp.hAPP _let_1 X_c _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_1) A_3)) (tptp.hAPP X_c X_c (tptp.hAPP X_c (tptp.fun X_c X_c) (tptp.times_times X_c) (tptp.hAPP X_b X_c G X_1)) (tptp.hAPP _let_1 X_c _let_2 A_3)))))))))) (forall ((X_b $$unsorted) (F $$unsorted) (A_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP (tptp.fun X_b tptp.nat) (tptp.fun _let_1 tptp.nat) (tptp.big_co1399186613setsum X_b tptp.nat) F))) (let ((_let_3 (tptp.hAPP _let_1 tptp.nat _let_2 A_3))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.hAPP _let_1 tptp.nat _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_4 (tptp.minus_minus _let_1) A_3) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_4 (tptp.insert X_b) A_2) (tptp.bot_bot _let_1)))))) (let ((_let_6 (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_2) A_3)))) (and (=> _let_6 (= _let_5 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) _let_3) (tptp.hAPP X_b tptp.nat F A_2)))) (=> (not _let_6) (= _let_5 _let_3)))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (Z_2 $$unsorted) (A_3 $$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_2) A_3) (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_2) A_3))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (Z_2 $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (F $$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_3)) (= (tptp.hAPP _let_2 X_c (tptp.hAPP X_c _let_3 _let_5 Z_2) (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_b (tptp.fun _let_2 _let_2) (tptp.insert X_b) X_1) A_3)) (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_2)) A_3)))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (Z_2 $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (F $$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_2))) (=> (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_3)) (= (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_3)) (tptp.hAPP X_c X_c (tptp.hAPP X_b _let_3 F X_1) (tptp.hAPP _let_1 X_c _let_5 A_3))))))))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (F $$unsorted) (F_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 X_b))) (let ((_let_3 (tptp.fun X_b (tptp.fun X_b X_b)))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_3 (tptp.fun _let_2 tptp.bool) (tptp.finite_folding_one X_b) F) F_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_1) A_3))) (= (tptp.hAPP _let_1 X_b F_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_1) A_3)) (tptp.hAPP _let_1 X_b (tptp.hAPP X_b _let_2 (tptp.hAPP _let_3 (tptp.fun X_b _let_2) (tptp.finite_fold X_b X_b) F) X_1) A_3))))))))) (forall ((X_b $$unsorted) (A_2 $$unsorted) (A_3 $$unsorted) (F $$unsorted) (F_2 $$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_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (= (tptp.hAPP _let_1 X_b F_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_2) A_3)) (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_2) A_3)))))))) (forall ((X_b $$unsorted)) (=> (tptp.ab_semigroup_mult X_b) (forall ((A_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.times_times X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun _let_2 X_b))) (let ((_let_4 (tptp.fun X_b (tptp.fun X_b X_b)))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (=> (not (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_b (tptp.fun _let_2 tptp.bool) (tptp.member X_b) A_2) A_3))) (= (tptp.hAPP _let_2 X_b (tptp.hAPP _let_4 _let_3 (tptp.finite_fold1 X_b) _let_1) (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_b (tptp.fun _let_2 _let_2) (tptp.insert X_b) A_2) A_3)) (tptp.hAPP _let_2 X_b (tptp.hAPP X_b _let_3 (tptp.hAPP _let_4 (tptp.fun X_b _let_3) (tptp.finite_fold X_b X_b) _let_1) A_2) A_3))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.ab_sem1668676832m_mult X_b) (forall ((A_2 $$unsorted) (A_3 $$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_3)) (= (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_2) A_3)) (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_2) A_3)))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (Z_2 $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (V $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (let ((_let_3 (tptp.fun _let_1 _let_2))) (let ((_let_4 (tptp.fun X_b (tptp.fun X_c X_c)))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.finite100568337ommute X_b X_c) F)) (=> (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.hAPP X_c _let_3 (tptp.hAPP _let_4 (tptp.fun X_c _let_3) (tptp.finite_fold_graph X_b X_c) F) Z_2) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_1) A_3)) V)) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_1) A_3))) (not (forall ((Y_1 $$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_1)) (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_2) A_3) Y_1)))))))))))))))))) (forall ((X_d $$unsorted) (X_b $$unsorted) (X_c $$unsorted)) (=> (tptp.comm_monoid_add X_c) (forall ((G $$unsorted) (F $$unsorted) (S_1 $$unsorted)) (let ((_let_1 (tptp.fun X_d tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun X_b X_d))) (let ((_let_4 (tptp.fun X_b _let_1))) (let ((_let_5 (tptp.fun X_d _let_2))) (let ((_let_6 (tptp.fun _let_2 _let_2))) (let ((_let_7 (tptp.fun tptp.bool tptp.bool))) (let ((_let_8 (tptp.fun X_b _let_7))) (let ((_let_9 (tptp.combb _let_2 _let_2 X_d))) (let ((_let_10 (tptp.fun _let_5 _let_5))) (let ((_let_11 (tptp.fun _let_2 X_c))) (let ((_let_12 (tptp.hAPP (tptp.fun X_b X_c) _let_11 (tptp.big_co1399186613setsum X_b X_c) G))) (let ((_let_13 (tptp.fun X_d X_c))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_b) S_1)) (= (tptp.hAPP _let_2 X_c _let_12 S_1) (tptp.hAPP _let_1 X_c (tptp.hAPP _let_13 (tptp.fun _let_1 X_c) (tptp.big_co1399186613setsum X_d X_c) (tptp.hAPP _let_5 _let_13 (tptp.hAPP _let_11 (tptp.fun _let_5 _let_13) (tptp.combb _let_2 X_c X_d) _let_12) (tptp.hAPP _let_5 _let_5 (tptp.hAPP _let_6 _let_10 _let_9 (tptp.collect X_b)) (tptp.hAPP _let_5 _let_5 (tptp.hAPP _let_6 _let_10 _let_9 (tptp.hAPP _let_8 _let_6 (tptp.combs X_b tptp.bool tptp.bool) (tptp.hAPP _let_2 _let_8 (tptp.hAPP (tptp.fun tptp.bool _let_7) (tptp.fun _let_2 _let_8) (tptp.combb tptp.bool _let_7 X_b) tptp.fconj) (tptp.hAPP _let_2 _let_2 (tptp.hAPP (tptp.fun X_b (tptp.fun _let_2 tptp.bool)) _let_6 (tptp.combc X_b _let_2 tptp.bool) (tptp.member X_b)) S_1)))) (tptp.hAPP _let_4 _let_5 (tptp.combc X_b X_d tptp.bool) (tptp.hAPP _let_3 _let_4 (tptp.hAPP (tptp.fun X_d _let_1) (tptp.fun _let_3 _let_4) (tptp.combb X_d _let_1 X_b) (tptp.fequal X_d)) F)))))) (tptp.hAPP _let_2 _let_1 (tptp.hAPP _let_3 (tptp.fun _let_2 _let_1) (tptp.image X_b X_d) F) S_1)))))))))))))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (tptp.comm_monoid_mult X_c) (forall ((G $$unsorted) (H $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.big_co302546470etprod X_b X_c))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun _let_2 X_c))) (let ((_let_4 (tptp.fun X_b X_c))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (=> (forall ((X_2 $$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_3)) (= (tptp.hAPP X_b X_c G X_2) (tptp.hAPP X_b X_c H X_2))))) (= (tptp.hAPP _let_2 X_c (tptp.hAPP _let_4 _let_3 _let_1 G) A_3) (tptp.hAPP _let_2 X_c (tptp.hAPP _let_4 _let_3 _let_1 H) A_3))))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (tptp.comm_monoid_add X_c) (forall ((G $$unsorted) (H $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.big_co1399186613setsum X_b X_c))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun _let_2 X_c))) (let ((_let_4 (tptp.fun X_b X_c))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (=> (forall ((X_2 $$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_3)) (= (tptp.hAPP X_b X_c G X_2) (tptp.hAPP X_b X_c H X_2))))) (= (tptp.hAPP _let_2 X_c (tptp.hAPP _let_4 _let_3 _let_1 G) A_3) (tptp.hAPP _let_2 X_c (tptp.hAPP _let_4 _let_3 _let_1 H) A_3))))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (X_d $$unsorted)) (=> (tptp.comm_monoid_add X_d) (forall ((F $$unsorted) (R_1 $$unsorted) (T_4 $$unsorted) (S_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_c _let_1))) (let ((_let_3 (tptp.fun X_c tptp.bool))) (let ((_let_4 (tptp.fun X_b _let_3))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (let ((_let_6 (tptp.fun tptp.bool tptp.bool))) (let ((_let_7 (tptp.fun X_b _let_6))) (let ((_let_8 (tptp.fun tptp.bool _let_6))) (let ((_let_9 (tptp.combb _let_1 _let_1 X_c))) (let ((_let_10 (tptp.fun _let_2 _let_2))) (let ((_let_11 (tptp.fun X_b X_d))) (let ((_let_12 (tptp.fun X_c _let_11))) (let ((_let_13 (tptp.fun X_c X_d))) (let ((_let_14 (tptp.fun X_b _let_13))) (let ((_let_15 (tptp.big_co1399186613setsum X_b X_d))) (let ((_let_16 (tptp.fun _let_1 X_d))) (let ((_let_17 (tptp.fun X_c _let_16))) (let ((_let_18 (tptp.big_co1399186613setsum X_c X_d))) (let ((_let_19 (tptp.fun _let_3 X_d))) (let ((_let_20 (tptp.fun _let_3 _let_3))) (let ((_let_21 (tptp.fun X_c _let_6))) (let ((_let_22 (tptp.combb _let_3 _let_3 X_b))) (let ((_let_23 (tptp.fun _let_4 _let_4))) (let ((_let_24 (tptp.fun X_b _let_19))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) S_1)) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.finite_finite_1 X_c) T_4)) (= (tptp.hAPP _let_1 X_d (tptp.hAPP _let_11 _let_16 _let_15 (tptp.hAPP _let_4 _let_11 (tptp.hAPP _let_24 (tptp.fun _let_4 _let_11) (tptp.combs X_b _let_3 X_d) (tptp.hAPP _let_14 _let_24 (tptp.hAPP (tptp.fun _let_13 _let_19) (tptp.fun _let_14 _let_24) (tptp.combb _let_13 _let_19 X_b) _let_18) F)) (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_20 _let_23 _let_22 (tptp.collect X_c)) (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_20 _let_23 _let_22 (tptp.hAPP _let_21 _let_20 (tptp.combs X_c tptp.bool tptp.bool) (tptp.hAPP _let_3 _let_21 (tptp.hAPP _let_8 (tptp.fun _let_3 _let_21) (tptp.combb tptp.bool _let_6 X_c) tptp.fconj) (tptp.hAPP _let_3 _let_3 (tptp.hAPP (tptp.fun X_c (tptp.fun _let_3 tptp.bool)) _let_20 (tptp.combc X_c _let_3 tptp.bool) (tptp.member X_c)) T_4)))) R_1)))) S_1) (tptp.hAPP _let_3 X_d (tptp.hAPP _let_13 _let_19 _let_18 (tptp.hAPP _let_2 _let_13 (tptp.hAPP _let_17 (tptp.fun _let_2 _let_13) (tptp.combs X_c _let_1 X_d) (tptp.hAPP _let_12 _let_17 (tptp.hAPP (tptp.fun _let_11 _let_16) (tptp.fun _let_12 _let_17) (tptp.combb _let_11 _let_16 X_c) _let_15) (tptp.hAPP _let_14 _let_12 (tptp.combc X_b X_c X_d) F))) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_5 _let_10 _let_9 (tptp.collect X_b)) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_5 _let_10 _let_9 (tptp.hAPP _let_7 _let_5 (tptp.combs X_b tptp.bool tptp.bool) (tptp.hAPP _let_1 _let_7 (tptp.hAPP _let_8 (tptp.fun _let_1 _let_7) (tptp.combb tptp.bool _let_6 X_b) tptp.fconj) (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_b (tptp.fun _let_1 tptp.bool)) _let_5 (tptp.combc X_b _let_1 tptp.bool) (tptp.member X_b)) S_1)))) (tptp.hAPP _let_4 _let_2 (tptp.combc X_b X_c tptp.bool) R_1))))) T_4))))))))))))))))))))))))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (tptp.comm_monoid_add X_c) (forall ((G $$unsorted) (X_1 $$unsorted) (A_3 $$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 X_c) (tptp.fun _let_1 X_c) (tptp.big_co1399186613setsum X_b X_c) G))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 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) X_1) A_3)) (= (tptp.hAPP _let_1 X_c _let_3 A_3) (tptp.hAPP X_c X_c (tptp.hAPP X_c (tptp.fun X_c X_c) (tptp.plus_plus X_c) (tptp.hAPP X_b X_c G X_1)) (tptp.hAPP _let_1 X_c _let_3 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.minus_minus _let_1) A_3) (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)) (=> (tptp.comm_monoid_add X_c) (forall ((F $$unsorted) (A_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun _let_1 X_c) (tptp.big_co1399186613setsum X_b X_c) F))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_2) A_3)) (= (tptp.hAPP _let_1 X_c _let_3 A_3) (tptp.hAPP X_c X_c (tptp.hAPP X_c (tptp.fun X_c X_c) (tptp.plus_plus X_c) (tptp.hAPP X_b X_c F A_2)) (tptp.hAPP _let_1 X_c _let_3 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.minus_minus _let_1) A_3) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_2 (tptp.insert X_b) A_2) (tptp.bot_bot _let_1)))))))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (tptp.comm_monoid_add X_c) (forall ((G $$unsorted) (X_1 $$unsorted) (A_3 $$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.hAPP (tptp.fun X_b X_c) (tptp.fun _let_1 X_c) (tptp.big_co1399186613setsum X_b X_c) G))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (= (tptp.hAPP _let_1 X_c _let_4 (tptp.hAPP _let_1 _let_1 _let_3 A_3)) (tptp.hAPP X_c X_c (tptp.hAPP X_c (tptp.fun X_c X_c) (tptp.plus_plus X_c) (tptp.hAPP X_b X_c G X_1)) (tptp.hAPP _let_1 X_c _let_4 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.minus_minus _let_1) A_3) (tptp.hAPP _let_1 _let_1 _let_3 (tptp.bot_bot _let_1)))))))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted)) (=> (tptp.comm_monoid_add X_b) (forall ((F $$unsorted) (G $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.big_co1399186613setsum X_c X_b))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (let ((_let_3 (tptp.fun _let_2 X_b))) (let ((_let_4 (tptp.fun X_c X_b))) (let ((_let_5 (tptp.plus_plus X_b))) (let ((_let_6 (tptp.fun X_b X_b))) (let ((_let_7 (tptp.fun X_c _let_6))) (= (tptp.hAPP _let_2 X_b (tptp.hAPP _let_4 _let_3 _let_1 (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_7 (tptp.fun _let_4 _let_4) (tptp.combs X_c X_b X_b) (tptp.hAPP _let_4 _let_7 (tptp.hAPP (tptp.fun X_b _let_6) (tptp.fun _let_4 _let_7) (tptp.combb X_b _let_6 X_c) _let_5) F)) G)) A_3) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_6 _let_5 (tptp.hAPP _let_2 X_b (tptp.hAPP _let_4 _let_3 _let_1 F) A_3)) (tptp.hAPP _let_2 X_b (tptp.hAPP _let_4 _let_3 _let_1 G) A_3))))))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (tptp.comm_monoid_add X_c) (forall ((G $$unsorted) (H $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.big_co1399186613setsum X_b 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 X_c))) (let ((_let_5 (tptp.plus_plus X_c))) (let ((_let_6 (tptp.fun X_c X_c))) (let ((_let_7 (tptp.fun X_b _let_6))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (= (tptp.hAPP _let_2 X_c (tptp.hAPP _let_4 _let_3 _let_1 (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_7 (tptp.fun _let_4 _let_4) (tptp.combs X_b X_c X_c) (tptp.hAPP _let_4 _let_7 (tptp.hAPP (tptp.fun X_c _let_6) (tptp.fun _let_4 _let_7) (tptp.combb X_c _let_6 X_b) _let_5) G)) H)) A_3) (tptp.hAPP X_c X_c (tptp.hAPP X_c _let_6 _let_5 (tptp.hAPP _let_2 X_c (tptp.hAPP _let_4 _let_3 _let_1 G) A_3)) (tptp.hAPP _let_2 X_c (tptp.hAPP _let_4 _let_3 _let_1 H) A_3)))))))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (tptp.comm_monoid_add X_c) (forall ((F $$unsorted) (A_2 $$unsorted) (F_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun _let_1 X_c) (tptp.big_co1399186613setsum X_b X_c) F))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) F_2)) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_2) F_2))) (= (tptp.hAPP _let_1 X_c _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_2) F_2)) (tptp.hAPP X_c X_c (tptp.hAPP X_c (tptp.fun X_c X_c) (tptp.plus_plus X_c) (tptp.hAPP X_b X_c F A_2)) (tptp.hAPP _let_1 X_c _let_2 F_2)))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (tptp.comm_monoid_add X_c) (forall ((G $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun _let_1 X_c) (tptp.big_co1399186613setsum X_b X_c) G))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (=> (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_3))) (= (tptp.hAPP _let_1 X_c _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_3)) (tptp.hAPP X_c X_c (tptp.hAPP X_c (tptp.fun X_c X_c) (tptp.plus_plus X_c) (tptp.hAPP X_b X_c G X_1)) (tptp.hAPP _let_1 X_c _let_2 A_3)))))))))) (forall ((X_b $$unsorted)) (=> (tptp.ring X_b) (forall ((A_2 $$unsorted) (E $$unsorted) (Ca $$unsorted) (Ba $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.fun X_b X_b))) (let ((_let_2 (tptp.times_times X_b))) (let ((_let_3 (tptp.plus_plus X_b))) (= (= (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_3 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_2 A_2) E)) Ca) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_3 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_2 Ba) E)) D)) (= (tptp.ti X_b Ca) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_3 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_2 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 (tptp.minus_minus X_b) Ba) A_2)) E)) D))))))))) (forall ((X_b $$unsorted)) (=> (tptp.ring X_b) (forall ((A_2 $$unsorted) (E $$unsorted) (Ca $$unsorted) (Ba $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.fun X_b X_b))) (let ((_let_2 (tptp.times_times X_b))) (let ((_let_3 (tptp.plus_plus X_b))) (= (= (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_3 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_2 A_2) E)) Ca) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_3 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_2 Ba) E)) D)) (= (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_3 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_2 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 (tptp.minus_minus X_b) A_2) Ba)) E)) Ca) (tptp.ti X_b D))))))))) (forall ((X_a $$unsorted)) (=> (tptp.group_add X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.plus_plus X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.minus_minus X_a) A_1) B)) B) (tptp.ti X_a A_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.group_add X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.minus_minus X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.plus_plus X_a) A_1) B)) B) (tptp.ti X_a A_1)))))) (forall ((X_b $$unsorted)) (=> (tptp.semiri456707255roduct X_b) (forall ((W_1 $$unsorted) (Y_2 $$unsorted) (X_1 $$unsorted) (Z_2 $$unsorted)) (let ((_let_1 (tptp.times_times X_b))) (let ((_let_2 (tptp.fun X_b X_b))) (let ((_let_3 (tptp.hAPP X_b _let_2 _let_1 X_1))) (let ((_let_4 (tptp.hAPP X_b _let_2 _let_1 W_1))) (let ((_let_5 (tptp.plus_plus X_b))) (= (= (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_2 _let_5 (tptp.hAPP X_b X_b _let_4 Y_2)) (tptp.hAPP X_b X_b _let_3 Z_2)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_2 _let_5 (tptp.hAPP X_b X_b _let_4 Z_2)) (tptp.hAPP X_b X_b _let_3 Y_2))) (or (= (tptp.ti X_b W_1) (tptp.ti X_b X_1)) (= (tptp.ti X_b Y_2) (tptp.ti X_b Z_2)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring X_a) (forall ((A_1 $$unsorted) (E_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.times_times X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 A_1) E_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 B) E_1)) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) B)) E_1)) C)))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (M $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.times_times X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 A_1) M)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 B) M)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) B)) M)))))))) (forall ((X_a $$unsorted)) (=> (tptp.cancel_semigroup_add X_a) (forall ((B $$unsorted) (A_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (=> (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) A_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 C) A_1)) (= (tptp.ti X_a B) (tptp.ti X_a C)))))))) (forall ((X_a $$unsorted)) (=> (tptp.cancel146912293up_add X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1))) (=> (= (tptp.hAPP X_a X_a _let_1 B) (tptp.hAPP X_a X_a _let_1 C)) (= (tptp.ti X_a B) (tptp.ti X_a C))))))) (forall ((X_a $$unsorted)) (=> (tptp.cancel_semigroup_add X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1))) (=> (= (tptp.hAPP X_a X_a _let_1 B) (tptp.hAPP X_a X_a _let_1 C)) (= (tptp.ti X_a B) (tptp.ti X_a C))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted) (D_1 $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 A_1))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 B)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 C) D_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) D_1))))))))) (forall ((X_b $$unsorted)) (=> (tptp.cancel_semigroup_add X_b) (forall ((Ba $$unsorted) (A_2 $$unsorted) (Ca $$unsorted)) (let ((_let_1 (tptp.plus_plus X_b))) (let ((_let_2 (tptp.fun X_b X_b))) (= (= (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_2 _let_1 Ba) A_2) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_2 _let_1 Ca) A_2)) (= (tptp.ti X_b Ba) (tptp.ti X_b Ca)))))))) (forall ((X_b $$unsorted)) (=> (tptp.cancel_semigroup_add X_b) (forall ((A_2 $$unsorted) (Ba $$unsorted) (Ca $$unsorted)) (let ((_let_1 (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.plus_plus X_b) A_2))) (= (= (tptp.hAPP X_b X_b _let_1 Ba) (tptp.hAPP X_b X_b _let_1 Ca)) (= (tptp.ti X_b Ba) (tptp.ti X_b Ca))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 A_1))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 B)) C) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 C)) B)))))))) (forall ((X_a $$unsorted)) (=> (tptp.ab_semigroup_add X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 A_1))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 B)) C) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) C))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 A_1))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 B)) C) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) C))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (C $$unsorted) (D_1 $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 A_1))) (= (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 C) D_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 C)) D_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (C $$unsorted) (D_1 $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 A_1))) (let ((_let_4 (tptp.hAPP X_a _let_2 _let_1 C))) (= (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a _let_4 D_1)) (tptp.hAPP X_a X_a _let_4 (tptp.hAPP X_a X_a _let_3 D_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 C) A_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((Lx $$unsorted) (Ly $$unsorted) (Rx $$unsorted) (Ry $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 Lx))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 Ly)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Rx) Ry)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 Rx)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Ly) Ry))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((Lx $$unsorted) (Ly $$unsorted) (Rx $$unsorted) (Ry $$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 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Lx) Ly)))) (let ((_let_4 (tptp.hAPP X_a _let_2 _let_1 Rx))) (= (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a _let_4 Ry)) (tptp.hAPP X_a X_a _let_4 (tptp.hAPP X_a X_a _let_3 Ry)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((Lx $$unsorted) (Ly $$unsorted) (Rx $$unsorted) (Ry $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Rx) Ry))) (let ((_let_4 (tptp.hAPP X_a _let_2 _let_1 Lx))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_4 Ly)) _let_3) (tptp.hAPP X_a X_a _let_4 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Ly) _let_3)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((Lx $$unsorted) (Ly $$unsorted) (Rx $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 Lx))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 Ly)) Rx) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 Rx)) Ly)))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((Lx $$unsorted) (Ly $$unsorted) (Rx $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 Lx))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 Ly)) Rx) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Ly) Rx))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ab_semigroup_mult X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 A_1))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 B)) C) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) C))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((Lx $$unsorted) (Rx $$unsorted) (Ry $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 Lx))) (= (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Rx) Ry)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 Rx)) Ry)))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((Lx $$unsorted) (Rx $$unsorted) (Ry $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 Lx))) (let ((_let_4 (tptp.hAPP X_a _let_2 _let_1 Rx))) (= (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a _let_4 Ry)) (tptp.hAPP X_a X_a _let_4 (tptp.hAPP X_a X_a _let_3 Ry)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) B) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) A_1))))))) (forall ((X_b $$unsorted)) (=> (tptp.ab_group_add X_b) (forall ((A_2 $$unsorted) (Ba $$unsorted) (Ca $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.minus_minus X_b))) (let ((_let_2 (tptp.fun X_b X_b))) (=> (= (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_2 _let_1 A_2) Ba) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_2 _let_1 Ca) D)) (= (= (tptp.ti X_b A_2) (tptp.ti X_b Ba)) (= (tptp.ti X_b Ca) (tptp.ti X_b D))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.times_times X_a) X))) (let ((_let_3 (tptp.plus_plus X_a))) (= (tptp.hAPP X_a X_a _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 Y) Z)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 (tptp.hAPP X_a X_a _let_2 Y)) (tptp.hAPP X_a X_a _let_2 Z))))))))) (forall ((X_b $$unsorted)) (=> (tptp.semiri456707255roduct X_b) (forall ((Ca $$unsorted) (D $$unsorted) (A_2 $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.times_times X_b))) (let ((_let_2 (tptp.fun X_b X_b))) (let ((_let_3 (tptp.hAPP X_b _let_2 _let_1 Ba))) (let ((_let_4 (tptp.hAPP X_b _let_2 _let_1 A_2))) (let ((_let_5 (tptp.plus_plus X_b))) (= (and (not (= (tptp.ti X_b A_2) (tptp.ti X_b Ba))) (not (= (tptp.ti X_b Ca) (tptp.ti X_b D)))) (not (= (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_2 _let_5 (tptp.hAPP X_b X_b _let_4 Ca)) (tptp.hAPP X_b X_b _let_3 D)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_2 _let_5 (tptp.hAPP X_b X_b _let_4 D)) (tptp.hAPP X_b X_b _let_3 Ca))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.plus_plus X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 A_1) B)) C) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) C))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.plus_plus X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 A_1) B)) C) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) C))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (tptp.comm_monoid_mult X_c) (forall ((F $$unsorted) (G $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.big_co302546470etprod X_b 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 X_c))) (=> (= (tptp.ti _let_2 A_3) (tptp.ti _let_2 B_2)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_2) B_2)) (= (tptp.hAPP X_b X_c F X_2) (tptp.hAPP X_b X_c G X_2))))) (= (tptp.hAPP _let_2 X_c (tptp.hAPP _let_4 _let_3 _let_1 F) A_3) (tptp.hAPP _let_2 X_c (tptp.hAPP _let_4 _let_3 _let_1 G) B_2))))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (tptp.comm_monoid_mult X_c) (forall ((H $$unsorted) (G $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.big_co302546470etprod X_b X_c))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun _let_2 X_c))) (let ((_let_4 (tptp.fun X_b X_c))) (=> (= (tptp.ti _let_2 A_3) (tptp.ti _let_2 B_2)) (=> (forall ((X_2 $$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_2)) (= (tptp.hAPP X_b X_c H X_2) (tptp.hAPP X_b X_c G X_2))))) (= (tptp.hAPP _let_2 X_c (tptp.hAPP _let_4 _let_3 _let_1 H) A_3) (tptp.hAPP _let_2 X_c (tptp.hAPP _let_4 _let_3 _let_1 G) B_2))))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (tptp.comm_monoid_add X_c) (forall ((F $$unsorted) (G $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.big_co1399186613setsum X_b X_c))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun _let_2 X_c))) (let ((_let_4 (tptp.fun X_b X_c))) (=> (forall ((X_2 $$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_3)) (= (tptp.hAPP X_b X_c F X_2) (tptp.hAPP X_b X_c G X_2))))) (= (tptp.hAPP _let_2 X_c (tptp.hAPP _let_4 _let_3 _let_1 F) A_3) (tptp.hAPP _let_2 X_c (tptp.hAPP _let_4 _let_3 _let_1 G) A_3)))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (tptp.comm_monoid_add X_c) (forall ((F $$unsorted) (G $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.big_co1399186613setsum X_b 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 X_c))) (=> (= (tptp.ti _let_2 A_3) (tptp.ti _let_2 B_2)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_2) B_2)) (= (tptp.hAPP X_b X_c F X_2) (tptp.hAPP X_b X_c G X_2))))) (= (tptp.hAPP _let_2 X_c (tptp.hAPP _let_4 _let_3 _let_1 F) A_3) (tptp.hAPP _let_2 X_c (tptp.hAPP _let_4 _let_3 _let_1 G) B_2))))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (tptp.comm_monoid_add X_c) (forall ((H $$unsorted) (G $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.big_co1399186613setsum X_b X_c))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun _let_2 X_c))) (let ((_let_4 (tptp.fun X_b X_c))) (=> (= (tptp.ti _let_2 A_3) (tptp.ti _let_2 B_2)) (=> (forall ((X_2 $$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_2)) (= (tptp.hAPP X_b X_c H X_2) (tptp.hAPP X_b X_c G X_2))))) (= (tptp.hAPP _let_2 X_c (tptp.hAPP _let_4 _let_3 _let_1 H) A_3) (tptp.hAPP _let_2 X_c (tptp.hAPP _let_4 _let_3 _let_1 G) B_2))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.order X_b) (forall ((K_1 $$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_1 (tptp.hAPP X_b _let_2 (tptp.insert X_b) K_1) (tptp.bot_bot _let_1)))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.minus_minus _let_1) _let_3) (tptp.hAPP X_b _let_1 (tptp.ord_lessThan X_b) K_1)) _let_3))))))) (forall ((X_b $$unsorted) (F $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP (tptp.fun X_b tptp.nat) (tptp.fun _let_1 tptp.nat) (tptp.big_co1399186613setsum X_b tptp.nat) F))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) B_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) B_2) A_3)) (= (tptp.hAPP _let_1 tptp.nat _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) A_3) B_2)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) (tptp.hAPP _let_1 tptp.nat _let_2 A_3)) (tptp.hAPP _let_1 tptp.nat _let_2 B_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 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.ord_less_eq _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 A_3) B_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 B_2) A_3)) (= (tptp.ti _let_1 A_3) (tptp.ti _let_1 B_2)))))))) (forall ((X_b $$unsorted) (Ca $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP X_b _let_2 (tptp.member X_b) Ca))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_3) B_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 A_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 B_2)))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) (tptp.bot_bot _let_1)) A_3)))) (forall ((X_b $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun _let_1 _let_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 _let_1) (tptp.hAPP _let_2 _let_2 (tptp.collect _let_1) (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_3 _let_3 (tptp.combc _let_1 _let_1 tptp.bool) (tptp.ord_less_eq _let_1)) A_3))))))))) (forall ((X_b $$unsorted) (R_1 $$unsorted) (S_1 $$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_1))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 R_1) S_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$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 $$unsorted)) (=> (tptp.order X_a) (forall ((C $$unsorted) (B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B) A_1)) (=> (= (tptp.ti X_a B) (tptp.ti X_a C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 C) A_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ord X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) A_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B)) (=> (= (tptp.ti X_a B) (tptp.ti X_a C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 C)))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) C))) (=> (= (tptp.ti X_a A_1) (tptp.ti X_a B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.ord X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (= (tptp.ti X_a A_1) (tptp.ti X_a B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) C))))))))) (forall ((X_b $$unsorted)) (=> (tptp.order X_b) (forall ((Y_2 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 Y_2) X_1)) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 X_1) Y_2)) (= (tptp.ti X_b X_1) (tptp.ti X_b Y_2))))))))) (forall ((X_b $$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 $$unsorted) (Y_2 $$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_2)) (and (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 X_1) Y_2)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 Y_2) X_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (or (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X) Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X)))))))) (forall ((X_b $$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 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.ord_less_eq _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (=> (= (tptp.ti _let_1 A_3) (tptp.ti _let_1 B_2)) (not (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 A_3) B_2)) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 B_2) A_3)))))))))) (forall ((X_b $$unsorted) (C_1 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.ord_less_eq _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.hAPP _let_1 _let_3 _let_2 A_3))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_4 B_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 B_2) C_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_4 C_1))))))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP X_b _let_2 (tptp.member X_b) X_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_3) B_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 A_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 B_2)))))))) (forall ((X_b $$unsorted) (B_2 $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP X_b _let_2 (tptp.member X_b) X_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 A_3)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_3) B_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 B_2)))))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP X_b _let_2 (tptp.member X_b) X_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_3) B_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 A_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 B_2)))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (= (tptp.ti _let_1 A_3) (tptp.ti _let_1 B_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) B_2) A_3))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (= (tptp.ti _let_1 A_3) (tptp.ti _let_1 B_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) A_3) B_2))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_2 $$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_3) (tptp.ti _let_1 B_2)) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 A_3) B_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 B_2) A_3)))))))) (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.