TSTP Solution File: NUM641+4 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM641+4 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 10:46:03 EDT 2023
% Result : Theorem 82.42s 82.70s
% Output : Proof 82.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.15 % Problem : NUM641+4 : TPTP v8.1.2. Released v7.3.0.
% 0.12/0.16 % Command : do_cvc5 %s %d
% 0.16/0.37 % Computer : n004.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Fri Aug 25 10:05:38 EDT 2023
% 0.23/0.37 % CPUTime :
% 0.23/0.53 %----Proving TF0_NAR, FOF, or CNF
% 82.42/82.70 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.B3BUxMDUij/cvc5---1.0.5_12647.p...
% 82.42/82.70 ------- get file name : TPTP file name is NUM641+4
% 82.42/82.70 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_12647.smt2...
% 82.42/82.70 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 82.42/82.70 --- Run --no-e-matching --full-saturate-quant at 5...
% 82.42/82.70 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 82.42/82.70 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 82.42/82.70 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 82.42/82.70 --- Run --trigger-sel=max --full-saturate-quant at 5...
% 82.42/82.70 --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 82.42/82.70 --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 82.42/82.70 --- Run --prenex-quant=none --full-saturate-quant at 5...
% 82.42/82.70 --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 5...
% 82.42/82.70 --- Run --relevant-triggers --full-saturate-quant at 5...
% 82.42/82.70 --- Run --finite-model-find --e-matching --sort-inference --uf-ss-fair at 5...
% 82.42/82.70 --- Run --pre-skolem-quant=on --full-saturate-quant at 10...
% 82.42/82.70 --- Run --cbqi-vo-exp --full-saturate-quant at 10...
% 82.42/82.70 % SZS status Theorem for NUM641+4
% 82.42/82.70 % SZS output start Proof for NUM641+4
% 82.42/82.70 (
% 82.42/82.70 (let ((_let_1 (tptp.scratc1829701671all_of tptp.aTP_Lamm_a))) (let ((_let_2 (tptp.pp (tptp.aa_fun171081125l_bool _let_1 tptp.aTP_Lamm_aa)))) (let ((_let_3 (not _let_2))) (let ((_let_4 (forall ((X7 $$unsorted) (Y $$unsorted)) (=> (and (tptp.gg_TPTP_ind X7) (tptp.gg_TPTP_ind Y)) (or (not (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.fequal_TPTP_ind X7) Y))) (= X7 Y)))))) (let ((_let_5 (forall ((X7 $$unsorted) (Y $$unsorted)) (or (not (= X7 Y)) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.fequal_TPTP_ind X7) Y)))))) (let ((_let_6 (forall ((Uu $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool tptp.aTP_Lamm_aa Uu)) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1083610823d_n_is (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc912327602rdsucc Uu)) (tptp.aa_TPTP_ind_TPTP_ind (tptp.scratc1084070009d_n_pl tptp.scratc45782132nd_n_1) Uu))))))) (let ((_let_7 (forall ((Uu $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool tptp.aTP_Lamm_bu Uu)) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1083610823d_n_is (tptp.aa_TPTP_ind_TPTP_ind (tptp.scratc1084070009d_n_pl tptp.scratc45782132nd_n_1) Uu)) (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc912327602rdsucc Uu))))))) (let ((_let_8 (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc912327602rdsucc tptp.scratc1745451206ptyset))) (let ((_let_9 (tptp.pp (tptp.aa_fun171081125l_bool _let_1 tptp.aTP_Lamm_bu)))) (let ((_let_10 (forall ((X $$unsorted) (Xa $$unsorted)) (= (tptp.pp (tptp.aa_fun171081125l_bool (tptp.scratc1829701671all_of X) Xa)) (forall ((X2 $$unsorted)) (=> (tptp.gg_TPTP_ind X2) (=> (tptp.scratc1451164978_is_of X2 X) (tptp.pp (tptp.aa_TPTP_ind_bool Xa X2))))))))) (let ((_let_11 (tptp.aa_fun1431113780TP_ind (tptp.scratc322369131_d_Sep (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc1770865966univof tptp.scratc1745451206ptyset)) tptp.scratc1337809184_nat_p))) (let ((_let_12 (= tptp.scratc315931824_omega _let_11))) (let ((_let_13 (= tptp.scratc1679165215d_Inj1 (tptp.scratc134999576In_rec tptp.aTP_Lamm_bk)))) (let ((_let_14 (= tptp.scratc339482526_d_Unj (tptp.scratc134999576In_rec tptp.aTP_Lamm_bj)))) (let ((_let_15 (= tptp.scratc153411835nd_imp tptp.fimplies))) (let ((_let_16 (= tptp.scratc1175657942bvious (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo1142376798l_bool tptp.scratc153411835nd_imp tptp.fFalse) tptp.fFalse))))) (let ((_let_17 (forall ((X $$unsorted)) (= (tptp.scratc1564950462d_e_is X) tptp.fequal_TPTP_ind)))) (let ((_let_18 (= tptp.scratc193932176nd_nat (tptp.aa_fun1431113780TP_ind (tptp.scratc322369131_d_Sep tptp.scratc315931824_omega) tptp.aTP_Lamm_ag)))) (let ((_let_19 (= tptp.scratc1083610823d_n_is (tptp.scratc1564950462d_e_is tptp.scratc193932176nd_nat)))) (let ((_let_20 (= tptp.scratc1083610818d_n_in (tptp.scratc1777039668d_esti tptp.scratc193932176nd_nat)))) (let ((_let_21 (= tptp.scratc1684187121n_some (tptp.scratc940362479l_some tptp.scratc193932176nd_nat)))) (let ((_let_22 (= tptp.scratc2011078052_n_all (tptp.scratc87254192nd_all tptp.scratc193932176nd_nat)))) (let ((_let_23 (= tptp.scratc2126870313_n_one (tptp.scratc203046453nd_one tptp.scratc193932176nd_nat)))) (let ((_let_24 (= tptp.scratc45782132nd_n_1 _let_8))) (let ((_let_25 (= tptp.scratc1161393342_cond1 (tptp.aa_TPT43085870d_bool tptp.scratc1083610818d_n_in tptp.scratc45782132nd_n_1)))) (let ((_let_26 (= tptp.scratc280311546d_i1_s (tptp.scratc322369131_d_Sep tptp.scratc193932176nd_nat)))) (let ((_let_27 (forall ((B_1 $$unsorted) (B_2 $$unsorted)) (tptp.gg_TPTP_ind (tptp.aa_TPTP_ind_TPTP_ind B_1 B_2))))) (let ((_let_28 (tptp.aa_fun1431113780TP_ind (tptp.scratc322369131_d_Sep _let_11) tptp.aTP_Lamm_ag))) (let ((_let_29 (tptp.scratc1564950462d_e_is _let_28))) (let ((_let_30 (= tptp.fequal_TPTP_ind _let_29))) (let ((_let_31 (tptp.scratc1084070009d_n_pl _let_8))) (let ((_let_32 (tptp.aa_TPTP_ind_TPTP_ind _let_31 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_33 (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc912327602rdsucc SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_34 (tptp.aa_TPT43085870d_bool _let_29 _let_33))) (let ((_let_35 (tptp.pp (tptp.aa_TPTP_ind_bool _let_34 _let_32)))) (let ((_let_36 (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.fequal_TPTP_ind _let_33) _let_33)))) (let ((_let_37 (= _let_33 _let_32))) (let ((_let_38 (forall ((X $$unsorted)) (= tptp.fequal_TPTP_ind (tptp.scratc1564950462d_e_is X))))) (let ((_let_39 (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_40 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_39 :args (_let_28 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.scratc1564950462d_e_is X) tptp.fequal_TPTP_ind))))) :args (_let_38))) _let_39 :args (_let_30 false _let_38)))) (let ((_let_41 (tptp.pp (tptp.aa_TPTP_ind_bool tptp.aTP_Lamm_aa SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10)))) (let ((_let_42 (= _let_41 _let_35))) (let ((_let_43 (not _let_35))) (let ((_let_44 (forall ((Uu $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool tptp.aTP_Lamm_aa Uu)) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.scratc1564950462d_e_is (tptp.aa_fun1431113780TP_ind (tptp.scratc322369131_d_Sep (tptp.aa_fun1431113780TP_ind (tptp.scratc322369131_d_Sep (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc1770865966univof tptp.scratc1745451206ptyset)) tptp.scratc1337809184_nat_p)) tptp.aTP_Lamm_ag)) (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc912327602rdsucc Uu)) (tptp.aa_TPTP_ind_TPTP_ind (tptp.scratc1084070009d_n_pl (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc912327602rdsucc tptp.scratc1745451206ptyset)) Uu))))))) (let ((_let_45 (AND_INTRO (ASSUME :args (_let_12)) (ASSUME :args (_let_13)) (ASSUME :args (_let_14)) (ASSUME :args (_let_15)) (ASSUME :args (_let_16)) (ASSUME :args (_let_18)) (ASSUME :args (_let_19)) (ASSUME :args (_let_20)) (ASSUME :args (_let_21)) (ASSUME :args (_let_22)) (ASSUME :args (_let_23)) (ASSUME :args (_let_24)) (ASSUME :args (_let_25)) (ASSUME :args (_let_26))))) (let ((_let_46 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO _let_45 :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_47 (tptp.scratc1451164978_is_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 tptp.aTP_Lamm_a))) (let ((_let_48 (not _let_47))) (let ((_let_49 (tptp.gg_TPTP_ind SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_50 (not _let_49))) (let ((_let_51 (or _let_50 _let_48 _let_41))) (let ((_let_52 (forall ((X2 $$unsorted)) (or (not (tptp.gg_TPTP_ind X2)) (not (tptp.scratc1451164978_is_of X2 tptp.aTP_Lamm_a)) (tptp.pp (tptp.aa_TPTP_ind_bool tptp.aTP_Lamm_aa X2)))))) (let ((_let_53 (not _let_51))) (let ((_let_54 (= _let_2 _let_52))) (let ((_let_55 (not _let_52))) (let ((_let_56 (forall ((X $$unsorted) (Xa $$unsorted)) (= (tptp.pp (tptp.aa_fun171081125l_bool (tptp.scratc1829701671all_of X) Xa)) (forall ((X2 $$unsorted)) (or (not (tptp.gg_TPTP_ind X2)) (not (tptp.scratc1451164978_is_of X2 X)) (tptp.pp (tptp.aa_TPTP_ind_bool Xa X2)))))))) (let ((_let_57 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_58 (_let_56))) (let ((_let_59 ((tptp.aa_fun171081125l_bool (tptp.scratc1829701671all_of X) Xa)))) (let ((_let_60 (or))) (let ((_let_61 (_let_55))) (let ((_let_62 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_61)) :args _let_61)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_55) _let_52))) (REFL :args (_let_53)) :args _let_60)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_54)) :args ((or _let_2 _let_55 (not _let_54)))) (ASSUME :args (_let_3)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_57 :args (tptp.aTP_Lamm_a tptp.aTP_Lamm_aa QUANTIFIERS_INST_E_MATCHING _let_59)) :args _let_58)) _let_57 :args (_let_54 false _let_56)) :args (_let_55 true _let_2 false _let_54)) :args (_let_53 true _let_52)))) (let ((_let_63 (forall ((Y $$unsorted)) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.fequal_TPTP_ind Y) Y))))) (let ((_let_64 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_65 (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.fequal_TPTP_ind _let_32) _let_33)))) (let ((_let_66 (not _let_65))) (let ((_let_67 (tptp.gg_TPTP_ind _let_33))) (let ((_let_68 (not _let_67))) (let ((_let_69 (tptp.gg_TPTP_ind _let_32))) (let ((_let_70 (not _let_69))) (let ((_let_71 (or _let_70 _let_68 _let_66 _let_37))) (let ((_let_72 (forall ((X7 $$unsorted) (Y $$unsorted)) (or (not (tptp.gg_TPTP_ind X7)) (not (tptp.gg_TPTP_ind Y)) (not (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.fequal_TPTP_ind X7) Y))) (= X7 Y))))) (let ((_let_73 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_74 (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool _let_29 _let_32) _let_33)))) (let ((_let_75 (tptp.pp (tptp.aa_TPTP_ind_bool tptp.aTP_Lamm_bu SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10)))) (let ((_let_76 (= _let_75 _let_74))) (let ((_let_77 (forall ((Uu $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool tptp.aTP_Lamm_bu Uu)) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.scratc1564950462d_e_is (tptp.aa_fun1431113780TP_ind (tptp.scratc322369131_d_Sep (tptp.aa_fun1431113780TP_ind (tptp.scratc322369131_d_Sep (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc1770865966univof tptp.scratc1745451206ptyset)) tptp.scratc1337809184_nat_p)) tptp.aTP_Lamm_ag)) (tptp.aa_TPTP_ind_TPTP_ind (tptp.scratc1084070009d_n_pl (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc912327602rdsucc tptp.scratc1745451206ptyset)) Uu)) (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc912327602rdsucc Uu))))))) (let ((_let_78 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO _let_45 :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_79 (or _let_50 _let_48 _let_75))) (let ((_let_80 (forall ((X2 $$unsorted)) (or (not (tptp.gg_TPTP_ind X2)) (not (tptp.scratc1451164978_is_of X2 tptp.aTP_Lamm_a)) (tptp.pp (tptp.aa_TPTP_ind_bool tptp.aTP_Lamm_bu X2)))))) (let ((_let_81 (= _let_9 _let_80))) (let ((_let_82 (_let_80))) (let ((_let_83 (REFL :args (_let_51)))) (let ((_let_84 (and _let_30 _let_74))) (let ((_let_85 (ASSUME :args (_let_74)))) (let ((_let_86 (APPLY_UF tptp.pp))) (let ((_let_87 (APPLY_UF tptp.aa_TPTP_ind_bool))) (let ((_let_88 (REFL :args (_let_33)))) (let ((_let_89 (APPLY_UF tptp.aa_TPT43085870d_bool))) (let ((_let_90 (ASSUME :args (_let_30)))) (let ((_let_91 (SYMM (SYMM _let_90)))) (let ((_let_92 (_let_27))) (let ((_let_93 (ASSUME :args _let_92))) (let ((_let_94 ((tptp.aa_TPTP_ind_TPTP_ind B_1 B_2)))) (let ((_let_95 (not _let_37))) (let ((_let_96 (not _let_36))) (let ((_let_97 (not _let_30))) (let ((_let_98 (ASSUME :args (_let_43)))) (let ((_let_99 (ASSUME :args (_let_37)))) (let ((_let_100 (ASSUME :args (_let_36)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_98 _let_99 _let_90 _let_100) :args (_let_30 _let_43 _let_36 _let_37)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_100)) (CONG (CONG (CONG _let_91 _let_88 :args _let_89) _let_88 :args _let_87) :args _let_86) (CONG (CONG (REFL :args (_let_34)) (SYMM (SYMM _let_99)) :args _let_87) :args _let_86) (FALSE_INTRO _let_98))) :args (_let_43 _let_37 _let_30 _let_36)) :args ((not (and _let_30 _let_43 _let_36 _let_37)) SB_LITERAL))) (CONG (REFL :args (_let_97)) (MACRO_SR_PRED_INTRO :args ((= (not _let_43) _let_35))) (REFL :args (_let_96)) (REFL :args (_let_95)) :args _let_60)) :args ((or _let_35 _let_97 _let_96 _let_95))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_71)) :args ((or _let_68 _let_70 _let_66 _let_37 (not _let_71)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_93 :args (tptp.scratc912327602rdsucc SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_94)) :args _let_92)) _let_93 :args (_let_67 false _let_27)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_93 :args (_let_31 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_94)) :args _let_92)) _let_93 :args (_let_69 false _let_27)) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_84)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_85 _let_90) (SCOPE (TRUE_ELIM (TRANS (CONG (CONG (CONG _let_91 (REFL :args (_let_32)) :args _let_89) _let_88 :args _let_87) :args _let_86) (TRUE_INTRO _let_85))) :args (_let_74 _let_30))) :args (_let_30 _let_74))) :args (true _let_84)) _let_40 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_76)) :args ((or (not _let_75) _let_74 (not _let_76)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_79)) :args ((or _let_50 _let_48 _let_75 (not _let_79)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_51 0)) (CONG _let_83 (MACRO_SR_PRED_INTRO :args ((= (not _let_50) _let_49))) :args _let_60)) :args ((or _let_49 _let_51))) _let_62 :args (_let_49 true _let_51)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_51 1)) (CONG _let_83 (MACRO_SR_PRED_INTRO :args ((= (not _let_48) _let_47))) :args _let_60)) :args ((or _let_47 _let_51))) _let_62 :args (_let_47 true _let_51)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_82) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.gg_TPTP_ind X2) false))))) :args _let_82)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_81)) :args ((or (not _let_9) _let_80 (not _let_81)))) (ASSUME :args (_let_9)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_57 :args (tptp.aTP_Lamm_a tptp.aTP_Lamm_bu QUANTIFIERS_INST_E_MATCHING _let_59)) :args _let_58)) _let_57 :args (_let_81 false _let_56)) :args (_let_80 false _let_9 false _let_81)) :args (_let_79 false _let_80)) :args (_let_75 false _let_49 false _let_47 false _let_79)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_78 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.aa_TPTP_ind_bool tptp.aTP_Lamm_bu Uu)))) :args (_let_77))) _let_78 :args (_let_76 false _let_77)) :args (_let_74 false _let_75 false _let_76)) :args (_let_65 false _let_30 false _let_74)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_73 :args (_let_32 _let_33 QUANTIFIERS_INST_CBQI_PROP)) :args (_let_72)))) _let_73 :args (_let_71 false _let_72)) :args (_let_37 false _let_67 false _let_69 false _let_65 false _let_71)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_64 :args (_let_33 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.aa_TPT43085870d_bool tptp.fequal_TPTP_ind Y)))) :args (_let_63))) _let_64 :args (_let_36 false _let_63)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_42)) :args ((or _let_41 _let_43 (not _let_42)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_51 2)) _let_62 :args ((not _let_41) true _let_51)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_46 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.aa_TPTP_ind_bool tptp.aTP_Lamm_aa Uu)))) :args (_let_44))) _let_46 :args (_let_42 false _let_44)) :args (_let_43 true _let_41 false _let_42)) _let_40 :args (false false _let_37 false _let_36 true _let_35 false _let_30)) :args ((tptp.gg_bool (tptp.undefined_bool tptp.bool)) (tptp.gg_TPTP_ind (tptp.undefined_TPTP_ind tptp.tPTP_ind)) (forall ((B_1 $$unsorted) (B_2 $$unsorted)) (tptp.gg_bool (tptp.scratc1624975209_amone B_1 B_2))) (forall ((B_1 $$unsorted) (B_2 $$unsorted)) (tptp.gg_bool (tptp.scratc438620580_d_and B_1 B_2))) (forall ((B_1 $$unsorted)) (tptp.gg_bool (tptp.scratc546085760_d_not B_1))) (forall ((B_1 $$unsorted) (B_2 $$unsorted) (B_3 $$unsorted)) (tptp.gg_bool (tptp.scratc119709764nd_ec3 B_1 B_2 B_3))) (forall ((B_1 $$unsorted) (B_2 $$unsorted)) (tptp.gg_TPTP_ind (tptp.scratc119709829nd_ect B_1 B_2))) (tptp.gg_TPTP_ind tptp.scratc1745451206ptyset) (forall ((B_1 $$unsorted)) (tptp.gg_TPTP_ind (tptp.scratc120562615nd_eps B_1))) (forall ((B_1 $$unsorted) (B_2 $$unsorted)) (tptp.gg_TPTP_ind (tptp.scratc153477422nd_ind B_1 B_2))) (forall ((B_1 $$unsorted) (B_2 $$unsorted)) (tptp.gg_bool (tptp.scratc951703481d_l_ec B_1 B_2))) (tptp.gg_TPTP_ind tptp.scratc45782132nd_n_1) (tptp.gg_TPTP_ind tptp.scratc193932176nd_nat) (tptp.gg_TPTP_ind tptp.scratc315931824_omega) (forall ((B_1 $$unsorted) (B_2 $$unsorted) (B_3 $$unsorted)) (tptp.gg_bool (tptp.scratc203308799nd_or3 B_1 B_2 B_3))) (forall ((B_1 $$unsorted) (B_2 $$unsorted)) (tptp.gg_bool (tptp.aa_bool_bool B_1 B_2))) (forall ((B_1 $$unsorted) (B_2 $$unsorted)) (tptp.gg_bool (tptp.aa_TPTP_ind_bool B_1 B_2))) _let_27 (forall ((B_1 $$unsorted) (B_2 $$unsorted)) (tptp.gg_bool (tptp.aa_fun171081125l_bool B_1 B_2))) (forall ((B_1 $$unsorted) (B_2 $$unsorted)) (tptp.gg_TPTP_ind (tptp.aa_fun1431113780TP_ind B_1 B_2))) (forall ((B_1 $$unsorted) (B_2 $$unsorted)) (tptp.gg_TPTP_ind (tptp.aa_fun277296641TP_ind B_1 B_2))) (forall ((B_1 $$unsorted)) (tptp.gg_bool (tptp.fEx_TPTP_ind B_1))) (tptp.gg_bool tptp.fFalse) (tptp.gg_bool tptp.fTrue) (forall ((X $$unsorted)) (= (tptp.scratc1084070009d_n_pl X) (tptp.aa_TPT1424761345TP_ind tptp.scratc1549486784bnd_ap (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc1715799339d_plus X)))) (forall ((X $$unsorted)) (= (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc1715799339d_plus X) (tptp.scratc153477422nd_ind (tptp.aa_fun277296641TP_ind (tptp.aa_TPT494704832TP_ind tptp.scratc423746188d_d_Pi tptp.scratc193932176nd_nat) tptp.aTP_Lamm_ab) (tptp.aa_TPT43085870d_bool tptp.scratc1657584698_prop2 X)))) (forall ((X $$unsorted)) (= (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc2122730866d_24_g X) (tptp.aa_fun277296641TP_ind (tptp.aa_TPT494704832TP_ind tptp.scratc1709589394_Sigma tptp.scratc193932176nd_nat) (tptp.aTP_Lamm_ac X)))) (forall ((X $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool tptp.scratc1146670208_prop4 X)) (tptp.pp (tptp.aa_fun171081125l_bool (tptp.scratc940362479l_some (tptp.aa_fun277296641TP_ind (tptp.aa_TPT494704832TP_ind tptp.scratc423746188d_d_Pi tptp.scratc193932176nd_nat) tptp.aTP_Lamm_ab)) (tptp.aa_TPT43085870d_bool tptp.scratc1657584698_prop2 X))))) (forall ((X $$unsorted) (Xa $$unsorted) (Xb $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.scratc1146670207_prop3 X) Xa) Xb)) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1083610823d_n_is (tptp.aa_TPTP_ind_TPTP_ind (tptp.aa_TPT1424761345TP_ind tptp.scratc1549486784bnd_ap X) Xb)) (tptp.aa_TPTP_ind_TPTP_ind (tptp.aa_TPT1424761345TP_ind tptp.scratc1549486784bnd_ap Xa) Xb))))) (forall ((X $$unsorted) (Xa $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1657584698_prop2 X) Xa)) (tptp.pp (tptp.scratc438620580_d_and (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1083610823d_n_is (tptp.aa_TPTP_ind_TPTP_ind (tptp.aa_TPT1424761345TP_ind tptp.scratc1549486784bnd_ap Xa) tptp.scratc45782132nd_n_1)) (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc912327602rdsucc X)) (tptp.aa_TPTP_ind_bool tptp.scratc1657584697_prop1 Xa))))) (forall ((X $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool tptp.scratc1657584697_prop1 X)) (tptp.pp (tptp.aa_fun171081125l_bool tptp.scratc2011078052_n_all (tptp.aa_TPT43085870d_bool tptp.aTP_Lamm_ad X))))) (forall ((X $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool tptp.scratc1069222522_prop1 X)) (tptp.pp (tptp.aa_bool_bool (tptp.scratc952359486d_l_or (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1083610823d_n_is X) tptp.scratc45782132nd_n_1)) (tptp.aa_fun171081125l_bool tptp.scratc1684187121n_some (tptp.aa_TPT43085870d_bool tptp.aTP_Lamm_ae X)))))) (forall ((X $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool tptp.scratc480860347_prop1 X)) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc194456967nd_nis (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc912327602rdsucc X)) X)))) _let_26 (forall ((X $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool tptp.scratc1161393343_cond2 X)) (tptp.pp (tptp.aa_fun171081125l_bool