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) A_3) A_3)))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (Pa $$unsorted) (Q_3 $$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) Pa) Q_3)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa X_1)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool Q_3 X_1)))))) (forall ((X_b $$unsorted) (Q_3 $$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_3)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool Q_3 X_1)))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.ord_lessThan X_b))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) (tptp.hAPP X_b _let_1 _let_2 X_1)) (tptp.hAPP X_b _let_1 _let_2 Y_2))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less_eq X_b) X_1) Y_2)))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.ord_lessThan X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (= (= (tptp.hAPP X_b _let_2 _let_1 X_1) (tptp.hAPP X_b _let_2 _let_1 Y_2)) (= (tptp.ti X_b X_1) (tptp.ti X_b Y_2)))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere236663937imp_le X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) C))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 A_1)) (tptp.hAPP X_a X_a _let_3 B))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere236663937imp_le X_a) (forall ((A_1 $$unsorted) (C $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.plus_plus X_a))) (let ((_let_4 (tptp.fun X_a X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 B) C))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere779506340up_add X_a) (forall ((C $$unsorted) (D_1 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less_eq X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 C) D_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) D_1)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere779506340up_add X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) C))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 A_1)) (tptp.hAPP X_a X_a _let_1 B)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere779506340up_add X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less_eq X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 A_1) B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) C))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.ordere236663937imp_le X_b) (forall ((Ca $$unsorted) (A_2 $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.plus_plus X_b) Ca))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 (tptp.hAPP X_b X_b _let_3 A_2)) (tptp.hAPP X_b X_b _let_3 Ba))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 A_2) Ba))))))))) (forall ((X_b $$unsorted)) (=> (tptp.ordere236663937imp_le X_b) (forall ((A_2 $$unsorted) (Ca $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.plus_plus X_b))) (let ((_let_4 (tptp.fun X_b X_b))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_4 _let_3 A_2) Ca)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_4 _let_3 Ba) Ca))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 A_2) Ba)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.bot X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.bot_bot X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) A_1) _let_1)) (= (tptp.ti X_a A_1) _let_1)))))) (forall ((X_b $$unsorted)) (=> (tptp.bot X_b) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.bot_bot X_b))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) A_2) _let_1)) (= (tptp.ti X_b A_2) _let_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.bot X_a) (forall ((A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.bot_bot X_a)) A_1))))) (forall ((X_b $$unsorted)) (=> (tptp.ordered_ab_group_add X_b) (forall ((A_2 $$unsorted) (Ba $$unsorted) (Ca $$unsorted) (D $$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_2) Ba) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_4 _let_3 Ca) D)) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 A_2) Ba)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 Ca) D))))))))))) (forall ((X_b $$unsorted) (A_3 $$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_3) _let_2)) (= (tptp.ti _let_1 A_3) _let_2))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.finite_finite_1 X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) A_3) B_2)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 B_2)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 A_3))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_2 $$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_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) A_3) B_2)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 A_3))))))) (forall ((X_b $$unsorted) (A_2 $$unsorted) (C_1 $$unsorted) (D_2 $$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_2))) (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_1) D_2)) (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_1)) (tptp.hAPP _let_1 _let_1 _let_2 D_2))))))))) (forall ((X_b $$unsorted) (Ba $$unsorted) (A_3 $$unsorted) (B_2 $$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_3))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B_2)) (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_2))))))) (forall ((X_b $$unsorted) (B_2 $$unsorted) (X_1 $$unsorted) (A_3 $$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_3))) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_2 (tptp.member X_b) X_1) A_3))) (= (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_2))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 B_2)))))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (B_2 $$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_3)) B_2)) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_3 (tptp.member X_b) X_1) B_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 A_3) B_2)))))))) (forall ((X_b $$unsorted) (B_2 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) B_2) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_2) B_2))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (A_3 $$unsorted) (B_2 $$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_3) B_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) (tptp.hAPP _let_2 _let_1 _let_3 A_3)) (tptp.hAPP _let_2 _let_1 _let_3 B_2)))))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (B_2 $$unsorted) (F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) B_2) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun _let_2 _let_1) (tptp.image X_c X_b) F) A_3))) (exists ((AA $$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_3)) (= (tptp.ti _let_1 B_2) (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_b $$unsorted) (C_1 $$unsorted) (A_3 $$unsorted) (B_2 $$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_3) B_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_5 _let_4 B_2) C_1)) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 B_2) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 C_1) A_3)) (tptp.ti _let_1 A_3)))))))))) (forall ((X_b $$unsorted) (D_2 $$unsorted) (B_2 $$unsorted) (A_3 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.minus_minus _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.ord_less_eq _let_1))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_5 _let_4 A_3) C_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_5 _let_4 D_2) B_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_5 _let_4 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 A_3) B_2)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 C_1) D_2))))))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_2 $$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_3) B_2)) A_3)))) (forall ((X_b $$unsorted) (Ts $$unsorted) (Ga $$unsorted) (Ts_1 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.hoare_2118899576triple X_b) tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP _let_1 _let_2 (tptp.hoare_1301688828derivs 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 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.hoare_2118899576triple X_b) tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) Ts) Ga)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.hoare_1301688828derivs X_b) Ga) Ts)))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (X_1 $$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_3))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) A_3) _let_3)) (or (= _let_4 _let_2) (= _let_4 _let_3)))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (B_2 $$unsorted) (F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) B_2) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun _let_2 _let_1) (tptp.image X_b X_c) F) A_3))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_c) B_2))))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (F $$unsorted) (A_3 $$unsorted) (B_2 $$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_3)) (tptp.hAPP _let_1 _let_2 _let_3 B_2))) (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_3) B_2)))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (B_2 $$unsorted) (A_3 $$unsorted) (F $$unsorted) (Z_2 $$unsorted) (G $$unsorted) (F_2 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.hAPP _let_1 X_b F_2 A_3))) (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_2) G) F_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_c) A_3)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) B_2) A_3)) (= (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_3 F (tptp.hAPP _let_1 X_b F_2 B_2)) _let_2) _let_2)))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.ordered_ring X_b) (forall ((A_2 $$unsorted) (E $$unsorted) (Ca $$unsorted) (Ba $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.fun X_b X_b))) (let ((_let_2 (tptp.times_times X_b))) (let ((_let_3 (tptp.plus_plus X_b))) (let ((_let_4 (tptp.ord_less_eq X_b))) (let ((_let_5 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_5 _let_4 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_3 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_2 A_2) E)) Ca)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_3 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_2 Ba) E)) D))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_5 _let_4 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_3 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_2 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 (tptp.minus_minus X_b) A_2) Ba)) E)) Ca)) D))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.ordered_ring X_b) (forall ((A_2 $$unsorted) (E $$unsorted) (Ca $$unsorted) (Ba $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.fun X_b X_b))) (let ((_let_2 (tptp.times_times X_b))) (let ((_let_3 (tptp.plus_plus X_b))) (let ((_let_4 (tptp.ord_less_eq X_b))) (let ((_let_5 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_5 _let_4 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_3 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_2 A_2) E)) Ca)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_3 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_2 Ba) E)) D))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_5 _let_4 Ca) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_3 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_2 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 (tptp.minus_minus X_b) Ba) A_2)) E)) D)))))))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (X_1 $$unsorted) (B_2 $$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_3) (tptp.hAPP _let_1 _let_1 _let_3 (tptp.bot_bot _let_1)))) B_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_5 (tptp.member X_b) X_1) A_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_5 _let_4 A_3) (tptp.hAPP _let_1 _let_1 _let_3 B_2))))))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (X_1 $$unsorted) (B_2 $$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_3))) (let ((_let_5 (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_3 (tptp.member X_b) X_1) A_3)))) (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_2))) (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_3) (tptp.hAPP _let_1 _let_1 _let_7 (tptp.bot_bot _let_1)))) B_2))) (=> (not _let_5) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_4 B_2))))))))))))) (forall ((X_b $$unsorted) (B_2 $$unsorted) (A_3 $$unsorted) (F $$unsorted) (F_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP _let_1 X_b F_2 A_3))) (let ((_let_3 (tptp.fun X_b X_b))) (let ((_let_4 (tptp.fun _let_1 X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP (tptp.fun X_b _let_3) (tptp.fun _let_4 tptp.bool) (tptp.finite2073411215e_idem X_b) F) F_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (=> (not (= (tptp.ti _let_1 B_2) (tptp.bot_bot _let_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) B_2) A_3)) (= (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_3 F (tptp.hAPP _let_1 X_b F_2 B_2)) _let_2) _let_2)))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (tptp.ab_group_add X_c) (forall ((F $$unsorted) (B_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun _let_1 X_c) (tptp.big_co1399186613setsum X_b X_c) F))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) B_2) A_3)) (= (tptp.hAPP _let_1 X_c _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) A_3) B_2)) (tptp.hAPP X_c X_c (tptp.hAPP X_c (tptp.fun X_c X_c) (tptp.minus_minus X_c) (tptp.hAPP _let_1 X_c _let_2 A_3)) (tptp.hAPP _let_1 X_c _let_2 B_2)))))))))) (forall ((X_b $$unsorted) (Pa $$unsorted) (A_3 $$unsorted) (F_2 $$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)) (=> (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_2) A_3)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa (tptp.bot_bot _let_1))) (=> (forall ((A_5 $$unsorted) (F_3 $$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_5))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) F_3)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_3)) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 F_3))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa F_3)) (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_5) F_3)))))))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa F_2)))))))) (forall ((X_b $$unsorted) (B_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (forall ((X_2 $$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_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B_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) A_3) B_2))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) B_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) B_2) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun _let_2 _let_1) (tptp.image X_c X_b) F) A_3))) (exists ((C_2 $$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_3)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_c) C_2)) (= (tptp.ti _let_1 B_2) (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 ((X_b $$unsorted) (X_c $$unsorted)) (=> (and (tptp.comm_monoid_add X_c) (tptp.ordere779506340up_add X_c)) (forall ((F $$unsorted) (G $$unsorted) (K_2 $$unsorted)) (let ((_let_1 (tptp.big_co1399186613setsum X_b X_c))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun _let_2 X_c))) (let ((_let_4 (tptp.fun X_b X_c))) (=> (forall ((I_2 $$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) I_2) K_2)) (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 I_2)) (tptp.hAPP X_b X_c G I_2)))))) (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 _let_2 X_c (tptp.hAPP _let_4 _let_3 _let_1 F) K_2)) (tptp.hAPP _let_2 X_c (tptp.hAPP _let_4 _let_3 _let_1 G) K_2))))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (B_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (forall ((X_2 $$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_3)) (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_2)))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun _let_2 _let_1) (tptp.image X_b X_c) F) A_3)) B_2)))))) (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 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less_eq X_c) (tptp.hAPP X_b X_c F X_2)) (tptp.hAPP X_b X_c G X_2)))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) F) G))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (Ba $$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_3))) (let ((_let_6 (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_4 (tptp.ord_less_eq _let_1) A_3) _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_3) _let_3))))))))))))) (forall ((N $$unsorted) (Q_3 $$unsorted) (Pa $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.hAPP tptp.nat _let_1 (tptp.ord_lessThan tptp.nat) N))) (let ((_let_3 (tptp.minus_minus tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.nat))) (let ((_let_5 (tptp.fun tptp.nat _let_4))) (let ((_let_6 (tptp.big_co1399186613setsum tptp.nat tptp.nat))) (let ((_let_7 (tptp.fun _let_1 tptp.nat))) (=> (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat Q_3 X_2)) (tptp.hAPP tptp.nat tptp.nat Pa X_2)))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_4 _let_3 (tptp.hAPP _let_1 tptp.nat (tptp.hAPP _let_4 _let_7 _let_6 Pa) _let_2)) (tptp.hAPP _let_1 tptp.nat (tptp.hAPP _let_4 _let_7 _let_6 Q_3) _let_2)) (tptp.hAPP _let_1 tptp.nat (tptp.hAPP _let_4 _let_7 _let_6 (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_5 (tptp.fun _let_4 _let_4) (tptp.combs tptp.nat tptp.nat tptp.nat) (tptp.hAPP _let_4 _let_5 (tptp.hAPP _let_5 (tptp.fun _let_4 _let_5) (tptp.combb tptp.nat _let_4 tptp.nat) _let_3) Pa)) Q_3)) _let_2))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((B_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun _let_1 X_b) (tptp.finite_fold1 X_b) (tptp.ord_min X_b)))) (=> (not (= (tptp.ti _let_1 A_3) (tptp.bot_bot _let_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) A_3) B_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) B_2)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less_eq X_b) (tptp.hAPP _let_1 X_b _let_2 B_2)) (tptp.hAPP _let_1 X_b _let_2 A_3))))))))))) (forall ((X_b $$unsorted) (Q_3 $$unsorted) (Pa $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa X_2)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool Q_3 X_2)))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) Pa) Q_3))))) (forall ((X_b $$unsorted) (Q_3 $$unsorted) (Pa $$unsorted)) (let ((_let_1 (tptp.collect X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa X_2)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool Q_3 X_2)))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) (tptp.hAPP _let_2 _let_2 _let_1 Pa)) (tptp.hAPP _let_2 _let_2 _let_1 Q_3))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((M_3 $$unsorted) (N_3 $$unsorted)) (let ((_let_1 (tptp.big_linorder_Min 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) M_3) N_3)) (=> (not (= (tptp.ti _let_2 M_3) (tptp.bot_bot _let_2))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_b) N_3)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 (tptp.ord_less_eq X_b) (tptp.hAPP _let_2 X_b _let_1 N_3)) (tptp.hAPP _let_2 X_b _let_1 M_3))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((M_3 $$unsorted) (N_3 $$unsorted)) (let ((_let_1 (tptp.big_linorder_Max X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) M_3) N_3)) (=> (not (= (tptp.ti _let_2 M_3) (tptp.bot_bot _let_2))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_b) N_3)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 (tptp.ord_less_eq X_b) (tptp.hAPP _let_2 X_b _let_1 M_3)) (tptp.hAPP _let_2 X_b _let_1 N_3))))))))))) (forall ((K_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 tptp.nat) (tptp.hAPP tptp.nat _let_1 (tptp.ord_lessThan tptp.nat) K_1))))) (forall ((K_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 tptp.nat) (tptp.hAPP _let_1 _let_1 (tptp.collect tptp.nat) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc tptp.nat tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat)) K_1))))))) (forall ((N_3 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat tptp.bool) tptp.bool (tptp.finite_finite_1 tptp.nat) N_3)) (exists ((M_2 $$unsorted)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.nat (tptp.fun _let_1 tptp.bool) (tptp.member tptp.nat) X_2) N_3)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) X_2) M_2)))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP _let_1 X_b (tptp.big_linorder_Min X_b) A_3))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_1) A_3)) (= (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.ord_min X_b) X_1) _let_2) _let_2)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_min X_a) X) X) (tptp.ti X_a X))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.ord_min X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 X))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 Y)) Z) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Y) Z))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.ord_min X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 A_1))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 B)) C) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) C))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.ord_min X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 X))) (let ((_let_4 (tptp.hAPP X_a _let_2 _let_1 Y))) (= (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a _let_4 Z)) (tptp.hAPP X_a X_a _let_4 (tptp.hAPP X_a X_a _let_3 Z)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((B $$unsorted) (A_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.ord_min X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 B))) (let ((_let_4 (tptp.hAPP X_a _let_2 _let_1 A_1))) (= (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a _let_4 C)) (tptp.hAPP X_a X_a _let_4 (tptp.hAPP X_a X_a _let_3 C)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_min X_a) X))) (let ((_let_2 (tptp.hAPP X_a X_a _let_1 Y))) (= (tptp.hAPP X_a X_a _let_1 _let_2) _let_2)))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_min X_a) A_1))) (let ((_let_2 (tptp.hAPP X_a X_a _let_1 B))) (= (tptp.hAPP X_a X_a _let_1 _let_2) _let_2)))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_min X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 X) Y) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Y) X))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_min X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) B) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) A_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_min X_a) A_1) A_1) (tptp.ti X_a A_1))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted) (Y_2 $$unsorted) (Z_2 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.ord_min X_b) X_1) Y_2)) Z_2)) (or (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 X_1) Z_2)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 Y_2) Z_2))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_min X_a) A_1) B))) (not (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_1)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((B $$unsorted) (D_1 $$unsorted) (A_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.ord_min X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less_eq X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 A_1) C)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 B) D_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) B)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 C) D_1)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((Z $$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.ord_min X_a) Y) Z))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((B $$unsorted) (X $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_min X_a) A_1) B))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((Y $$unsorted) (X $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) Y) X)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_min X_a) X) Y) (tptp.ti X_a Y)))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X) Y)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_min X_a) X) Y) (tptp.ti X_a X)))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B) X)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_min X_a) A_1) B)) X)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((B $$unsorted) (A_1 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) X)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_min X_a) A_1) B)) X)))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted) (Y_2 $$unsorted) (Z_2 $$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.ord_min X_b) Y_2) Z_2))) (and (tptp.hBOOL (tptp.hAPP X_b tptp.bool _let_1 Y_2)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool _let_1 Z_2)))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) X_1) Y_2)) (= (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.ord_min X_b) X_1) Y_2) (tptp.ti X_b X_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_min X_a) X) Y)) Y))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_min X_a) X) Y)) X))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere236663937imp_le X_a) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_min X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 X) Y)) Z) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 X) Z)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Y) Z))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ab_group_add X_a) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.minus_minus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_min X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 X) Y)) Z) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 X) Z)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Y) Z))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (= (tptp.hAPP _let_1 X_b (tptp.big_linorder_Min X_b) A_3) (tptp.hAPP _let_1 X_b (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun _let_1 X_b) (tptp.finite_fold1 X_b) (tptp.ord_min X_b)) A_3))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder 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.ord_min X_b))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.big_linorder_Min X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (=> (not (= (tptp.ti _let_2 A_3) (tptp.bot_bot _let_2))) (= (tptp.hAPP _let_2 X_b _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_b (tptp.fun _let_2 _let_2) (tptp.insert X_b) X_1) A_3)) (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.ord_min X_b) X_1) (tptp.hAPP _let_2 X_b _let_1 A_3)))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.big_linorder_Min 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_3)) (=> (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_3))) (=> (not (= (tptp.ti _let_2 A_3) (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_3)) (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.ord_min X_b) X_1) (tptp.hAPP _let_2 X_b _let_1 A_3))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((B_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.big_linorder_Min X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.hAPP _let_2 X_b _let_1 A_3))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (=> (not (= (tptp.ti _let_2 B_2) (tptp.bot_bot _let_2))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) B_2) A_3)) (= (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.ord_min X_b) (tptp.hAPP _let_2 X_b _let_1 B_2)) _let_3) _let_3)))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted) (A_3 $$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_3)) (=> (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_3))) (= (tptp.hAPP _let_1 X_b (tptp.big_linorder_Min 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_3)) (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.ord_min X_b)) X_1) A_3))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((A_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (= (tptp.hAPP _let_1 X_b (tptp.big_linorder_Min X_b) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_2) A_3)) (tptp.hAPP _let_1 X_b (tptp.hAPP X_b _let_2 (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun X_b _let_2) (tptp.finite_fold X_b X_b) (tptp.ord_min X_b)) A_2) A_3)))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.bot_bot _let_1))) (let ((_let_3 (tptp.fun _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_3) (tptp.hAPP _let_1 _let_1 _let_4 _let_2)))) (let ((_let_6 (tptp.big_linorder_Min X_b))) (let ((_let_7 (tptp.hAPP _let_1 X_b _let_6 (tptp.hAPP _let_1 _let_1 _let_4 A_3)))) (let ((_let_8 (= _let_5 _let_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (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.ord_min X_b) X_1) (tptp.hAPP _let_1 X_b _let_6 _let_5))))))))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.bot_bot _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 (tptp.minus_minus _let_1) A_3) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_3 (tptp.insert X_b) X_1) _let_2)))) (let ((_let_5 (tptp.big_linorder_Min X_b))) (let ((_let_6 (tptp.hAPP _let_1 X_b _let_5 A_3))) (let ((_let_7 (= _let_4 _let_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_1) A_3)) (and (=> _let_7 (= _let_6 (tptp.ti X_b X_1))) (=> (not _let_7) (= _let_6 (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.ord_min X_b) X_1) (tptp.hAPP _let_1 X_b _let_5 _let_4))))))))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted) (A_3 $$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)) (=> (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_3)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less_eq X_b) X_1) (tptp.hAPP _let_1 X_b (tptp.big_linorder_Max X_b) A_3))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_1) A_3)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less_eq X_b) (tptp.hAPP _let_1 X_b (tptp.big_linorder_Min X_b) A_3)) X_1)))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (=> (not (= (tptp.ti _let_1 A_3) (tptp.bot_bot _let_1))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) (tptp.hAPP _let_1 X_b (tptp.big_linorder_Max X_b) A_3)) A_3)))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (=> (not (= (tptp.ti _let_1 A_3) (tptp.bot_bot _let_1))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) (tptp.hAPP _let_1 X_b (tptp.big_linorder_Min X_b) A_3)) A_3)))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (tptp.hAPP _let_1 X_b (tptp.big_linorder_Min X_b) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_1) (tptp.bot_bot _let_1))) (tptp.ti X_b X_1)))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (tptp.hAPP _let_1 X_b (tptp.big_linorder_Max X_b) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_1) (tptp.bot_bot _let_1))) (tptp.ti X_b X_1)))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((Ba $$unsorted) (A_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.ord_min X_b))) (let ((_let_2 (tptp.fun X_b X_b))) (let ((_let_3 (tptp.fun X_b tptp.bool))) (let ((_let_4 (tptp.fun _let_3 X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_b (tptp.fun _let_3 tptp.bool) (tptp.member X_b) A_2) A_3)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_3 (tptp.ord_less_eq X_b) (tptp.hAPP _let_3 X_b (tptp.hAPP X_b _let_4 (tptp.hAPP (tptp.fun X_b _let_2) (tptp.fun X_b _let_4) (tptp.finite_fold X_b X_b) _let_1) Ba) A_3)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_2 _let_1 A_2) Ba)))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((Ba $$unsorted) (A_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.ord_min X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun _let_2 X_b))) (let ((_let_4 (tptp.fun X_b X_b))) (let ((_let_5 (tptp.hAPP X_b _let_3 (tptp.hAPP (tptp.fun X_b _let_4) (tptp.fun X_b _let_3) (tptp.finite_fold X_b X_b) _let_1) Ba))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (= (tptp.hAPP _let_2 X_b _let_5 (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_b (tptp.fun _let_2 _let_2) (tptp.insert X_b) A_2) A_3)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_4 _let_1 A_2) (tptp.hAPP _let_2 X_b _let_5 A_3)))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((A_2 $$unsorted) (A_3 $$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)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_2) A_3)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less_eq 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.ord_min X_b)) A_3)) A_2)))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (=> (not (= (tptp.ti _let_1 A_3) (tptp.bot_bot _let_1))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less_eq X_b) (tptp.hAPP _let_1 X_b (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun _let_1 X_b) (tptp.finite_fold1 X_b) (tptp.ord_min X_b)) A_3)) X_1)) (exists ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_2) A_3)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less_eq X_b) X_2) X_1)))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (=> (not (= (tptp.ti _let_1 A_3) (tptp.bot_bot _let_1))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less_eq X_b) X_1) (tptp.hAPP _let_1 X_b (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun _let_1 X_b) (tptp.finite_fold1 X_b) (tptp.ord_min X_b)) A_3))) (forall ((X_2 $$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_3)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less_eq X_b) X_1) X_2)))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((N_3 $$unsorted) (H $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.big_linorder_Min X_b))) (=> (forall ((X_2 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.ord_min X_b))) (let ((_let_2 (tptp.fun X_b X_b))) (= (tptp.hAPP X_b X_b H (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_2 _let_1 X_2) Y_1)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_2 _let_1 (tptp.hAPP X_b X_b H X_2)) (tptp.hAPP X_b X_b H Y_1)))))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) N_3)) (=> (not (= (tptp.ti _let_1 N_3) (tptp.bot_bot _let_1))) (= (tptp.hAPP X_b X_b H (tptp.hAPP _let_1 X_b _let_2 N_3)) (tptp.hAPP _let_1 X_b _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_b X_b) (tptp.fun _let_1 _let_1) (tptp.image X_b X_b) H) N_3))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (=> (not (= (tptp.ti _let_1 A_3) (tptp.bot_bot _let_1))) (=> (forall ((X_2 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.insert X_b))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.ord_min X_b) X_2) Y_1)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_3 _let_2 X_2) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_3 _let_2 Y_1) (tptp.bot_bot _let_1))))))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) (tptp.hAPP _let_1 X_b (tptp.big_linorder_Min X_b) A_3)) A_3))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((Ca $$unsorted) (Ba $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.ord_min X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun _let_2 X_b))) (let ((_let_4 (tptp.fun X_b X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (=> (forall ((X_2 $$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_3)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less_eq X_b) Ba) X_2))))) (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 Ba) Ca)) (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) Ca) A_3)))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (=> (forall ((Y_1 $$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) Y_1) A_3)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less_eq X_b) X_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) X_1) A_3)) (= (tptp.hAPP _let_1 X_b (tptp.big_linorder_Min X_b) A_3) (tptp.ti X_b X_1))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (=> (forall ((Y_1 $$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) Y_1) A_3)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less_eq X_b) Y_1) X_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_3)) (= (tptp.hAPP _let_1 X_b (tptp.big_linorder_Max X_b) A_3) (tptp.ti X_b X_1))))))))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.fun X_b (tptp.fun X_b tptp.bool)))) (=> (tptp.linorder X_b) (= (tptp.hAPP _let_1 (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.max X_b) (tptp.hAPP _let_1 _let_1 (tptp.combc X_b X_b tptp.bool) (tptp.ord_less_eq X_b))) (tptp.ord_min X_b))))) (forall ((U $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (let ((_let_3 (tptp.fun tptp.nat tptp.nat))) (=> (forall ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N_2) (tptp.hAPP tptp.nat tptp.nat F N_2)))) (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_a $$unsorted)) (=> (tptp.order X_a) (forall ((X $$unsorted) (Least $$unsorted)) (=> (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) Least) X_2))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_min X_a) X) Least) (tptp.ti X_a Least)))))) (forall ((X_a $$unsorted)) (=> (tptp.ord X_a) (forall ((X $$unsorted) (Least $$unsorted)) (=> (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) Least) X_2))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_min X_a) Least) X) (tptp.ti X_a Least)))))) (forall ((X_b $$unsorted)) (=> (tptp.ord X_b) (= (tptp.ord_min X_b) (tptp.hAPP (tptp.fun X_b (tptp.fun X_b tptp.bool)) (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.min X_b) (tptp.ord_less_eq X_b))))) (forall ((N $$unsorted) (K_1 $$unsorted) (M_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.minus_minus tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.nat))) (let ((_let_5 (tptp.hAPP tptp.nat _let_2 _let_1 K_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_5 M_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_5 N)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_4 _let_3 M_1) K_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_4 _let_3 N) K_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M_1) N))))))))))) (forall ((K $$unsorted) (L_1 $$unsorted) (I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.times_times tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.ord_less_eq tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 I) J)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 K) L_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 I) K)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 J) L_1)))))))))) (forall ((K $$unsorted) (I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) K))) (let ((_let_2 (tptp.ord_less_eq tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 I) J)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.nat tptp.nat _let_1 I)) (tptp.hAPP tptp.nat tptp.nat _let_1 J)))))))) (forall ((K $$unsorted) (I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.times_times tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.ord_less_eq tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 I) J)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 I) K)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 J) K))))))))) (forall ((M $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) M))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M) (tptp.hAPP tptp.nat tptp.nat _let_1 (tptp.hAPP tptp.nat tptp.nat _let_1 M)))))) (forall ((M $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) M) M)))) (forall ((N_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N_1) N_1))) (forall ((M $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 N_1) M)))))) (forall ((M $$unsorted) (N_1 $$unsorted)) (=> (= M N_1) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M) N_1)))) (forall ((K $$unsorted) (I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 I))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 J)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 J) K)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 K)))))))) (forall ((M $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) N_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 N_1) M)) (= M N_1)))))) (forall ((M $$unsorted) (K $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M) K)) N_1)) (not (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) N_1)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 K) N_1))))))))) (forall ((M $$unsorted) (K $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M) K)) N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) N_1)))))) (forall ((M $$unsorted) (K $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M) K)) N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 K) N_1)))))) (forall ((K $$unsorted) (L_1 $$unsorted) (I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.ord_less_eq tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 I) J)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 K) L_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 I) K)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 J) L_1)))))))))) (forall ((K $$unsorted) (I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.ord_less_eq tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 I) J)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 I) K)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 J) K))))))))) (forall ((M $$unsorted) (I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) I))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 J)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M) J)))))) (forall ((M $$unsorted) (I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) I))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 J)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) J) M)))))) (forall ((K_1 $$unsorted) (M_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) K_1))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 M_1)) (tptp.hAPP tptp.nat tptp.nat _let_3 N))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M_1) N))))))) (forall ((M_1 $$unsorted) (N $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M_1) N)) (exists ((K_3 $$unsorted)) (= N (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M_1) K_3))))) (forall ((N_1 $$unsorted) (M $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) N_1) M)))) (forall ((N_1 $$unsorted) (M $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M) N_1)))) (forall ((M $$unsorted) (I $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.ord_min tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.minus_minus tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 M) I)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 N_1) I)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M) N_1)) I)))))) (forall ((K $$unsorted) (M $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.nat _let_1 (tptp.times_times tptp.nat) K))) (let ((_let_3 (tptp.minus_minus tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 M) N_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat _let_2 M)) (tptp.hAPP tptp.nat tptp.nat _let_2 N_1))))))) (forall ((M $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) M) N_1)) N_1) M))) (forall ((N_1 $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) N_1) M)) N_1) M))) (forall ((I $$unsorted) (J $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.minus_minus tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat _let_1 _let_2 I))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.hAPP tptp.nat tptp.nat _let_3 J)) K) (tptp.hAPP tptp.nat tptp.nat _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) J) K))))))) (forall ((I $$unsorted) (J $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 I))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 J)) K) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 K)) J)))))) (forall ((M $$unsorted) (N_1 $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.times_times tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.minus_minus tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 M) N_1)) K) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M) K)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 N_1) K))))))) (forall ((K $$unsorted) (M $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 (tptp.plus_plus tptp.nat) K))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 M)) (tptp.hAPP tptp.nat tptp.nat _let_3 N_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M) N_1)))))) (forall ((M $$unsorted) (K $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.plus_plus tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 M) K)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 N_1) K)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M) N_1)))))) (forall ((M $$unsorted) (N_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) M) N_1)) M))) (forall ((I $$unsorted) (K $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.minus_minus tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K) J)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 I) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 J) K)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) I) K)) J)))))) (forall ((J_1 $$unsorted) (K_1 $$unsorted) (I_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.ord_less_eq tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) J_1) K_1)) I_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 J_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) I_1) K_1)))))))) (forall ((M $$unsorted) (K $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.ord_less_eq tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 K) N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 M) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) N_1) M)) K)))))))) (forall ((L_1 $$unsorted) (M $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) L_1))) (let ((_let_2 (tptp.ord_less_eq tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 M) N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.nat tptp.nat _let_1 N_1)) (tptp.hAPP tptp.nat tptp.nat _let_1 M)))))))) (forall ((L_1 $$unsorted) (M $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.ord_less_eq tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 M) N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M) L_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 N_1) L_1))))))))) (forall ((I $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) N_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) I) N_1)) (= (tptp.hAPP tptp.nat tptp.nat _let_1 (tptp.hAPP tptp.nat tptp.nat _let_1 I)) I)))) (forall ((N_1 $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N_1) M)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) N_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) M) N_1)) M)))) (forall ((I $$unsorted) (K $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) I))) (let ((_let_3 (tptp.minus_minus tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K) J)) (= (tptp.hAPP tptp.nat tptp.nat _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 J) K)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat _let_2 J)) K))))))) (forall ((I_1 $$unsorted) (K_1 $$unsorted) (J_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.ord_less_eq tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 K_1) J_1)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 I_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) J_1) K_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) I_1) K_1)) J_1)))))))) (forall ((N_1 $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N_1) M)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) M) N_1)) N_1) M)))) (forall ((K_1 $$unsorted) (I_1 $$unsorted) (J_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) I_1) J_1)) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) J_1) I_1) K_1) (= J_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) K_1) I_1)))))) (forall ((I $$unsorted) (K $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 (tptp.plus_plus tptp.nat) I))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K) J)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 J)) K) (tptp.hAPP tptp.nat tptp.nat _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 J) K)))))))) (forall ((I $$unsorted) (K $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.minus_minus tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K) J)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 J) K)) I) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 J) I)) K))))))) (forall ((I $$unsorted) (K $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.plus_plus tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K) J)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 J) I)) K) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 J) K)) I))))))) (forall ((N $$unsorted) (K_1 $$unsorted) (M_1 $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 M_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 N)) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M_1) K_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 N) K_1)) (= M_1 N)))))))) (forall ((N_1 $$unsorted) (K $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 M))) (let ((_let_4 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_4 M)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_4 N_1)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 K)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 N_1) K)) (tptp.hAPP tptp.nat tptp.nat _let_3 N_1))))))))) (forall ((U $$unsorted) (M_1 $$unsorted) (N $$unsorted) (I_1 $$unsorted) (J_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.times_times tptp.nat))) (let ((_let_3 (tptp.plus_plus tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) I_1) J_1)) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 I_1) U)) M_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 J_1) U)) N)) (= M_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) J_1) I_1)) U)) N)))))))) (forall ((U_1 $$unsorted) (M $$unsorted) (N_1 $$unsorted) (I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.times_times tptp.nat))) (let ((_let_4 (tptp.plus_plus tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) I) J)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 I) U_1)) M)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 J) U_1)) N_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 J) I)) U_1)) N_1))))))))) (forall ((U $$unsorted) (M_1 $$unsorted) (N $$unsorted) (I_1 $$unsorted) (J_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.times_times tptp.nat))) (let ((_let_3 (tptp.plus_plus tptp.nat))) (let ((_let_4 (tptp.ord_less_eq tptp.nat))) (let ((_let_5 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_5 _let_4 I_1) J_1)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_5 _let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 I_1) U)) M_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 J_1) U)) N))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_5 _let_4 M_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) J_1) I_1)) U)) N))))))))))) (forall ((U $$unsorted) (M_1 $$unsorted) (N $$unsorted) (J_1 $$unsorted) (I_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.times_times tptp.nat))) (let ((_let_3 (tptp.plus_plus tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) J_1) I_1)) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 I_1) U)) M_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 J_1) U)) N)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) I_1) J_1)) U)) M_1) N))))))) (forall ((U_1 $$unsorted) (M $$unsorted) (N_1 $$unsorted) (J $$unsorted) (I $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.times_times tptp.nat))) (let ((_let_4 (tptp.plus_plus tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) J) I)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 I) U_1)) M)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 J) U_1)) N_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 I) J)) U_1)) M)) N_1)))))))) (forall ((M $$unsorted) (N_1 $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.times_times tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 M))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 N_1)) K) (tptp.hAPP tptp.nat tptp.nat _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 N_1) K))))))) (forall ((M $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.times_times tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M) N_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 N_1) M))))) (forall ((M_1 $$unsorted) (K_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M_1) K_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 N) K_1)) (= M_1 N))))) (forall ((K_1 $$unsorted) (M_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) K_1))) (= (= (tptp.hAPP tptp.nat tptp.nat _let_1 M_1) (tptp.hAPP tptp.nat tptp.nat _let_1 N)) (= M_1 N)))) (forall ((M $$unsorted) (N_1 $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 M))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 N_1)) K) (tptp.hAPP tptp.nat tptp.nat _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 N_1) K))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 X))) (let ((_let_4 (tptp.hAPP tptp.nat _let_2 _let_1 Y))) (= (tptp.hAPP tptp.nat tptp.nat _let_3 (tptp.hAPP tptp.nat tptp.nat _let_4 Z)) (tptp.hAPP tptp.nat tptp.nat _let_4 (tptp.hAPP tptp.nat tptp.nat _let_3 Z)))))))) (forall ((M $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M) N_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 N_1) M))))) (forall ((K $$unsorted) (M $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.nat _let_1 (tptp.times_times tptp.nat) K))) (let ((_let_3 (tptp.plus_plus tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 M) N_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat _let_2 M)) (tptp.hAPP tptp.nat tptp.nat _let_2 N_1))))))) (forall ((M $$unsorted) (N_1 $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.times_times tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.plus_plus tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 M) N_1)) K) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M) K)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 N_1) K))))))) (forall ((I $$unsorted) (U_1 $$unsorted) (J $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.times_times tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 I) U_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 J) U_1)) K)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 I) J)) U_1)) K)))))) (forall ((U $$unsorted) (M_1 $$unsorted) (N $$unsorted) (J_1 $$unsorted) (I_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.times_times tptp.nat))) (let ((_let_3 (tptp.plus_plus tptp.nat))) (let ((_let_4 (tptp.ord_less_eq tptp.nat))) (let ((_let_5 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_5 _let_4 J_1) I_1)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_5 _let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 I_1) U)) M_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 J_1) U)) N))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_5 _let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) I_1) J_1)) U)) M_1)) N)))))))))) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) X))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) Y) Z)))))) (forall ((Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) X))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 Z)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) Y) Z)))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.bot_bot _let_1))) (let ((_let_3 (tptp.fun _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_3) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_3 (tptp.insert X_b) X_1) _let_2)))) (let ((_let_5 (tptp.ord_min X_b))) (let ((_let_6 (tptp.fun X_b X_b))) (let ((_let_7 (tptp.hAPP (tptp.fun X_b _let_6) (tptp.fun _let_1 X_b) (tptp.big_Inf_fin X_b) _let_5))) (let ((_let_8 (tptp.hAPP _let_1 X_b _let_7 A_3))) (let ((_let_9 (= _let_4 _let_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 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) X_1) A_3)) (and (=> _let_9 (= _let_8 (tptp.ti X_b X_1))) (=> (not _let_9) (= _let_8 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_6 _let_5 X_1) (tptp.hAPP _let_1 X_b _let_7 _let_4))))))))))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.bot_bot _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.hAPP X_b _let_3 (tptp.insert X_b) X_1))) (let ((_let_5 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 (tptp.minus_minus _let_1) A_3) (tptp.hAPP _let_1 _let_1 _let_4 _let_2)))) (let ((_let_6 (tptp.ord_min X_b))) (let ((_let_7 (tptp.fun X_b X_b))) (let ((_let_8 (tptp.hAPP (tptp.fun X_b _let_7) (tptp.fun _let_1 X_b) (tptp.big_Inf_fin X_b) _let_6))) (let ((_let_9 (tptp.hAPP _let_1 X_b _let_8 (tptp.hAPP _let_1 _let_1 _let_4 A_3)))) (let ((_let_10 (= _let_5 _let_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (and (=> _let_10 (= _let_9 (tptp.ti X_b X_1))) (=> (not _let_10) (= _let_9 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_7 _let_6 X_1) (tptp.hAPP _let_1 X_b _let_8 _let_5))))))))))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.ord_min 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 _let_2 X_b (tptp.hAPP (tptp.fun X_b _let_3) (tptp.fun _let_2 X_b) (tptp.big_Inf_fin X_b) _let_1) A_3))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (=> (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_3)) (= (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_3 _let_1 X_1) _let_4) _let_4)))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$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.big_Inf_fin X_b) (tptp.ord_min 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 $$unsorted)) (=> (tptp.linorder X_b) (forall ((A_3 $$unsorted)) (let ((_let_1 (tptp.ord_min 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_3)) (= (tptp.hAPP _let_2 X_b (tptp.hAPP _let_4 _let_3 (tptp.big_Inf_fin X_b) _let_1) A_3) (tptp.hAPP _let_2 X_b (tptp.hAPP _let_4 _let_3 (tptp.finite_fold1 X_b) _let_1) A_3)))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.ord_min X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun X_b X_b))) (let ((_let_4 (tptp.hAPP (tptp.fun X_b _let_3) (tptp.fun _let_2 X_b) (tptp.big_Inf_fin X_b) _let_1))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (=> (not (= (tptp.ti _let_2 A_3) (tptp.bot_bot _let_2))) (= (tptp.hAPP _let_2 X_b _let_4 (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_b (tptp.fun _let_2 _let_2) (tptp.insert X_b) X_1) A_3)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_3 _let_1 X_1) (tptp.hAPP _let_2 X_b _let_4 A_3)))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.ord_min 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.big_Inf_fin X_b) _let_1))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (=> (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_3))) (=> (not (= (tptp.ti _let_2 A_3) (tptp.bot_bot _let_2))) (= (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_3)) (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_3))))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((B_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.ord_min X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun X_b X_b))) (let ((_let_4 (tptp.hAPP (tptp.fun X_b _let_3) (tptp.fun _let_2 X_b) (tptp.big_Inf_fin X_b) _let_1))) (let ((_let_5 (tptp.hAPP _let_2 X_b _let_4 A_3))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (=> (not (= (tptp.ti _let_2 B_2) (tptp.bot_bot _let_2))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) B_2) A_3)) (= (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_3 _let_1 (tptp.hAPP _let_2 X_b _let_4 B_2)) _let_5) _let_5)))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.ord_min 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_3)) (=> (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_3))) (= (tptp.hAPP _let_2 X_b (tptp.hAPP _let_4 _let_3 (tptp.big_Inf_fin 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_3)) (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) X_1) A_3))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((A_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.ord_min X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun _let_2 X_b))) (let ((_let_4 (tptp.fun X_b (tptp.fun X_b X_b)))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (= (tptp.hAPP _let_2 X_b (tptp.hAPP _let_4 _let_3 (tptp.big_Inf_fin X_b) _let_1) (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_b (tptp.fun _let_2 _let_2) (tptp.insert X_b) A_2) A_3)) (tptp.hAPP _let_2 X_b (tptp.hAPP X_b _let_3 (tptp.hAPP _let_4 (tptp.fun X_b _let_3) (tptp.finite_fold X_b X_b) _let_1) A_2) A_3)))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((N_3 $$unsorted) (H $$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.big_Inf_fin X_b) (tptp.ord_min X_b)))) (=> (forall ((X_2 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.ord_min 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_1)) (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_1)))))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) N_3)) (=> (not (= (tptp.ti _let_1 N_3) (tptp.bot_bot _let_1))) (= (tptp.hAPP X_b X_b H (tptp.hAPP _let_1 X_b _let_3 N_3)) (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_3)))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((A_3 $$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)) (=> (not (= (tptp.ti _let_1 A_3) (tptp.bot_bot _let_1))) (=> (forall ((X_2 $$unsorted) (Y_1 $$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))) (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.ord_min X_b) X_2) Y_1)) (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_1) (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.big_Inf_fin X_b) (tptp.ord_min X_b)) A_3)) A_3))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linord219039673up_add X_b) (forall ((S_1 $$unsorted)) (let ((_let_1 (tptp.uminus_uminus 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) S_1)) (=> (not (= (tptp.ti _let_2 S_1) (tptp.bot_bot _let_2))) (= (tptp.hAPP X_b X_b _let_1 (tptp.hAPP _let_2 X_b (tptp.big_linorder_Max X_b) S_1)) (tptp.hAPP _let_2 X_b (tptp.big_linorder_Min X_b) (tptp.hAPP _let_2 _let_2 (tptp.hAPP (tptp.fun X_b X_b) (tptp.fun _let_2 _let_2) (tptp.image X_b X_b) _let_1) S_1)))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linord219039673up_add X_b) (forall ((S_1 $$unsorted)) (let ((_let_1 (tptp.uminus_uminus 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) S_1)) (=> (not (= (tptp.ti _let_2 S_1) (tptp.bot_bot _let_2))) (= (tptp.hAPP X_b X_b _let_1 (tptp.hAPP _let_2 X_b (tptp.big_linorder_Min X_b) S_1)) (tptp.hAPP _let_2 X_b (tptp.big_linorder_Max X_b) (tptp.hAPP _let_2 _let_2 (tptp.hAPP (tptp.fun X_b X_b) (tptp.fun _let_2 _let_2) (tptp.image X_b X_b) _let_1) S_1)))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (tptp.uminus X_c) (forall ((A_3 $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b X_c))) (= (tptp.hAPP X_b X_c (tptp.hAPP _let_1 _let_1 (tptp.uminus_uminus _let_1) A_3) X_2) (tptp.hAPP X_c X_c (tptp.uminus_uminus X_c) (tptp.hAPP X_b X_c A_3 X_2))))))) (forall ((X_a $$unsorted)) (=> (tptp.boolean_algebra X_a) (forall ((X $$unsorted)) (let ((_let_1 (tptp.uminus_uminus X_a))) (= (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a _let_1 X)) (tptp.ti X_a X)))))) (forall ((X_c $$unsorted) (X_b $$unsorted)) (=> (tptp.uminus X_b) (forall ((A_3 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c X_b))) (= (tptp.hAPP X_c X_b (tptp.hAPP _let_1 _let_1 (tptp.uminus_uminus _let_1) A_3) X_1) (tptp.hAPP X_b X_b (tptp.uminus_uminus X_b) (tptp.hAPP X_c X_b A_3 X_1))))))) (forall ((X_b $$unsorted)) (=> (tptp.boolean_algebra X_b) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.uminus_uminus X_b))) (= (= (tptp.hAPP X_b X_b _let_1 X_1) (tptp.hAPP X_b X_b _let_1 Y_2)) (= (tptp.ti X_b X_1) (tptp.ti X_b Y_2))))))) (forall ((X_a $$unsorted)) (=> (tptp.group_add X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.uminus_uminus X_a))) (= (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a _let_1 A_1)) (tptp.ti X_a A_1)))))) (forall ((X_b $$unsorted)) (=> (tptp.group_add X_b) (forall ((A_2 $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.uminus_uminus X_b))) (= (= (tptp.ti X_b A_2) (tptp.hAPP X_b X_b _let_1 Ba)) (= (tptp.ti X_b Ba) (tptp.hAPP X_b X_b _let_1 A_2))))))) (forall ((X_b $$unsorted)) (=> (tptp.group_add X_b) (forall ((A_2 $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.uminus_uminus X_b))) (= (= (tptp.hAPP X_b X_b _let_1 A_2) (tptp.ti X_b Ba)) (= (tptp.hAPP X_b X_b _let_1 Ba) (tptp.ti X_b A_2))))))) (forall ((X_b $$unsorted)) (=> (tptp.group_add X_b) (forall ((A_2 $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.uminus_uminus X_b))) (= (= (tptp.hAPP X_b X_b _let_1 A_2) (tptp.hAPP X_b X_b _let_1 Ba)) (= (tptp.ti X_b A_2) (tptp.ti X_b Ba))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.uminus_uminus _let_1))) (let ((_let_3 (tptp.ord_less_eq _let_1))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_4 _let_3 A_3) B_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_4 _let_3 (tptp.hAPP _let_1 _let_1 _let_2 B_2)) (tptp.hAPP _let_1 _let_1 _let_2 A_3))))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_2 $$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.uminus_uminus _let_1))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 (tptp.hAPP _let_1 _let_1 _let_4 A_3)) (tptp.hAPP _let_1 _let_1 _let_4 B_2))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 B_2) A_3)))))))) (forall ((X_a $$unsorted)) (=> (tptp.ab_group_add X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.minus_minus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) B)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) A_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ab_group_add X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.uminus_uminus X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 B)) (tptp.hAPP X_a X_a _let_1 A_1)))))))))) (forall ((X_b $$unsorted)) (=> (tptp.ordered_ab_group_add X_b) (forall ((Ba $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.uminus_uminus X_b))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 (tptp.hAPP X_b X_b _let_3 Ba)) (tptp.hAPP X_b X_b _let_3 A_2))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 A_2) Ba))))))))) (forall ((X_b $$unsorted)) (=> (tptp.ordered_ab_group_add X_b) (forall ((A_2 $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.uminus_uminus X_b))) (let ((_let_2 (tptp.ord_less_eq X_b))) (let ((_let_3 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_3 _let_2 (tptp.hAPP X_b X_b _let_1 A_2)) Ba)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_3 _let_2 (tptp.hAPP X_b X_b _let_1 Ba)) A_2))))))))) (forall ((X_b $$unsorted)) (=> (tptp.ordered_ab_group_add X_b) (forall ((A_2 $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.uminus_uminus X_b))) (let ((_let_2 (tptp.ord_less_eq X_b))) (let ((_let_3 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_3 _let_2 A_2) (tptp.hAPP X_b X_b _let_1 Ba))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_3 _let_2 Ba) (tptp.hAPP X_b X_b _let_1 A_2)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.boolean_algebra X_a) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.uminus_uminus X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 Y)) X)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 X)) Y))))))))) (forall ((X_a $$unsorted)) (=> (tptp.boolean_algebra X_a) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.uminus_uminus X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 Y) (tptp.hAPP X_a X_a _let_1 X))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 X) (tptp.hAPP X_a X_a _let_1 Y)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.boolean_algebra X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.uminus_uminus X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 X) Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 Y)) (tptp.hAPP X_a X_a _let_1 X)))))))))) (forall ((X_b $$unsorted)) (=> (tptp.boolean_algebra X_b) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.uminus_uminus X_b))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 (tptp.hAPP X_b X_b _let_3 X_1)) (tptp.hAPP X_b X_b _let_3 Y_2))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 Y_2) X_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ab_group_add X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.uminus_uminus X_a))) (let ((_let_2 (tptp.plus_plus X_a))) (let ((_let_3 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 A_1) B)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 A_1)) (tptp.hAPP X_a X_a _let_1 B))))))))) (forall ((X_a $$unsorted)) (=> (tptp.group_add X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.uminus_uminus X_a))) (let ((_let_2 (tptp.plus_plus X_a))) (let ((_let_3 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 A_1) B)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 B)) (tptp.hAPP X_a X_a _let_1 A_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.group_add X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) A_1)) B)) (tptp.ti X_a B))))))) (forall ((X_a $$unsorted)) (=> (tptp.group_add X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) A_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) B)) (tptp.ti X_a B))))))) (forall ((X_a $$unsorted)) (=> (tptp.ring X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.uminus_uminus X_a))) (let ((_let_2 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1))) (= (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a _let_2 B)) (tptp.hAPP X_a X_a _let_2 (tptp.hAPP X_a X_a _let_1 B)))))))) (forall ((X_a $$unsorted)) (=> (tptp.ring X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.uminus_uminus X_a))) (let ((_let_2 (tptp.times_times X_a))) (let ((_let_3 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 A_1) B)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 A_1)) B)))))))) (forall ((X_a $$unsorted)) (=> (tptp.ring X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.uminus_uminus X_a))) (let ((_let_2 (tptp.times_times X_a))) (let ((_let_3 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 A_1)) B) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 A_1) (tptp.hAPP X_a X_a _let_1 B))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ring X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.uminus_uminus X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 A_1)) (tptp.hAPP X_a X_a _let_3 B)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) B)))))))) (forall ((X_b $$unsorted)) (=> (tptp.idom X_b) (forall ((A_2 $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.ti X_b A_2))) (let ((_let_2 (tptp.times_times X_b))) (let ((_let_3 (tptp.fun X_b X_b))) (= (= (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_3 _let_2 A_2) A_2) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_3 _let_2 Ba) Ba)) (or (= _let_1 (tptp.ti X_b Ba)) (= _let_1 (tptp.hAPP X_b X_b (tptp.uminus_uminus X_b) Ba)))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted)) (=> (tptp.ab_group_add X_b) (forall ((F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.big_co1399186613setsum X_c X_b))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (let ((_let_3 (tptp.fun _let_2 X_b))) (let ((_let_4 (tptp.fun X_c X_b))) (let ((_let_5 (tptp.uminus_uminus X_b))) (= (tptp.hAPP _let_2 X_b (tptp.hAPP _let_4 _let_3 _let_1 (tptp.hAPP _let_4 _let_4 (tptp.hAPP (tptp.fun X_b X_b) (tptp.fun _let_4 _let_4) (tptp.combb X_b X_b X_c) _let_5) F)) A_3) (tptp.hAPP X_b X_b _let_5 (tptp.hAPP _let_2 X_b (tptp.hAPP _let_4 _let_3 _let_1 F) A_3))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.group_add X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.minus_minus X_a) A_1) (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) B)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.plus_plus X_a) A_1) B)))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_ring_1 X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.minus_minus X_a) X) Y) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.plus_plus X_a) X) (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) Y))))))) (forall ((X_a $$unsorted)) (=> (tptp.ab_group_add X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.minus_minus X_a) A_1) B) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.plus_plus X_a) A_1) (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) B))))))) (forall ((X_a $$unsorted)) (=> (tptp.group_add X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.minus_minus X_a) A_1) B) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.plus_plus X_a) A_1) (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) B))))))) (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.