tptp.scratc2011078052_n_all (tptp.aa_TPT43085870d_bool tptp.aTP_Lamm_af X))))) _let_25 _let_24 _let_23 _let_22 _let_21 _let_20 (forall ((X $$unsorted) (Xa $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc194456967nd_nis X) Xa)) (tptp.pp (tptp.scratc546085760_d_not (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1083610823d_n_is X) Xa))))) _let_19 _let_18 (forall ((X $$unsorted) (Xa $$unsorted) (Xb $$unsorted) (Xc $$unsorted) (Xd $$unsorted)) (= (tptp.scratc1853463352indeq2 X Xa Xb Xc Xd) (tptp.aa_TPT1424761345TP_ind (tptp.scratc693191546_indeq X Xa Xb) (tptp.aa_TPTP_ind_TPTP_ind (tptp.aa_TPT1424761345TP_ind (tptp.scratc788888630d_11_i X Xa Xb) Xc) Xd)))) (forall ((X $$unsorted) (Xa $$unsorted) (Xb $$unsorted)) (= (tptp.scratc788888630d_11_i X Xa Xb) (tptp.scratc693191546_indeq X Xa (tptp.aa_fun277296641TP_ind (tptp.aa_TPT494704832TP_ind tptp.scratc423746188d_d_Pi X) (tptp.aTP_Lamm_ah Xb))))) (forall ((X $$unsorted) (Xa $$unsorted) (Xb $$unsorted) (Xc $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.scratc2069953503fixfu2 X Xa) Xb) Xc)) (tptp.pp (tptp.aa_fun171081125l_bool (tptp.scratc1829701671all_of (tptp.aa_TPT43085870d_bool tptp.aTP_Lamm_ai X)) (tptp.aa_TPT43085870d_bool (tptp.aa_TPT60673477d_bool (tptp.aa_fun987228051d_bool (tptp.aTP_Lamm_am X) Xa) Xb) Xc))))) (forall ((X $$unsorted) (Xa $$unsorted) (Xb $$unsorted) (Xc $$unsorted) (Xd $$unsorted)) (= (tptp.aa_TPTP_ind_TPTP_ind (tptp.aa_TPT1424761345TP_ind (tptp.scratc693191546_indeq X Xa Xb) Xc) Xd) (tptp.scratc153477422nd_ind Xb (tptp.aa_TPT43085870d_bool (tptp.scratc1146670206_prop2 X Xa Xb Xc) Xd)))) (forall ((X $$unsorted) (Xa $$unsorted) (Xb $$unsorted) (Xc $$unsorted) (Xd $$unsorted) (Xe $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.scratc1146670206_prop2 X Xa Xb Xc) Xd) Xe)) (tptp.pp (tptp.aa_fun171081125l_bool (tptp.scratc940362479l_some X) (tptp.aa_TPT43085870d_bool (tptp.scratc57423676_prop1 X Xa Xb Xc Xd) Xe))))) (forall ((X $$unsorted) (Xa $$unsorted) (Xb $$unsorted) (Xc $$unsorted) (Xd $$unsorted) (Xe $$unsorted) (Xf $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.scratc57423676_prop1 X Xa Xb Xc Xd) Xe) Xf)) (tptp.pp (tptp.scratc438620580_d_and (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.scratc1777039668d_esti X) Xf) (tptp.aa_TPTP_ind_TPTP_ind (tptp.scratc441507399_ecect X Xa) Xd)) (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.scratc1564950462d_e_is Xb) (tptp.aa_TPTP_ind_TPTP_ind (tptp.aa_TPT1424761345TP_ind tptp.scratc1549486784bnd_ap Xc) Xf)) Xe))))) (forall ((X $$unsorted) (Xa $$unsorted) (Xb $$unsorted) (Xc $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.scratc2126792979_fixfu X Xa) Xb) Xc)) (tptp.pp (tptp.aa_fun171081125l_bool (tptp.scratc1829701671all_of (tptp.aa_TPT43085870d_bool tptp.aTP_Lamm_ai X)) (tptp.aa_TPT43085870d_bool (tptp.aa_TPT60673477d_bool (tptp.aa_fun987228051d_bool (tptp.aTP_Lamm_ao X) Xa) Xb) Xc))))) (forall ((X $$unsorted) (Xa $$unsorted)) (= (tptp.scratc441507399_ecect X Xa) (tptp.scratc1564950457d_e_in (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc1017762772_power X) (tptp.scratc759883004d_anec X Xa)))) (forall ((X $$unsorted) (Xa $$unsorted) (Xb $$unsorted)) (= (tptp.aa_TPTP_ind_TPTP_ind (tptp.scratc319294504ectelt X Xa) Xb) (tptp.aa_TPTP_ind_TPTP_ind (tptp.scratc434496381ectset X Xa) (tptp.aa_TPTP_ind_TPTP_ind (tptp.scratc442097790_ecelt X Xa) Xb)))) (forall ((X $$unsorted) (Xa $$unsorted)) (= (tptp.scratc434496381ectset X Xa) (tptp.scratc203505661nd_out (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc1017762772_power X) (tptp.scratc759883004d_anec X Xa)))) (forall ((X $$unsorted) (Xa $$unsorted)) (= (tptp.scratc119709829nd_ect X Xa) (tptp.aa_fun1431113780TP_ind (tptp.scratc322369131_d_Sep (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc1017762772_power X)) (tptp.scratc759883004d_anec X Xa)))) (forall ((X $$unsorted) (Xa $$unsorted) (Xb $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.scratc759883004d_anec X Xa) Xb)) (tptp.pp (tptp.aa_fun171081125l_bool (tptp.scratc940362479l_some X) (tptp.aa_TPT43085870d_bool (tptp.scratc119709825nd_ecp X Xa) Xb))))) (forall ((X $$unsorted) (Xa $$unsorted) (Xb $$unsorted) (Xc $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.scratc119709825nd_ecp X Xa) Xb) Xc)) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.scratc1564950462d_e_is (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc1017762772_power X)) Xb) (tptp.aa_TPTP_ind_TPTP_ind (tptp.scratc442097790_ecelt X Xa) Xc))))) (forall ((X $$unsorted) (Xa $$unsorted) (Xb $$unsorted)) (= (tptp.aa_TPTP_ind_TPTP_ind (tptp.scratc442097790_ecelt X Xa) Xb) (tptp.aa_fun1431113780TP_ind (tptp.scratc322369131_d_Sep X) (tptp.aa_TPT43085870d_bool Xa Xb)))) (forall ((X $$unsorted) (Xa $$unsorted) (Xb $$unsorted)) (= (tptp.aa_TPTP_ind_TPTP_ind (tptp.scratc540613727unmore X Xa) Xb) (tptp.aa_fun1431113780TP_ind (tptp.scratc322369131_d_Sep X) (tptp.aa_TPT43085870d_bool (tptp.aa_TPT60673477d_bool (tptp.aTP_Lamm_aq X) Xa) Xb)))) (forall ((X $$unsorted) (Xa $$unsorted) (Xb $$unsorted) (Xc $$unsorted)) (let ((_let_1 (tptp.aa_TPT43085870d_bool (tptp.scratc1777039668d_esti X) Xc))) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.scratc1991259070etprop X Xa) Xb) Xc)) (tptp.pp (tptp.scratc438620580_d_and (tptp.aa_TPTP_ind_bool _let_1 Xa) (tptp.scratc546085760_d_not (tptp.aa_TPTP_ind_bool _let_1 Xb))))))) (forall ((X $$unsorted) (Xa $$unsorted) (Xb $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.scratc1290387246t_disj X) Xa) Xb)) (tptp.pp (tptp.aa_fun171081125l_bool (tptp.scratc87254192nd_all X) (tptp.aa_TPT43085870d_bool (tptp.aa_TPT60673477d_bool (tptp.aTP_Lamm_ar X) Xa) Xb))))) (forall ((X $$unsorted) (Xa $$unsorted) (Xb $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.scratc561998463d_incl X) Xa) Xb)) (tptp.pp (tptp.aa_fun171081125l_bool (tptp.scratc87254192nd_all X) (tptp.aa_TPT43085870d_bool (tptp.aa_TPT60673477d_bool (tptp.aTP_Lamm_as X) Xa) Xb))))) (forall ((X $$unsorted) (Xa $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc2031046193nempty X) Xa)) (tptp.pp (tptp.aa_fun171081125l_bool (tptp.scratc940362479l_some X) (tptp.aa_TPT43085870d_bool (tptp.aTP_Lamm_at X) Xa))))) (forall ((X $$unsorted) (Xa $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1896920188_empty X) Xa)) (tptp.pp (tptp.aa_fun171081125l_bool (tptp.scratc1829701671all_of (tptp.aa_TPT43085870d_bool tptp.aTP_Lamm_ai X)) (tptp.scratc194850556nd_non X (tptp.aa_TPT43085870d_bool (tptp.aTP_Lamm_at X) Xa)))))) (forall ((X $$unsorted)) (= (tptp.scratc1777039668d_esti X) tptp.scratc1550011574bnd_in)) (forall ((X $$unsorted) (Xa $$unsorted)) (= (tptp.scratc1346638271d_r_ec X Xa) (=> (tptp.pp X) (tptp.pp (tptp.scratc546085760_d_not Xa))))) (forall ((X $$unsorted) (Xa $$unsorted) (Xb $$unsorted) (Xc $$unsorted) (Xd $$unsorted)) (= (tptp.aa_TPTP_ind_TPTP_ind (tptp.scratc324534245hangef X Xa Xb Xc) Xd) (tptp.aa_fun277296641TP_ind (tptp.aa_TPT494704832TP_ind tptp.scratc1709589394_Sigma X) (tptp.aa_TPT1424761345TP_ind (tptp.aa_TPT1791839040TP_ind (tptp.aa_TPT1781712639TP_ind (tptp.aTP_Lamm_au X) Xb) Xc) Xd)))) (forall ((X $$unsorted) (Xa $$unsorted) (Xb $$unsorted)) (= (tptp.aa_TPTP_ind_TPTP_ind (tptp.scratc302523178wissel X Xa) Xb) (tptp.aa_fun277296641TP_ind (tptp.aa_TPT494704832TP_ind tptp.scratc1709589394_Sigma X) (tptp.scratc1930628757sel_wb X Xa Xb)))) (forall ((X $$unsorted) (Xa $$unsorted) (Xb $$unsorted) (Xc $$unsorted)) (= (tptp.aa_TPTP_ind_TPTP_ind (tptp.scratc1930628757sel_wb X Xa Xb) Xc) (tptp.aa_TPTP_ind_TPTP_ind (tptp.scratc153871017nd_ite (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.scratc1564950462d_e_is X) Xc) Xb) X Xa) (tptp.aa_TPTP_ind_TPTP_ind (tptp.scratc1930628756sel_wa X Xa Xb) Xc)))) (forall ((X $$unsorted) (Xa $$unsorted) (Xb $$unsorted) (Xc $$unsorted)) (= (tptp.aa_TPTP_ind_TPTP_ind (tptp.scratc1930628756sel_wa X Xa Xb) Xc) (tptp.aa_TPTP_ind_TPTP_ind (tptp.scratc153871017nd_ite (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.scratc1564950462d_e_is X) Xc) Xa) X Xb) Xc))) (forall ((X $$unsorted) (Xa $$unsorted) (Xb $$unsorted) (Xc $$unsorted)) (= (tptp.aa_TPTP_ind_TPTP_ind (tptp.scratc153871017nd_ite X Xa Xb) Xc) (tptp.scratc153477422nd_ind Xa (tptp.aa_TPT43085870d_bool (tptp.scratc1146670205_prop1 X Xa Xb) Xc)))) (forall ((X $$unsorted) (Xa $$unsorted) (Xb $$unsorted) (Xc $$unsorted) (Xd $$unsorted)) (let ((_let_1 (tptp.aa_TPT43085870d_bool (tptp.scratc1564950462d_e_is Xa) Xd))) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.scratc1146670205_prop1 X Xa Xb) Xc) Xd)) (tptp.pp (tptp.scratc438620580_d_and (tptp.aa_bool_bool (tptp.aa_boo1142376798l_bool tptp.scratc153411835nd_imp X) (tptp.aa_TPTP_ind_bool _let_1 Xb)) (tptp.aa_bool_bool (tptp.aa_boo1142376798l_bool tptp.scratc153411835nd_imp (tptp.scratc546085760_d_not X)) (tptp.aa_TPTP_ind_bool _let_1 Xc))))))) (forall ((X $$unsorted) (Xa $$unsorted)) (= (tptp.scratc1061739109second X Xa) tptp.scratc1146276611_proj1)) (forall ((X $$unsorted) (Xa $$unsorted)) (= (tptp.scratc2078076735_first X Xa) tptp.scratc1146276610_proj0)) (forall ((X $$unsorted) (Xa $$unsorted)) (= (tptp.scratc1949829805d_pair X Xa) tptp.scratc1624135595d_pair)) (forall ((X $$unsorted) (Xa $$unsorted)) (let ((_let_1 (tptp.aa_fun1431113780TP_ind (tptp.scratc322369131_d_Sep X) Xa))) (= (tptp.scratc203505661nd_out X Xa) (tptp.scratc1933877819d_soft _let_1 X (tptp.aa_fun277296641TP_ind (tptp.aa_TPT494704832TP_ind tptp.scratc1709589394_Sigma _let_1) (tptp.scratc1564950457d_e_in X Xa)))))) (forall ((X $$unsorted) (Xa $$unsorted) (Xb $$unsorted)) (=> (tptp.gg_TPTP_ind Xb) (= (tptp.aa_TPTP_ind_TPTP_ind (tptp.scratc1564950457d_e_in X Xa) Xb) Xb))) (forall ((X $$unsorted) (Xa $$unsorted) (Xb $$unsorted) (Xc $$unsorted) (Xd $$unsorted)) (= (tptp.aa_TPTP_ind_TPTP_ind (tptp.scratc43785844_inj_h X Xa Xb Xc) Xd) (tptp.aa_fun277296641TP_ind (tptp.aa_TPT494704832TP_ind tptp.scratc1709589394_Sigma X) (tptp.aa_TPT1424761345TP_ind (tptp.aTP_Lamm_av Xc) Xd)))) (forall ((X $$unsorted) (Xa $$unsorted) (Xb $$unsorted)) (= (tptp.aa_TPTP_ind_TPTP_ind (tptp.scratc563244838d_invf X Xa) Xb) (tptp.aa_fun277296641TP_ind (tptp.aa_TPT494704832TP_ind tptp.scratc1709589394_Sigma Xa) (tptp.scratc1933877819d_soft X Xa Xb)))) (forall ((X $$unsorted) (Xa $$unsorted) (Xb $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.scratc370955156ective X) Xa) Xb)) (tptp.pp (tptp.scratc438620580_d_and (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.scratc187235926ective X) Xa) Xb) (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.scratc1527004365ective X) Xa) Xb))))) (forall ((X $$unsorted) (Xa $$unsorted) (Xb $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.scratc1527004365ective X) Xa) Xb)) (tptp.pp (tptp.aa_fun171081125l_bool (tptp.scratc87254192nd_all Xa) (tptp.aa_TPT43085870d_bool (tptp.scratc2035434666_image X Xa) Xb))))) (forall ((X $$unsorted) (Xa $$unsorted) (Xb $$unsorted)) (= (tptp.aa_TPTP_ind_TPTP_ind (tptp.scratc310575295nverse X Xa) Xb) (tptp.aa_fun277296641TP_ind (tptp.aa_TPT494704832TP_ind tptp.scratc1709589394_Sigma Xa) (tptp.aa_TPT1424761345TP_ind (tptp.aa_TPT1791839040TP_ind (tptp.aTP_Lamm_aw X) Xa) Xb)))) (forall ((X $$unsorted) (Xa $$unsorted) (Xb $$unsorted) (Xc $$unsorted)) (= (tptp.aa_TPTP_ind_TPTP_ind (tptp.scratc1933877819d_soft X Xa Xb) Xc) (tptp.scratc153477422nd_ind X (tptp.aa_TPT43085870d_bool (tptp.aa_TPT60673477d_bool (tptp.aTP_Lamm_ax Xa) Xb) Xc)))) (forall ((X $$unsorted) (Xa $$unsorted)) (= (tptp.scratc566981369d_tofs X Xa) tptp.scratc1549486784bnd_ap)) (forall ((X $$unsorted) (Xa $$unsorted) (Xb $$unsorted) (Xc $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.scratc2035434666_image X Xa) Xb) Xc)) (tptp.pp (tptp.aa_fun171081125l_bool (tptp.scratc940362479l_some X) (tptp.aa_TPT43085870d_bool (tptp.aa_TPT60673477d_bool (tptp.aTP_Lamm_ax Xa) Xb) Xc))))) (forall ((X $$unsorted) (Xa $$unsorted) (Xb $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.scratc187235926ective X) Xa) Xb)) (tptp.pp (tptp.aa_fun171081125l_bool (tptp.scratc87254192nd_all X) (tptp.aa_TPT43085870d_bool (tptp.aa_TPT60673477d_bool (tptp.aTP_Lamm_az X) Xa) Xb))))) (forall ((X $$unsorted) (Xa $$unsorted)) (= (tptp.scratc153477422nd_ind X Xa) (tptp.scratc120562615nd_eps (tptp.aa_fun1584354236d_bool (tptp.aTP_Lamm_ba X) Xa)))) (forall ((X $$unsorted) (Xa $$unsorted)) (= (tptp.pp (tptp.aa_fun171081125l_bool (tptp.scratc203046453nd_one X) Xa)) (tptp.pp (tptp.scratc438620580_d_and (tptp.scratc1624975209_amone X Xa) (tptp.aa_fun171081125l_bool (tptp.scratc940362479l_some X) Xa))))) (forall ((X $$unsorted) (Xa $$unsorted)) (= (tptp.pp (tptp.scratc1624975209_amone X Xa)) (tptp.pp (tptp.aa_fun171081125l_bool (tptp.scratc1829701671all_of (tptp.aa_TPT43085870d_bool tptp.aTP_Lamm_ai X)) (tptp.aa_fun1584354236d_bool (tptp.aTP_Lamm_bc X) Xa))))) _let_17 (forall ((X $$unsorted) (Xa $$unsorted) (Xb $$unsorted)) (= (tptp.scratc2071121729_orec3 X Xa Xb) (tptp.pp (tptp.scratc438620580_d_and (tptp.scratc203308799nd_or3 X Xa Xb) (tptp.scratc119709764nd_ec3 X Xa Xb))))) (forall ((X $$unsorted) (Xa $$unsorted) (Xb $$unsorted)) (= (tptp.pp (tptp.scratc119709764nd_ec3 X Xa Xb)) (tptp.scratc759817357d_and3 (tptp.scratc951703481d_l_ec X Xa) (tptp.scratc951703481d_l_ec Xa Xb) (tptp.scratc951703481d_l_ec Xb X)))) (forall ((X $$unsorted) (Xa $$unsorted) (Xb $$unsorted)) (= (tptp.scratc759817357d_and3 X Xa Xb) (tptp.pp (tptp.scratc438620580_d_and X (tptp.scratc438620580_d_and Xa Xb))))) (forall ((X $$unsorted) (Xa $$unsorted) (Xb $$unsorted)) (= (tptp.pp (tptp.scratc203308799nd_or3 X Xa Xb)) (tptp.pp (tptp.aa_bool_bool (tptp.scratc952359486d_l_or X) (tptp.aa_bool_bool (tptp.scratc952359486d_l_or Xa) Xb))))) (forall ((X $$unsorted) (Xa $$unsorted)) (= (tptp.pp (tptp.aa_fun171081125l_bool (tptp.scratc940362479l_some X) Xa)) (tptp.pp (tptp.scratc546085760_d_not (tptp.aa_fun171081125l_bool (tptp.scratc1829701671all_of (tptp.aa_TPT43085870d_bool tptp.aTP_Lamm_ai X)) (tptp.scratc194850556nd_non X Xa)))))) (forall ((X $$unsorted) (Xa $$unsorted) (Xb $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.scratc194850556nd_non X Xa) Xb)) (tptp.pp (tptp.scratc546085760_d_not (tptp.aa_TPTP_ind_bool Xa Xb))))) (forall ((X $$unsorted)) (= (tptp.scratc87254192nd_all X) (tptp.scratc1829701671all_of (tptp.aa_TPT43085870d_bool tptp.aTP_Lamm_ai X)))) (forall ((X $$unsorted) (Xa $$unsorted)) (= (tptp.scratc1332762030_l_iff X Xa) (tptp.pp (tptp.scratc438620580_d_and (tptp.aa_bool_bool (tptp.aa_boo1142376798l_bool tptp.scratc153411835nd_imp X) Xa) (tptp.aa_bool_bool (tptp.aa_boo1142376798l_bool tptp.scratc153411835nd_imp Xa) X))))) (forall ((X $$unsorted) (Xa $$unsorted)) (= (tptp.scratc983731570d_orec X Xa) (tptp.pp (tptp.scratc438620580_d_and (tptp.aa_bool_bool (tptp.scratc952359486d_l_or X) Xa) (tptp.scratc951703481d_l_ec X Xa))))) (forall ((X $$unsorted)) (= (tptp.scratc952359486d_l_or X) (tptp.aa_boo1142376798l_bool tptp.scratc153411835nd_imp (tptp.scratc546085760_d_not X)))) (forall ((X $$unsorted) (Xa $$unsorted)) (= (tptp.pp (tptp.scratc438620580_d_and X Xa)) (tptp.pp (tptp.scratc546085760_d_not (tptp.scratc951703481d_l_ec X Xa))))) (forall ((X $$unsorted) (Xa $$unsorted)) (= (tptp.pp (tptp.scratc951703481d_l_ec X Xa)) (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo1142376798l_bool tptp.scratc153411835nd_imp X) (tptp.scratc546085760_d_not Xa))))) _let_16 (forall ((X $$unsorted)) (= (tptp.scratc268548109nd_wel X) (tptp.pp (tptp.scratc546085760_d_not (tptp.scratc546085760_d_not X))))) (forall ((X $$unsorted)) (= (tptp.pp (tptp.scratc546085760_d_not X)) (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo1142376798l_bool tptp.scratc153411835nd_imp X) tptp.fFalse)))) _let_15 (forall ((X $$unsorted) (Xa $$unsorted)) (= (tptp.aa_fun277296641TP_ind (tptp.aa_TPT494704832TP_ind tptp.scratc423746188d_d_Pi X) Xa) (tptp.aa_fun1431113780TP_ind (tptp.scratc322369131_d_Sep (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc1017762772_power (tptp.aa_fun277296641TP_ind (tptp.aa_TPT494704832TP_ind tptp.scratc1709589394_Sigma X) (tptp.aTP_Lamm_bd Xa)))) (tptp.aa_fun1913827119d_bool (tptp.aTP_Lamm_be X) Xa)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.aa_TPT1424761345TP_ind tptp.scratc1549486784bnd_ap X))) (=> (tptp.gg_TPTP_ind X) (= (tptp.pp (tptp.aa_TPTP_ind_bool tptp.scratc769077573pair_p X)) (= (tptp.aa_TPTP_ind_TPTP_ind (tptp.aa_TPT1424761345TP_ind tptp.scratc1624135595d_pair (tptp.aa_TPTP_ind_TPTP_ind _let_1 tptp.scratc1745451206ptyset)) (tptp.aa_TPTP_ind_TPTP_ind _let_1 (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc912327602rdsucc tptp.scratc1745451206ptyset))) X))))) (forall ((X $$unsorted) (Xa $$unsorted)) (= (tptp.aa_TPTP_ind_TPTP_ind (tptp.aa_TPT1424761345TP_ind tptp.scratc1549486784bnd_ap X) Xa) (tptp.aa_fun277296641TP_ind (tptp.scratc407235996eplSep X (tptp.aa_TPT43085870d_bool tptp.aTP_Lamm_bf Xa)) tptp.scratc1146276611_proj1))) (forall ((X $$unsorted) (Xa $$unsorted)) (= (tptp.aa_TPTP_ind_TPTP_ind (tptp.scratc546250696etprod X) Xa) (tptp.aa_fun277296641TP_ind (tptp.aa_TPT494704832TP_ind tptp.scratc1709589394_Sigma X) (tptp.aTP_Lamm_ah Xa)))) (forall ((X $$unsorted) (Xa $$unsorted)) (= (tptp.aa_fun277296641TP_ind (tptp.aa_TPT494704832TP_ind tptp.scratc1709589394_Sigma X) Xa) (tptp.aa_fun277296641TP_ind (tptp.aa_TPT494704832TP_ind tptp.scratc2110891758munion X) (tptp.aTP_Lamm_bg Xa)))) (forall ((X $$unsorted)) (= (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc1146276611_proj1 X) (tptp.aa_fun277296641TP_ind (tptp.scratc407235996eplSep X tptp.aTP_Lamm_bh) tptp.scratc339482526_d_Unj))) (forall ((X $$unsorted)) (= (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc1146276610_proj0 X) (tptp.aa_fun277296641TP_ind (tptp.scratc407235996eplSep X tptp.aTP_Lamm_bi) tptp.scratc339482526_d_Unj))) (forall ((X $$unsorted) (Xa $$unsorted)) (= (tptp.aa_TPTP_ind_TPTP_ind (tptp.aa_TPT1424761345TP_ind tptp.scratc1624135595d_pair X) Xa) (tptp.aa_TPTP_ind_TPTP_ind (tptp.scratc957265209nunion (tptp.aa_fun277296641TP_ind (tptp.aa_TPT494704832TP_ind tptp.scratc1071331552d_repl X) tptp.scratc1679165214d_Inj0)) (tptp.aa_fun277296641TP_ind (tptp.aa_TPT494704832TP_ind tptp.scratc1071331552d_repl Xa) tptp.scratc1679165215d_Inj1)))) _let_14 (forall ((X $$unsorted)) (= (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc1679165214d_Inj0 X) (tptp.aa_fun277296641TP_ind (tptp.aa_TPT494704832TP_ind tptp.scratc1071331552d_repl X) tptp.scratc1679165215d_Inj1))) _let_13 _let_12 (forall ((X $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool tptp.scratc1337809184_nat_p X)) (forall ((X1 $$unsorted)) (=> (tptp.pp (tptp.aa_TPTP_ind_bool X1 tptp.scratc1745451206ptyset)) (=> (forall ((X2 $$unsorted)) (=> (tptp.gg_TPTP_ind X2) (=> (tptp.pp (tptp.aa_TPTP_ind_bool X1 X2)) (tptp.pp (tptp.aa_TPTP_ind_bool X1 (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc912327602rdsucc X2)))))) (tptp.pp (tptp.aa_TPTP_ind_bool X1 X))))))) (forall ((X $$unsorted)) (= (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc912327602rdsucc X) (tptp.aa_TPTP_ind_TPTP_ind (tptp.scratc957265209nunion X) (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc854057538d_Sing X)))) (forall ((X $$unsorted) (Xa $$unsorted)) (= (tptp.aa_TPTP_ind_TPTP_ind (tptp.scratc134999576In_rec X) Xa) (tptp.scratc120562615nd_eps (tptp.aa_TPT43085870d_bool (tptp.scratc1376844911_rec_G X) Xa)))) (forall ((X $$unsorted) (Xa $$unsorted) (Xb $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.scratc1376844911_rec_G X) Xa) Xb)) (forall ((X3 $$unsorted)) (=> (forall ((X4 $$unsorted) (X5 $$unsorted)) (=> (tptp.gg_TPTP_ind X4) (=> (forall ((X6 $$unsorted)) (=> (tptp.gg_TPTP_ind X6) (=> (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1550011574bnd_in X6) X4)) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool X3 X6) (tptp.aa_TPTP_ind_TPTP_ind X5 X6)))))) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool X3 X4) (tptp.aa_fun277296641TP_ind (tptp.aa_TPT494704832TP_ind X X4) X5)))))) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool X3 Xa) Xb)))))) (forall ((X $$unsorted) (Xa $$unsorted)) (= (tptp.aa_TPTP_ind_TPTP_ind (tptp.scratc873550751tminus X) Xa) (tptp.aa_fun1431113780TP_ind (tptp.scratc322369131_d_Sep X) (tptp.aa_TPT43085870d_bool tptp.aTP_Lamm_bl Xa)))) (forall ((X $$unsorted) (Xa $$unsorted)) (= (tptp.scratc407235996eplSep X Xa) (tptp.aa_TPT494704832TP_ind tptp.scratc1071331552d_repl (tptp.aa_fun1431113780TP_ind (tptp.scratc322369131_d_Sep X) Xa)))) (forall ((X $$unsorted) (Xa $$unsorted)) (= (tptp.aa_fun1431113780TP_ind (tptp.scratc322369131_d_Sep X) Xa) (tptp.aa_TPTP_ind_TPTP_ind (tptp.scratc1550011566bnd_if (tptp.fEx_TPTP_ind (tptp.cOMBS_2003118649l_bool (tptp.cOMBB_658106424TP_ind tptp.fconj (tptp.aa_TPT43085870d_bool (tptp.cOMBC_1555011498d_bool tptp.scratc1550011574bnd_in) X)) Xa)) (tptp.aa_fun277296641TP_ind (tptp.aa_TPT494704832TP_ind tptp.scratc1071331552d_repl X) (tptp.aa_fun1235454963TP_ind (tptp.aTP_Lamm_bm X) Xa))) tptp.scratc1745451206ptyset))) (forall ((X $$unsorted) (Xa $$unsorted)) (= (tptp.aa_fun277296641TP_ind (tptp.aa_TPT494704832TP_ind tptp.scratc2110891758munion X) Xa) (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc1525024638_union (tptp.aa_fun277296641TP_ind (tptp.aa_TPT494704832TP_ind tptp.scratc1071331552d_repl X) Xa)))) (forall ((X $$unsorted) (Xa $$unsorted)) (= (tptp.aa_TPTP_ind_TPTP_ind (tptp.scratc957265209nunion X) Xa) (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc1525024638_union (tptp.aa_TPTP_ind_TPTP_ind (tptp.scratc1604075772_UPair X) Xa)))) (forall ((X $$unsorted)) (= (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc854057538d_Sing X) (tptp.aa_TPTP_ind_TPTP_ind (tptp.scratc1604075772_UPair X) X))) (forall ((X $$unsorted) (Xa $$unsorted)) (= (tptp.aa_TPTP_ind_TPTP_ind (tptp.scratc1604075772_UPair X) Xa) (tptp.aa_fun277296641TP_ind (tptp.aa_TPT494704832TP_ind tptp.scratc1071331552d_repl (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc1017762772_power (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc1017762772_power tptp.scratc1745451206ptyset))) (tptp.aa_TPT1424761345TP_ind (tptp.aTP_Lamm_bn X) Xa)))) (forall ((X $$unsorted) (Xa $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc192357794nd_nIn X) Xa)) (not (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1550011574bnd_in X) Xa))))) (forall ((X $$unsorted) (Xa $$unsorted) (Xb $$unsorted)) (= (tptp.aa_TPTP_ind_TPTP_ind (tptp.scratc1550011566bnd_if X Xa) Xb) (tptp.scratc120562615nd_eps (tptp.aa_TPT43085870d_bool (tptp.aa_TPT60673477d_bool (tptp.aTP_Lamm_bo X) Xa) Xb)))) (forall ((X $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool tptp.scratc1675368811closed X)) (and (tptp.pp (tptp.aa_TPTP_ind_bool tptp.scratc468858728closed X)) (tptp.pp (tptp.aa_TPTP_ind_bool tptp.scratc633591742closed X)) (tptp.pp (tptp.aa_TPTP_ind_bool tptp.scratc1137838734closed X))))) (forall ((X $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool tptp.scratc1137838734closed X)) (forall ((X1 $$unsorted)) (=> (tptp.gg_TPTP_ind X1) (=> (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1550011574bnd_in X1) X)) (forall ((X2 $$unsorted)) (=> (forall ((X3 $$unsorted)) (=> (tptp.gg_TPTP_ind X3) (=> (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1550011574bnd_in X3) X1)) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1550011574bnd_in (tptp.aa_TPTP_ind_TPTP_ind X2 X3)) X))))) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1550011574bnd_in (tptp.aa_fun277296641TP_ind (tptp.aa_TPT494704832TP_ind tptp.scratc1071331552d_repl X1) X2)) X))))))))) (forall ((X $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool tptp.scratc633591742closed X)) (forall ((X1 $$unsorted)) (=> (tptp.gg_TPTP_ind X1) (=> (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1550011574bnd_in X1) X)) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1550011574bnd_in (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc1017762772_power X1)) X))))))) (forall ((X $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool tptp.scratc468858728closed X)) (forall ((X1 $$unsorted)) (=> (tptp.gg_TPTP_ind X1) (=> (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1550011574bnd_in X1) X)) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1550011574bnd_in (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc1525024638_union X1)) X))))))) (forall ((X $$unsorted) (Xa $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc952408420d_Subq X) Xa)) (forall ((X2 $$unsorted)) (let ((_let_1 (tptp.aa_TPT43085870d_bool tptp.scratc1550011574bnd_in X2))) (=> (tptp.gg_TPTP_ind X2) (=> (tptp.pp (tptp.aa_TPTP_ind_bool _let_1 X)) (tptp.pp (tptp.aa_TPTP_ind_bool _let_1 Xa)))))))) _let_10 (forall ((X $$unsorted) (Xa $$unsorted)) (= (tptp.scratc1451164978_is_of X Xa) (tptp.pp (tptp.aa_TPTP_ind_bool Xa X)))) (tptp.pp (tptp.aa_fun171081125l_bool _let_1 tptp.aTP_Lamm_bq)) (tptp.pp (tptp.aa_fun171081125l_bool _let_1 tptp.aTP_Lamm_br)) (tptp.pp (tptp.aa_fun171081125l_bool _let_1 tptp.aTP_Lamm_bt)) _let_9 (tptp.pp (tptp.aa_fun171081125l_bool _let_1 tptp.aTP_Lamm_bw)) (tptp.pp (tptp.aa_fun171081125l_bool _let_1 tptp.aTP_Lamm_bx)) (tptp.pp (tptp.aa_fun171081125l_bool _let_1 tptp.aTP_Lamm_bz)) (tptp.pp (tptp.aa_fun171081125l_bool _let_1 tptp.aTP_Lamm_ca)) (tptp.pp (tptp.aa_fun171081125l_bool _let_1 tptp.aTP_Lamm_cb)) (tptp.pp (tptp.aa_fun171081125l_bool _let_1 tptp.aTP_Lamm_cc)) (tptp.pp (tptp.aa_fun171081125l_bool _let_1 tptp.aTP_Lamm_ce)) (tptp.pp (tptp.aa_fun171081125l_bool (tptp.scratc1829701671all_of tptp.aTP_Lamm_cf) tptp.aTP_Lamm_ch)) (tptp.pp (tptp.aa_fun171081125l_bool _let_1 tptp.aTP_Lamm_cj)) (tptp.pp (tptp.aa_fun171081125l_bool _let_1 tptp.aTP_Lamm_ck)) (tptp.pp (tptp.aa_fun171081125l_bool _let_1 tptp.aTP_Lamm_cl)) (tptp.scratc1451164978_is_of tptp.scratc45782132nd_n_1 tptp.aTP_Lamm_a) (forall ((X0 $$unsorted)) (tptp.pp (tptp.aa_fun171081125l_bool (tptp.scratc1829701671all_of (tptp.aa_TPT43085870d_bool tptp.aTP_Lamm_cm X0)) (tptp.aa_TPT43085870d_bool tptp.aTP_Lamm_co X0)))) (forall ((X0 $$unsorted) (X12 $$unsorted)) (tptp.pp (tptp.aa_fun171081125l_bool (tptp.scratc1829701671all_of (tptp.aa_TPT43085870d_bool tptp.aTP_Lamm_ai X0)) (tptp.aa_fun1584354236d_bool (tptp.aTP_Lamm_cp X0) X12)))) (forall ((X0 $$unsorted) (X12 $$unsorted)) (tptp.pp (tptp.aa_fun171081125l_bool (tptp.scratc1829701671all_of (tptp.aa_TPT43085870d_bool tptp.aTP_Lamm_ai X0)) (tptp.aa_fun1584354236d_bool (tptp.aTP_Lamm_cq X0) X12)))) (forall ((X0 $$unsorted) (X12 $$unsorted)) (tptp.scratc1451164978_is_of (tptp.aa_fun1431113780TP_ind (tptp.scratc322369131_d_Sep X0) X12) (tptp.aa_TPT43085870d_bool tptp.aTP_Lamm_cm X0))) (forall ((X0 $$unsorted) (X12 $$unsorted)) (tptp.pp (tptp.aa_fun171081125l_bool (tptp.scratc1829701671all_of (tptp.aa_TPT43085870d_bool tptp.aTP_Lamm_ai X0)) (tptp.aa_TPT43085870d_bool (tptp.aTP_Lamm_cs X0) X12)))) (forall ((X0 $$unsorted) (X12 $$unsorted)) (tptp.pp (tptp.aa_fun171081125l_bool (tptp.scratc1829701671all_of (tptp.aa_TPT43085870d_bool tptp.aTP_Lamm_ai X0)) (tptp.aa_TPT43085870d_bool (tptp.aTP_Lamm_cu X0) X12)))) (forall ((X0 $$unsorted) (X12 $$unsorted)) (tptp.pp (tptp.aa_fun171081125l_bool (tptp.scratc1829701671all_of (tptp.aa_TPT43085870d_bool (tptp.aTP_Lamm_cv X0) X12)) (tptp.aa_TPT43085870d_bool (tptp.aTP_Lamm_cw X0) X12)))) (forall ((X0 $$unsorted) (X12 $$unsorted)) (tptp.pp (tptp.aa_fun171081125l_bool (tptp.scratc1829701671all_of (tptp.aa_TPT43085870d_bool (tptp.aTP_Lamm_cv X0) X12)) (tptp.aa_TPT43085870d_bool (tptp.aTP_Lamm_cx X0) X12)))) (forall ((X0 $$unsorted) (X12 $$unsorted)) (tptp.pp (tptp.aa_fun171081125l_bool (tptp.scratc1829701671all_of (tptp.aa_TPT43085870d_bool (tptp.aTP_Lamm_cv X0) X12)) (tptp.aa_TPT43085870d_bool (tptp.aTP_Lamm_cy X0) X12)))) (forall ((X0 $$unsorted) (X12 $$unsorted)) (tptp.pp (tptp.aa_fun171081125l_bool (tptp.scratc1829701671all_of (tptp.aa_TPT43085870d_bool tptp.aTP_Lamm_ai X0)) (tptp.aa_TPT43085870d_bool (tptp.aTP_Lamm_da X0) X12)))) (forall ((X0 $$unsorted) (X12 $$unsorted)) (tptp.pp (tptp.aa_fun171081125l_bool (tptp.scratc1829701671all_of (tptp.aa_TPT43085870d_bool tptp.aTP_Lamm_ai X0)) (tptp.aa_fun1584354236d_bool (tptp.aTP_Lamm_db X0) X12)))) (forall ((X0 $$unsorted) (X12 $$unsorted)) (let ((_let_1 (tptp.aa_fun1431113780TP_ind (tptp.scratc322369131_d_Sep X0) X12))) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.scratc187235926ective _let_1) X0) (tptp.aa_fun277296641TP_ind (tptp.aa_TPT494704832TP_ind tptp.scratc1709589394_Sigma _let_1) (tptp.scratc1564950457d_e_in X0 X12)))))) (forall ((X0 $$unsorted) (X12 $$unsorted)) (tptp.pp (tptp.aa_fun171081125l_bool (tptp.scratc1829701671all_of (tptp.aa_fun1584354236d_bool (tptp.aTP_Lamm_dc X0) X12)) (tptp.aa_fun1584354236d_bool (tptp.aTP_Lamm_dd X0) X12)))) (forall ((X0 $$unsorted) (X12 $$unsorted)) (tptp.pp (tptp.aa_fun171081125l_bool (tptp.scratc1829701671all_of (tptp.aa_fun1584354236d_bool (tptp.aTP_Lamm_dc X0) X12)) (tptp.aa_fun1584354236d_bool (tptp.aTP_Lamm_de X0) X12)))) (forall ((X0 $$unsorted) (X12 $$unsorted)) (tptp.pp (tptp.aa_fun171081125l_bool (tptp.scratc1829701671all_of (tptp.aa_TPT43085870d_bool (tptp.aTP_Lamm_df X0) X12)) (tptp.aa_TPT43085870d_bool (tptp.aTP_Lamm_di X0) X12)))) (forall ((X0 $$unsorted) (X12 $$unsorted)) (=> (tptp.pp (tptp.aa_fun171081125l_bool (tptp.scratc203046453nd_one X0) X12)) (tptp.pp (tptp.aa_TPTP_ind_bool X12 (tptp.scratc153477422nd_ind X0 X12))))) (forall ((X0 $$unsorted) (X12 $$unsorted)) (=> (tptp.pp (tptp.aa_fun171081125l_bool (tptp.scratc203046453nd_one X0) X12)) (tptp.scratc1451164978_is_of (tptp.scratc153477422nd_ind X0 X12) (tptp.aa_TPT43085870d_bool tptp.aTP_Lamm_ai X0)))) (forall ((X0 $$unsorted) (X12 $$unsorted)) (tptp.pp (tptp.aa_fun171081125l_bool (tptp.scratc1829701671all_of (tptp.aa_TPT43085870d_bool tptp.aTP_Lamm_ai X0)) (tptp.aa_fun1584354236d_bool (tptp.aTP_Lamm_dk X0) X12)))) (forall ((X0 $$unsorted)) (tptp.pp (tptp.aa_fun171081125l_bool (tptp.scratc1829701671all_of (tptp.aa_TPT43085870d_bool tptp.aTP_Lamm_ai X0)) (tptp.aa_TPT43085870d_bool tptp.aTP_Lamm_dl X0)))) (forall ((X0 $$unsorted)) (=> (tptp.scratc268548109nd_wel X0) (tptp.pp X0))) (forall ((X0 $$unsorted) (X12 $$unsorted) (X22 $$unsorted) (X32 $$unsorted)) (let ((_let_1 (tptp.aa_TPT43085870d_bool tptp.scratc1550011574bnd_in X12))) (=> (tptp.pp X0) (=> (tptp.pp (tptp.aa_TPTP_ind_bool _let_1 (tptp.aa_TPTP_ind_TPTP_ind (tptp.scratc1550011566bnd_if X0 X22) X32))) (tptp.pp (tptp.aa_TPTP_ind_bool _let_1 X22)))))) (forall ((X0 $$unsorted) (X12 $$unsorted) (X22 $$unsorted)) (=> (=> (tptp.pp X0) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1550011574bnd_in X12) X22))) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1550011574bnd_in (tptp.aa_TPTP_ind_TPTP_ind (tptp.scratc1550011566bnd_if X0 X12) tptp.scratc1745451206ptyset)) (tptp.aa_TPTP_ind_TPTP_ind (tptp.scratc1550011566bnd_if X0 X22) (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc912327602rdsucc tptp.scratc1745451206ptyset)))))) (forall ((X0 $$unsorted) (X12 $$unsorted) (X22 $$unsorted)) (let ((_let_1 (tptp.aa_TPT494704832TP_ind tptp.scratc1709589394_Sigma X0))) (=> (forall ((X33 $$unsorted)) (=> (tptp.gg_TPTP_ind X33) (=> (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1550011574bnd_in X33) X0)) (= (tptp.aa_TPTP_ind_TPTP_ind X12 X33) (tptp.aa_TPTP_ind_TPTP_ind X22 X33))))) (= (tptp.aa_fun277296641TP_ind _let_1 X12) (tptp.aa_fun277296641TP_ind _let_1 X22))))) (forall ((X0 $$unsorted) (X12 $$unsorted) (X22 $$unsorted)) (=> (tptp.gg_TPTP_ind X22) (=> (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1550011574bnd_in X22) (tptp.aa_fun277296641TP_ind (tptp.aa_TPT494704832TP_ind tptp.scratc423746188d_d_Pi X0) X12))) (forall ((X32 $$unsorted)) (=> (tptp.gg_TPTP_ind X32) (=> (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1550011574bnd_in X32) (tptp.aa_fun277296641TP_ind (tptp.aa_TPT494704832TP_ind tptp.scratc423746188d_d_Pi X0) X12))) (=> (forall ((X42 $$unsorted)) (=> (tptp.gg_TPTP_ind X42) (=> (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1550011574bnd_in X42) X0)) (= (tptp.aa_TPTP_ind_TPTP_ind (tptp.aa_TPT1424761345TP_ind tptp.scratc1549486784bnd_ap X22) X42) (tptp.aa_TPTP_ind_TPTP_ind (tptp.aa_TPT1424761345TP_ind tptp.scratc1549486784bnd_ap X32) X42))))) (= X22 X32)))))))) (forall ((X0 $$unsorted) (X12 $$unsorted) (X22 $$unsorted) (X32 $$unsorted)) (=> (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1550011574bnd_in X22) (tptp.aa_fun277296641TP_ind (tptp.aa_TPT494704832TP_ind tptp.scratc423746188d_d_Pi X0) X12))) (=> (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1550011574bnd_in X32) X0)) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1550011574bnd_in (tptp.aa_TPTP_ind_TPTP_ind (tptp.aa_TPT1424761345TP_ind tptp.scratc1549486784bnd_ap X22) X32)) (tptp.aa_TPTP_ind_TPTP_ind X12 X32)))))) (forall ((X0 $$unsorted) (X12 $$unsorted) (X22 $$unsorted)) (=> (forall ((X33 $$unsorted)) (=> (tptp.gg_TPTP_ind X33) (=> (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1550011574bnd_in X33) X0)) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1550011574bnd_in (tptp.aa_TPTP_ind_TPTP_ind X22 X33)) (tptp.aa_TPTP_ind_TPTP_ind X12 X33)))))) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1550011574bnd_in (tptp.aa_fun277296641TP_ind (tptp.aa_TPT494704832TP_ind tptp.scratc1709589394_Sigma X0) X22)) (tptp.aa_fun277296641TP_ind (tptp.aa_TPT494704832TP_ind tptp.scratc423746188d_d_Pi X0) X12))))) (forall ((X0 $$unsorted) (X12 $$unsorted) (X22 $$unsorted)) (=> (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1550011574bnd_in X22) X0)) (= (tptp.aa_TPTP_ind_TPTP_ind (tptp.aa_TPT1424761345TP_ind tptp.scratc1549486784bnd_ap (tptp.aa_fun277296641TP_ind (tptp.aa_TPT494704832TP_ind tptp.scratc1709589394_Sigma X0) X12)) X22) (tptp.aa_TPTP_ind_TPTP_ind X12 X22)))) (forall ((X0 $$unsorted) (X12 $$unsorted) (X22 $$unsorted)) (=> (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1550011574bnd_in X22) (tptp.aa_fun277296641TP_ind (tptp.aa_TPT494704832TP_ind tptp.scratc1709589394_Sigma X0) X12))) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1550011574bnd_in (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc1146276611_proj1 X22)) (tptp.aa_TPTP_ind_TPTP_ind X12 (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc1146276610_proj0 X22)))))) (forall ((X0 $$unsorted) (X12 $$unsorted) (X22 $$unsorted)) (=> (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1550011574bnd_in X22) (tptp.aa_fun277296641TP_ind (tptp.aa_TPT494704832TP_ind tptp.scratc1709589394_Sigma X0) X12))) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1550011574bnd_in (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc1146276610_proj0 X22)) X0)))) (forall ((X0 $$unsorted) (X12 $$unsorted) (X22 $$unsorted)) (=> (tptp.gg_TPTP_ind X22) (=> (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1550011574bnd_in X22) (tptp.aa_fun277296641TP_ind (tptp.aa_TPT494704832TP_ind tptp.scratc1709589394_Sigma X0) X12))) (= (tptp.aa_TPTP_ind_TPTP_ind (tptp.aa_TPT1424761345TP_ind tptp.scratc1624135595d_pair (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc1146276610_proj0 X22)) (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc1146276611_proj1 X22)) X22)))) (forall ((X0 $$unsorted) (X12 $$unsorted) (X22 $$unsorted)) (let ((_let_1 (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc1146276610_proj0 X22))) (let ((_let_2 (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc1146276611_proj1 X22))) (=> (tptp.gg_TPTP_ind X22) (=> (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1550011574bnd_in X22) (tptp.aa_fun277296641TP_ind (tptp.aa_TPT494704832TP_ind tptp.scratc1709589394_Sigma X0) X12))) (and (= (tptp.aa_TPTP_ind_TPTP_ind (tptp.aa_TPT1424761345TP_ind tptp.scratc1624135595d_pair _let_1) _let_2) X22) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1550011574bnd_in _let_1) X0)) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1550011574bnd_in _let_2) (tptp.aa_TPTP_ind_TPTP_ind X12 _let_1))))))))) (forall ((X0 $$unsorted) (X12 $$unsorted) (X22 $$unsorted)) (=> (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1550011574bnd_in X22) X0)) (forall ((X32 $$unsorted)) (=> (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1550011574bnd_in X32) (tptp.aa_TPTP_ind_TPTP_ind X12 X22))) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1550011574bnd_in (tptp.aa_TPTP_ind_TPTP_ind (tptp.aa_TPT1424761345TP_ind tptp.scratc1624135595d_pair X22) X32)) (tptp.aa_fun277296641TP_ind (tptp.aa_TPT494704832TP_ind tptp.scratc1709589394_Sigma X0) X12))))))) (forall ((X0 $$unsorted) (X12 $$unsorted)) (=> (tptp.gg_TPTP_ind X12) (= (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc1146276611_proj1 (tptp.aa_TPTP_ind_TPTP_ind (tptp.aa_TPT1424761345TP_ind tptp.scratc1624135595d_pair X0) X12)) X12))) (forall ((X0 $$unsorted) (X12 $$unsorted)) (=> (tptp.gg_TPTP_ind X0) (= (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc1146276610_proj0 (tptp.aa_TPTP_ind_TPTP_ind (tptp.aa_TPT1424761345TP_ind tptp.scratc1624135595d_pair X0) X12)) X0))) (forall ((X0 $$unsorted)) (=> (tptp.pp (tptp.aa_TPTP_ind_bool tptp.scratc1337809184_nat_p X0)) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1550011574bnd_in X0) tptp.scratc315931824_omega)))) (forall ((X0 $$unsorted)) (=> (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1550011574bnd_in X0) tptp.scratc315931824_omega)) (tptp.pp (tptp.aa_TPTP_ind_bool tptp.scratc1337809184_nat_p X0)))) (forall ((X0 $$unsorted)) (=> (tptp.gg_TPTP_ind X0) (=> (tptp.pp (tptp.aa_TPTP_ind_bool tptp.scratc1337809184_nat_p X0)) (or (= X0 tptp.scratc1745451206ptyset) (exists ((X13 $$unsorted)) (and (tptp.gg_TPTP_ind X13) (tptp.pp (tptp.aa_TPTP_ind_bool tptp.scratc1337809184_nat_p X13)) (= X0 (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc912327602rdsucc X13)))))))) (forall ((X0 $$unsorted)) (=> (tptp.pp (tptp.aa_TPTP_ind_bool X0 tptp.scratc1745451206ptyset)) (=> (forall ((X13 $$unsorted)) (=> (tptp.gg_TPTP_ind X13) (=> (tptp.pp (tptp.aa_TPTP_ind_bool tptp.scratc1337809184_nat_p X13)) (=> (tptp.pp (tptp.aa_TPTP_ind_bool X0 X13)) (tptp.pp (tptp.aa_TPTP_ind_bool X0 (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc912327602rdsucc X13))))))) (forall ((X12 $$unsorted)) (=> (tptp.pp (tptp.aa_TPTP_ind_bool tptp.scratc1337809184_nat_p X12)) (tptp.pp (tptp.aa_TPTP_ind_bool X0 X12))))))) (tptp.pp (tptp.aa_TPTP_ind_bool tptp.scratc1337809184_nat_p _let_8)) (forall ((X0 $$unsorted)) (=> (tptp.pp (tptp.aa_TPTP_ind_bool tptp.scratc1337809184_nat_p X0)) (tptp.pp (tptp.aa_TPTP_ind_bool tptp.scratc1337809184_nat_p (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc912327602rdsucc X0))))) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1550011574bnd_in tptp.scratc1745451206ptyset) _let_8)) (forall ((X0 $$unsorted) (X12 $$unsorted)) (=> (and (tptp.gg_TPTP_ind X0) (tptp.gg_TPTP_ind X12)) (=> (= (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc912327602rdsucc X0) (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc912327602rdsucc X12)) (= X0 X12)))) (forall ((X0 $$unsorted)) (not (= (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc912327602rdsucc X0) tptp.scratc1745451206ptyset))) (forall ((X0 $$unsorted) (X12 $$unsorted) (X22 $$unsorted)) (=> (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1550011574bnd_in X22) (tptp.aa_fun1431113780TP_ind (tptp.scratc322369131_d_Sep X0) X12))) (tptp.pp (tptp.aa_TPTP_ind_bool X12 X22)))) (forall ((X0 $$unsorted) (X12 $$unsorted) (X22 $$unsorted)) (let ((_let_1 (tptp.aa_TPT43085870d_bool tptp.scratc1550011574bnd_in X22))) (=> (tptp.pp (tptp.aa_TPTP_ind_bool _let_1 (tptp.aa_fun1431113780TP_ind (tptp.scratc322369131_d_Sep X0) X12))) (tptp.pp (tptp.aa_TPTP_ind_bool _let_1 X0))))) (forall ((X0 $$unsorted) (X12 $$unsorted) (X22 $$unsorted)) (let ((_let_1 (tptp.aa_TPT43085870d_bool tptp.scratc1550011574bnd_in X22))) (=> (tptp.pp (tptp.aa_TPTP_ind_bool _let_1 X0)) (=> (tptp.pp (tptp.aa_TPTP_ind_bool X12 X22)) (tptp.pp (tptp.aa_TPTP_ind_bool _let_1 (tptp.aa_fun1431113780TP_ind (tptp.scratc322369131_d_Sep X0) X12))))))) (forall ((X0 $$unsorted)) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1550011574bnd_in X0) (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc1017762772_power X0)))) (forall ((X0 $$unsorted) (X12 $$unsorted)) (=> (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc952408420d_Subq X12) X0)) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1550011574bnd_in X12) (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc1017762772_power X0))))) (forall ((X0 $$unsorted) (X12 $$unsorted)) (=> (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1550011574bnd_in X12) (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc1017762772_power X0))) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc952408420d_Subq X12) X0)))) (forall ((X0 $$unsorted) (X12 $$unsorted) (X22 $$unsorted)) (let ((_let_1 (tptp.aa_TPTP_ind_TPTP_ind (tptp.scratc1550011566bnd_if X0 X12) X22))) (=> (and (tptp.gg_TPTP_ind X12) (tptp.gg_TPTP_ind X22)) (or (= _let_1 X12) (= _let_1 X22))))) (forall ((X0 $$unsorted) (X12 $$unsorted) (X22 $$unsorted)) (=> (tptp.gg_TPTP_ind X12) (=> (tptp.pp X0) (= (tptp.aa_TPTP_ind_TPTP_ind (tptp.scratc1550011566bnd_if X0 X12) X22) X12)))) (forall ((X0 $$unsorted) (X12 $$unsorted) (X22 $$unsorted)) (=> (tptp.gg_TPTP_ind X22) (=> (not (tptp.pp X0)) (= (tptp.aa_TPTP_ind_TPTP_ind (tptp.scratc1550011566bnd_if X0 X12) X22) X22)))) (forall ((X0 $$unsorted) (X12 $$unsorted) (X22 $$unsorted)) (let ((_let_1 (tptp.aa_TPTP_ind_TPTP_ind (tptp.scratc1550011566bnd_if X0 X12) X22))) (let ((_let_2 (tptp.pp X0))) (=> (and (tptp.gg_TPTP_ind X12) (tptp.gg_TPTP_ind X22)) (or (and _let_2 (= _let_1 X12)) (and (not _let_2) (= _let_1 X22))))))) (forall ((X0 $$unsorted)) (tptp.pp (tptp.aa_TPTP_ind_bool tptp.scratc1675368811closed (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc1770865966univof X0)))) (forall ((X0 $$unsorted)) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1550011574bnd_in X0) (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc1770865966univof X0)))) (forall ((X0 $$unsorted) (X12 $$unsorted) (X22 $$unsorted)) (=> (tptp.gg_TPTP_ind X22) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1550011574bnd_in X22) (tptp.aa_fun277296641TP_ind (tptp.aa_TPT494704832TP_ind tptp.scratc1071331552d_repl X0) X12))) (exists ((X3 $$unsorted)) (and (tptp.gg_TPTP_ind X3) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1550011574bnd_in X3) X0)) (= X22 (tptp.aa_TPTP_ind_TPTP_ind X12 X3))))))) (forall ((X0 $$unsorted) (X12 $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1550011574bnd_in X12) (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc1017762772_power X0))) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc952408420d_Subq X12) X0)))) (forall ((X0 $$unsorted) (X12 $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1550011574bnd_in X12) (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc1525024638_union X0))) (exists ((X2 $$unsorted)) (and (tptp.gg_TPTP_ind X2) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1550011574bnd_in