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) A_3) (tptp.hAPP _let_1 _let_1 (tptp.uminus_uminus _let_1) A_3))) (= (tptp.ti _let_1 A_3) (tptp.bot_bot _let_1))))) (forall ((X_b $$unsorted)) (=> (tptp.ordered_ab_group_add X_b) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.uminus_uminus X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (= (tptp.hAPP _let_2 _let_2 (tptp.hAPP (tptp.fun X_b X_b) (tptp.fun _let_2 _let_2) (tptp.image X_b X_b) _let_1) (tptp.hAPP X_b _let_2 (tptp.ord_lessThan X_b) X_1)) (tptp.hAPP X_b _let_2 (tptp.ord_greaterThan X_b) (tptp.hAPP X_b X_b _let_1 X_1)))))))) (forall ((X_b $$unsorted)) (=> (tptp.ordered_ab_group_add X_b) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.uminus_uminus X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (= (tptp.hAPP _let_2 _let_2 (tptp.hAPP (tptp.fun X_b X_b) (tptp.fun _let_2 _let_2) (tptp.image X_b X_b) _let_1) (tptp.hAPP X_b _let_2 (tptp.ord_greaterThan X_b) X_1)) (tptp.hAPP X_b _let_2 (tptp.ord_lessThan X_b) (tptp.hAPP X_b X_b _let_1 X_1)))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.bot_bot _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 (tptp.minus_minus _let_1) A_3) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_3 (tptp.insert X_b) X_1) _let_2)))) (let ((_let_5 (tptp.big_linorder_Max X_b))) (let ((_let_6 (tptp.hAPP _let_1 X_b _let_5 A_3))) (let ((_let_7 (= _let_4 _let_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_1) A_3)) (and (=> _let_7 (= _let_6 (tptp.ti X_b X_1))) (=> (not _let_7) (= _let_6 (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.ord_max X_b) X_1) (tptp.hAPP _let_1 X_b _let_5 _let_4))))))))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.bot_bot _let_1))) (let ((_let_3 (tptp.fun _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_3) (tptp.hAPP _let_1 _let_1 _let_4 _let_2)))) (let ((_let_6 (tptp.big_linorder_Max X_b))) (let ((_let_7 (tptp.hAPP _let_1 X_b _let_6 (tptp.hAPP _let_1 _let_1 _let_4 A_3)))) (let ((_let_8 (= _let_5 _let_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (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.ord_max X_b) X_1) (tptp.hAPP _let_1 X_b _let_6 _let_5))))))))))))))))) (forall ((X_b $$unsorted) (Ca $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) Ca))) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_3))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.uminus_uminus _let_1) A_3))))))) (forall ((X_b $$unsorted) (Pa $$unsorted)) (let ((_let_1 (tptp.collect X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (= (tptp.hAPP _let_2 _let_2 _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP (tptp.fun tptp.bool tptp.bool) (tptp.fun _let_2 _let_2) (tptp.combb tptp.bool tptp.bool X_b) tptp.fNot) Pa)) (tptp.hAPP _let_2 _let_2 (tptp.uminus_uminus _let_2) (tptp.hAPP _let_2 _let_2 _let_1 Pa)))))) (forall ((X_b $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (= (tptp.hAPP _let_1 _let_1 (tptp.uminus_uminus _let_1) A_3) (tptp.hAPP _let_1 _let_1 (tptp.collect X_b) (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun tptp.bool tptp.bool) _let_2 (tptp.combb tptp.bool tptp.bool X_b) tptp.fNot) (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_b (tptp.fun _let_1 tptp.bool)) _let_2 (tptp.combc X_b _let_1 tptp.bool) (tptp.member X_b)) A_3))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.uminus_uminus _let_1))) (= (tptp.hAPP _let_1 _let_1 _let_2 (tptp.hAPP _let_1 _let_1 _let_2 A_3)) (tptp.ti _let_1 A_3))))) (forall ((X_b $$unsorted) (Ca $$unsorted) (A_3 $$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.uminus_uminus _let_1) A_3))) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_3))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.uminus_uminus _let_1))) (= (= (tptp.hAPP _let_1 _let_1 _let_2 A_3) (tptp.hAPP _let_1 _let_1 _let_2 B_2)) (= (tptp.ti _let_1 A_3) (tptp.ti _let_1 B_2)))))) (forall ((X_b $$unsorted) (Ca $$unsorted) (A_3 $$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.uminus_uminus _let_1) A_3))) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_3))))))) (forall ((X_b $$unsorted) (Ca $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) Ca))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.uminus_uminus _let_1) A_3))) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_3))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ord_min X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_max X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 Y) Z)) X) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Y) X)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Z) X))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ord_max X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_min X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 Y) Z)) X) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Y) X)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Z) X))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.ord_min X_a) X))) (let ((_let_3 (tptp.ord_max X_a))) (= (tptp.hAPP X_a X_a _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 Y) Z)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 (tptp.hAPP X_a X_a _let_2 Y)) (tptp.hAPP X_a X_a _let_2 Z))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.ord_max X_a) X))) (let ((_let_3 (tptp.ord_min X_a))) (= (tptp.hAPP X_a X_a _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 Y) Z)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 (tptp.hAPP X_a X_a _let_2 Y)) (tptp.hAPP X_a X_a _let_2 Z))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.ord_min X_a) X) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.ord_max X_a) X) Y)) (tptp.ti X_a X)))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.ord_max X_a) X) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.ord_min X_a) X) Y)) (tptp.ti X_a X)))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere236663937imp_le X_a) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_max X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 X) Y)) Z) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 X) Z)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Y) Z))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ab_group_add X_a) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.minus_minus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_max X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 X) Y)) Z) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 X) Z)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Y) Z))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_max X_a) X) X) (tptp.ti X_a X))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.ord_max X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 X))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 Y)) Z) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Y) Z))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.ord_max X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 A_1))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 B)) C) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) C))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.ord_max X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 X))) (let ((_let_4 (tptp.hAPP X_a _let_2 _let_1 Y))) (= (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a _let_4 Z)) (tptp.hAPP X_a X_a _let_4 (tptp.hAPP X_a X_a _let_3 Z)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((B $$unsorted) (A_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.ord_max X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 B))) (let ((_let_4 (tptp.hAPP X_a _let_2 _let_1 A_1))) (= (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a _let_4 C)) (tptp.hAPP X_a X_a _let_4 (tptp.hAPP X_a X_a _let_3 C)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_max X_a) X))) (let ((_let_2 (tptp.hAPP X_a X_a _let_1 Y))) (= (tptp.hAPP X_a X_a _let_1 _let_2) _let_2)))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_max X_a) A_1))) (let ((_let_2 (tptp.hAPP X_a X_a _let_1 B))) (= (tptp.hAPP X_a X_a _let_1 _let_2) _let_2)))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_max X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 X) Y) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Y) X))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_max X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) B) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) A_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_max X_a) A_1) A_1) (tptp.ti X_a A_1))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.ord_greaterThan X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (= (= (tptp.hAPP X_b _let_2 _let_1 X_1) (tptp.hAPP X_b _let_2 _let_1 Y_2)) (= (tptp.ti X_b X_1) (tptp.ti X_b Y_2)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_max X_a) X) Y)))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((Y $$unsorted) (X $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) Y) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_max X_a) X) Y)))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) X_1) Y_2)) (= (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.ord_max X_b) X_1) Y_2) (tptp.ti X_b Y_2)))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted) (Y_2 $$unsorted) (Z_2 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.ord_max X_b) X_1) Y_2)) Z_2)) (and (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 X_1) Z_2)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 Y_2) Z_2))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((B $$unsorted) (X $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_max X_a) A_1) B)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((A_1 $$unsorted) (X $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_max X_a) A_1) B)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X) Y)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_max X_a) X) Y) (tptp.ti X_a Y)))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((Y $$unsorted) (X $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) Y) X)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_max X_a) X) Y) (tptp.ti X_a X)))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((B $$unsorted) (A_1 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) X)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B) X)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_max X_a) A_1) B)) X))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((Z $$unsorted) (Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Z) X)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_max X_a) Y) Z)) X))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((B $$unsorted) (D_1 $$unsorted) (A_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.ord_max X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less_eq X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 A_1) C)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 B) D_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) B)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 C) D_1)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_max X_a) A_1) B)) X)) (not (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) X)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B) X))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((Z_2 $$unsorted) (X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) Z_2))) (= (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.ord_max X_b) X_1) Y_2))) (or (tptp.hBOOL (tptp.hAPP X_b tptp.bool _let_1 X_1)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool _let_1 Y_2)))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) tptp.bool (tptp.finite_comp_fun_idem X_b X_b) (tptp.ord_max X_b))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.ord_max X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 (tptp.ord_min X_a) X))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 Y)) (tptp.hAPP X_a X_a _let_3 Z))) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Y) Z)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.ord_max X_a) X))) (let ((_let_3 (tptp.ord_min X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP X_a X_a _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 Y) Z))) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 (tptp.hAPP X_a X_a _let_2 Y)) (tptp.hAPP X_a X_a _let_2 Z)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord219039673up_add X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.uminus_uminus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 (tptp.ord_min X_a) X) Y)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 (tptp.ord_max X_a) (tptp.hAPP X_a X_a _let_1 X)) (tptp.hAPP X_a X_a _let_1 Y)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord219039673up_add X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.uminus_uminus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 (tptp.ord_max X_a) X) Y)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 (tptp.ord_min X_a) (tptp.hAPP X_a X_a _let_1 X)) (tptp.hAPP X_a X_a _let_1 Y)))))))) (forall ((N_1 $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) N_1) M)) M) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.ord_max tptp.nat) N_1) M)))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP _let_1 X_b (tptp.big_linorder_Max X_b) A_3))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 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) X_1) A_3)) (= (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.ord_max X_b) X_1) _let_2) _let_2)))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((Ba $$unsorted) (A_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.ord_max 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_3)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_b (tptp.fun _let_2 tptp.bool) (tptp.member X_b) A_2) A_3)) (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_2) 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_3)))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.ord X_b) (= (tptp.ord_max X_b) (tptp.hAPP (tptp.fun X_b (tptp.fun X_b tptp.bool)) (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.max X_b) (tptp.ord_less_eq X_b))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((Ba $$unsorted) (A_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.ord_max X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun _let_2 X_b))) (let ((_let_4 (tptp.fun X_b X_b))) (let ((_let_5 (tptp.hAPP X_b _let_3 (tptp.hAPP (tptp.fun X_b _let_4) (tptp.fun X_b _let_3) (tptp.finite_fold X_b X_b) _let_1) Ba))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (= (tptp.hAPP _let_2 X_b _let_5 (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_b (tptp.fun _let_2 _let_2) (tptp.insert X_b) A_2) A_3)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_4 _let_1 A_2) (tptp.hAPP _let_2 X_b _let_5 A_3)))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((A_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_b X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 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_2) A_3)) (= (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_2 (tptp.ord_max X_b) A_2) (tptp.hAPP _let_1 X_b (tptp.hAPP (tptp.fun X_b _let_2) (tptp.fun _let_1 X_b) (tptp.big_Inf_fin X_b) (tptp.ord_min X_b)) A_3)) (tptp.ti X_b A_2))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.ord_greaterThan X_b))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) (tptp.hAPP X_b _let_1 _let_2 X_1)) (tptp.hAPP X_b _let_1 _let_2 Y_2))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less_eq X_b) Y_2) X_1)))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (= (tptp.hAPP _let_1 X_b (tptp.big_linorder_Max X_b) A_3) (tptp.hAPP _let_1 X_b (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun _let_1 X_b) (tptp.finite_fold1 X_b) (tptp.ord_max X_b)) A_3))))))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.fun X_b (tptp.fun X_b tptp.bool)))) (=> (tptp.linorder X_b) (= (tptp.hAPP _let_1 (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.min X_b) (tptp.hAPP _let_1 _let_1 (tptp.combc X_b X_b tptp.bool) (tptp.ord_less_eq X_b))) (tptp.ord_max X_b))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.big_linorder_Max X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (=> (not (= (tptp.ti _let_2 A_3) (tptp.bot_bot _let_2))) (= (tptp.hAPP _let_2 X_b _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_b (tptp.fun _let_2 _let_2) (tptp.insert X_b) X_1) A_3)) (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.ord_max X_b) X_1) (tptp.hAPP _let_2 X_b _let_1 A_3)))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.big_linorder_Max 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_3)) (=> (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_3))) (=> (not (= (tptp.ti _let_2 A_3) (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_3)) (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.ord_max X_b) X_1) (tptp.hAPP _let_2 X_b _let_1 A_3))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((B_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.big_linorder_Max X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.hAPP _let_2 X_b _let_1 A_3))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (=> (not (= (tptp.ti _let_2 B_2) (tptp.bot_bot _let_2))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) B_2) A_3)) (= (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.ord_max X_b) (tptp.hAPP _let_2 X_b _let_1 B_2)) _let_3) _let_3)))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted) (A_3 $$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_3)) (=> (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_3))) (= (tptp.hAPP _let_1 X_b (tptp.big_linorder_Max 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_3)) (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.ord_max X_b)) X_1) A_3))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((A_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (= (tptp.hAPP _let_1 X_b (tptp.big_linorder_Max X_b) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_2) A_3)) (tptp.hAPP _let_1 X_b (tptp.hAPP X_b _let_2 (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun X_b _let_2) (tptp.finite_fold X_b X_b) (tptp.ord_max X_b)) A_2) A_3)))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((N_3 $$unsorted) (H $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.big_linorder_Max X_b))) (=> (forall ((X_2 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.ord_max 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_1)) (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_1)))))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) N_3)) (=> (not (= (tptp.ti _let_1 N_3) (tptp.bot_bot _let_1))) (= (tptp.hAPP X_b X_b H (tptp.hAPP _let_1 X_b _let_2 N_3)) (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_3))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((A_3 $$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)) (=> (not (= (tptp.ti _let_1 A_3) (tptp.bot_bot _let_1))) (=> (forall ((X_2 $$unsorted) (Y_1 $$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))) (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.ord_max X_b) X_2) Y_1)) (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_1) (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_linorder_Max X_b) A_3)) A_3))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((Ca $$unsorted) (Ba $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.ord_max 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_3)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_2) A_3)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less_eq X_b) X_2) Ba))))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_3 (tptp.ord_less_eq X_b) (tptp.hAPP _let_3 X_b (tptp.hAPP X_b _let_4 (tptp.hAPP (tptp.fun X_b _let_2) (tptp.fun X_b _let_4) (tptp.finite_fold X_b X_b) _let_1) Ca) A_3)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_2 _let_1 Ba) Ca)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.ord_max X_a) X))) (let ((_let_3 (tptp.ord_min X_a))) (=> (forall ((X_2 $$unsorted) (Y_1 $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.ord_min X_a) X_2))) (let ((_let_3 (tptp.ord_max X_a))) (= (tptp.hAPP X_a X_a _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 Y_1) Z_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 (tptp.hAPP X_a X_a _let_2 Y_1)) (tptp.hAPP X_a X_a _let_2 Z_1))))))) (= (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 $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.ord_min X_a) X))) (let ((_let_3 (tptp.ord_max X_a))) (=> (forall ((X_2 $$unsorted) (Y_1 $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.ord_max X_a) X_2))) (let ((_let_3 (tptp.ord_min X_a))) (= (tptp.hAPP X_a X_a _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 Y_1) Z_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 (tptp.hAPP X_a X_a _let_2 Y_1)) (tptp.hAPP X_a X_a _let_2 Z_1))))))) (= (tptp.hAPP X_a X_a _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 Y) Z)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 (tptp.hAPP X_a X_a _let_2 Y)) (tptp.hAPP X_a X_a _let_2 Z)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ord X_a) (forall ((X $$unsorted) (Least $$unsorted)) (=> (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) Least) X_2))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_max X_a) Least) X) (tptp.ti X_a X)))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((X $$unsorted) (Least $$unsorted)) (=> (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) Least) X_2))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_max X_a) X) Least) (tptp.ti X_a X)))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 X_b))) (let ((_let_3 (tptp.fun X_b (tptp.fun X_b X_b)))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (=> (not (= (tptp.ti _let_1 A_3) (tptp.bot_bot _let_1))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less_eq X_b) (tptp.hAPP _let_1 X_b (tptp.hAPP _let_3 _let_2 (tptp.big_Inf_fin X_b) (tptp.ord_min X_b)) A_3)) (tptp.hAPP _let_1 X_b (tptp.hAPP _let_3 _let_2 (tptp.big_Sup_fin X_b) (tptp.ord_max X_b)) A_3))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((B_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.hAPP (tptp.fun X_b _let_3) _let_2 (tptp.combc X_b _let_1 tptp.bool) (tptp.member X_b)))) (let ((_let_5 (tptp.fun tptp.bool tptp.bool))) (let ((_let_6 (tptp.fun X_b _let_5))) (let ((_let_7 (tptp.fun _let_1 _let_6))) (let ((_let_8 (tptp.hAPP (tptp.fun tptp.bool _let_5) _let_7 (tptp.combb tptp.bool _let_5 X_b) tptp.fconj))) (let ((_let_9 (tptp.fun X_b _let_2))) (let ((_let_10 (tptp.fun X_b _let_1))) (let ((_let_11 (tptp.ord_max X_b))) (let ((_let_12 (tptp.fun X_b X_b))) (let ((_let_13 (tptp.fun _let_12 _let_1))) (let ((_let_14 (tptp.fun X_b _let_13))) (let ((_let_15 (tptp.fun X_b _let_12))) (let ((_let_16 (tptp.fun _let_15 _let_10))) (let ((_let_17 (tptp.fun X_b _let_16))) (let ((_let_18 (tptp.fun X_b _let_10))) (let ((_let_19 (tptp.fun X_b _let_6))) (let ((_let_20 (tptp.fun _let_10 _let_19))) (let ((_let_21 (tptp.fun X_b _let_19))) (let ((_let_22 (tptp.fun _let_19 _let_9))) (let ((_let_23 (tptp.fun X_b _let_9))) (let ((_let_24 (tptp.fun _let_10 _let_10))) (let ((_let_25 (tptp.fun X_b _let_24))) (let ((_let_26 (tptp.fun _let_10 _let_1))) (let ((_let_27 (tptp.hAPP _let_3 _let_26 (tptp.combb _let_1 tptp.bool X_b) (tptp.fEx X_b)))) (let ((_let_28 (tptp.hAPP _let_15 (tptp.fun _let_1 X_b) (tptp.big_Inf_fin X_b) (tptp.ord_min X_b)))) (let ((_let_29 (tptp.bot_bot _let_1))) (let ((_let_30 (tptp.finite_finite_1 X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_30 A_3)) (=> (not (= (tptp.ti _let_1 A_3) _let_29)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_30 B_2)) (=> (not (= (tptp.ti _let_1 B_2) _let_29)) (= (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_12 _let_11 (tptp.hAPP _let_1 X_b _let_28 A_3)) (tptp.hAPP _let_1 X_b _let_28 B_2)) (tptp.hAPP _let_1 X_b _let_28 (tptp.hAPP _let_1 _let_1 (tptp.collect X_b) (tptp.hAPP _let_10 _let_1 _let_27 (tptp.hAPP _let_18 _let_10 (tptp.hAPP _let_26 (tptp.fun _let_18 _let_10) (tptp.combb _let_10 _let_1 X_b) _let_27) (tptp.hAPP _let_10 _let_18 (tptp.hAPP _let_25 (tptp.fun _let_10 _let_18) (tptp.combc X_b _let_10 _let_10) (tptp.hAPP _let_23 _let_25 (tptp.hAPP (tptp.fun _let_9 _let_24) (tptp.fun _let_23 _let_25) (tptp.combb _let_9 _let_24 X_b) (tptp.combs X_b _let_1 _let_1)) (tptp.hAPP _let_21 _let_23 (tptp.hAPP _let_22 (tptp.fun _let_21 _let_23) (tptp.combb _let_19 _let_9 X_b) (tptp.hAPP (tptp.fun _let_6 _let_2) _let_22 (tptp.combb _let_6 _let_2 X_b) (tptp.combs X_b tptp.bool tptp.bool))) (tptp.hAPP _let_18 _let_21 (tptp.hAPP _let_20 (tptp.fun _let_18 _let_21) (tptp.combb _let_10 _let_19 X_b) (tptp.hAPP _let_7 _let_20 (tptp.combb _let_1 _let_6 X_b) _let_8)) (tptp.hAPP _let_15 _let_18 (tptp.hAPP _let_17 (tptp.fun _let_15 _let_18) (tptp.combc X_b _let_15 _let_10) (tptp.hAPP _let_14 _let_17 (tptp.hAPP (tptp.fun _let_13 _let_16) (tptp.fun _let_14 _let_17) (tptp.combb _let_13 _let_16 X_b) (tptp.combb _let_12 _let_1 X_b)) (tptp.hAPP _let_10 _let_14 (tptp.hAPP (tptp.fun _let_1 _let_13) (tptp.fun _let_10 _let_14) (tptp.combb _let_1 _let_13 X_b) (tptp.combb X_b tptp.bool X_b)) (tptp.fequal X_b)))) _let_11))))) (tptp.hAPP _let_1 _let_10 (tptp.hAPP _let_9 (tptp.fun _let_1 _let_10) (tptp.combc X_b _let_1 _let_1) (tptp.hAPP _let_6 _let_9 (tptp.hAPP (tptp.fun _let_5 _let_2) (tptp.fun _let_6 _let_9) (tptp.combb _let_5 _let_2 X_b) (tptp.combb tptp.bool tptp.bool X_b)) (tptp.hAPP _let_1 _let_6 _let_8 (tptp.hAPP _let_1 _let_1 _let_4 A_3)))) (tptp.hAPP _let_1 _let_1 _let_4 B_2))))))))))))))))))))))))))))))))))))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun X_b X_b))) (let ((_let_5 (tptp.hAPP X_b _let_4 (tptp.ord_max X_b) X_1))) (let ((_let_6 (tptp.fun _let_4 _let_1))) (let ((_let_7 (tptp.fun X_b _let_6))) (let ((_let_8 (tptp.fun X_b _let_1))) (let ((_let_9 (tptp.fun tptp.bool tptp.bool))) (let ((_let_10 (tptp.fun X_b _let_9))) (let ((_let_11 (tptp.fun _let_1 _let_10))) (let ((_let_12 (tptp.fun X_b _let_10))) (let ((_let_13 (tptp.fun X_b _let_2))) (let ((_let_14 (tptp.hAPP (tptp.fun X_b _let_4) (tptp.fun _let_1 X_b) (tptp.big_Inf_fin X_b) (tptp.ord_min X_b)))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (=> (not (= (tptp.ti _let_1 A_3) (tptp.bot_bot _let_1))) (= (tptp.hAPP X_b X_b _let_5 (tptp.hAPP _let_1 X_b _let_14 A_3)) (tptp.hAPP _let_1 X_b _let_14 (tptp.hAPP _let_1 _let_1 (tptp.collect X_b) (tptp.hAPP _let_8 _let_1 (tptp.hAPP _let_3 (tptp.fun _let_8 _let_1) (tptp.combb _let_1 tptp.bool X_b) (tptp.fEx X_b)) (tptp.hAPP _let_1 _let_8 (tptp.hAPP _let_13 (tptp.fun _let_1 _let_8) (tptp.combc X_b _let_1 _let_1) (tptp.hAPP _let_12 _let_13 (tptp.hAPP (tptp.fun _let_10 _let_2) (tptp.fun _let_12 _let_13) (tptp.combb _let_10 _let_2 X_b) (tptp.combs X_b tptp.bool tptp.bool)) (tptp.hAPP _let_8 _let_12 (tptp.hAPP _let_11 (tptp.fun _let_8 _let_12) (tptp.combb _let_1 _let_10 X_b) (tptp.hAPP (tptp.fun tptp.bool _let_9) _let_11 (tptp.combb tptp.bool _let_9 X_b) tptp.fconj)) (tptp.hAPP _let_4 _let_8 (tptp.hAPP _let_7 (tptp.fun _let_4 _let_8) (tptp.combc X_b _let_4 _let_1) (tptp.hAPP _let_8 _let_7 (tptp.hAPP (tptp.fun _let_1 _let_6) (tptp.fun _let_8 _let_7) (tptp.combb _let_1 _let_6 X_b) (tptp.combb X_b tptp.bool X_b)) (tptp.fequal X_b))) _let_5)))) (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_b _let_3) _let_2 (tptp.combc X_b _let_1 tptp.bool) (tptp.member X_b)) A_3))))))))))))))))))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (Q_3 $$unsorted) (Pa $$unsorted)) (let ((_let_1 (tptp.fun tptp.bool tptp.bool))) (let ((_let_2 (tptp.fun X_b _let_1))) (let ((_let_3 (tptp.fun X_b tptp.bool))) (let ((_let_4 (tptp.fun _let_3 _let_3))) (let ((_let_5 (tptp.fun X_c _let_3))) (let ((_let_6 (tptp.fun X_c tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.finite_finite_1 X_b) (tptp.hAPP _let_3 _let_3 (tptp.collect X_b) Pa))) (= (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.finite_finite_1 X_c) (tptp.hAPP _let_6 _let_6 (tptp.collect X_c) (tptp.hAPP _let_5 _let_6 (tptp.hAPP (tptp.fun _let_3 tptp.bool) (tptp.fun _let_5 _let_6) (tptp.combb _let_3 tptp.bool X_c) (tptp.fEx X_b)) (tptp.hAPP _let_5 _let_5 (tptp.hAPP _let_4 (tptp.fun _let_5 _let_5) (tptp.combb _let_3 _let_3 X_c) (tptp.hAPP _let_2 _let_4 (tptp.combs X_b tptp.bool tptp.bool) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun tptp.bool _let_1) (tptp.fun _let_3 _let_2) (tptp.combb tptp.bool _let_1 X_b) tptp.fconj) Pa))) Q_3))))) (forall ((Y_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa Y_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_c) (tptp.hAPP _let_1 _let_1 (tptp.collect X_c) (tptp.hAPP X_b _let_1 (tptp.hAPP (tptp.fun X_c (tptp.fun X_b tptp.bool)) (tptp.fun X_b _let_1) (tptp.combc X_c X_b tptp.bool) Q_3) Y_1)))))))))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (Pa $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_b X_c))) (let ((_let_3 (tptp.fun _let_2 _let_1))) (let ((_let_4 (tptp.fun X_c tptp.bool))) (let ((_let_5 (tptp.fun X_c _let_3))) (let ((_let_6 (tptp.fun X_c _let_4))) (let ((_let_7 (tptp.fun X_c _let_1))) (let ((_let_8 (tptp.fun tptp.bool tptp.bool))) (let ((_let_9 (tptp.fun X_b _let_8))) (let ((_let_10 (tptp.fun _let_1 _let_9))) (let ((_let_11 (tptp.fun X_c _let_9))) (let ((_let_12 (tptp.fun _let_1 _let_1))) (let ((_let_13 (tptp.fun X_c _let_12))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) (tptp.hAPP _let_1 _let_1 (tptp.collect X_b) Pa))) (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.finite_finite_1 X_c) (tptp.hAPP _let_4 _let_4 (tptp.collect X_c) (tptp.hAPP _let_7 _let_4 (tptp.hAPP (tptp.fun _let_1 tptp.bool) (tptp.fun _let_7 _let_4) (tptp.combb _let_1 tptp.bool X_c) (tptp.fEx X_b)) (tptp.hAPP _let_1 _let_7 (tptp.hAPP _let_13 (tptp.fun _let_1 _let_7) (tptp.combc X_c _let_1 _let_1) (tptp.hAPP _let_11 _let_13 (tptp.hAPP (tptp.fun _let_9 _let_12) (tptp.fun _let_11 _let_13) (tptp.combb _let_9 _let_12 X_c) (tptp.combs X_b tptp.bool tptp.bool)) (tptp.hAPP _let_7 _let_11 (tptp.hAPP _let_10 (tptp.fun _let_7 _let_11) (tptp.combb _let_1 _let_9 X_c) (tptp.hAPP (tptp.fun tptp.bool _let_8) _let_10 (tptp.combb tptp.bool _let_8 X_b) tptp.fconj)) (tptp.hAPP _let_2 _let_7 (tptp.hAPP _let_5 (tptp.fun _let_2 _let_7) (tptp.combc X_c _let_2 _let_1) (tptp.hAPP _let_6 _let_5 (tptp.hAPP (tptp.fun _let_4 _let_3) (tptp.fun _let_6 _let_5) (tptp.combb _let_4 _let_3 X_c) (tptp.combb X_c tptp.bool X_b)) (tptp.fequal X_c))) F)))) Pa)))))))))))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun X_b X_b))) (let ((_let_5 (tptp.hAPP X_b _let_4 (tptp.ord_min X_b) X_1))) (let ((_let_6 (tptp.fun _let_4 _let_1))) (let ((_let_7 (tptp.fun X_b _let_6))) (let ((_let_8 (tptp.fun X_b _let_1))) (let ((_let_9 (tptp.fun tptp.bool tptp.bool))) (let ((_let_10 (tptp.fun X_b _let_9))) (let ((_let_11 (tptp.fun _let_1 _let_10))) (let ((_let_12 (tptp.fun X_b _let_10))) (let ((_let_13 (tptp.fun X_b _let_2))) (let ((_let_14 (tptp.hAPP (tptp.fun X_b _let_4) (tptp.fun _let_1 X_b) (tptp.big_Sup_fin X_b) (tptp.ord_max X_b)))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (=> (not (= (tptp.ti _let_1 A_3) (tptp.bot_bot _let_1))) (= (tptp.hAPP X_b X_b _let_5 (tptp.hAPP _let_1 X_b _let_14 A_3)) (tptp.hAPP _let_1 X_b _let_14 (tptp.hAPP _let_1 _let_1 (tptp.collect X_b) (tptp.hAPP _let_8 _let_1 (tptp.hAPP _let_3 (tptp.fun _let_8 _let_1) (tptp.combb _let_1 tptp.bool X_b) (tptp.fEx X_b)) (tptp.hAPP _let_1 _let_8 (tptp.hAPP _let_13 (tptp.fun _let_1 _let_8) (tptp.combc X_b _let_1 _let_1) (tptp.hAPP _let_12 _let_13 (tptp.hAPP (tptp.fun _let_10 _let_2) (tptp.fun _let_12 _let_13) (tptp.combb _let_10 _let_2 X_b) (tptp.combs X_b tptp.bool tptp.bool)) (tptp.hAPP _let_8 _let_12 (tptp.hAPP _let_11 (tptp.fun _let_8 _let_12) (tptp.combb _let_1 _let_10 X_b) (tptp.hAPP (tptp.fun tptp.bool _let_9) _let_11 (tptp.combb tptp.bool _let_9 X_b) tptp.fconj)) (tptp.hAPP _let_4 _let_8 (tptp.hAPP _let_7 (tptp.fun _let_4 _let_8) (tptp.combc X_b _let_4 _let_1) (tptp.hAPP _let_8 _let_7 (tptp.hAPP (tptp.fun _let_1 _let_6) (tptp.fun _let_8 _let_7) (tptp.combb _let_1 _let_6 X_b) (tptp.combb X_b tptp.bool X_b)) (tptp.fequal X_b))) _let_5)))) (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_b _let_3) _let_2 (tptp.combc X_b _let_1 tptp.bool) (tptp.member X_b)) A_3))))))))))))))))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((B_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.hAPP (tptp.fun X_b _let_3) _let_2 (tptp.combc X_b _let_1 tptp.bool) (tptp.member X_b)))) (let ((_let_5 (tptp.fun tptp.bool tptp.bool))) (let ((_let_6 (tptp.fun X_b _let_5))) (let ((_let_7 (tptp.fun _let_1 _let_6))) (let ((_let_8 (tptp.hAPP (tptp.fun tptp.bool _let_5) _let_7 (tptp.combb tptp.bool _let_5 X_b) tptp.fconj))) (let ((_let_9 (tptp.fun X_b _let_2))) (let ((_let_10 (tptp.fun X_b _let_1))) (let ((_let_11 (tptp.ord_min X_b))) (let ((_let_12 (tptp.fun X_b X_b))) (let ((_let_13 (tptp.fun _let_12 _let_1))) (let ((_let_14 (tptp.fun X_b _let_13))) (let ((_let_15 (tptp.fun X_b _let_12))) (let ((_let_16 (tptp.fun _let_15 _let_10))) (let ((_let_17 (tptp.fun X_b _let_16))) (let ((_let_18 (tptp.fun X_b _let_10))) (let ((_let_19 (tptp.fun X_b _let_6))) (let ((_let_20 (tptp.fun _let_10 _let_19))) (let ((_let_21 (tptp.fun X_b _let_19))) (let ((_let_22 (tptp.fun _let_19 _let_9))) (let ((_let_23 (tptp.fun X_b _let_9))) (let ((_let_24 (tptp.fun _let_10 _let_10))) (let ((_let_25 (tptp.fun X_b _let_24))) (let ((_let_26 (tptp.fun _let_10 _let_1))) (let ((_let_27 (tptp.hAPP _let_3 _let_26 (tptp.combb _let_1 tptp.bool X_b) (tptp.fEx X_b)))) (let ((_let_28 (tptp.hAPP _let_15 (tptp.fun _let_1 X_b) (tptp.big_Sup_fin X_b) (tptp.ord_max X_b)))) (let ((_let_29 (tptp.bot_bot _let_1))) (let ((_let_30 (tptp.finite_finite_1 X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_30 A_3)) (=> (not (= (tptp.ti _let_1 A_3) _let_29)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_30 B_2)) (=> (not (= (tptp.ti _let_1 B_2) _let_29)) (= (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_12 _let_11 (tptp.hAPP _let_1 X_b _let_28 A_3)) (tptp.hAPP _let_1 X_b _let_28 B_2)) (tptp.hAPP _let_1 X_b _let_28 (tptp.hAPP _let_1 _let_1 (tptp.collect X_b) (tptp.hAPP _let_10 _let_1 _let_27 (tptp.hAPP _let_18 _let_10 (tptp.hAPP _let_26 (tptp.fun _let_18 _let_10) (tptp.combb _let_10 _let_1 X_b) _let_27) (tptp.hAPP _let_10 _let_18 (tptp.hAPP _let_25 (tptp.fun _let_10 _let_18) (tptp.combc X_b _let_10 _let_10) (tptp.hAPP _let_23 _let_25 (tptp.hAPP (tptp.fun _let_9 _let_24) (tptp.fun _let_23 _let_25) (tptp.combb _let_9 _let_24 X_b) (tptp.combs X_b _let_1 _let_1)) (tptp.hAPP _let_21 _let_23 (tptp.hAPP _let_22 (tptp.fun _let_21 _let_23) (tptp.combb _let_19 _let_9 X_b) (tptp.hAPP (tptp.fun _let_6 _let_2) _let_22 (tptp.combb _let_6 _let_2 X_b) (tptp.combs X_b tptp.bool tptp.bool))) (tptp.hAPP _let_18 _let_21 (tptp.hAPP _let_20 (tptp.fun _let_18 _let_21) (tptp.combb _let_10 _let_19 X_b) (tptp.hAPP _let_7 _let_20 (tptp.combb _let_1 _let_6 X_b) _let_8)) (tptp.hAPP _let_15 _let_18 (tptp.hAPP _let_17 (tptp.fun _let_15 _let_18) (tptp.combc X_b _let_15 _let_10) (tptp.hAPP _let_14 _let_17 (tptp.hAPP (tptp.fun _let_13 _let_16) (tptp.fun _let_14 _let_17) (tptp.combb _let_13 _let_16 X_b) (tptp.combb _let_12 _let_1 X_b)) (tptp.hAPP _let_10 _let_14 (tptp.hAPP (tptp.fun _let_1 _let_13) (tptp.fun _let_10 _let_14) (tptp.combb _let_1 _let_13 X_b) (tptp.combb X_b tptp.bool X_b)) (tptp.fequal X_b)))) _let_11))))) (tptp.hAPP _let_1 _let_10 (tptp.hAPP _let_9 (tptp.fun _let_1 _let_10) (tptp.combc X_b _let_1 _let_1) (tptp.hAPP _let_6 _let_9 (tptp.hAPP (tptp.fun _let_5 _let_2) (tptp.fun _let_6 _let_9) (tptp.combb _let_5 _let_2 X_b) (tptp.combb tptp.bool tptp.bool X_b)) (tptp.hAPP _let_1 _let_6 _let_8 (tptp.hAPP _let_1 _let_1 _let_4 A_3)))) (tptp.hAPP _let_1 _let_1 _let_4 B_2))))))))))))))))))))))))))))))))))))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.ord_max X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun X_b X_b))) (let ((_let_4 (tptp.hAPP _let_2 X_b (tptp.hAPP (tptp.fun X_b _let_3) (tptp.fun _let_2 X_b) (tptp.big_Sup_fin X_b) _let_1) A_3))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_b (tptp.fun _let_2 tptp.bool) (tptp.member X_b) X_1) A_3)) (= (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_3 _let_1 X_1) _let_4) _let_4)))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (tptp.hAPP _let_1 X_b (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun _let_1 X_b) (tptp.big_Sup_fin X_b) (tptp.ord_max X_b)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_1) (tptp.bot_bot _let_1))) (tptp.ti X_b X_1)))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((A_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_b X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 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_2) A_3)) (= (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_2 (tptp.ord_min X_b) A_2) (tptp.hAPP _let_1 X_b (tptp.hAPP (tptp.fun X_b _let_2) (tptp.fun _let_1 X_b) (tptp.big_Sup_fin X_b) (tptp.ord_max X_b)) A_3)) (tptp.ti X_b A_2))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((A_3 $$unsorted)) (let ((_let_1 (tptp.ord_max 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_3)) (= (tptp.hAPP _let_2 X_b (tptp.hAPP _let_4 _let_3 (tptp.big_Sup_fin X_b) _let_1) A_3) (tptp.hAPP _let_2 X_b (tptp.hAPP _let_4 _let_3 (tptp.finite_fold1 X_b) _let_1) A_3)))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.ord_max X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun X_b X_b))) (let ((_let_4 (tptp.hAPP (tptp.fun X_b _let_3) (tptp.fun _let_2 X_b) (tptp.big_Sup_fin X_b) _let_1))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (=> (not (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_b (tptp.fun _let_2 tptp.bool) (tptp.member X_b) X_1) A_3))) (=> (not (= (tptp.ti _let_2 A_3) (tptp.bot_bot _let_2))) (= (tptp.hAPP _let_2 X_b _let_4 (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_b (tptp.fun _let_2 _let_2) (tptp.insert X_b) X_1) A_3)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_3 _let_1 X_1) (tptp.hAPP _let_2 X_b _let_4 A_3))))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.ord_max 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.big_Sup_fin X_b) _let_1))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (=> (not (= (tptp.ti _let_2 A_3) (tptp.bot_bot _let_2))) (= (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_3)) (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_3)))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((B_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.ord_max X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun X_b X_b))) (let ((_let_4 (tptp.hAPP (tptp.fun X_b _let_3) (tptp.fun _let_2 X_b) (tptp.big_Sup_fin X_b) _let_1))) (let ((_let_5 (tptp.hAPP _let_2 X_b _let_4 A_3))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (=> (not (= (tptp.ti _let_2 B_2) (tptp.bot_bot _let_2))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) B_2) A_3)) (= (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_3 _let_1 (tptp.hAPP _let_2 X_b _let_4 B_2)) _let_5) _let_5)))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linord2061991079up_add X_b) (forall ((K_1 $$unsorted) (N_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun X_b X_b))) (let ((_let_5 (tptp.hAPP X_b _let_4 (tptp.plus_plus X_b) K_1))) (let ((_let_6 (tptp.fun _let_4 _let_1))) (let ((_let_7 (tptp.fun X_b _let_6))) (let ((_let_8 (tptp.fun X_b _let_1))) (let ((_let_9 (tptp.fun tptp.bool tptp.bool))) (let ((_let_10 (tptp.fun X_b _let_9))) (let ((_let_11 (tptp.fun _let_1 _let_10))) (let ((_let_12 (tptp.fun X_b _let_10))) (let ((_let_13 (tptp.fun X_b _let_2))) (let ((_let_14 (tptp.big_linorder_Max X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) N_3)) (=> (not (= (tptp.ti _let_1 N_3) (tptp.bot_bot _let_1))) (= (tptp.hAPP X_b X_b _let_5 (tptp.hAPP _let_1 X_b _let_14 N_3)) (tptp.hAPP _let_1 X_b _let_14 (tptp.hAPP _let_1 _let_1 (tptp.collect X_b) (tptp.hAPP _let_8 _let_1 (tptp.hAPP _let_3 (tptp.fun _let_8 _let_1) (tptp.combb _let_1 tptp.bool X_b) (tptp.fEx X_b)) (tptp.hAPP _let_1 _let_8 (tptp.hAPP _let_13 (tptp.fun _let_1 _let_8) (tptp.combc X_b _let_1 _let_1) (tptp.hAPP _let_12 _let_13 (tptp.hAPP (tptp.fun _let_10 _let_2) (tptp.fun _let_12 _let_13) (tptp.combb _let_10 _let_2 X_b) (tptp.combs X_b tptp.bool tptp.bool)) (tptp.hAPP _let_8 _let_12 (tptp.hAPP _let_11 (tptp.fun _let_8 _let_12) (tptp.combb _let_1 _let_10 X_b) (tptp.hAPP (tptp.fun tptp.bool _let_9) _let_11 (tptp.combb tptp.bool _let_9 X_b) tptp.fconj)) (tptp.hAPP _let_4 _let_8 (tptp.hAPP _let_7 (tptp.fun _let_4 _let_8) (tptp.combc X_b _let_4 _let_1) (tptp.hAPP _let_8 _let_7 (tptp.hAPP (tptp.fun _let_1 _let_6) (tptp.fun _let_8 _let_7) (tptp.combb _let_1 _let_6 X_b) (tptp.combb X_b tptp.bool X_b)) (tptp.fequal X_b))) _let_5)))) (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_b _let_3) _let_2 (tptp.combc X_b _let_1 tptp.bool) (tptp.member X_b)) N_3))))))))))))))))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linord2061991079up_add X_b) (forall ((K_1 $$unsorted) (N_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun X_b X_b))) (let ((_let_5 (tptp.hAPP X_b _let_4 (tptp.plus_plus X_b) K_1))) (let ((_let_6 (tptp.fun _let_4 _let_1))) (let ((_let_7 (tptp.fun X_b _let_6))) (let ((_let_8 (tptp.fun X_b _let_1))) (let ((_let_9 (tptp.fun tptp.bool tptp.bool))) (let ((_let_10 (tptp.fun X_b _let_9))) (let ((_let_11 (tptp.fun _let_1 _let_10))) (let ((_let_12 (tptp.fun X_b _let_10))) (let ((_let_13 (tptp.fun X_b _let_2))) (let ((_let_14 (tptp.big_linorder_Min X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) N_3)) (=> (not (= (tptp.ti _let_1 N_3) (tptp.bot_bot _let_1))) (= (tptp.hAPP X_b X_b _let_5 (tptp.hAPP _let_1 X_b _let_14 N_3)) (tptp.hAPP _let_1 X_b _let_14 (tptp.hAPP _let_1 _let_1 (tptp.collect X_b) (tptp.hAPP _let_8 _let_1 (tptp.hAPP _let_3 (tptp.fun _let_8 _let_1) (tptp.combb _let_1 tptp.bool X_b) (tptp.fEx X_b)) (tptp.hAPP _let_1 _let_8 (tptp.hAPP _let_13 (tptp.fun _let_1 _let_8) (tptp.combc X_b _let_1 _let_1) (tptp.hAPP _let_12 _let_13 (tptp.hAPP (tptp.fun _let_10 _let_2) (tptp.fun _let_12 _let_13) (tptp.combb _let_10 _let_2 X_b) (tptp.combs X_b tptp.bool tptp.bool)) (tptp.hAPP _let_8 _let_12 (tptp.hAPP _let_11 (tptp.fun _let_8 _let_12) (tptp.combb _let_1 _let_10 X_b) (tptp.hAPP (tptp.fun tptp.bool _let_9) _let_11 (tptp.combb tptp.bool _let_9 X_b) tptp.fconj)) (tptp.hAPP _let_4 _let_8 (tptp.hAPP _let_7 (tptp.fun _let_4 _let_8) (tptp.combc X_b _let_4 _let_1) (tptp.hAPP _let_8 _let_7 (tptp.hAPP (tptp.fun _let_1 _let_6) (tptp.fun _let_8 _let_7) (tptp.combb _let_1 _let_6 X_b) (tptp.combb X_b tptp.bool X_b)) (tptp.fequal X_b))) _let_5)))) (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_b _let_3) _let_2 (tptp.combc X_b _let_1 tptp.bool) (tptp.member X_b)) N_3))))))))))))))))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((A_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.ord_max 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_3)) (= (tptp.hAPP _let_2 X_b (tptp.hAPP _let_4 _let_3 (tptp.big_Sup_fin 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_2) A_3)) (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_2) A_3)))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.ord_max X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun _let_2 X_b))) (let ((_let_4 (tptp.fun X_b (tptp.fun X_b X_b)))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (=> (not (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_b (tptp.fun _let_2 tptp.bool) (tptp.member X_b) X_1) A_3))) (= (tptp.hAPP _let_2 X_b (tptp.hAPP _let_4 _let_3 (tptp.big_Sup_fin X_b) _let_1) (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_b (tptp.fun _let_2 _let_2) (tptp.insert X_b) X_1) A_3)) (tptp.hAPP _let_2 X_b (tptp.hAPP X_b _let_3 (tptp.hAPP _let_4 (tptp.fun X_b _let_3) (tptp.finite_fold X_b X_b) _let_1) X_1) A_3))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.bot_bot _let_1))) (let ((_let_3 (tptp.fun _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_3) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_3 (tptp.insert X_b) X_1) _let_2)))) (let ((_let_5 (tptp.ord_max X_b))) (let ((_let_6 (tptp.fun X_b X_b))) (let ((_let_7 (tptp.hAPP (tptp.fun X_b _let_6) (tptp.fun _let_1 X_b) (tptp.big_Sup_fin X_b) _let_5))) (let ((_let_8 (tptp.hAPP _let_1 X_b _let_7 A_3))) (let ((_let_9 (= _let_4 _let_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 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) X_1) A_3)) (and (=> _let_9 (= _let_8 (tptp.ti X_b X_1))) (=> (not _let_9) (= _let_8 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_6 _let_5 X_1) (tptp.hAPP _let_1 X_b _let_7 _let_4))))))))))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.bot_bot _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.hAPP X_b _let_3 (tptp.insert X_b) X_1))) (let ((_let_5 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 (tptp.minus_minus _let_1) A_3) (tptp.hAPP _let_1 _let_1 _let_4 _let_2)))) (let ((_let_6 (tptp.ord_max X_b))) (let ((_let_7 (tptp.fun X_b X_b))) (let ((_let_8 (tptp.hAPP (tptp.fun X_b _let_7) (tptp.fun _let_1 X_b) (tptp.big_Sup_fin X_b) _let_6))) (let ((_let_9 (tptp.hAPP _let_1 X_b _let_8 (tptp.hAPP _let_1 _let_1 _let_4 A_3)))) (let ((_let_10 (= _let_5 _let_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (and (=> _let_10 (= _let_9 (tptp.ti X_b X_1))) (=> (not _let_10) (= _let_9 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_7 _let_6 X_1) (tptp.hAPP _let_1 X_b _let_8 _let_5))))))))))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((N_3 $$unsorted) (H $$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.big_Sup_fin X_b) (tptp.ord_max X_b)))) (=> (forall ((X_2 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.ord_max 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_1)) (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_1)))))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) N_3)) (=> (not (= (tptp.ti _let_1 N_3) (tptp.bot_bot _let_1))) (= (tptp.hAPP X_b X_b H (tptp.hAPP _let_1 X_b _let_3 N_3)) (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_3)))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((A_3 $$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)) (=> (not (= (tptp.ti _let_1 A_3) (tptp.bot_bot _let_1))) (=> (forall ((X_2 $$unsorted) (Y_1 $$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))) (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.ord_max X_b) X_2) Y_1)) (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_1) (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.big_Sup_fin X_b) (tptp.ord_max X_b)) A_3)) A_3))))))))) (forall ((X_b $$unsorted) (Pa $$unsorted)) (= (exists ((X1 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa X1))) (forall ((Q_2 $$unsorted)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa X_2)) (tptp.hBOOL Q_2))) (tptp.hBOOL Q_2))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.finite_card X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP _let_2 tptp.nat _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_3 (tptp.minus_minus _let_2) A_3) (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_b _let_3 (tptp.insert X_b) X_1) (tptp.bot_bot _let_2))))) (tptp.hAPP _let_2 tptp.nat _let_1 A_3)))))))) (forall ((X_c $$unsorted) (X_b $$unsorted)) (=> (and (tptp.order X_b) (tptp.ord X_c)) (forall ((Ca $$unsorted) (F $$unsorted) (Ba $$unsorted) (A_2 $$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_c X_b F Ba)) A_2)) (=> (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less_eq X_c) Ca) Ba)) (=> (forall ((X_2 $$unsorted) (Y_1 $$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) Y_1) X_2)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) (tptp.hAPP X_c X_b F Y_1)) (tptp.hAPP X_c X_b F X_2))))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 (tptp.hAPP X_c X_b F Ca)) A_2)))))))))) (forall ((X_b $$unsorted)) (=> (tptp.order X_b) (forall ((Ca $$unsorted) (A_2 $$unsorted) (F $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (= (tptp.ti X_b A_2) (tptp.hAPP X_b X_b F Ba)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 Ca) Ba)) (=> (forall ((X_2 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 Y_1) X_2)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 (tptp.hAPP X_b X_b F Y_1)) (tptp.hAPP X_b X_b F X_2))))))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 (tptp.hAPP X_b X_b F Ca)) A_2)))))))))) (forall ((U $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hAPP _let_1 tptp.nat (tptp.finite_card tptp.nat) (tptp.hAPP tptp.nat _let_1 (tptp.ord_lessThan tptp.nat) U)) U))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.finite_card X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP _let_1 tptp.nat _let_2 A_3)) (tptp.hAPP _let_1 tptp.nat _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_1) A_3)))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.finite_card X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) B_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) A_3) B_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP _let_1 tptp.nat _let_2 B_2)) (tptp.hAPP _let_1 tptp.nat _let_2 A_3))) (= (tptp.ti _let_1 A_3) (tptp.ti _let_1 B_2)))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.finite_card X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_b) B_2)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) A_3) B_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP _let_2 tptp.nat _let_1 A_3)) (tptp.hAPP _let_2 tptp.nat _let_1 B_2)))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP _let_2 tptp.nat (tptp.finite_card X_c) (tptp.hAPP _let_1 _let_2 (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun _let_1 _let_2) (tptp.image X_b X_c) F) A_3))) (tptp.hAPP _let_1 tptp.nat (tptp.finite_card X_b) A_3))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.finite_card 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) B_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_2) A_3)) (= (tptp.hAPP _let_2 tptp.nat _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 (tptp.fun _let_2 _let_2) (tptp.minus_minus _let_2) A_3) B_2)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) (tptp.hAPP _let_2 tptp.nat _let_1 A_3)) (tptp.hAPP _let_2 tptp.nat _let_1 B_2)))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.finite_card X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) B_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) (tptp.hAPP _let_1 tptp.nat _let_2 A_3)) (tptp.hAPP _let_1 tptp.nat _let_2 B_2))) (tptp.hAPP _let_1 tptp.nat _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) A_3) B_2)))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (R_1 $$unsorted) (K_1 $$unsorted) (T_4 $$unsorted) (S_1 $$unsorted)) (let ((_let_1 (tptp.finite_card X_c))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (let ((_let_4 (tptp.fun tptp.bool tptp.bool))) (let ((_let_5 (tptp.fun X_c _let_4))) (let ((_let_6 (tptp.combb _let_2 _let_2 X_b))) (let ((_let_7 (tptp.fun X_b _let_2))) (let ((_let_8 (tptp.fun _let_7 _let_7))) (let ((_let_9 (tptp.fun X_b tptp.nat))) (let ((_let_10 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_10 tptp.bool (tptp.finite_finite_1 X_b) S_1)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_c) T_4)) (=> (forall ((X_2 $$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_1))) (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 (tptp.hAPP X_c (tptp.fun _let_2 tptp.bool) (tptp.member X_c) X_2) T_4)) (= (tptp.hAPP _let_1 tptp.nat (tptp.finite_card X_b) (tptp.hAPP _let_1 _let_1 (tptp.collect X_b) (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.fconj) (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_b (tptp.fun _let_1 tptp.bool)) _let_3 (tptp.combc X_b _let_1 tptp.bool) (tptp.member X_b)) S_1))) (tptp.hAPP X_c _let_1 (tptp.hAPP (tptp.fun X_b _let_2) (tptp.fun X_c _let_1) (tptp.combc X_b X_c tptp.bool) R_1) X_2)))) K_1)))))))) (= (tptp.hAPP _let_10 tptp.nat (tptp.hAPP _let_9 (tptp.fun _let_10 tptp.nat) (tptp.big_co1399186613setsum X_b tptp.nat) (tptp.hAPP _let_7 _let_9 (tptp.hAPP (tptp.fun _let_2 tptp.nat) (tptp.fun _let_7 _let_9) (tptp.combb _let_2 tptp.nat X_b) _let_1) (tptp.hAPP _let_7 _let_7 (tptp.hAPP _let_3 _let_8 _let_6 (tptp.collect X_c)) (tptp.hAPP _let_7 _let_7 (tptp.hAPP _let_3 _let_8 _let_6 (tptp.hAPP _let_5 _let_3 (tptp.combs X_c 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_c) tptp.fconj) (tptp.hAPP _let_2 _let_2 (tptp.hAPP (tptp.fun X_c (tptp.fun _let_2 tptp.bool)) _let_3 (tptp.combc X_c _let_2 tptp.bool) (tptp.member X_c)) T_4)))) R_1)))) S_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) K_1) (tptp.hAPP _let_2 tptp.nat _let_1 T_4))))))))))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (R_1 $$unsorted) (K_1 $$unsorted) (T_5 $$unsorted) (S_2 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.nat))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.fun tptp.bool tptp.bool))) (let ((_let_5 (tptp.fun X_c _let_4))) (let ((_let_6 (tptp.combb _let_1 _let_1 X_b))) (let ((_let_7 (tptp.fun X_b _let_1))) (let ((_let_8 (tptp.fun _let_7 _let_7))) (let ((_let_9 (tptp.fun X_b tptp.nat))) (let ((_let_10 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_10 tptp.bool (tptp.finite_finite_1 X_b) S_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_c) T_5)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.fun tptp.bool tptp.bool))) (let ((_let_5 (tptp.fun X_b _let_4))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_c (tptp.fun _let_2 tptp.bool) (tptp.member X_c) X_2) T_5)) (= (tptp.hAPP _let_1 tptp.nat (tptp.finite_card X_b) (tptp.hAPP _let_1 _let_1 (tptp.collect X_b) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_5 _let_3 (tptp.combs X_b tptp.bool tptp.bool) (tptp.hAPP _let_1 _let_5 (tptp.hAPP (tptp.fun tptp.bool _let_4) (tptp.fun _let_1 _let_5) (tptp.combb tptp.bool _let_4 X_b) tptp.fconj) (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_b (tptp.fun _let_1 tptp.bool)) _let_3 (tptp.combc X_b _let_1 tptp.bool) (tptp.member X_b)) S_2))) (tptp.hAPP X_c _let_1 (tptp.hAPP (tptp.fun X_b _let_2) (tptp.fun X_c _let_1) (tptp.combc X_b X_c tptp.bool) R_1) X_2)))) (tptp.hAPP X_c tptp.nat K_1 X_2))))))))) (= (tptp.hAPP _let_10 tptp.nat (tptp.hAPP _let_9 (tptp.fun _let_10 tptp.nat) (tptp.big_co1399186613setsum X_b tptp.nat) (tptp.hAPP _let_7 _let_9 (tptp.hAPP _let_2 (tptp.fun _let_7 _let_9) (tptp.combb _let_1 tptp.nat X_b) (tptp.finite_card X_c)) (tptp.hAPP _let_7 _let_7 (tptp.hAPP _let_3 _let_8 _let_6 (tptp.collect X_c)) (tptp.hAPP _let_7 _let_7 (tptp.hAPP _let_3 _let_8 _let_6 (tptp.hAPP _let_5 _let_3 (tptp.combs X_c tptp.bool tptp.bool) (tptp.hAPP _let_1 _let_5 (tptp.hAPP (tptp.fun tptp.bool _let_4) (tptp.fun _let_1 _let_5) (tptp.combb tptp.bool _let_4 X_c) tptp.fconj) (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_c (tptp.fun _let_1 tptp.bool)) _let_3 (tptp.combc X_c _let_1 tptp.bool) (tptp.member X_c)) T_5)))) R_1)))) S_2) (tptp.hAPP _let_1 tptp.nat (tptp.hAPP (tptp.fun X_c tptp.nat) _let_2 (tptp.big_co1399186613setsum X_c tptp.nat) K_1) T_5)))))))))))))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.finite_card X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (=> (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_3)) (= (tptp.hAPP _let_2 tptp.nat _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_3 (tptp.minus_minus _let_2) A_3) (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_b _let_3 (tptp.insert X_b) X_1) (tptp.bot_bot _let_2)))) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) (tptp.hAPP _let_2 tptp.nat _let_1 A_3)) (tptp.one_one tptp.nat))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted)) (=> (tptp.comm_monoid_mult X_b) (forall ((A_3 $$unsorted)) (let ((_let_1 (tptp.one_one X_b))) (let ((_let_2 (tptp.fun X_c X_b))) (let ((_let_3 (tptp.fun X_c tptp.bool))) (= (tptp.hAPP _let_3 X_b (tptp.hAPP _let_2 (tptp.fun _let_3 X_b) (tptp.big_co302546470etprod X_c X_b) (tptp.hAPP X_b _let_2 (tptp.combk X_b X_c) _let_1)) A_3) _let_1))))))) (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.one_one tptp.nat))) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) M_1) N) _let_1) (and (= M_1 _let_1) (= N _let_1))))) (forall ((N_1 $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) N_1) (tptp.one_one tptp.nat)) N_1)) (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.one_one tptp.nat))) (= (= _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) M_1) N)) (and (= M_1 _let_1) (= N _let_1))))) (forall ((N_1 $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) (tptp.one_one tptp.nat)) N_1) N_1)) (forall ((X_a $$unsorted)) (=> (tptp.comm_monoid_mult X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1) (tptp.one_one X_a)) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1) (tptp.one_one X_a)) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.monoid_mult X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1) (tptp.one_one X_a)) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_monoid_mult X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) (tptp.one_one X_a)) A_1) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) (tptp.one_one X_a)) A_1) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.monoid_mult X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) (tptp.one_one X_a)) A_1) (tptp.ti X_a A_1))))) (forall ((X_b $$unsorted) (F $$unsorted) (F_2 $$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)) (= (= (tptp.hAPP _let_1 tptp.nat (tptp.hAPP (tptp.fun X_b tptp.nat) (tptp.fun _let_1 tptp.nat) (tptp.big_co302546470etprod X_b tptp.nat) F) F_2) (tptp.one_one tptp.nat)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_2) F_2)) (= (tptp.hAPP X_b tptp.nat F X_2) (tptp.one_one tptp.nat))))))))) (forall ((X_b $$unsorted)) (=> (tptp.one X_b) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.one_one X_b))) (let ((_let_2 (tptp.ti X_b X_1))) (= (= _let_1 _let_2) (= _let_2 _let_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.times_times X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 A_1) M)) M) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) (tptp.one_one X_a))) M)))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((M $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.times_times X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 M) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 A_1) M)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) (tptp.one_one X_a))) M)))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((M $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (let ((_let_2 (tptp.plus_plus X_a))) (let ((_let_3 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 M) M) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 (tptp.times_times X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 _let_1) _let_1)) M)))))))) (forall ((X_b $$unsorted)) (=> (tptp.ring_11004092258visors X_b) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.one_one X_b))) (let ((_let_2 (tptp.ti X_b X_1))) (= (= (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.times_times X_b) X_1) X_1) _let_1) (or (= _let_2 _let_1) (= _let_2 (tptp.hAPP X_b X_b (tptp.uminus_uminus X_b) _let_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_ring_1 X_a) (forall ((X $$unsorted)) (let ((_let_1 (tptp.uminus_uminus X_a))) (= (tptp.hAPP X_a X_a _let_1 X) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) (tptp.hAPP X_a X_a _let_1 (tptp.one_one X_a))) X)))))) (forall ((X_c $$unsorted) (X_b $$unsorted)) (=> (tptp.comm_monoid_mult X_b) (forall ((G $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (= (tptp.hAPP _let_1 X_b (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun _let_1 X_b) (tptp.big_co302546470etprod X_c X_b) G) (tptp.bot_bot _let_1)) (tptp.one_one X_b)))))) (forall ((X_c $$unsorted) (X_b $$unsorted)) (=> (tptp.comm_monoid_mult X_b) (forall ((F $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (= (tptp.hAPP _let_1 X_b (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun _let_1 X_b) (tptp.big_co302546470etprod X_c X_b) F) (tptp.bot_bot _let_1)) (tptp.one_one X_b)))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (tptp.comm_monoid_mult X_c) (forall ((F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_3))) (= (tptp.hAPP _let_1 X_c (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun _let_1 X_c) (tptp.big_co302546470etprod X_b X_c) F) A_3) (tptp.one_one X_c))))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (tptp.comm_monoid_mult X_c) (forall ((G $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_3))) (= (tptp.hAPP _let_1 X_c (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun _let_1 X_c) (tptp.big_co302546470etprod X_b X_c) G) A_3) (tptp.one_one X_c))))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (tptp.comm_monoid_mult X_c) (forall ((Ba $$unsorted) (A_2 $$unsorted) (S_1 $$unsorted)) (let ((_let_1 (tptp.one_one X_c))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun X_c X_c))) (let ((_let_4 (tptp.fun X_c _let_3))) (let ((_let_5 (tptp.fun X_b _let_4))) (let ((_let_6 (tptp.fun X_b _let_3))) (let ((_let_7 (tptp.fun X_b X_c))) (let ((_let_8 (tptp.hAPP _let_2 X_c (tptp.hAPP _let_7 (tptp.fun _let_2 X_c) (tptp.big_co302546470etprod X_b X_c) (tptp.hAPP X_c _let_7 (tptp.hAPP _let_6 (tptp.fun X_c _let_7) (tptp.combc X_b X_c X_c) (tptp.hAPP _let_7 _let_6 (tptp.hAPP _let_5 (tptp.fun _let_7 _let_6) (tptp.combs X_b X_c _let_3) (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.if X_c)) (tptp.hAPP X_b _let_2 (tptp.fequal X_b) A_2))) Ba)) _let_1)) S_1))) (let ((_let_9 (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_b (tptp.fun _let_2 tptp.bool) (tptp.member X_b) A_2) S_1)))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_b) S_1)) (and (=> _let_9 (= _let_8 (tptp.hAPP X_b X_c Ba A_2))) (=> (not _let_9) (= _let_8 _let_1)))))))))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (tptp.comm_monoid_mult X_c) (forall ((Ba $$unsorted) (A_2 $$unsorted) (S_1 $$unsorted)) (let ((_let_1 (tptp.one_one X_c))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun X_b _let_2))) (let ((_let_4 (tptp.fun X_c X_c))) (let ((_let_5 (tptp.fun X_c _let_4))) (let ((_let_6 (tptp.fun X_b _let_5))) (let ((_let_7 (tptp.fun X_b _let_4))) (let ((_let_8 (tptp.fun X_b X_c))) (let ((_let_9 (tptp.hAPP _let_2 X_c (tptp.hAPP _let_8 (tptp.fun _let_2 X_c) (tptp.big_co302546470etprod X_b X_c) (tptp.hAPP X_c _let_8 (tptp.hAPP _let_7 (tptp.fun X_c _let_8) (tptp.combc X_b X_c X_c) (tptp.hAPP _let_8 _let_7 (tptp.hAPP _let_6 (tptp.fun _let_8 _let_7) (tptp.combs X_b X_c _let_4) (tptp.hAPP _let_2 _let_6 (tptp.hAPP (tptp.fun tptp.bool _let_5) (tptp.fun _let_2 _let_6) (tptp.combb tptp.bool _let_5 X_b) (tptp.if X_c)) (tptp.hAPP X_b _let_2 (tptp.hAPP _let_3 _let_3 (tptp.combc X_b X_b tptp.bool) (tptp.fequal X_b)) A_2))) Ba)) _let_1)) S_1))) (let ((_let_10 (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_b (tptp.fun _let_2 tptp.bool) (tptp.member X_b) A_2) S_1)))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_b) S_1)) (and (=> _let_10 (= _let_9 (tptp.hAPP X_b X_c Ba A_2))) (=> (not _let_10) (= _let_9 _let_1))))))))))))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.nat))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (= (tptp.hAPP _let_2 tptp.nat (tptp.finite_card X_b) A_3) (tptp.hAPP _let_2 tptp.nat (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.nat) (tptp.big_co1399186613setsum X_b tptp.nat) (tptp.hAPP tptp.nat _let_1 (tptp.combk tptp.nat X_b) (tptp.one_one tptp.nat))) A_3))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.finite_card 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_3)) (=> (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_3))) (= (tptp.hAPP _let_2 tptp.nat _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_3)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) (tptp.one_one tptp.nat)) (tptp.hAPP _let_2 tptp.nat _let_1 A_3)))))))) (forall ((X_b $$unsorted) (B_2 $$unsorted) (A_2 $$unsorted) (A_3 $$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_3))) (let ((_let_4 (tptp.finite_card X_b))) (let ((_let_5 (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_5 A_3)) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_5 B_2))) (= (tptp.hAPP _let_1 tptp.nat _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_2) B_2))) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) (tptp.hAPP _let_1 tptp.nat _let_4 (tptp.hAPP _let_1 _let_1 _let_3 B_2))) (tptp.one_one tptp.nat)))))))))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP X_b _let_2 (tptp.insert X_b) X_1))) (let ((_let_4 (tptp.finite_card X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (= (tptp.hAPP _let_1 tptp.nat _let_4 (tptp.hAPP _let_1 _let_1 _let_3 A_3)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) (tptp.one_one tptp.nat)) (tptp.hAPP _let_1 tptp.nat _let_4 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.minus_minus _let_1) A_3) (tptp.hAPP _let_1 _let_1 _let_3 (tptp.bot_bot _let_1)))))))))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.finite_card X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 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) X_1) A_3)) (= (tptp.hAPP _let_1 tptp.nat _let_3 A_3) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) (tptp.one_one tptp.nat)) (tptp.hAPP _let_1 tptp.nat _let_3 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.minus_minus _let_1) A_3) (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 $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.finite_card X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.hAPP _let_2 tptp.nat _let_1 A_3))) (let ((_let_4 (tptp.fun _let_2 _let_2))) (let ((_let_5 (tptp.hAPP _let_2 tptp.nat _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_4 (tptp.minus_minus _let_2) A_3) (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_b _let_4 (tptp.insert X_b) X_1) (tptp.bot_bot _let_2)))))) (let ((_let_6 (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_b (tptp.fun _let_2 tptp.bool) (tptp.member X_b) X_1) A_3)))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (and (=> _let_6 (= _let_5 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) _let_3) (tptp.one_one tptp.nat)))) (=> (not _let_6) (= _let_5 _let_3))))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (tptp.comm_monoid_mult X_c) (forall ((F $$unsorted) (S_1 $$unsorted) (T_4 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun _let_1 X_c) (tptp.big_co302546470etprod X_b X_c) F))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) T_4)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) S_1) T_4)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_2) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) T_4) S_1))) (= (tptp.hAPP X_b X_c F X_2) (tptp.one_one X_c))))) (= (tptp.hAPP _let_1 X_c _let_2 T_4) (tptp.hAPP _let_1 X_c _let_2 S_1)))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (tptp.comm_monoid_mult X_c) (forall ((F $$unsorted) (S_1 $$unsorted) (T_4 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun _let_1 X_c) (tptp.big_co302546470etprod X_b X_c) F))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) T_4)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) S_1) T_4)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_2) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) T_4) S_1))) (= (tptp.hAPP X_b X_c F X_2) (tptp.one_one X_c))))) (= (tptp.hAPP _let_1 X_c _let_2 S_1) (tptp.hAPP _let_1 X_c _let_2 T_4)))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (tptp.comm_monoid_mult X_c) (forall ((G $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (=> (forall ((X_2 $$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_3)) (= (tptp.hAPP X_b X_c G X_2) (tptp.one_one X_c))))) (= (tptp.hAPP _let_1 X_c (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun _let_1 X_c) (tptp.big_co302546470etprod X_b X_c) G) A_3) (tptp.one_one X_c)))))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (tptp.comm_monoid_mult X_c) (forall ((F $$unsorted) (F_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_2) F_2)) (= (tptp.hAPP X_b X_c F X_2) (tptp.one_one X_c))))) (= (tptp.hAPP _let_1 X_c (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun _let_1 X_c) (tptp.big_co302546470etprod X_b X_c) F) F_2) (tptp.one_one X_c))))))) (forall ((X_b $$unsorted)) (=> (tptp.comm_semiring_1 X_b) (forall ((A_2 $$unsorted) (D $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat X_b))) (let ((_let_2 (tptp.times_times X_b))) (let ((_let_3 (tptp.fun X_b X_b))) (let ((_let_4 (tptp.plus_plus X_b))) (let ((_let_5 (tptp.hAPP X_b _let_3 _let_4 A_2))) (let ((_let_6 (tptp.fun tptp.nat tptp.bool))) (let ((_let_7 (tptp.fun tptp.nat _let_3))) (let ((_let_8 (tptp.fun tptp.nat X_b))) (let ((_let_9 (tptp.one_one X_b))) (= (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_3 _let_2 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_3 _let_4 _let_9) _let_9)) (tptp.hAPP _let_6 X_b (tptp.hAPP _let_8 (tptp.fun _let_6 X_b) (tptp.big_co1399186613setsum tptp.nat X_b) (tptp.hAPP _let_8 _let_8 (tptp.hAPP _let_3 (tptp.fun _let_8 _let_8) (tptp.combb X_b X_b tptp.nat) _let_5) (tptp.hAPP X_b _let_8 (tptp.hAPP _let_7 (tptp.fun X_b _let_8) (tptp.combc tptp.nat X_b X_b) (tptp.hAPP _let_8 _let_7 (tptp.hAPP (tptp.fun X_b _let_3) (tptp.fun _let_8 _let_7) (tptp.combb X_b _let_3 tptp.nat) _let_2) _let_1)) D))) (tptp.hAPP tptp.nat _let_6 (tptp.ord_lessThan tptp.nat) N))) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_3 _let_2 (tptp.hAPP tptp.nat X_b _let_1 N)) (tptp.hAPP X_b X_b _let_5 (tptp.hAPP X_b X_b _let_5 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_3 _let_2 (tptp.hAPP tptp.nat X_b _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) N) (tptp.one_one tptp.nat)))) D))))))))))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted)) (=> (tptp.comm_monoid_mult X_b) (forall ((H $$unsorted) (G $$unsorted) (S_1 $$unsorted) (R_1 $$unsorted)) (let ((_let_1 (tptp.big_co302546470etprod X_c X_b))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (let ((_let_3 (tptp.fun _let_2 X_b))) (let ((_let_4 (tptp.fun X_c X_b))) (let ((_let_5 (tptp.fun X_b tptp.bool))) (let ((_let_6 (tptp.one_one X_b))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_5 R_1 _let_6) _let_6)) (=> (forall ((X1 $$unsorted) (Y1 $$unsorted) (X2 $$unsorted) (Y2 $$unsorted)) (let ((_let_1 (tptp.times_times X_b))) (let ((_let_2 (tptp.fun X_b X_b))) (let ((_let_3 (tptp.fun X_b tptp.bool))) (=> (and (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_3 R_1 X1) X2)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_3 R_1 Y1) Y2))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_3 R_1 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_2 _let_1 X1) Y1)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_2 _let_1 X2) Y2)))))))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_c) S_1)) (=> (forall ((X_2 $$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) S_1)) (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_5 R_1 (tptp.hAPP _let_2 X_b (tptp.hAPP _let_4 _let_3 _let_1 H) S_1)) (tptp.hAPP _let_2 X_b (tptp.hAPP _let_4 _let_3 _let_1 G) S_1)))))))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.semiring_char_0 X_b) (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat X_b))) (= (= (tptp.hAPP tptp.nat X_b _let_1 M_1) (tptp.hAPP tptp.nat X_b _let_1 N)) (= M_1 N)))))) (forall ((X_b $$unsorted)) (=> (tptp.linordered_semidom X_b) (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat 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) (tptp.hAPP tptp.nat X_b _let_1 M_1)) (tptp.hAPP tptp.nat X_b _let_1 N))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M_1) N))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_1 X_a) (forall ((M $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat X_a))) (= (tptp.hAPP tptp.nat X_a _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M) N_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) (tptp.hAPP tptp.nat X_a _let_1 M)) (tptp.hAPP tptp.nat X_a _let_1 N_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_1 X_a) (forall ((M $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat X_a))) (= (tptp.hAPP tptp.nat X_a _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) M) N_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) (tptp.hAPP tptp.nat X_a _let_1 M)) (tptp.hAPP tptp.nat X_a _let_1 N_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_1 X_a) (= (tptp.hAPP tptp.nat X_a (tptp.semiring_1_of_nat X_a) (tptp.one_one tptp.nat)) (tptp.one_one X_a)))) (forall ((X_a $$unsorted)) (=> (tptp.ring_1 X_a) (forall ((N_1 $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat X_a))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N_1) M)) (= (tptp.hAPP tptp.nat X_a _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) M) N_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.minus_minus X_a) (tptp.hAPP tptp.nat X_a _let_1 M)) (tptp.hAPP tptp.nat X_a _let_1 N_1)))))))) (forall ((X_c $$unsorted) (X_b $$unsorted)) (=> (tptp.semiring_1 X_b) (forall ((Y_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_c X_b))) (= (tptp.hAPP _let_1 X_b (tptp.hAPP _let_2 (tptp.fun _let_1 X_b) (tptp.big_co1399186613setsum X_c X_b) (tptp.hAPP X_b _let_2 (tptp.combk X_b X_c) Y_2)) A_3) (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.times_times X_b) (tptp.hAPP tptp.nat X_b (tptp.semiring_1_of_nat X_b) (tptp.hAPP _let_1 tptp.nat (tptp.finite_card X_c) A_3))) Y_2))))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (and (tptp.ordere779506340up_add X_c) (tptp.semiring_1 X_c)) (forall ((F $$unsorted) (K_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (forall ((I_2 $$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) I_2) A_3)) (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 I_2)) K_2))))) (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 _let_1 X_c (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun _let_1 X_c) (tptp.big_co1399186613setsum X_b X_c) F) A_3)) (tptp.hAPP X_c X_c (tptp.hAPP X_c (tptp.fun X_c X_c) (tptp.times_times X_c) (tptp.hAPP tptp.nat X_c (tptp.semiring_1_of_nat X_c) (tptp.hAPP _let_1 tptp.nat (tptp.finite_card X_b) A_3))) K_2)))))))) (forall ((X_c $$unsorted) (X_b $$unsorted)) (=> (and (tptp.comm_monoid_mult X_b) (tptp.semiring_1 X_b)) (forall ((F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat X_b))) (let ((_let_2 (tptp.fun X_c X_b))) (let ((_let_3 (tptp.fun X_c tptp.nat))) (let ((_let_4 (tptp.fun X_c tptp.bool))) (= (tptp.hAPP tptp.nat X_b _let_1 (tptp.hAPP _let_4 tptp.nat (tptp.hAPP _let_3 (tptp.fun _let_4 tptp.nat) (tptp.big_co302546470etprod X_c tptp.nat) F) A_3)) (tptp.hAPP _let_4 X_b (tptp.hAPP _let_2 (tptp.fun _let_4 X_b) (tptp.big_co302546470etprod X_c X_b) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun tptp.nat X_b) (tptp.fun _let_3 _let_2) (tptp.combb tptp.nat X_b X_c) _let_1) F)) A_3))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted)) (=> (tptp.semiring_1 X_b) (forall ((F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat X_b))) (let ((_let_2 (tptp.fun X_c X_b))) (let ((_let_3 (tptp.fun X_c tptp.nat))) (let ((_let_4 (tptp.fun X_c tptp.bool))) (= (tptp.hAPP tptp.nat X_b _let_1 (tptp.hAPP _let_4 tptp.nat (tptp.hAPP _let_3 (tptp.fun _let_4 tptp.nat) (tptp.big_co1399186613setsum X_c tptp.nat) F) A_3)) (tptp.hAPP _let_4 X_b (tptp.hAPP _let_2 (tptp.fun _let_4 X_b) (tptp.big_co1399186613setsum X_c X_b) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun tptp.nat X_b) (tptp.fun _let_3 _let_2) (tptp.combb tptp.nat X_b X_c) _let_1) F)) A_3))))))))) (forall ((M $$unsorted) (N_1 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (let ((_let_2 (tptp.plus_plus tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 _let_2 (tptp.hAPP tptp.nat tptp.int _let_1 M)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 _let_2 (tptp.hAPP tptp.nat tptp.int _let_1 N_1)) Z)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 _let_2 (tptp.hAPP tptp.nat tptp.int _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M) N_1))) Z)))))) (forall ((M $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) (tptp.hAPP tptp.nat tptp.int _let_1 M)) (tptp.hAPP tptp.nat tptp.int _let_1 N_1)) (tptp.hAPP tptp.nat tptp.int _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M) N_1))))) (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.hAPP tptp.nat tptp.int _let_1 M_1)) (tptp.hAPP tptp.nat tptp.int _let_1 N))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M_1) N))))) (forall ((M $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) (tptp.hAPP tptp.nat tptp.int _let_1 M)) (tptp.hAPP tptp.nat tptp.int _let_1 N_1)) (tptp.hAPP tptp.nat tptp.int _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) M) N_1))))) (forall ((M $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (tptp.hAPP tptp.nat tptp.int _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) M) N_1)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) (tptp.hAPP tptp.nat tptp.int _let_1 M)) (tptp.hAPP tptp.nat tptp.int _let_1 N_1))))) (= _let_34 _let_29) (forall ((X_b $$unsorted) (F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (let ((_let_2 (tptp.fun X_b tptp.int))) (let ((_let_3 (tptp.fun X_b tptp.nat))) (let ((_let_4 (tptp.fun X_b tptp.bool))) (= (tptp.hAPP tptp.nat tptp.int _let_1 (tptp.hAPP _let_4 tptp.nat (tptp.hAPP _let_3 (tptp.fun _let_4 tptp.nat) (tptp.big_co1399186613setsum X_b tptp.nat) F) A_3)) (tptp.hAPP _let_4 tptp.int (tptp.hAPP _let_2 (tptp.fun _let_4 tptp.int) (tptp.big_co1399186613setsum X_b tptp.int) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun tptp.nat tptp.int) (tptp.fun _let_3 _let_2) (tptp.combb tptp.nat tptp.int X_b) _let_1) F)) A_3))))))) (forall ((X_b $$unsorted) (F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (let ((_let_2 (tptp.fun X_b tptp.int))) (let ((_let_3 (tptp.fun X_b tptp.nat))) (let ((_let_4 (tptp.fun X_b tptp.bool))) (= (tptp.hAPP tptp.nat tptp.int _let_1 (tptp.hAPP _let_4 tptp.nat (tptp.hAPP _let_3 (tptp.fun _let_4 tptp.nat) (tptp.big_co302546470etprod X_b tptp.nat) F) A_3)) (tptp.hAPP _let_4 tptp.int (tptp.hAPP _let_2 (tptp.fun _let_4 tptp.int) (tptp.big_co302546470etprod X_b tptp.int) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun tptp.nat tptp.int) (tptp.fun _let_3 _let_2) (tptp.combb tptp.nat tptp.int X_b) _let_1) F)) A_3))))))) (forall ((N_1 $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N_1) M)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) (tptp.hAPP tptp.nat tptp.int _let_1 M)) (tptp.hAPP tptp.nat tptp.int _let_1 N_1)) (tptp.hAPP tptp.nat tptp.int _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) M) N_1)))))) (forall ((X_b $$unsorted)) (=> (tptp.comm_semiring_1 X_b) (forall ((N $$unsorted)) (let ((_let_1 (tptp.one_one X_b))) (let ((_let_2 (tptp.semiring_1_of_nat X_b))) (let ((_let_3 (tptp.hAPP tptp.nat X_b _let_2 N))) (let ((_let_4 (tptp.plus_plus X_b))) (let ((_let_5 (tptp.fun X_b X_b))) (let ((_let_6 (tptp.times_times X_b))) (let ((_let_7 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_5 _let_6 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_5 _let_4 _let_1) _let_1)) (tptp.hAPP _let_7 X_b (tptp.hAPP (tptp.fun tptp.nat X_b) (tptp.fun _let_7 X_b) (tptp.big_co1399186613setsum tptp.nat X_b) _let_2) (tptp.hAPP tptp.nat _let_7 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_7) (tptp.ord_atLeastAtMost tptp.nat) (tptp.one_one tptp.nat)) N))) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_5 _let_6 _let_3) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_5 _let_4 _let_3) _let_1))))))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (tptp.comm_monoid_mult X_c) (forall ((Ba $$unsorted) (Ca $$unsorted) (A_2 $$unsorted) (S_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP _let_1 tptp.nat (tptp.finite_card X_b) S_1))) (let ((_let_3 (tptp.hAPP X_c (tptp.fun tptp.nat X_c) (tptp.power_power X_c) Ca))) (let ((_let_4 (tptp.fun X_b _let_1))) (let ((_let_5 (tptp.fun X_c X_c))) (let ((_let_6 (tptp.fun X_c _let_5))) (let ((_let_7 (tptp.fun X_b _let_6))) (let ((_let_8 (tptp.fun X_b _let_5))) (let ((_let_9 (tptp.fun X_b X_c))) (let ((_let_10 (tptp.hAPP _let_1 X_c (tptp.hAPP _let_9 (tptp.fun _let_1 X_c) (tptp.big_co302546470etprod X_b X_c) (tptp.hAPP X_c _let_9 (tptp.hAPP _let_8 (tptp.fun X_c _let_9) (tptp.combc X_b X_c X_c) (tptp.hAPP _let_9 _let_8 (tptp.hAPP _let_7 (tptp.fun _let_9 _let_8) (tptp.combs X_b X_c _let_5) (tptp.hAPP _let_1 _let_7 (tptp.hAPP (tptp.fun tptp.bool _let_6) (tptp.fun _let_1 _let_7) (tptp.combb tptp.bool _let_6 X_b) (tptp.if X_c)) (tptp.hAPP X_b _let_1 (tptp.hAPP _let_4 _let_4 (tptp.combc X_b X_b tptp.bool) (tptp.fequal X_b)) A_2))) Ba)) Ca)) S_1))) (let ((_let_11 (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_2) S_1)))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) S_1)) (and (=> _let_11 (= _let_10 (tptp.hAPP X_c X_c (tptp.hAPP X_c _let_5 (tptp.times_times X_c) (tptp.hAPP X_b X_c Ba A_2)) (tptp.hAPP tptp.nat X_c _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) _let_2) (tptp.one_one tptp.nat)))))) (=> (not _let_11) (= _let_10 (tptp.hAPP tptp.nat X_c _let_3 _let_2))))))))))))))))))) (forall ((X_b $$unsorted) (Y_2 $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.finite_card X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.bot_bot _let_2))) (let ((_let_4 (tptp.insert X_b))) (let ((_let_5 (tptp.fun _let_2 _let_2))) (let ((_let_6 (tptp.minus_minus _let_2))) (let ((_let_7 (tptp.member X_b))) (let ((_let_8 (tptp.fun _let_2 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_b _let_8 _let_7 X_1) A_3)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_b _let_8 _let_7 Y_2) A_3)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP _let_2 tptp.nat _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_5 _let_6 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_5 _let_6 A_3) (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_b _let_5 _let_4 X_1) _let_3))) (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_b _let_5 _let_4 Y_2) _let_3)))) (tptp.hAPP _let_2 tptp.nat _let_1 A_3))))))))))))))) (forall ((N_1 $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.uminus_uminus tptp.int) (tptp.hAPP tptp.nat tptp.int _let_1 N_1))) (tptp.hAPP tptp.nat tptp.int _let_1 M))))) (forall ((L $$unsorted) (U $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 tptp.nat) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_1) (tptp.ord_atLeastAtMost tptp.nat) L) U))))) (forall ((K_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 tptp.nat) (tptp.hAPP _let_1 _let_1 (tptp.collect tptp.nat) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc tptp.nat tptp.nat tptp.bool) (tptp.ord_less tptp.nat)) K_1))))))) (forall ((W_1 $$unsorted) (Z_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) W_1) Z_2)) (exists ((N_2 $$unsorted)) (= Z_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) W_1) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) N_2)))))) (forall ((M $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (tptp.hAPP tptp.nat tptp.int _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.power_power tptp.nat) M) N_1)) (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.nat tptp.int) (tptp.power_power tptp.int) (tptp.hAPP tptp.nat tptp.int _let_1 M)) N_1)))) (forall ((M $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.nat tptp.int) (tptp.power_power tptp.int) (tptp.hAPP tptp.nat tptp.int _let_1 M)) N_1) (tptp.hAPP tptp.nat tptp.int _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.power_power tptp.nat) M) N_1))))) (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (= (tptp.hAPP tptp.nat tptp.int _let_1 M_1) (tptp.hAPP tptp.nat tptp.int _let_1 N)) (= M_1 N)))) (forall ((Z $$unsorted) (W_2 $$unsorted)) (let ((_let_1 (tptp.times_times tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.uminus_uminus tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int _let_3 Z)) W_2) (tptp.hAPP tptp.int tptp.int _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 Z) W_2))))))) (forall ((Z $$unsorted) (W_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.plus_plus tptp.int) Z) (tptp.hAPP tptp.int tptp.int (tptp.uminus_uminus tptp.int) W_2)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.minus_minus tptp.int) Z) W_2)))) (forall ((Z $$unsorted) (W_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.minus_minus tptp.int) Z) W_2) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.plus_plus tptp.int) Z) (tptp.hAPP tptp.int tptp.int (tptp.uminus_uminus tptp.int) W_2))))) (forall ((Z $$unsorted) (W_2 $$unsorted)) (let ((_let_1 (tptp.uminus_uminus tptp.int))) (let ((_let_2 (tptp.plus_plus tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (= (tptp.hAPP tptp.int tptp.int _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 _let_2 Z) W_2)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 _let_2 (tptp.hAPP tptp.int tptp.int _let_1 Z)) (tptp.hAPP tptp.int tptp.int _let_1 W_2))))))) (forall ((W_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) W_2) W_2))) (forall ((Z $$unsorted) (W_2 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (or (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 Z) W_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 W_2) Z)))))) (forall ((K $$unsorted) (I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 _let_1 I))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 J)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 J) K)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 K)))))))) (forall ((Z $$unsorted) (W_2 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 Z) W_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 W_2) Z)) (= Z W_2)))))) (forall ((Z1 $$unsorted) (Z2 $$unsorted) (Z3 $$unsorted)) (let ((_let_1 (tptp.times_times tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 _let_1 Z1))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int _let_3 Z2)) Z3) (tptp.hAPP tptp.int tptp.int _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 Z2) Z3))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.power_power tptp.int))) (let ((_let_2 (tptp.fun tptp.nat tptp.int))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 _let_1 X))) (= (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.nat tptp.int _let_3 Y)) Z) (tptp.hAPP tptp.nat tptp.int _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) Y) Z))))))) (forall ((Z $$unsorted) (W_2 $$unsorted)) (let ((_let_1 (tptp.times_times tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 Z) W_2) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 W_2) Z))))) (forall ((Z1 $$unsorted) (Z2 $$unsorted) (W_2 $$unsorted)) (let ((_let_1 (tptp.times_times tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.minus_minus tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_3 Z1) Z2)) W_2) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 Z1) W_2)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 Z2) W_2))))))) (forall ((W_2 $$unsorted) (Z1 $$unsorted) (Z2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) W_2))) (let ((_let_3 (tptp.minus_minus tptp.int))) (= (tptp.hAPP tptp.int tptp.int _let_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 _let_3 Z1) Z2)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 _let_3 (tptp.hAPP tptp.int tptp.int _let_2 Z1)) (tptp.hAPP tptp.int tptp.int _let_2 Z2))))))) (forall ((Z1 $$unsorted) (Z2 $$unsorted) (Z3 $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 _let_1 Z1))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int _let_3 Z2)) Z3) (tptp.hAPP tptp.int tptp.int _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 Z2) Z3))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 _let_1 X))) (let ((_let_4 (tptp.hAPP tptp.int _let_2 _let_1 Y))) (= (tptp.hAPP tptp.int tptp.int _let_3 (tptp.hAPP tptp.int tptp.int _let_4 Z)) (tptp.hAPP tptp.int tptp.int _let_4 (tptp.hAPP tptp.int tptp.int _let_3 Z)))))))) (forall ((Z $$unsorted) (W_2 $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 Z) W_2) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 W_2) Z))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.nat tptp.int) (tptp.power_power tptp.int) X))) (= (tptp.hAPP tptp.nat tptp.int _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) Y) Z)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) (tptp.hAPP tptp.nat tptp.int _let_1 Y)) (tptp.hAPP tptp.nat tptp.int _let_1 Z))))) (forall ((W_2 $$unsorted) (Z1 $$unsorted) (Z2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) W_2))) (let ((_let_3 (tptp.plus_plus tptp.int))) (= (tptp.hAPP tptp.int tptp.int _let_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 _let_3 Z1) Z2)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 _let_3 (tptp.hAPP tptp.int tptp.int _let_2 Z1)) (tptp.hAPP tptp.int tptp.int _let_2 Z2))))))) (forall ((Z1 $$unsorted) (Z2 $$unsorted) (W_2 $$unsorted)) (let ((_let_1 (tptp.times_times tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.plus_plus tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_3 Z1) Z2)) W_2) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 Z1) W_2)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 Z2) W_2))))))) (forall ((K $$unsorted) (I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) K))) (let ((_let_2 (tptp.ord_less_eq tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 I) J)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 (tptp.hAPP tptp.int tptp.int _let_1 I)) (tptp.hAPP tptp.int tptp.int _let_1 J)))))))) (forall ((Z $$unsorted)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) Z) (tptp.one_one tptp.int)) Z)) (forall ((Z $$unsorted)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) (tptp.one_one tptp.int)) Z) Z)) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((X $$unsorted)) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) X) (tptp.one_one tptp.nat)) (tptp.ti X_a X))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted) (Y_2 $$unsorted) (Z_2 $$unsorted)) (let ((_let_1 (tptp.ord_less X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.ord_max X_b) X_1) Y_2)) Z_2)) (and (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 X_1) Z_2)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 Y_2) Z_2))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((Z_2 $$unsorted) (X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) Z_2))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool _let_1 (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.ord_max X_b) X_1) Y_2))) (or (tptp.hBOOL (tptp.hAPP X_b tptp.bool _let_1 X_1)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool _let_1 Y_2)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((A_1 $$unsorted) (X $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) X))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_max X_a) A_1) B)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((B $$unsorted) (X $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) X))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_max X_a) A_1) B)))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (F $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (=> (= (tptp.ti _let_1 A_3) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun tptp.nat X_b) (tptp.fun _let_2 _let_1) (tptp.image tptp.nat X_b) F) (tptp.hAPP _let_2 _let_2 (tptp.collect tptp.nat) (tptp.hAPP tptp.nat _let_2 (tptp.hAPP _let_3 _let_3 (tptp.combc tptp.nat tptp.nat tptp.bool) (tptp.ord_less tptp.nat)) N)))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_3))))))) (forall ((I $$unsorted) (J $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) I) J)) K)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 I) K)))))) (forall ((M $$unsorted) (N_1 $$unsorted) (K $$unsorted) (L_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.plus_plus tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 K) L_1)) (=> (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_4 _let_3 M) L_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_4 _let_3 K) N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) N_1))))))))) (forall ((K $$unsorted) (L_1 $$unsorted) (I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.ord_less tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 I) J)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 K) L_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 I) K)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 J) L_1)))))))))) (forall ((K $$unsorted) (I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.ord_less tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 I) J)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 I) K)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 J) K))))))))) (forall ((M $$unsorted) (I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 J)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M) J)))))) (forall ((M $$unsorted) (I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 J)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) J) M)))))) (forall ((K_1 $$unsorted) (M_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) K_1))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 M_1)) (tptp.hAPP tptp.nat tptp.nat _let_3 N))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M_1) N))))))) (forall ((J $$unsorted) (I $$unsorted)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) J) I)) I)))) (forall ((I $$unsorted) (J $$unsorted)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) I) J)) I)))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((X $$unsorted) (P_2 $$unsorted) (Q_1 $$unsorted)) (let ((_let_1 (tptp.power_power X_a))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 X))) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP tptp.nat X_a _let_3 P_2)) Q_1) (tptp.hAPP tptp.nat X_a _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) P_2) Q_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere236663937imp_le X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) C))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 A_1)) (tptp.hAPP X_a X_a _let_3 B))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere236663937imp_le X_a) (forall ((A_1 $$unsorted) (C $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.plus_plus X_a))) (let ((_let_4 (tptp.fun X_a X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 B) C))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere223160158up_add X_a) (forall ((C $$unsorted) (D_1 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 C) D_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) D_1)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere223160158up_add X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) C))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 A_1)) (tptp.hAPP X_a X_a _let_1 B)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere223160158up_add X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 A_1) B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) C))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.ordere236663937imp_le X_b) (forall ((Ca $$unsorted) (A_2 $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.ord_less X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.plus_plus X_b) Ca))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 (tptp.hAPP X_b X_b _let_3 A_2)) (tptp.hAPP X_b X_b _let_3 Ba))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 A_2) Ba))))))))) (forall ((X_b $$unsorted)) (=> (tptp.ordere236663937imp_le X_b) (forall ((A_2 $$unsorted) (Ca $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.ord_less X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.plus_plus X_b))) (let ((_let_4 (tptp.fun X_b X_b))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_4 _let_3 A_2) Ca)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_4 _let_3 Ba) Ca))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 A_2) Ba)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((X $$unsorted) (Y $$unsorted) (Q_1 $$unsorted)) (let ((_let_1 (tptp.power_power X_a))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (let ((_let_3 (tptp.times_times X_a))) (let ((_let_4 (tptp.fun X_a X_a))) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 X) Y)) Q_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_2 _let_1 X) Q_1)) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_2 _let_1 Y) Q_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((B $$unsorted) (A_1 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) X)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_min X_a) A_1) B)) X)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B) X)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_min X_a) A_1) B)) X)))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((Z_2 $$unsorted) (X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) Z_2))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool _let_1 (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.ord_min X_b) X_1) Y_2))) (and (tptp.hBOOL (tptp.hAPP X_b tptp.bool _let_1 X_1)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool _let_1 Y_2)))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted) (Y_2 $$unsorted) (Z_2 $$unsorted)) (let ((_let_1 (tptp.ord_less X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.ord_min X_b) X_1) Y_2)) Z_2)) (or (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 X_1) Z_2)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 Y_2) Z_2))))))))) (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) M_1) N)) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) M_1) N)) (not (= M_1 N)))))) (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) M_1) N)) (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) M_1) N)) (= M_1 N))))) (forall ((M $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) M) N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) M) N_1))))) (forall ((M $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) M) N_1)) (=> (not (= M N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) M) N_1)))))) (forall ((M $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) M) N_1)) (= M N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) M) N_1))))) (forall ((N_1 $$unsorted) (J $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 J) K)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) J) N_1)) K)))))) (forall ((L_1 $$unsorted) (M $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) L_1))) (let ((_let_2 (tptp.ord_less tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (let ((_let_4 (tptp.hAPP tptp.nat _let_3 _let_2 M))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_4 N_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_4 L_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.nat tptp.nat _let_1 N_1)) (tptp.hAPP tptp.nat tptp.nat _let_1 M)))))))))) (forall ((X_b $$unsorted)) (=> (tptp.ord X_b) (forall ((I_1 $$unsorted) (K_1 $$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) I_1) (tptp.hAPP X_b _let_1 (tptp.ord_lessThan X_b) K_1))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less X_b) I_1) K_1))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (not (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less X_b) X_1) Y_2))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less_eq X_b) Y_2) X_1))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (not (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less_eq X_b) X_1) Y_2))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less X_b) Y_2) X_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (or (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) X) Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) Y) X))))))) (forall ((X_b $$unsorted)) (=> (tptp.order X_b) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less X_b) X_1) Y_2)) (and (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less_eq X_b) X_1) Y_2)) (not (= (tptp.ti X_b X_1) (tptp.ti X_b Y_2))))))))) (forall ((X_b $$unsorted)) (=> (tptp.preorder X_b) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 (tptp.ord_less X_b) X_1) Y_2)) (and (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 X_1) Y_2)) (not (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 Y_2) X_1)))))))))) (forall ((X_b $$unsorted)) (=> (tptp.order X_b) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less_eq X_b) X_1) Y_2)) (or (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less X_b) X_1) Y_2)) (= (tptp.ti X_b X_1) (tptp.ti X_b Y_2)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) X) Y))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) Y) X))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) Y) X))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) X) Y))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (not (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less X_b) X_1) Y_2))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less_eq X_b) X_1) Y_2)) (= (tptp.ti X_b X_1) (tptp.ti X_b Y_2)))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (not (= (tptp.ti X_a A_1) (tptp.ti X_a B))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) A_1) B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) A_1) B)))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (not (= (tptp.ti X_a A_1) (tptp.ti X_a B))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) B) A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) B) A_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) Y) X)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) X) Y)))))))) (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) X) Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) X) Y))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less_eq X_b) X_1) Y_2)) (= (not (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less X_b) X_1) Y_2))) (= (tptp.ti X_b X_1) (tptp.ti X_b Y_2)))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) X) Y)) (or (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) X) Y)) (= (tptp.ti X_a X) (tptp.ti X_a Y)))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) A_1) B)) (=> (not (= (tptp.ti X_a A_1) (tptp.ti X_a B))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) A_1) B)))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) B) A_1)) (=> (not (= (tptp.ti X_a A_1) (tptp.ti X_a B))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) B) A_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) X))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_2 Y)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) Y) Z)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_2 Z))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((Z $$unsorted) (Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) Z) Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Z) X))))))))) (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) X) Y)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) Z)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X) Z))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((Z $$unsorted) (Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) Z))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) Y) X)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_2 Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_2 X))))))))) (forall ((X_a $$unsorted)) (=> (tptp.bot X_a) (forall ((A_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) A_1) (tptp.bot_bot X_a))))))) (forall ((X_b $$unsorted)) (=> (tptp.bot X_b) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.bot_bot X_b))) (= (not (= (tptp.ti X_b A_2) _let_1)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) _let_1) A_2))))))) (forall ((X_b $$unsorted)) (=> (tptp.ordered_ab_group_add X_b) (forall ((A_2 $$unsorted) (Ba $$unsorted) (Ca $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.ord_less 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_2) Ba) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_4 _let_3 Ca) D)) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 A_2) Ba)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 Ca) D))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (not (= (tptp.ti X_a X) (tptp.ti X_a Y))) (=> (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X) Y))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X) Y))) (=> (not (= (tptp.ti X_a X) (tptp.ti X_a Y))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X))))))))) (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X) Y)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((Z $$unsorted) (Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 Z))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 X)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 X))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 Y)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) Z)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 Z)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((C $$unsorted) (B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B) A_1)) (=> (= (tptp.ti X_a B) (tptp.ti X_a C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 C) A_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ord X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) A_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B)) (=> (= (tptp.ti X_a B) (tptp.ti X_a C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 C)))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) C))) (=> (= (tptp.ti X_a A_1) (tptp.ti X_a B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.ord X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (= (tptp.ti X_a A_1) (tptp.ti X_a B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) C))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B) A_1)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B))))))))) (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B) A_1))))))))) (forall ((X_b $$unsorted)) (=> (tptp.preorder X_b) (forall ((Pa $$unsorted) (X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.ord_less X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 X_1) Y_2)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 Y_2) X_1)) (tptp.hBOOL Pa)))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) X) Y)) (not (= (tptp.ti X_a Y) (tptp.ti X_a X))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) X) Y)) (not (= (tptp.ti X_a X) (tptp.ti X_a Y))))))) (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X) Y)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X))))))))) (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X) Y)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) X) Y)) (not (= (tptp.ti X_a X) (tptp.ti X_a Y))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (not (= (tptp.ti X_a X) (tptp.ti X_a Y))) (=> (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X) Y))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((Y_2 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (not (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 Y_2) X_1))) (= (not (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 X_1) Y_2))) (= (tptp.ti X_b X_1) (tptp.ti X_b Y_2))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (or (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X) Y)) (= (tptp.ti X_a X) (tptp.ti X_a Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X)))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.ord_less X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (= (not (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 X_1) Y_2))) (or (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 Y_2) X_1)) (= (tptp.ti X_b X_1) (tptp.ti X_b Y_2))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.ord_less X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (= (not (= (tptp.ti X_b X_1) (tptp.ti X_b Y_2))) (or (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 X_1) Y_2)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 Y_2) X_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((X $$unsorted)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) X) X)))))) (forall ((X_b $$unsorted)) (=> (tptp.order X_b) (forall ((Ba $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less X_b) Ba) A_2)) (= (tptp.hAPP X_b _let_1 (tptp.hAPP X_b (tptp.fun X_b _let_1) (tptp.ord_atLeastAtMost X_b) A_2) Ba) (tptp.bot_bot _let_1))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.ord_lessThan X_b))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less _let_1) (tptp.hAPP X_b _let_1 _let_2 M_1)) (tptp.hAPP X_b _let_1 _let_2 N))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less X_b) M_1) N)))))))) (forall ((X_b $$unsorted)) (=> (tptp.order X_b) (forall ((A_2 $$unsorted) (Ba $$unsorted) (Ca $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.hAPP X_b _let_2 _let_1 Ca))) (let ((_let_4 (tptp.ord_less X_b))) (let ((_let_5 (tptp.ord_atLeastAtMost X_b))) (let ((_let_6 (tptp.fun X_b _let_2))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less _let_2) (tptp.hAPP X_b _let_2 (tptp.hAPP X_b _let_6 _let_5 A_2) Ba)) (tptp.hAPP X_b _let_2 (tptp.hAPP X_b _let_6 _let_5 Ca) D))) (and (or (not (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 A_2) Ba))) (and (tptp.hBOOL (tptp.hAPP X_b tptp.bool _let_3 A_2)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 Ba) D)) (or (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_4 Ca) A_2)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_4 Ba) D))))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool _let_3 D))))))))))))) (forall ((Pa $$unsorted) (M_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 Pa N) M_1)))) (let ((_let_3 (tptp.ord_less tptp.nat))) (=> (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 _let_3 M_1) N)) _let_2) (=> (=> (= M_1 N) _let_2) (=> (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 _let_3 N) M_1)) _let_2) _let_2))))))) (forall ((S $$unsorted) (T_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) S) T_3)) (not (= S T_3)))) (forall ((N_1 $$unsorted) (M $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N_1) M)) (not (= M N_1)))) (forall ((N_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N_1) N_1)))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (not (= X Y)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 X) Y))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Y) X))))))) (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (not (= M_1 N)) (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M_1) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 N) M_1))))))) (forall ((N_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N_1) N_1)))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) X) Y)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) X) Y))))) (forall ((Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) X))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 Z)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) Y) Z)))))) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) X))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) Y) Z)))))) (forall ((K_1 $$unsorted) (I_1 $$unsorted) (J_1 $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.ord_atLeastAtMost tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.bool))) (let ((_let_5 (tptp.fun tptp.nat _let_4))) (let ((_let_6 (tptp.fun tptp.nat _let_2))) (= (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_2 (tptp.fun _let_4 _let_4) (tptp.image tptp.nat tptp.nat) (tptp.hAPP tptp.nat _let_2 (tptp.hAPP _let_6 _let_6 (tptp.combc tptp.nat tptp.nat tptp.nat) _let_1) K_1)) (tptp.hAPP tptp.nat _let_4 (tptp.hAPP tptp.nat _let_5 _let_3 I_1) J_1)) (tptp.hAPP tptp.nat _let_4 (tptp.hAPP tptp.nat _let_5 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 I_1) K_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 J_1) K_1)))))))))) (forall ((N_3 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat tptp.bool) tptp.bool (tptp.finite_finite_1 tptp.nat) N_3)) (exists ((M_2 $$unsorted)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.nat (tptp.fun _let_1 tptp.bool) (tptp.member tptp.nat) X_2) N_3)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) X_2) M_2)))))))) (forall ((X_b $$unsorted)) (=> (tptp.ord X_b) (forall ((I_1 $$unsorted) (K_1 $$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) I_1) (tptp.hAPP X_b _let_1 (tptp.ord_greaterThan X_b) K_1))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less X_b) K_1) I_1))))))) (forall ((X_b $$unsorted)) (=> (tptp.ordered_ab_group_add X_b) (forall ((Ba $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.ord_less X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.uminus_uminus X_b))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 (tptp.hAPP X_b X_b _let_3 Ba)) (tptp.hAPP X_b X_b _let_3 A_2))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 A_2) Ba))))))))) (forall ((X_b $$unsorted)) (=> (tptp.ordered_ab_group_add X_b) (forall ((A_2 $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.uminus_uminus X_b))) (let ((_let_2 (tptp.ord_less X_b))) (let ((_let_3 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_3 _let_2 (tptp.hAPP X_b X_b _let_1 A_2)) Ba)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_3 _let_2 (tptp.hAPP X_b X_b _let_1 Ba)) A_2))))))))) (forall ((X_b $$unsorted)) (=> (tptp.ordered_ab_group_add X_b) (forall ((A_2 $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.uminus_uminus X_b))) (let ((_let_2 (tptp.ord_less X_b))) (let ((_let_3 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_3 _let_2 A_2) (tptp.hAPP X_b X_b _let_1 Ba))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_3 _let_2 Ba) (tptp.hAPP X_b X_b _let_1 A_2)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.boolean_algebra X_a) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.uminus_uminus X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 Y)) X)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 X)) Y))))))))) (forall ((X_a $$unsorted)) (=> (tptp.boolean_algebra X_a) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.uminus_uminus X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 Y) (tptp.hAPP X_a X_a _let_1 X))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 X) (tptp.hAPP X_a X_a _let_1 Y)))))))))) (forall ((X_b $$unsorted)) (=> (tptp.boolean_algebra X_b) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.ord_less X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.uminus_uminus X_b))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 (tptp.hAPP X_b X_b _let_3 X_1)) (tptp.hAPP X_b X_b _let_3 Y_2))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 Y_2) X_1))))))))) (forall ((Pa $$unsorted) (I_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (let ((_let_3 (tptp.fun tptp.bool tptp.bool))) (let ((_let_4 (tptp.fun tptp.nat _let_3))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 tptp.nat) (tptp.hAPP _let_1 _let_1 (tptp.collect tptp.nat) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_4 (tptp.fun _let_1 _let_1) (tptp.combs tptp.nat tptp.bool tptp.bool) (tptp.hAPP _let_1 _let_4 (tptp.hAPP (tptp.fun tptp.bool _let_3) (tptp.fun _let_1 _let_4) (tptp.combb tptp.bool _let_3 tptp.nat) tptp.fconj) Pa)) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc tptp.nat tptp.nat tptp.bool) (tptp.ord_less tptp.nat)) I_1)))))))))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (= (tptp.hAPP _let_1 tptp.nat (tptp.finite_card tptp.nat) (tptp.hAPP _let_1 _let_1 (tptp.collect tptp.nat) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc tptp.nat tptp.nat tptp.bool) (tptp.ord_less tptp.nat)) N))) N)))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((X $$unsorted) (P_2 $$unsorted) (Q_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) X))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) (tptp.hAPP tptp.nat X_a _let_1 P_2)) (tptp.hAPP tptp.nat X_a _let_1 Q_1)) (tptp.hAPP tptp.nat X_a _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) P_2) Q_1))))))) (forall ((X_b $$unsorted)) (=> (tptp.linordered_semidom X_b) (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat X_b))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) (tptp.hAPP tptp.nat X_b _let_1 M_1)) (tptp.hAPP tptp.nat X_b _let_1 N))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M_1) N))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((M $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat X_a))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M) N_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.hAPP tptp.nat X_a _let_1 M)) (tptp.hAPP tptp.nat X_a _let_1 N_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((M $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.hAPP tptp.nat X_a _let_1 M)) (tptp.hAPP tptp.nat X_a _let_1 N_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M) N_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere223160158up_add X_a) (forall ((C $$unsorted) (D_1 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 (tptp.ord_less_eq X_a) C) D_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) D_1)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere223160158up_add X_a) (forall ((C $$unsorted) (D_1 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 (tptp.ord_less_eq X_a) A_1) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 C) D_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) D_1)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) A_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) (tptp.one_one X_a))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((N_1 $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.one_one X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 M)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 N_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) M) N_1))))))))) (forall ((M $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M) N_1))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) N_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) M) N_1)) M)))) (forall ((I_1 $$unsorted) (J_1 $$unsorted) (K_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.ord_less tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 I_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) J_1) K_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) I_1) K_1)) J_1))))))) (forall ((N $$unsorted) (K_1 $$unsorted) (M_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.minus_minus tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.nat))) (let ((_let_5 (tptp.hAPP tptp.nat _let_2 (tptp.ord_less_eq tptp.nat) K_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_5 M_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_5 N)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_4 _let_3 M_1) K_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_4 _let_3 N) K_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M_1) N))))))))))) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.ord_less tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 (tptp.ord_less_eq tptp.nat) C) A_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 A_1) C)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 B) C)))))))))) (forall ((X_b $$unsorted)) (=> (tptp.order X_b) (forall ((A_2 $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (= (tptp.hAPP X_b _let_1 (tptp.hAPP X_b (tptp.fun X_b _let_1) (tptp.ord_atLeastAtMost X_b) A_2) Ba) (tptp.bot_bot _let_1)) (not (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less_eq X_b) A_2) Ba)))))))) (forall ((X_b $$unsorted)) (=> (tptp.order X_b) (forall ((A_2 $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (= (tptp.bot_bot _let_1) (tptp.hAPP X_b _let_1 (tptp.hAPP X_b (tptp.fun X_b _let_1) (tptp.ord_atLeastAtMost X_b) A_2) Ba)) (not (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less_eq X_b) A_2) Ba)))))))) (forall ((X_b $$unsorted)) (=> (tptp.order X_b) (forall ((A_2 $$unsorted) (Ba $$unsorted) (Ca $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.ord_atLeastAtMost X_b))) (let ((_let_4 (tptp.fun X_b _let_2))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) (tptp.hAPP X_b _let_2 (tptp.hAPP X_b _let_4 _let_3 A_2) Ba)) (tptp.hAPP X_b _let_2 (tptp.hAPP X_b _let_4 _let_3 Ca) D))) (or (not (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 A_2) Ba))) (and (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 Ca) A_2)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 Ba) D)))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.order X_b) (forall ((A_2 $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (= (tptp.ti X_b A_2) (tptp.ti X_b Ba)) (= (tptp.hAPP X_b _let_1 (tptp.hAPP X_b (tptp.fun X_b _let_1) (tptp.ord_atLeastAtMost X_b) A_2) Ba) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_2) (tptp.bot_bot _let_1)))))))) (forall ((X_b $$unsorted)) (=> (tptp.order X_b) (forall ((A_2 $$unsorted) (Ba $$unsorted) (Ca $$unsorted)) (let ((_let_1 (tptp.ti X_b Ba))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (= (= (tptp.hAPP X_b _let_2 (tptp.hAPP X_b (tptp.fun X_b _let_2) (tptp.ord_atLeastAtMost X_b) A_2) Ba) (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_b (tptp.fun _let_2 _let_2) (tptp.insert X_b) Ca) (tptp.bot_bot _let_2))) (and (= (tptp.ti X_b A_2) _let_1) (= _let_1 (tptp.ti X_b Ca))))))))) (forall ((X_b $$unsorted)) (=> (tptp.order X_b) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (tptp.hAPP X_b _let_1 (tptp.hAPP X_b (tptp.fun X_b _let_1) (tptp.ord_atLeastAtMost X_b) A_2) A_2) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_2) (tptp.bot_bot _let_1))))))) (forall ((X_b $$unsorted)) (=> (tptp.ordered_ab_group_add X_b) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.uminus_uminus X_b))) (let ((_let_2 (tptp.ord_atLeastAtMost X_b))) (let ((_let_3 (tptp.fun X_b tptp.bool))) (let ((_let_4 (tptp.fun X_b _let_3))) (= (tptp.hAPP _let_3 _let_3 (tptp.hAPP (tptp.fun X_b X_b) (tptp.fun _let_3 _let_3) (tptp.image X_b X_b) _let_1) (tptp.hAPP X_b _let_3 (tptp.hAPP X_b _let_4 _let_2 X_1) Y_2)) (tptp.hAPP X_b _let_3 (tptp.hAPP X_b _let_4 _let_2 (tptp.hAPP X_b X_b _let_1 Y_2)) (tptp.hAPP X_b X_b _let_1 X_1)))))))))) (forall ((X_b $$unsorted)) (=> (tptp.comm_monoid_add X_b) (forall ((F $$unsorted) (M_1 $$unsorted) (K_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_atLeastAtMost tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (let ((_let_4 (tptp.plus_plus tptp.nat))) (let ((_let_5 (tptp.fun tptp.nat tptp.nat))) (let ((_let_6 (tptp.fun tptp.nat _let_5))) (let ((_let_7 (tptp.fun tptp.nat X_b))) (let ((_let_8 (tptp.big_co1399186613setsum tptp.nat X_b))) (let ((_let_9 (tptp.fun _let_2 X_b))) (= (tptp.hAPP _let_2 X_b (tptp.hAPP _let_7 _let_9 _let_8 F) (tptp.hAPP tptp.nat _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_5 _let_4 M_1) K_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_5 _let_4 N) K_1))) (tptp.hAPP _let_2 X_b (tptp.hAPP _let_7 _let_9 _let_8 (tptp.hAPP _let_5 _let_7 (tptp.hAPP _let_7 (tptp.fun _let_5 _let_7) (tptp.combb tptp.nat X_b tptp.nat) F) (tptp.hAPP tptp.nat _let_5 (tptp.hAPP _let_6 _let_6 (tptp.combc tptp.nat tptp.nat tptp.nat) _let_4) K_1))) (tptp.hAPP tptp.nat _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 M_1) N))))))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.ordered_ring X_b) (forall ((A_2 $$unsorted) (E $$unsorted) (Ca $$unsorted) (Ba $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.fun X_b X_b))) (let ((_let_2 (tptp.times_times X_b))) (let ((_let_3 (tptp.plus_plus X_b))) (let ((_let_4 (tptp.ord_less X_b))) (let ((_let_5 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_5 _let_4 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_3 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_2 A_2) E)) Ca)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_3 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_2 Ba) E)) D))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_5 _let_4 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_3 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_2 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 (tptp.minus_minus X_b) A_2) Ba)) E)) Ca)) D))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.ordered_ring X_b) (forall ((A_2 $$unsorted) (E $$unsorted) (Ca $$unsorted) (Ba $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.fun X_b X_b))) (let ((_let_2 (tptp.times_times X_b))) (let ((_let_3 (tptp.plus_plus X_b))) (let ((_let_4 (tptp.ord_less X_b))) (let ((_let_5 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_5 _let_4 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_3 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_2 A_2) E)) Ca)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_3 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_2 Ba) E)) D))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_5 _let_4 Ca) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_3 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_2 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 (tptp.minus_minus X_b) Ba) A_2)) E)) D)))))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (tptp.comm_monoid_mult X_c) (forall ((Y_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_b X_c))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (= (tptp.hAPP _let_1 X_c (tptp.hAPP _let_2 (tptp.fun _let_1 X_c) (tptp.big_co302546470etprod X_b X_c) (tptp.hAPP X_c _let_2 (tptp.combk X_c X_b) Y_2)) A_3) (tptp.hAPP tptp.nat X_c (tptp.hAPP X_c (tptp.fun tptp.nat X_c) (tptp.power_power X_c) Y_2) (tptp.hAPP _let_1 tptp.nat (tptp.finite_card X_b) A_3))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (=> (not (= (tptp.ti _let_1 A_3) (tptp.bot_bot _let_1))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less X_b) (tptp.hAPP _let_1 X_b (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun _let_1 X_b) (tptp.finite_fold1 X_b) (tptp.ord_min X_b)) A_3)) X_1)) (exists ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_2) A_3)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less X_b) X_2) X_1)))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (=> (not (= (tptp.ti _let_1 A_3) (tptp.bot_bot _let_1))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less X_b) X_1) (tptp.hAPP _let_1 X_b (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun _let_1 X_b) (tptp.finite_fold1 X_b) (tptp.ord_min X_b)) A_3))) (forall ((X_2 $$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_3)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less X_b) X_1) X_2)))))))))))) (forall ((U $$unsorted) (M_1 $$unsorted) (N $$unsorted) (J_1 $$unsorted) (I_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.times_times tptp.nat))) (let ((_let_3 (tptp.plus_plus tptp.nat))) (let ((_let_4 (tptp.ord_less tptp.nat))) (let ((_let_5 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_5 (tptp.ord_less_eq tptp.nat) J_1) I_1)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_5 _let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 I_1) U)) M_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 J_1) U)) N))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_5 _let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) I_1) J_1)) U)) M_1)) N)))))))))) (forall ((U $$unsorted) (M_1 $$unsorted) (N $$unsorted) (I_1 $$unsorted) (J_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.times_times tptp.nat))) (let ((_let_3 (tptp.plus_plus tptp.nat))) (let ((_let_4 (tptp.ord_less tptp.nat))) (let ((_let_5 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_5 (tptp.ord_less_eq tptp.nat) I_1) J_1)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_5 _let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 I_1) U)) M_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 J_1) U)) N))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_5 _let_4 M_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) J_1) I_1)) U)) N))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.comm_monoid_add X_b) (forall ((F $$unsorted) (P_1 $$unsorted) (M_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) N))) (let ((_let_2 (tptp.hAPP tptp.nat tptp.nat _let_1 P_1))) (let ((_let_3 (tptp.hAPP tptp.nat tptp.nat _let_1 (tptp.one_one tptp.nat)))) (let ((_let_4 (tptp.ord_atLeastAtMost tptp.nat))) (let ((_let_5 (tptp.fun tptp.nat tptp.bool))) (let ((_let_6 (tptp.fun tptp.nat _let_5))) (let ((_let_7 (tptp.hAPP (tptp.fun tptp.nat X_b) (tptp.fun _let_5 X_b) (tptp.big_co1399186613setsum tptp.nat X_b) F))) (let ((_let_8 (tptp.hAPP tptp.nat _let_6 _let_4 M_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_5 (tptp.ord_less_eq tptp.nat) M_1) _let_3)) (= (tptp.hAPP _let_5 X_b _let_7 (tptp.hAPP tptp.nat _let_5 _let_8 _let_2)) (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.plus_plus X_b) (tptp.hAPP _let_5 X_b _let_7 (tptp.hAPP tptp.nat _let_5 _let_8 N))) (tptp.hAPP _let_5 X_b _let_7 (tptp.hAPP tptp.nat _let_5 (tptp.hAPP tptp.nat _let_6 _let_4 _let_3) _let_2)))))))))))))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.finite_card X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (=> (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_3)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP _let_2 tptp.nat _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_3 (tptp.minus_minus _let_2) A_3) (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_b _let_3 (tptp.insert X_b) X_1) (tptp.bot_bot _let_2))))) (tptp.hAPP _let_2 tptp.nat _let_1 A_3))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((M $$unsorted) (N_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) A_1))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less X_a) (tptp.one_one X_a)) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) (tptp.hAPP tptp.nat X_a _let_1 M)) (tptp.hAPP tptp.nat X_a _let_1 N_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M) N_1))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linordered_semidom X_b) (forall ((X_1 $$unsorted) (Y_2 $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.hAPP X_b (tptp.fun tptp.nat X_b) (tptp.power_power X_b) Ba))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 (tptp.ord_less X_b) (tptp.one_one X_b)) Ba)) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 (tptp.ord_less_eq X_b) (tptp.hAPP tptp.nat X_b _let_1 X_1)) (tptp.hAPP tptp.nat X_b _let_1 Y_2))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) X_1) Y_2))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (and (tptp.comm_monoid_add X_c) (tptp.ordere223160158up_add X_c)) (forall ((F $$unsorted) (G $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.big_co1399186613setsum X_b X_c))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun _let_2 X_c))) (let ((_let_4 (tptp.fun X_b X_c))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (=> (not (= (tptp.ti _let_2 A_3) (tptp.bot_bot _let_2))) (=> (forall ((X_2 $$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) A_3)) (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less X_c) (tptp.hAPP X_b X_c F X_2)) (tptp.hAPP X_b X_c G X_2)))))) (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less X_c) (tptp.hAPP _let_2 X_c (tptp.hAPP _let_4 _let_3 _let_1 F) A_3)) (tptp.hAPP _let_2 X_c (tptp.hAPP _let_4 _let_3 _let_1 G) A_3))))))))))))) (forall ((N_1 $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.hAPP tptp.nat tptp.int _let_1 N_1)) (tptp.hAPP tptp.int tptp.int (tptp.uminus_uminus tptp.int) (tptp.hAPP tptp.nat tptp.int _let_1 M))))))) (forall ((Z_2 $$unsorted) (W_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) Z_2) W_1)) (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) Z_2) W_1)) (not (= Z_2 W_1)))))) (forall ((K $$unsorted) (I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.ord_less tptp.int))) (let ((_let_4 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_3 I) J)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 I) K)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 J) K))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (tptp.ord X_c) (forall ((F $$unsorted) (G $$unsorted)) (let ((_let_1 (tptp.fun X_b X_c))) (let ((_let_2 (tptp.ord_less_eq _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 (tptp.ord_less _let_1) F) G)) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 F) G)) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 G) F))))))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less _let_1) A_3) (tptp.bot_bot _let_1)))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun 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 _let_1) A_3) B_2)) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_3) B_2)) (not (= (tptp.ti _let_1 A_3) (tptp.ti _let_1 B_2)))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_3) B_2)) (or (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less _let_1) A_3) B_2)) (= (tptp.ti _let_1 A_3) (tptp.ti _let_1 B_2))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun 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 _let_1) A_3) B_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_3) B_2)))))) (forall ((X_b $$unsorted) (C_1 $$unsorted) (A_3 $$unsorted) (B_2 $$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 _let_1) A_3))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 B_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) B_2) C_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 C_1)))))))) (forall ((X_b $$unsorted) (C_1 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.ord_less _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 (tptp.ord_less_eq _let_1) A_3) B_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 B_2) C_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 A_3) C_1)))))))) (forall ((X_b $$unsorted) (C_1 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.ord_less _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.hAPP _let_1 _let_3 _let_2 A_3))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_4 B_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 B_2) C_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_4 C_1))))))))) (forall ((X_b $$unsorted) (Ca $$unsorted) (A_3 $$unsorted) (B_2 $$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 _let_1) A_3) B_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 A_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 B_2)))))))) (forall ((Z $$unsorted)) (let ((_let_1 (tptp.uminus_uminus tptp.int))) (= (tptp.hAPP tptp.int tptp.int _let_1 (tptp.hAPP tptp.int tptp.int _let_1 Z)) Z))) (forall ((Z_3 $$unsorted) (Z $$unsorted) (W_3 $$unsorted) (W_2 $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.ord_less tptp.int))) (let ((_let_4 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_3 W_3) W_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 (tptp.ord_less_eq tptp.int) Z_3) Z)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 W_3) Z_3)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 W_2) Z)))))))))) (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.hAPP tptp.nat tptp.int _let_1 M_1)) (tptp.hAPP tptp.nat tptp.int _let_1 N))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M_1) N))))) (forall ((W_1 $$unsorted) (Z_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) W_1))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) Z_2) (tptp.one_one tptp.int)))) (or (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 Z_2)) (= W_1 Z_2))))) (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) (tptp.ord_atLeastAtMost tptp.int) M_1))) (let ((_let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) (tptp.one_one tptp.int)) N))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) M_1) _let_3)) (= (tptp.hAPP tptp.int _let_1 _let_2 _let_3) (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.int (tptp.fun _let_1 _let_1) (tptp.insert tptp.int) _let_3) (tptp.hAPP tptp.int _let_1 _let_2 N)))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.finite_card 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) B_2)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less _let_2) A_3) B_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP _let_2 tptp.nat _let_1 A_3)) (tptp.hAPP _let_2 tptp.nat _let_1 B_2)))))))) (forall ((W_2 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) W_2) Z)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) W_2) (tptp.one_one tptp.int))) Z))))) (forall ((W_1 $$unsorted) (Z_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) W_1) (tptp.one_one tptp.int))) Z_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) W_1) Z_2))))) (forall ((W_1 $$unsorted) (Z_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) W_1) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) Z_2) (tptp.one_one tptp.int)))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) W_1) Z_2))))) (forall ((W_1 $$unsorted) (Z_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) W_1) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) Z_2) (tptp.one_one tptp.int)))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) W_1) Z_2))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (X_1 $$unsorted) (B_2 $$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))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 A_3)))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (let ((_let_6 (tptp.hAPP X_b _let_5 (tptp.insert X_b) X_1))) (let ((_let_7 (tptp.ord_less _let_1))) (let ((_let_8 (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 B_2)))) (let ((_let_9 (tptp.hAPP _let_1 _let_2 _let_7 A_3))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_9 (tptp.hAPP _let_1 _let_1 _let_6 B_2))) (and (=> _let_8 (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_9 B_2))) (=> (not _let_8) (and (=> _let_4 (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 _let_7 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_5 (tptp.minus_minus _let_1) A_3) (tptp.hAPP _let_1 _let_1 _let_6 (tptp.bot_bot _let_1)))) B_2))) (=> (not _let_4) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_3) B_2))))))))))))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.finite_card X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) B_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_3) B_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP _let_1 tptp.nat _let_3 A_3)) (tptp.hAPP _let_1 tptp.nat _let_3 B_2))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less _let_1) A_3) B_2))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_monoid_mult X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.power_power X_a))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (let ((_let_3 (tptp.times_times X_a))) (let ((_let_4 (tptp.fun X_a X_a))) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 A_1) B)) N_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_2 _let_1 A_1) N_1)) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_2 _let_1 B) N_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.monoid_mult X_a) (forall ((A_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) A_1) N_1))) (let ((_let_2 (tptp.times_times X_a))) (let ((_let_3 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 _let_1) A_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 A_1) _let_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.monoid_mult X_a) (forall ((N_1 $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) _let_1) N_1) _let_1))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_1 X_a) (forall ((M $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat X_a))) (= (tptp.hAPP tptp.nat X_a _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.power_power tptp.nat) M) N_1)) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) (tptp.hAPP tptp.nat X_a _let_1 M)) N_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.monoid_mult X_a) (forall ((A_1 $$unsorted) (M $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.power_power X_a))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 A_1))) (= (tptp.hAPP tptp.nat X_a _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) M) N_1)) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP tptp.nat X_a _let_3 M)) N_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.monoid_mult X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) A_1) (tptp.one_one tptp.nat)) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((N_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.one_one X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) A_1) N_1)))))))) (forall ((X_b $$unsorted)) (=> (tptp.linordered_semidom X_b) (forall ((M_1 $$unsorted) (N $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.hAPP X_b (tptp.fun tptp.nat X_b) (tptp.power_power X_b) A_2))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) (tptp.one_one X_b)) A_2)) (= (= (tptp.hAPP tptp.nat X_b _let_1 M_1) (tptp.hAPP tptp.nat X_b _let_1 N)) (= M_1 N))))))) (forall ((X_a $$unsorted)) (=> (tptp.monoid_mult X_a) (forall ((A_1 $$unsorted) (M $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) A_1))) (= (tptp.hAPP tptp.nat X_a _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M) N_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) (tptp.hAPP tptp.nat X_a _let_1 M)) (tptp.hAPP tptp.nat X_a _let_1 N_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((N_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) A_1) N_1))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.one_one X_a)) A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 _let_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((N_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.one_one X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_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.times_times X_a) A_1) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) A_1) N_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((A_1 $$unsorted) (N_1 $$unsorted) (N_4 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) A_1))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N_1) N_4)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.one_one X_a)) A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP tptp.nat X_a _let_1 N_1)) (tptp.hAPP tptp.nat X_a _let_1 N_4))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((M $$unsorted) (N_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) A_1))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.one_one X_a)) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP tptp.nat X_a _let_1 M)) (tptp.hAPP tptp.nat X_a _let_1 N_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M) N_1)))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linordered_semidom X_b) (forall ((X_1 $$unsorted) (Y_2 $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.hAPP X_b (tptp.fun tptp.nat X_b) (tptp.power_power X_b) Ba))) (let ((_let_2 (tptp.ord_less X_b))) (let ((_let_3 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_3 _let_2 (tptp.one_one X_b)) Ba)) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_3 _let_2 (tptp.hAPP tptp.nat X_b _let_1 X_1)) (tptp.hAPP tptp.nat X_b _let_1 Y_2))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) X_1) Y_2)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((A_1 $$unsorted) (N_1 $$unsorted) (N_4 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) A_1))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N_1) N_4)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.one_one X_a)) A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP tptp.nat X_a _let_1 N_1)) (tptp.hAPP tptp.nat X_a _let_1 N_4))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ring_1 X_a) (forall ((A_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.power_power X_a))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (let ((_let_3 (tptp.uminus_uminus X_a))) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 A_1)) N_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 (tptp.one_one X_a))) N_1)) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_2 _let_1 A_1) N_1))))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite_1 X_b) A_3)) (exists ((N_2 $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (let ((_let_3 (tptp.fun X_b tptp.bool))) (= (tptp.ti _let_3 A_3) (tptp.hAPP _let_1 _let_3 (tptp.hAPP (tptp.fun tptp.nat X_b) (tptp.fun _let_1 _let_3) (tptp.image tptp.nat X_b) F_1) (tptp.hAPP _let_1 _let_1 (tptp.collect tptp.nat) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc tptp.nat tptp.nat tptp.bool) (tptp.ord_less tptp.nat)) N_2)))))))))) (forall ((Pa $$unsorted) (I_1 $$unsorted) (K_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) I_1) K_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa K_1)) (=> (forall ((I_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) I_2) K_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa I_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) I_2) (tptp.one_one tptp.int))))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa I_1)))))) (forall ((L $$unsorted) (U $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 tptp.int) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) (tptp.ord_atLeastAtMost tptp.int) L) U))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (or (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 X) Y)) (= X Y) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 Y) X)))))) (forall ((J_1 $$unsorted) (I_1 $$unsorted)) (let ((_let_1 (tptp.ord_atLeastAtMost tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.fun tptp.int _let_2))) (let ((_let_4 (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int _let_3 _let_1 I_1) J_1))) (let ((_let_5 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) J_1) I_1)))) (and (=> _let_5 (= _let_4 (tptp.bot_bot _let_2))) (=> (not _let_5) (= _let_4 (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.int (tptp.fun _let_2 _let_2) (tptp.insert tptp.int) I_1) (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int _let_3 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) I_1) (tptp.one_one tptp.int))) J_1))))))))))) (forall ((Pa $$unsorted) (I_1 $$unsorted) (K_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) I_1) K_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) K_1) (tptp.one_one tptp.int)))) (=> (forall ((I_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) I_2) K_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa I_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) I_2) (tptp.one_one tptp.int))))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa I_1)))))) (forall ((A_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 tptp.nat) A_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 tptp.int) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun tptp.nat tptp.int) (tptp.fun _let_2 _let_1) (tptp.image tptp.nat tptp.int) (tptp.semiring_1_of_nat tptp.int)) A_3))))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP (tptp.fun tptp.nat tptp.int) (tptp.fun _let_2 _let_1) (tptp.image tptp.nat tptp.int) (tptp.semiring_1_of_nat tptp.int)))) (= (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_3) B_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) (tptp.hAPP _let_2 _let_1 _let_3 A_3)) (tptp.hAPP _let_2 _let_1 _let_3 B_2)))))))) (forall ((X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP tptp.nat (tptp.fun _let_3 tptp.bool) (tptp.member tptp.nat) X_1) A_3)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_2 tptp.bool) (tptp.member tptp.int) (tptp.hAPP tptp.nat tptp.int _let_1 X_1)) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun tptp.nat tptp.int) (tptp.fun _let_3 _let_2) (tptp.image tptp.nat tptp.int) _let_1) A_3)))))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP (tptp.fun tptp.nat tptp.int) (tptp.fun _let_2 _let_1) (tptp.image tptp.nat tptp.int) (tptp.semiring_1_of_nat tptp.int)))) (= (= A_3 B_2) (= (tptp.hAPP _let_2 _let_1 _let_3 A_3) (tptp.hAPP _let_2 _let_1 _let_3 B_2))))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted) (Pa $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.semiring_1_of_nat tptp.int))) (let ((_let_3 (tptp.hAPP tptp.nat tptp.int _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.bool (tptp.fun tptp.nat _let_1) (tptp.if tptp.nat) Pa) X_1) Y_2)))) (let ((_let_4 (tptp.hBOOL Pa))) (and (=> _let_4 (= (tptp.hAPP tptp.nat tptp.int _let_2 X_1) _let_3)) (=> (not _let_4) (= (tptp.hAPP tptp.nat tptp.int _let_2 Y_2) _let_3)))))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (= (tptp.hAPP tptp.nat tptp.int _let_1 X_1) (tptp.hAPP tptp.nat tptp.int _let_1 Y_2)) (= X_1 Y_2)))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP (tptp.fun tptp.nat tptp.int) (tptp.fun _let_2 _let_1) (tptp.image tptp.nat tptp.int) (tptp.semiring_1_of_nat tptp.int)))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less _let_2) A_3) B_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less _let_1) (tptp.hAPP _let_2 _let_1 _let_3 A_3)) (tptp.hAPP _let_2 _let_1 _let_3 B_2)))))))) (forall ((A_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hAPP _let_2 tptp.nat (tptp.finite_card tptp.nat) A_3) (tptp.hAPP _let_1 tptp.nat (tptp.finite_card tptp.int) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun tptp.nat tptp.int) (tptp.fun _let_2 _let_1) (tptp.image tptp.nat tptp.int) (tptp.semiring_1_of_nat tptp.int)) A_3)))))) (= (tptp.bot_bot _let_31) (tptp.hAPP _let_35 _let_31 (tptp.hAPP (tptp.fun tptp.nat tptp.int) (tptp.fun _let_35 _let_31) (tptp.image tptp.nat tptp.int) _let_33) (tptp.bot_bot _let_35))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.hAPP tptp.nat tptp.int _let_1 X_1)) (tptp.hAPP tptp.nat tptp.int _let_1 Y_2))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) X_1) Y_2))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.hAPP tptp.nat tptp.int _let_1 X_1)) (tptp.hAPP tptp.nat tptp.int _let_1 Y_2))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) X_1) Y_2))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) (tptp.hAPP tptp.nat tptp.int _let_1 X)) (tptp.hAPP tptp.nat tptp.int _let_1 Y)) (tptp.hAPP tptp.nat tptp.int _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) X) Y))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) (tptp.hAPP tptp.nat tptp.int _let_1 X)) (tptp.hAPP tptp.nat tptp.int _let_1 Y)) (tptp.hAPP tptp.nat tptp.int _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) X) Y))))) (= _let_29 _let_34) (forall ((X $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.nat tptp.int) (tptp.power_power tptp.int) (tptp.hAPP tptp.nat tptp.int _let_1 X)) N_1) (tptp.hAPP tptp.nat tptp.int _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.power_power tptp.nat) X) N_1))))) (forall ((Pa $$unsorted) (K_1 $$unsorted) (I_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) K_1) I_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) K_1) (tptp.one_one tptp.int)))) (=> (forall ((I_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) K_1) I_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa I_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) I_2) (tptp.one_one tptp.int))))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa I_1)))))) (forall ((Pa $$unsorted) (K_1 $$unsorted) (I_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) K_1) I_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa K_1)) (=> (forall ((I_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) K_1) I_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa I_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) I_2) (tptp.one_one tptp.int))))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa I_1)))))) (forall ((M_1 $$unsorted) (K_1 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (=> (forall ((M_2 $$unsorted) (N_2 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M_2) N_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat F M_2)) (tptp.hAPP tptp.nat tptp.nat F N_2))))))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat F M_1)) K_1)) (tptp.hAPP tptp.nat tptp.nat F (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M_1) K_1)))))))) (forall ((N $$unsorted) (N_3 $$unsorted)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.nat (tptp.fun _let_1 tptp.bool) (tptp.member tptp.nat) X_2) N_3)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) X_2) N))))) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat tptp.bool) tptp.bool (tptp.finite_finite_1 tptp.nat) N_3)))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less _let_1) A_3) B_2)) (exists ((B_1 $$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) B_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) B_2) A_3)))))))) (forall ((Z $$unsorted)) (not (forall ((M_2 $$unsorted) (N_2 $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (not (= Z (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) (tptp.hAPP tptp.nat tptp.int _let_1 M_2)) (tptp.hAPP tptp.nat tptp.int _let_1 N_2)))))))) (forall ((I_1 $$unsorted) (J_1 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (forall ((I_2 $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 I_2) J_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat F I_2)) (tptp.hAPP tptp.nat tptp.nat F J_2))))))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 I_1) J_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat F I_1)) (tptp.hAPP tptp.nat tptp.nat F J_1)))))))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.fun X_b (tptp.fun tptp.nat X_b)))) (let ((_let_2 (tptp.fun X_b (tptp.fun X_b X_b)))) (=> (tptp.power X_b) (= (tptp.power_power X_b) (tptp.hAPP _let_2 _let_1 (tptp.hAPP X_b (tptp.fun _let_2 _let_1) (tptp.power_1 X_b) (tptp.one_one X_b)) (tptp.times_times X_b))))))) (forall ((X_a $$unsorted)) (=> (tptp.dense_linorder X_a) (forall ((Z $$unsorted) (Y $$unsorted)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) X_2) Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) X_2) Z))))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) Y) Z)))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((T_3 $$unsorted)) (exists ((Z_1 $$unsorted)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) X_2) Z_1)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) T_3) X_2)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((T_3 $$unsorted)) (exists ((Z_1 $$unsorted)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) Z_1) X_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) T_3) X_2))))))))) (forall ((X_a $$unsorted)) (=> (tptp.dense_linorder X_a) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) X) Y)) (=> (forall ((W $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.ord_less X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 _let_2 X) W)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 _let_2 W) Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) W) Z))))))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) Y) Z)))))))) (forall ((X_c $$unsorted) (X_b $$unsorted)) (=> (and (tptp.order X_b) (tptp.order X_c)) (forall ((Ca $$unsorted) (F $$unsorted) (Ba $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) Ba) A_2)) (=> (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c _let_1 (tptp.ord_less_eq X_c) Ca) (tptp.hAPP X_b X_c F Ba))) (=> (forall ((X_2 $$unsorted) (Y_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) Y_1) X_2)) (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less X_c) (tptp.hAPP X_b X_c F Y_1)) (tptp.hAPP X_b X_c F X_2))))) (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c _let_1 (tptp.ord_less X_c) Ca) (tptp.hAPP X_b X_c F A_2)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((T_3 $$unsorted)) (exists ((Z_1 $$unsorted)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) X_2) Z_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) X_2) T_3))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((T_3 $$unsorted)) (exists ((Z_1 $$unsorted)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) Z_1) X_2)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) X_2) T_3)))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted)) (=> (and (tptp.order X_b) (tptp.order X_c)) (forall ((Ca $$unsorted) (F $$unsorted) (Ba $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less X_c) Ca))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) Ba) A_2)) (=> (tptp.hBOOL (tptp.hAPP X_c tptp.bool _let_1 (tptp.hAPP X_b X_c F Ba))) (=> (forall ((X_2 $$unsorted) (Y_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) Y_1) X_2)) (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 Y_1)) (tptp.hAPP X_b X_c F X_2))))) (tptp.hBOOL (tptp.hAPP X_c tptp.bool _let_1 (tptp.hAPP X_b X_c F A_2)))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (and (tptp.order X_c) (tptp.order X_b)) (forall ((F $$unsorted) (Ca $$unsorted) (A_2 $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) A_2) Ba)) (=> (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c _let_1 (tptp.ord_less_eq X_c) (tptp.hAPP X_b X_c F Ba)) Ca)) (=> (forall ((X_2 $$unsorted) (Y_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) X_2) Y_1)) (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less X_c) (tptp.hAPP X_b X_c F X_2)) (tptp.hAPP X_b X_c F Y_1))))) (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c _let_1 (tptp.ord_less X_c) (tptp.hAPP X_b X_c F A_2)) Ca))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted)) (=> (and (tptp.order X_b) (tptp.ord X_c)) (forall ((Ca $$unsorted) (F $$unsorted) (Ba $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less_eq X_b) (tptp.hAPP X_c X_b F Ba)) A_2)) (=> (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less X_c) Ca) Ba)) (=> (forall ((X_2 $$unsorted) (Y_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less X_c) Y_1) X_2)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) (tptp.hAPP X_c X_b F Y_1)) (tptp.hAPP X_c X_b F X_2))))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less X_b) (tptp.hAPP X_c X_b F Ca)) A_2))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted)) (=> (and (tptp.order X_b) (tptp.order X_c)) (forall ((Ca $$unsorted) (F $$unsorted) (Ba $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.ord_less 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_c X_b F Ba)) A_2)) (=> (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less_eq X_c) Ca) Ba)) (=> (forall ((X_2 $$unsorted) (Y_1 $$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) Y_1) X_2)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) (tptp.hAPP X_c X_b F Y_1)) (tptp.hAPP X_c X_b F X_2))))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 (tptp.hAPP X_c X_b F Ca)) A_2)))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (and (tptp.order X_c) (tptp.order X_b)) (forall ((F $$unsorted) (Ca $$unsorted) (A_2 $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.ord_less X_c))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (=> (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_2) Ba)) (=> (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c _let_2 _let_1 (tptp.hAPP X_b X_c F Ba)) Ca)) (=> (forall ((X_2 $$unsorted) (Y_1 $$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_2) Y_1)) (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 F Y_1))))) (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c _let_2 _let_1 (tptp.hAPP X_b X_c F A_2)) Ca)))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (and (tptp.order X_c) (tptp.order X_b)) (forall ((Ca $$unsorted) (A_2 $$unsorted) (F $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) A_2))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool _let_1 (tptp.hAPP X_c X_b F Ba))) (=> (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less_eq X_c) Ba) Ca)) (=> (forall ((X_2 $$unsorted) (Y_1 $$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) X_2) Y_1)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) (tptp.hAPP X_c X_b F X_2)) (tptp.hAPP X_c X_b F Y_1))))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool _let_1 (tptp.hAPP X_c X_b F Ca)))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (and (tptp.order X_c) (tptp.order X_b)) (forall ((Ca $$unsorted) (A_2 $$unsorted) (F $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less_eq X_b) A_2) (tptp.hAPP X_c X_b F Ba))) (=> (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less X_c) Ba) Ca)) (=> (forall ((X_2 $$unsorted) (Y_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less X_c) X_2) Y_1)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) (tptp.hAPP X_c X_b F X_2)) (tptp.hAPP X_c X_b F Y_1))))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less X_b) A_2) (tptp.hAPP X_c X_b F Ca)))))))))) (forall ((I_1 $$unsorted) (Pa $$unsorted) (K_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa K_1)) (=> (forall ((I_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) K_1) I_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa I_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) I_2) (tptp.one_one tptp.int))))))) (=> (forall ((I_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) I_2) K_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa I_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) I_2) (tptp.one_one tptp.int))))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa I_1)))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((Pa $$unsorted) (A_3 $$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)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa (tptp.bot_bot _let_1))) (=> (forall ((B_1 $$unsorted) (A_4 $$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_4)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_2) A_4)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less X_b) X_2) B_1))))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa A_4)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) B_1) A_4)))))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa A_3))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((Pa $$unsorted) (A_3 $$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)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa (tptp.bot_bot _let_1))) (=> (forall ((B_1 $$unsorted) (A_4 $$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_4)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_2) A_4)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less X_b) B_1) X_2))))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa A_4)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) B_1) A_4)))))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa A_3))))))))) (forall ((X_b $$unsorted)) (=> (tptp.ab_group_add X_b) (forall ((F $$unsorted) (M_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.one_one tptp.nat))) (let ((_let_3 (tptp.plus_plus tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.nat))) (let ((_let_5 (tptp.fun tptp.nat _let_4))) (let ((_let_6 (tptp.fun tptp.nat X_b))) (let ((_let_7 (tptp.minus_minus X_b))) (let ((_let_8 (tptp.fun X_b X_b))) (let ((_let_9 (tptp.fun tptp.nat _let_8))) (let ((_let_10 (tptp.hAPP _let_1 X_b (tptp.hAPP _let_6 (tptp.fun _let_1 X_b) (tptp.big_co1399186613setsum tptp.nat X_b) (tptp.hAPP _let_6 _let_6 (tptp.hAPP _let_9 (tptp.fun _let_6 _let_6) (tptp.combs tptp.nat X_b X_b) (tptp.hAPP _let_6 _let_9 (tptp.hAPP (tptp.fun X_b _let_8) (tptp.fun _let_6 _let_9) (tptp.combb X_b _let_8 tptp.nat) _let_7) F)) (tptp.hAPP _let_4 _let_6 (tptp.hAPP _let_6 (tptp.fun _let_4 _let_6) (tptp.combb tptp.nat X_b tptp.nat) F) (tptp.hAPP tptp.nat _let_4 (tptp.hAPP _let_5 _let_5 (tptp.combc tptp.nat tptp.nat tptp.nat) _let_3) _let_2)))) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_1) (tptp.ord_atLeastAtMost tptp.nat) M_1) N)))) (let ((_let_11 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) M_1) N)))) (and (=> _let_11 (= _let_10 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_8 _let_7 (tptp.hAPP tptp.nat X_b F M_1)) (tptp.hAPP tptp.nat X_b F (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_4 _let_3 N) _let_2))))) (=> (not _let_11) (= _let_10 (tptp.zero_zero X_b)))))))))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.comm_monoid_add X_b) (forall ((Pa $$unsorted) (M_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (let ((_let_3 (tptp.hAPP (tptp.fun tptp.nat X_b) (tptp.fun _let_1 X_b) (tptp.big_co1399186613setsum tptp.nat X_b) Pa))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) M_1) N)) (= (tptp.hAPP _let_1 X_b _let_3 (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.nat _let_2 (tptp.ord_atLeastAtMost tptp.nat) M_1) N)) (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.plus_plus X_b) (tptp.hAPP tptp.nat X_b Pa M_1)) (tptp.hAPP _let_1 X_b _let_3 (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.nat _let_2 (tptp.ord_gr1471790799AtMost tptp.nat) M_1) N))))))))))) (forall ((N_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N_1) (tptp.zero_zero tptp.nat))))) (forall ((N_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.zero_zero tptp.nat)) N_1))) (forall ((L $$unsorted) (U $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 tptp.nat) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_1) (tptp.ord_gr1471790799AtMost tptp.nat) L) U))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((A_1 $$unsorted) (N_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.power_power X_a))) (let ((_let_4 (tptp.fun tptp.nat X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_4 _let_3 A_1) N_1)) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_4 _let_3 B) N_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom 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))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 (tptp.zero_zero X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 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) (tptp.one_one X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) X) Y)) X))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 (tptp.zero_zero X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 X)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 Y)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) (tptp.one_one X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) Y) X)) X))))))))))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (=> (tptp.linordered_semidom X_a) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.zero_zero X_a)) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) _let_1) _let_1)))))) (forall ((X_b $$unsorted) (One $$unsorted) (Times $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat X_b))) (let ((_let_2 (tptp.fun X_b _let_1))) (let ((_let_3 (tptp.fun X_b (tptp.fun X_b X_b)))) (= (tptp.hAPP tptp.nat X_b (tptp.hAPP X_b _let_1 (tptp.hAPP _let_3 _let_2 (tptp.hAPP X_b (tptp.fun _let_3 _let_2) (tptp.power_1 X_b) One) Times) A_2) (tptp.zero_zero tptp.nat)) (tptp.ti X_b One)))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 (tptp.ord_less X_a) _let_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) _let_1) B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) B))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 (tptp.ord_less X_a) _let_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) _let_1) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) B))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B $$unsorted) (C $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.zero_zero X_a)) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) B) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) C)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B $$unsorted) (C $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) B))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_2 C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) C)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) _let_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 (tptp.ord_less_eq X_a) B) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) B)) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 (tptp.ord_less_eq X_a) A_1) _let_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) B)) _let_1)))))))))) (forall ((N_1 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 X)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.nat tptp.int) (tptp.power_power tptp.int) X) N_1)))))) (forall ((Pa $$unsorted)) (= (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) X_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa X_2)))) (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) X_2)))))) (forall ((Pa $$unsorted)) (= (exists ((X_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) X_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa X_2)))) (exists ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) X_2)))))) (forall ((Z $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) Z)))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_32 _let_30)) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 X)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) X) Y))))))) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 X)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) X) Y))))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_32 _let_29)) (forall ((K $$unsorted)) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) K)) (tptp.zero_zero tptp.int))))) (forall ((N $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) N))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N)))) (forall ((K_1 $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K_1) L)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) K_1) L)) (tptp.zero_zero tptp.int))))))) (forall ((K $$unsorted) (I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) K))) (let ((_let_2 (tptp.ord_less tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 I) J)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 (tptp.zero_zero tptp.int)) K)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 (tptp.hAPP tptp.int tptp.int _let_1 I)) (tptp.hAPP tptp.int tptp.int _let_1 J))))))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_31 (tptp.ord_less tptp.int) _let_30) _let_29)) (forall ((X_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) _let_1))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.power_power tptp.nat) X_1) N))) (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 X_1)) (= N _let_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((N_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.zero_zero X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) A_1) N_1)))))))) (forall ((M $$unsorted) (N_1 $$unsorted) (I $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.power_power tptp.nat) I))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.zero_zero tptp.nat)) I)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 M)) (tptp.hAPP tptp.nat tptp.nat _let_3 N_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) N_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((A_1 $$unsorted) (N_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)))) (let ((_let_2 (tptp.power_power X_a))) (let ((_let_3 (tptp.fun tptp.nat X_a))) (=> (= (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_3 _let_2 A_1) N_1) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_3 _let_2 B) N_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N_1)) (= (tptp.ti X_a A_1) (tptp.ti X_a B)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((N_1 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.power_power X_a))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (let ((_let_3 (tptp.ord_less X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) A_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_2 _let_1 A_1) N_1)) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_2 _let_1 B) N_1))))))))))))) (forall ((N_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (=> (not (= N_1 _let_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) _let_1) N_1))))) (forall ((M $$unsorted) (N_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M) N_1)) (not (= N_1 (tptp.zero_zero tptp.nat))))) (forall ((N_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N_1) (tptp.zero_zero tptp.nat))))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (= (not (= N _let_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) _let_1) N))))) (forall ((N_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N_1) (tptp.zero_zero tptp.nat))))) (forall ((X_b $$unsorted)) (=> (tptp.linordered_semidom X_b) (forall ((N $$unsorted)) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) (tptp.zero_zero X_b)) (tptp.hAPP tptp.nat X_b (tptp.semiring_1_of_nat X_b) N))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N)))))) (forall ((X_b $$unsorted)) (=> (tptp.linord219039673up_add X_b) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) (tptp.zero_zero X_b)))) (= (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.plus_plus X_b) A_2) A_2))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool _let_1 A_2))))))) (forall ((X_b $$unsorted)) (=> (tptp.linord219039673up_add X_b) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_b))) (let ((_let_2 (tptp.ord_less X_b))) (let ((_let_3 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_3 _let_2 (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.plus_plus X_b) A_2) A_2)) _let_1)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_3 _let_2 A_2) _let_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.zero_zero X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) B))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((B $$unsorted) (C $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 B))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.zero_zero X_a)) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) C))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) _let_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) B)) _let_1)))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linordered_idom X_b) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_b))) (let ((_let_2 (tptp.ord_less X_b))) (let ((_let_3 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_3 _let_2 (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.plus_plus X_b) A_2) A_2)) _let_1)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_3 _let_2 A_2) _let_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_ring X_a) (forall ((A_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1) A_1)) (tptp.zero_zero X_a))))))) (forall ((X_b $$unsorted)) (=> (tptp.linord581940658strict X_b) (forall ((A_2 $$unsorted) (Ca $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.ord_less X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.zero_zero X_b))) (let ((_let_4 (tptp.times_times X_b))) (let ((_let_5 (tptp.fun X_b X_b))) (= (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 _let_5 _let_4 A_2) Ca)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_5 _let_4 Ba) Ca))) (or (and (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 _let_3) Ca)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 A_2) Ba))) (and (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 Ca) _let_3)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 Ba) A_2))))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linord581940658strict X_b) (forall ((Ca $$unsorted) (A_2 $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.ord_less X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.zero_zero X_b))) (let ((_let_4 (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.times_times X_b) Ca))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 (tptp.hAPP X_b X_b _let_4 A_2)) (tptp.hAPP X_b X_b _let_4 Ba))) (or (and (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 _let_3) Ca)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 A_2) Ba))) (and (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 Ca) _let_3)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 Ba) A_2)))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linord581940658strict X_b) (forall ((A_2 $$unsorted) (Ba $$unsorted) (Ca $$unsorted)) (let ((_let_1 (tptp.ord_less X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.times_times X_b) Ca))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 (tptp.zero_zero X_b)) Ca)) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 (tptp.hAPP X_b X_b _let_3 A_2)) (tptp.hAPP X_b X_b _let_3 Ba))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 A_2) Ba)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord20386208strict X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.zero_zero X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1) B))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord20386208strict X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 _let_1) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1) B)) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord20386208strict X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 _let_1) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) B) A_1)) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord20386208strict X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.zero_zero X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1) B))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord20386208strict X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.zero_zero X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) B) A_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B)))))))) (forall ((X_b $$unsorted)) (=> (tptp.linord581940658strict X_b) (forall ((A_2 $$unsorted) (Ba $$unsorted) (Ca $$unsorted)) (let ((_let_1 (tptp.ord_less X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.times_times X_b) Ca))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 Ca) (tptp.zero_zero X_b))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 (tptp.hAPP X_b X_b _let_3 A_2)) (tptp.hAPP X_b X_b _let_3 Ba))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 Ba) A_2)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord20386208strict X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) _let_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 _let_1) B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1) B)) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord581940658strict X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) _let_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 _let_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1) B))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord20386208strict X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.zero_zero X_a)) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) C)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord20386208strict X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) C))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.zero_zero X_a)) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 A_1)) (tptp.hAPP X_a X_a _let_1 B))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord893533164strict X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) C))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.zero_zero X_a)) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 A_1)) (tptp.hAPP X_a X_a _let_1 B))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord581940658strict X_a) (forall ((C $$unsorted) (B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 B) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 C) (tptp.zero_zero X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) C)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord581940658strict X_a) (forall ((C $$unsorted) (B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) C))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 C) (tptp.zero_zero X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 A_1)) (tptp.hAPP X_a X_a _let_1 B))))))))))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.boolean_algebra T_1) (tptp.boolean_algebra (tptp.fun T_2 T_1)))) (forall ((T_2 $$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 $$unsorted)) (=> (tptp.order T_1) (tptp.order (tptp.fun T_2 T_1)))) (forall ((T_2 $$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 $$unsorted)) (=> (tptp.uminus T_1) (tptp.uminus (tptp.fun T_2 T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.minus T_1) (tptp.minus (tptp.fun T_2 T_1)))) (tptp.semiri456707255roduct tptp.int) (tptp.ordere223160158up_add tptp.int) (tptp.ordere236663937imp_le tptp.int) (tptp.linord893533164strict tptp.int) (tptp.linord2061991079up_add tptp.int) (tptp.linord20386208strict tptp.int) (tptp.ordere779506340up_add tptp.int) (tptp.ordere216010020id_add tptp.int) (tptp.linord219039673up_add tptp.int) (tptp.cancel146912293up_add tptp.int) (tptp.ring_11004092258visors tptp.int) (tptp.linord581940658strict tptp.int) (tptp.ordered_ab_group_add tptp.int) (tptp.cancel_semigroup_add tptp.int) (tptp.linordered_semidom tptp.int) (tptp.ab_semigroup_mult tptp.int) (tptp.comm_monoid_mult tptp.int) (tptp.ab_semigroup_add tptp.int) (tptp.comm_monoid_add tptp.int) (tptp.linordered_ring tptp.int) (tptp.linordered_idom tptp.int) (tptp.comm_semiring_1 tptp.int) (tptp.comm_semiring tptp.int) (tptp.semiring_char_0 tptp.int) (tptp.ab_group_add tptp.int) (tptp.ordered_ring tptp.int) (tptp.preorder tptp.int) (tptp.linorder tptp.int) (tptp.monoid_mult tptp.int) (tptp.comm_ring_1 tptp.int) (tptp.semiring_1 tptp.int) (tptp.semiring_0 tptp.int) (tptp.group_add tptp.int) (tptp.order tptp.int) (tptp.semiring tptp.int) (tptp.ord tptp.int) (tptp.uminus tptp.int) (tptp.ring_1 tptp.int) (tptp.minus tptp.int) (tptp.power tptp.int) (tptp.ring tptp.int) (tptp.idom tptp.int) (tptp.one tptp.int) (tptp.semiri456707255roduct tptp.nat) (tptp.ordere223160158up_add tptp.nat) (tptp.ordere236663937imp_le tptp.nat) (tptp.linord893533164strict tptp.nat) (tptp.linord2061991079up_add tptp.nat) (tptp.linord20386208strict tptp.nat) (tptp.ordere779506340up_add tptp.nat) (tptp.ordere216010020id_add tptp.nat) (tptp.cancel146912293up_add tptp.nat) (tptp.cancel_semigroup_add tptp.nat) (tptp.linordered_semidom tptp.nat) (tptp.ab_semigroup_mult tptp.nat) (tptp.comm_monoid_mult tptp.nat) (tptp.ab_semigroup_add tptp.nat) (tptp.comm_monoid_add tptp.nat) (tptp.comm_semiring_1 tptp.nat) (tptp.comm_semiring tptp.nat) (tptp.semiring_char_0 tptp.nat) (tptp.preorder tptp.nat) (tptp.linorder tptp.nat) (tptp.monoid_mult tptp.nat) (tptp.semiring_1 tptp.nat) (tptp.semiring_0 tptp.nat) (tptp.order tptp.nat) (tptp.semiring tptp.nat) (tptp.ord tptp.nat) (tptp.bot tptp.nat) (tptp.minus tptp.nat) (tptp.power tptp.nat) (tptp.one tptp.nat) (tptp.boolean_algebra tptp.bool) (tptp.preorder tptp.bool) (tptp.finite_finite tptp.bool) (tptp.order tptp.bool) (tptp.ord tptp.bool) (tptp.bot tptp.bool) (tptp.uminus tptp.bool) (tptp.minus tptp.bool) (forall ((T $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.ti T A))) (= (tptp.ti T _let_1) _let_1))) (forall ((X_a $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.hAPP tptp.bool (tptp.fun X_a _let_1) (tptp.if X_a) tptp.fTrue) X) Y) (tptp.ti X_a X)))) (forall ((X_a $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.hAPP tptp.bool (tptp.fun X_a _let_1) (tptp.if X_a) tptp.fFalse) X) Y) (tptp.ti X_a Y)))) (forall ((P $$unsorted)) (let ((_let_1 (tptp.ti tptp.bool P))) (or (= _let_1 tptp.fTrue) (= _let_1 tptp.fFalse)))) (forall ((X_a $$unsorted) (P $$unsorted) (X $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool P X))) (tptp.hBOOL (tptp.hAPP (tptp.fun X_a tptp.bool) tptp.bool (tptp.fEx X_a) P)))) (forall ((P $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool tptp.fNot P))) (not (tptp.hBOOL P)))) (forall ((P $$unsorted)) (or (tptp.hBOOL P) (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool tptp.fNot P)))) (forall ((X_a $$unsorted) (X_c $$unsorted) (X_b $$unsorted) (P $$unsorted) (Q $$unsorted) (R $$unsorted)) (let ((_let_1 (tptp.fun X_a X_c))) (let ((_let_2 (tptp.fun X_a X_b))) (= (tptp.hAPP X_a X_c (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun _let_2 _let_1) (tptp.combb X_b X_c X_a) P) Q) R) (tptp.hAPP X_b X_c P (tptp.hAPP X_a X_b Q R)))))) (forall ((X_a $$unsorted) (X_c $$unsorted) (X_b $$unsorted) (P $$unsorted) (Q $$unsorted) (R $$unsorted)) (let ((_let_1 (tptp.fun X_b X_c))) (let ((_let_2 (tptp.fun X_a X_c))) (= (tptp.hAPP X_a X_c (tptp.hAPP X_b _let_2 (tptp.hAPP (tptp.fun X_a _let_1) (tptp.fun X_b _let_2) (tptp.combc X_a X_b X_c) P) Q) R) (tptp.hAPP X_b X_c (tptp.hAPP X_a _let_1 P R) Q))))) (forall ((X_a $$unsorted) (P $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.combi X_a) P) (tptp.ti X_a P))) _let_28 (forall ((X_a $$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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 91.48/86.72 )
% 91.48/86.72 % SZS output end Proof for SWW470+7
% 91.48/86.73 % cvc5---1.0.5 exiting
% 91.48/86.73 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------