X12) X2)) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1550011574bnd_in X2) X0)))))) (not (exists ((X0 $$unsorted)) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1550011574bnd_in X0) tptp.scratc1745451206ptyset)))) (forall ((X0 $$unsorted)) (=> (forall ((X13 $$unsorted)) (=> (tptp.gg_TPTP_ind X13) (=> (forall ((X22 $$unsorted)) (=> (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1550011574bnd_in X22) X13)) (tptp.pp (tptp.aa_TPTP_ind_bool X0 X22)))) (tptp.pp (tptp.aa_TPTP_ind_bool X0 X13))))) (forall ((X14 $$unsorted)) (tptp.pp (tptp.aa_TPTP_ind_bool X0 X14))))) (forall ((X0 $$unsorted) (X12 $$unsorted)) (=> (and (tptp.gg_TPTP_ind X0) (tptp.gg_TPTP_ind X12)) (=> (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc952408420d_Subq X0) X12)) (=> (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc952408420d_Subq X12) X0)) (= X0 X12))))) (forall ((Uu $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool tptp.aTP_Lamm_cb Uu)) (=> (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc194456967nd_nis Uu) tptp.scratc45782132nd_n_1)) (tptp.pp (tptp.aa_fun171081125l_bool tptp.scratc1684187121n_some (tptp.aa_TPT43085870d_bool tptp.aTP_Lamm_ae Uu)))))) (forall ((Uu $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool tptp.aTP_Lamm_ca Uu)) (=> (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc194456967nd_nis Uu) tptp.scratc45782132nd_n_1)) (tptp.pp (tptp.aa_fun171081125l_bool tptp.scratc2126870313_n_one (tptp.aa_TPT43085870d_bool tptp.aTP_Lamm_ae Uu)))))) (forall ((Uu $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool tptp.aTP_Lamm_bx Uu)) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1083610823d_n_is (tptp.aa_TPTP_ind_TPTP_ind (tptp.scratc1084070009d_n_pl Uu) tptp.scratc45782132nd_n_1)) (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc912327602rdsucc Uu))))) _let_7 (forall ((Uu $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool tptp.aTP_Lamm_bz Uu)) (tptp.pp (tptp.aa_fun171081125l_bool (tptp.scratc203046453nd_one (tptp.aa_fun277296641TP_ind (tptp.aa_TPT494704832TP_ind tptp.scratc423746188d_d_Pi tptp.scratc193932176nd_nat) tptp.aTP_Lamm_ab)) (tptp.aa_TPT43085870d_bool tptp.aTP_Lamm_by Uu))))) (forall ((Uu $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool tptp.aTP_Lamm_ch Uu)) (=> (tptp.pp (tptp.aa_TPTP_ind_bool tptp.scratc1161393342_cond1 Uu)) (=> (tptp.pp (tptp.aa_TPTP_ind_bool tptp.scratc1161393343_cond2 Uu)) (tptp.pp (tptp.aa_fun171081125l_bool (tptp.scratc1829701671all_of tptp.aTP_Lamm_a) (tptp.aa_TPT43085870d_bool tptp.aTP_Lamm_cg Uu))))))) (forall ((Uu $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool tptp.aTP_Lamm_br Uu)) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1083610823d_n_is (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc912327602rdsucc Uu)) (tptp.aa_TPTP_ind_TPTP_ind (tptp.scratc1084070009d_n_pl Uu) tptp.scratc45782132nd_n_1))))) _let_6 (forall ((Uu $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool tptp.aTP_Lamm_cc Uu)) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc194456967nd_nis (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc912327602rdsucc Uu)) Uu)))) (forall ((Uu $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool tptp.aTP_Lamm_cl Uu)) (tptp.scratc1451164978_is_of (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc912327602rdsucc Uu) tptp.aTP_Lamm_a))) (forall ((Uu $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool tptp.aTP_Lamm_ck Uu)) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc194456967nd_nis (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc912327602rdsucc Uu)) tptp.scratc45782132nd_n_1)))) (forall ((Uu $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool tptp.aTP_Lamm_cf Uu)) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1550011574bnd_in Uu) (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc1017762772_power tptp.scratc193932176nd_nat))))) (forall ((Uu $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool tptp.aTP_Lamm_a Uu)) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1550011574bnd_in Uu) tptp.scratc193932176nd_nat)))) (forall ((Uu $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool tptp.aTP_Lamm_cj Uu)) (tptp.pp (tptp.aa_fun171081125l_bool (tptp.scratc1829701671all_of tptp.aTP_Lamm_a) (tptp.aa_TPT43085870d_bool tptp.aTP_Lamm_ci Uu))))) (forall ((Uu $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool tptp.aTP_Lamm_ce Uu)) (tptp.pp (tptp.aa_fun171081125l_bool (tptp.scratc1829701671all_of tptp.aTP_Lamm_a) (tptp.aa_TPT43085870d_bool tptp.aTP_Lamm_cd Uu))))) (forall ((Uu $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool tptp.aTP_Lamm_bw Uu)) (tptp.pp (tptp.aa_fun171081125l_bool (tptp.scratc1829701671all_of tptp.aTP_Lamm_a) (tptp.aa_TPT43085870d_bool tptp.aTP_Lamm_bv Uu))))) (forall ((Uu $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool tptp.aTP_Lamm_bt Uu)) (tptp.pp (tptp.aa_fun171081125l_bool (tptp.scratc1829701671all_of tptp.aTP_Lamm_a) (tptp.aa_TPT43085870d_bool tptp.aTP_Lamm_bs Uu))))) (forall ((Uu $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool tptp.aTP_Lamm_bq Uu)) (tptp.pp (tptp.aa_fun171081125l_bool (tptp.scratc1829701671all_of tptp.aTP_Lamm_a) (tptp.aa_TPT43085870d_bool tptp.aTP_Lamm_bp Uu))))) (forall ((Uu $$unsorted)) (= (tptp.aa_TPT494704832TP_ind tptp.aTP_Lamm_bj Uu) (tptp.aa_TPT494704832TP_ind tptp.scratc1071331552d_repl (tptp.aa_TPTP_ind_TPTP_ind (tptp.scratc873550751tminus Uu) (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc854057538d_Sing tptp.scratc1745451206ptyset))))) (forall ((Uu $$unsorted)) (=> (tptp.gg_TPTP_ind Uu) (= (tptp.pp (tptp.aa_TPTP_ind_bool tptp.aTP_Lamm_ag Uu)) (not (= Uu tptp.scratc1745451206ptyset))))) (forall ((Uu $$unsorted)) (=> (tptp.gg_TPTP_ind Uu) (= (tptp.pp (tptp.aa_TPTP_ind_bool tptp.aTP_Lamm_bh Uu)) (exists ((X2 $$unsorted)) (and (tptp.gg_TPTP_ind X2) (= (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc1679165215d_Inj1 X2) Uu)))))) (forall ((Uu $$unsorted)) (=> (tptp.gg_TPTP_ind Uu) (= (tptp.pp (tptp.aa_TPTP_ind_bool tptp.aTP_Lamm_bi Uu)) (exists ((X2 $$unsorted)) (and (tptp.gg_TPTP_ind X2) (= (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc1679165214d_Inj0 X2) Uu)))))) (forall ((Uu $$unsorted) (Uua $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.aTP_Lamm_dl Uu) Uua)) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.scratc1564950462d_e_is Uu) Uua) Uua)))) (forall ((Uu $$unsorted) (Uua $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.aTP_Lamm_by Uu) Uua)) (tptp.pp (tptp.scratc438620580_d_and (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1083610823d_n_is (tptp.aa_TPTP_ind_TPTP_ind (tptp.aa_TPT1424761345TP_ind tptp.scratc1549486784bnd_ap Uua) tptp.scratc45782132nd_n_1)) (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc912327602rdsucc Uu)) (tptp.aa_fun171081125l_bool tptp.scratc2011078052_n_all (tptp.aa_TPT43085870d_bool tptp.aTP_Lamm_ad Uua)))))) (forall ((Uu $$unsorted) (Uua $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.aTP_Lamm_ci Uu) Uua)) (=> (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1083610823d_n_is (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc912327602rdsucc Uu)) (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc912327602rdsucc Uua))) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1083610823d_n_is Uu) Uua))))) (forall ((Uu $$unsorted) (Uua $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.aTP_Lamm_bs Uu) Uua)) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1083610823d_n_is (tptp.aa_TPTP_ind_TPTP_ind (tptp.scratc1084070009d_n_pl (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc912327602rdsucc Uu)) Uua)) (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc912327602rdsucc (tptp.aa_TPTP_ind_TPTP_ind (tptp.scratc1084070009d_n_pl Uu) Uua)))))) (forall ((Uu $$unsorted) (Uua $$unsorted)) (let ((_let_1 (tptp.scratc1084070009d_n_pl Uu))) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.aTP_Lamm_bv Uu) Uua)) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1083610823d_n_is (tptp.aa_TPTP_ind_TPTP_ind _let_1 (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc912327602rdsucc Uua))) (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc912327602rdsucc (tptp.aa_TPTP_ind_TPTP_ind _let_1 Uua))))))) (forall ((Uu $$unsorted) (Uua $$unsorted)) (let ((_let_1 (tptp.aa_TPT1424761345TP_ind tptp.scratc1549486784bnd_ap Uu))) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.aTP_Lamm_ad Uu) Uua)) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1083610823d_n_is (tptp.aa_TPTP_ind_TPTP_ind _let_1 (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc912327602rdsucc Uua))) (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc912327602rdsucc (tptp.aa_TPTP_ind_TPTP_ind _let_1 Uua))))))) (forall ((Uu $$unsorted) (Uua $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.aTP_Lamm_cd Uu) Uua)) (=> (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc194456967nd_nis Uu) Uua)) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc194456967nd_nis (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc912327602rdsucc Uu)) (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc912327602rdsucc Uua)))))) (forall ((Uu $$unsorted) (Uua $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.aTP_Lamm_af Uu) Uua)) (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo1142376798l_bool tptp.scratc153411835nd_imp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1083610818d_n_in Uua) Uu)) (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1083610818d_n_in (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc912327602rdsucc Uua)) Uu))))) (forall ((Uu $$unsorted) (Uua $$unsorted)) (= (tptp.aa_TPTP_ind_TPTP_ind (tptp.aTP_Lamm_bg Uu) Uua) (tptp.aa_fun277296641TP_ind (tptp.aa_TPT494704832TP_ind tptp.scratc1071331552d_repl (tptp.aa_TPTP_ind_TPTP_ind Uu Uua)) (tptp.aa_TPT1424761345TP_ind tptp.scratc1624135595d_pair Uua)))) (forall ((Uu $$unsorted) (Uua $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.aTP_Lamm_co Uu) Uua)) (tptp.pp (tptp.aa_fun171081125l_bool (tptp.scratc1829701671all_of (tptp.aa_TPT43085870d_bool tptp.aTP_Lamm_cm Uu)) (tptp.aa_TPT43085870d_bool (tptp.aTP_Lamm_cn Uu) Uua))))) (forall ((Uu $$unsorted) (Uua $$unsorted)) (let ((_let_1 (tptp.scratc1084070009d_n_pl Uu))) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.aTP_Lamm_bp Uu) Uua)) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1083610823d_n_is (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc912327602rdsucc (tptp.aa_TPTP_ind_TPTP_ind _let_1 Uua))) (tptp.aa_TPTP_ind_TPTP_ind _let_1 (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc912327602rdsucc Uua))))))) (forall ((Uu $$unsorted) (Uua $$unsorted)) (= (tptp.aa_fun277296641TP_ind (tptp.aa_TPT494704832TP_ind tptp.aTP_Lamm_bk Uu) Uua) (tptp.aa_TPTP_ind_TPTP_ind (tptp.scratc957265209nunion (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc854057538d_Sing tptp.scratc1745451206ptyset)) (tptp.aa_fun277296641TP_ind (tptp.aa_TPT494704832TP_ind tptp.scratc1071331552d_repl Uu) Uua)))) (forall ((Uu $$unsorted) (Uua $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.aTP_Lamm_ae Uu) Uua)) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1083610823d_n_is Uu) (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc912327602rdsucc Uua))))) (forall ((Uu $$unsorted) (Uua $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.aTP_Lamm_cm Uu) Uua)) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1550011574bnd_in Uua) (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc1017762772_power Uu))))) (forall ((Uu $$unsorted) (Uua $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.aTP_Lamm_cg Uu) Uua)) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1083610818d_n_in Uua) Uu)))) (forall ((Uu $$unsorted) (Uua $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.aTP_Lamm_bl Uu) Uua)) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc192357794nd_nIn Uua) Uu)))) (forall ((Uu $$unsorted) (Uua $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.aTP_Lamm_ai Uu) Uua)) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1550011574bnd_in Uua) Uu)))) (forall ((Uu $$unsorted) (Uua $$unsorted)) (= (tptp.aa_TPTP_ind_TPTP_ind (tptp.aTP_Lamm_ac Uu) Uua) (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc912327602rdsucc (tptp.aa_TPTP_ind_TPTP_ind (tptp.aa_TPT1424761345TP_ind tptp.scratc1549486784bnd_ap Uu) Uua)))) (forall ((Uu $$unsorted) (Uua $$unsorted)) (= (tptp.aa_TPTP_ind_TPTP_ind (tptp.aTP_Lamm_bd Uu) Uua) (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc1525024638_union (tptp.aa_TPTP_ind_TPTP_ind Uu Uua)))) (forall ((Uu $$unsorted) (Uua $$unsorted)) (=> (tptp.gg_TPTP_ind Uua) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.aTP_Lamm_bf Uu) Uua)) (exists ((X3 $$unsorted)) (and (tptp.gg_TPTP_ind X3) (= Uua (tptp.aa_TPTP_ind_TPTP_ind (tptp.aa_TPT1424761345TP_ind tptp.scratc1624135595d_pair Uu) X3))))))) (forall ((Uu $$unsorted) (Uua $$unsorted) (Uub $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.aTP_Lamm_cw Uu) Uua) Uub)) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.scratc1564950462d_e_is (tptp.aa_TPTP_ind_TPTP_ind (tptp.scratc546250696etprod Uu) Uua)) (tptp.aa_TPTP_ind_TPTP_ind (tptp.aa_TPT1424761345TP_ind (tptp.scratc1949829805d_pair Uu Uua) (tptp.aa_TPTP_ind_TPTP_ind (tptp.scratc2078076735_first Uu Uua) Uub)) (tptp.aa_TPTP_ind_TPTP_ind (tptp.scratc1061739109second Uu Uua) Uub))) Uub)))) (forall ((Uu $$unsorted) (Uua $$unsorted) (Uub $$unsorted)) (= (tptp.aa_TPTP_ind_TPTP_ind (tptp.aa_TPT1424761345TP_ind (tptp.aTP_Lamm_bn Uu) Uua) Uub) (tptp.aa_TPTP_ind_TPTP_ind (tptp.scratc1550011566bnd_if (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1550011574bnd_in tptp.scratc1745451206ptyset) Uub) Uu) Uua))) (forall ((Uu $$unsorted) (Uua $$unsorted) (Uub $$unsorted)) (= (tptp.aa_TPTP_ind_TPTP_ind (tptp.aa_fun1235454963TP_ind (tptp.aTP_Lamm_bm Uu) Uua) Uub) (tptp.aa_TPTP_ind_TPTP_ind (tptp.scratc1550011566bnd_if (tptp.aa_TPTP_ind_bool Uua Uub) Uub) (tptp.scratc120562615nd_eps (tptp.aa_fun1584354236d_bool (tptp.aTP_Lamm_ba Uu) Uua))))) (forall ((Uu $$unsorted) (Uua $$unsorted) (Uub $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.aTP_Lamm_at Uu) Uua) Uub)) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.scratc1777039668d_esti Uu) Uub) Uua)))) (forall ((Uu $$unsorted) (Uua $$unsorted) (Uub $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_fun1584354236d_bool (tptp.aTP_Lamm_cp Uu) Uua) Uub)) (=> (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.scratc1777039668d_esti Uu) Uub) (tptp.aa_fun1431113780TP_ind (tptp.scratc322369131_d_Sep Uu) Uua))) (tptp.pp (tptp.aa_TPTP_ind_bool Uua Uub))))) (forall ((Uu $$unsorted) (Uua $$unsorted) (Uub $$unsorted)) (let ((_let_1 (tptp.scratc561998463d_incl Uu))) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.aTP_Lamm_cn Uu) Uua) Uub)) (=> (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool _let_1 Uua) Uub)) (=> (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool _let_1 Uub) Uua)) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.scratc1564950462d_e_is (tptp.aa_TPTP_ind_TPTP_ind tptp.scratc1017762772_power Uu)) Uua) Uub))))))) (forall ((Uu $$unsorted) (Uua $$unsorted) (Uub $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.aTP_Lamm_cx Uu) Uua) Uub)) (tptp.scratc1451164978_is_of (tptp.aa_TPTP_ind_TPTP_ind (tptp.scratc1061739109second Uu Uua) Uub) (tptp.aa_TPT43085870d_bool tptp.aTP_Lamm_ai Uua)))) (forall ((Uu $$unsorted) (Uua $$unsorted) (Uub $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.aTP_Lamm_cy Uu) Uua) Uub)) (tptp.scratc1451164978_is_of (tptp.aa_TPTP_ind_TPTP_ind (tptp.scratc2078076735_first Uu Uua) Uub) (tptp.aa_TPT43085870d_bool tptp.aTP_Lamm_ai Uu)))) (forall ((Uu $$unsorted) (Uua $$unsorted) (Uub $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_fun1584354236d_bool (tptp.aTP_Lamm_de Uu) Uua) Uub)) (tptp.scratc1451164978_is_of (tptp.aa_TPTP_ind_TPTP_ind (tptp.scratc1564950457d_e_in Uu Uua) Uub) (tptp.aa_TPT43085870d_bool tptp.aTP_Lamm_ai Uu)))) (forall ((Uu $$unsorted) (Uua $$unsorted) (Uub $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.aTP_Lamm_di Uu) Uua) Uub)) (tptp.pp (tptp.aa_fun171081125l_bool (tptp.scratc1829701671all_of (tptp.aa_TPT43085870d_bool (tptp.aTP_Lamm_df Uu) Uua)) (tptp.aa_TPT43085870d_bool (tptp.aa_TPT60673477d_bool (tptp.aTP_Lamm_dh Uu) Uua) Uub))))) (forall ((Uu $$unsorted) (Uua $$unsorted) (Uub $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_fun1584354236d_bool (tptp.aTP_Lamm_ba Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1550011574bnd_in Uub) Uu)) (tptp.pp (tptp.aa_TPTP_ind_bool Uua Uub))))) (forall ((Uu $$unsorted) (Uua $$unsorted) (Uub $$unsorted)) (let ((_let_1 (tptp.aa_fun1431113780TP_ind (tptp.scratc322369131_d_Sep Uu) Uua))) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_fun1584354236d_bool (tptp.aTP_Lamm_db Uu) Uua) Uub)) (=> (tptp.pp (tptp.aa_TPTP_ind_bool Uua Uub)) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.scratc2035434666_image _let_1 Uu) (tptp.aa_fun277296641TP_ind (tptp.aa_TPT494704832TP_ind tptp.scratc1709589394_Sigma _let_1) (tptp.scratc1564950457d_e_in Uu Uua))) Uub)))))) (forall ((Uu $$unsorted) (Uua $$unsorted) (Uub $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_fun1584354236d_bool (tptp.aTP_Lamm_cq Uu) Uua) Uub)) (=> (tptp.pp (tptp.aa_TPTP_ind_bool Uua Uub)) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.scratc1777039668d_esti Uu) Uub) (tptp.aa_fun1431113780TP_ind (tptp.scratc322369131_d_Sep Uu) Uua)))))) (forall ((Uu $$unsorted) (Uua $$unsorted) (Uub $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_fun1584354236d_bool (tptp.aTP_Lamm_dk Uu) Uua) Uub)) (tptp.pp (tptp.aa_fun171081125l_bool (tptp.scratc1829701671all_of (tptp.aa_TPT43085870d_bool tptp.aTP_Lamm_ai Uu)) (tptp.aa_TPT43085870d_bool (tptp.aa_fun1212484691d_bool (tptp.aTP_Lamm_dj Uu) Uua) Uub))))) (forall ((Uu $$unsorted) (Uua $$unsorted) (Uub $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_fun1584354236d_bool (tptp.aTP_Lamm_bc Uu) Uua) Uub)) (tptp.pp (tptp.aa_fun171081125l_bool (tptp.scratc1829701671all_of (tptp.aa_TPT43085870d_bool tptp.aTP_Lamm_ai Uu)) (tptp.aa_TPT43085870d_bool (tptp.aa_fun1212484691d_bool (tptp.aTP_Lamm_bb Uu) Uua) Uub))))) (forall ((Uu $$unsorted) (Uua $$unsorted) (Uub $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.aTP_Lamm_da Uu) Uua) Uub)) (tptp.pp (tptp.aa_fun171081125l_bool (tptp.scratc1829701671all_of (tptp.aa_TPT43085870d_bool tptp.aTP_Lamm_ai Uua)) (tptp.aa_TPT43085870d_bool (tptp.aa_TPT60673477d_bool (tptp.aTP_Lamm_cz Uu) Uua) Uub))))) (forall ((Uu $$unsorted) (Uua $$unsorted) (Uub $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.aTP_Lamm_cu Uu) Uua) Uub)) (tptp.pp (tptp.aa_fun171081125l_bool (tptp.scratc1829701671all_of (tptp.aa_TPT43085870d_bool tptp.aTP_Lamm_ai Uua)) (tptp.aa_TPT43085870d_bool (tptp.aa_TPT60673477d_bool (tptp.aTP_Lamm_ct Uu) Uua) Uub))))) (forall ((Uu $$unsorted) (Uua $$unsorted) (Uub $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.aTP_Lamm_cs Uu) Uua) Uub)) (tptp.pp (tptp.aa_fun171081125l_bool (tptp.scratc1829701671all_of (tptp.aa_TPT43085870d_bool tptp.aTP_Lamm_ai Uua)) (tptp.aa_TPT43085870d_bool (tptp.aa_TPT60673477d_bool (tptp.aTP_Lamm_cr Uu) Uua) Uub))))) (forall ((Uu $$unsorted) (Uua $$unsorted) (Uub $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.aTP_Lamm_df Uu) Uua) Uub)) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1550011574bnd_in Uub) (tptp.aa_fun277296641TP_ind (tptp.aa_TPT494704832TP_ind tptp.scratc423746188d_d_Pi Uu) (tptp.aTP_Lamm_ah Uua)))))) (forall ((Uu $$unsorted) (Uua $$unsorted) (Uub $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.aTP_Lamm_cv Uu) Uua) Uub)) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1550011574bnd_in Uub) (tptp.aa_TPTP_ind_TPTP_ind (tptp.scratc546250696etprod Uu) Uua))))) (forall ((Uu $$unsorted) (Uua $$unsorted) (Uub $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_fun1584354236d_bool (tptp.aTP_Lamm_dc Uu) Uua) Uub)) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1550011574bnd_in Uub) (tptp.aa_fun1431113780TP_ind (tptp.scratc322369131_d_Sep Uu) Uua))))) (forall ((Uu $$unsorted) (Uua $$unsorted) (Uub $$unsorted)) (= (tptp.aa_TPTP_ind_TPTP_ind (tptp.aa_TPT1424761345TP_ind (tptp.aTP_Lamm_av Uu) Uua) Uub) (tptp.aa_TPTP_ind_TPTP_ind (tptp.aa_TPT1424761345TP_ind tptp.scratc1549486784bnd_ap Uua) (tptp.aa_TPTP_ind_TPTP_ind (tptp.aa_TPT1424761345TP_ind tptp.scratc1549486784bnd_ap Uu) Uub)))) (forall ((Uu $$unsorted) (Uua $$unsorted) (Uub $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_fun1584354236d_bool (tptp.aTP_Lamm_dd Uu) Uua) Uub)) (tptp.pp (tptp.aa_TPTP_ind_bool Uua (tptp.aa_TPTP_ind_TPTP_ind (tptp.scratc1564950457d_e_in Uu Uua) Uub))))) (forall ((Uu $$unsorted) (Uua $$unsorted) (Uub $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_fun1913827119d_bool (tptp.aTP_Lamm_be Uu) Uua) Uub)) (forall ((X3 $$unsorted)) (=> (tptp.gg_TPTP_ind X3) (=> (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1550011574bnd_in X3) Uu)) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool tptp.scratc1550011574bnd_in (tptp.aa_TPTP_ind_TPTP_ind (tptp.aa_TPT1424761345TP_ind tptp.scratc1549486784bnd_ap Uub) X3)) (tptp.aa_TPTP_ind_TPTP_ind Uua X3)))))))) (forall ((Uu $$unsorted) (Uua $$unsorted) (Uub $$unsorted) (Uuc $$unsorted)) (= (tptp.aa_TPTP_ind_TPTP_ind (tptp.aa_TPT1424761345TP_ind (tptp.aa_TPT1791839040TP_ind (tptp.aTP_Lamm_aw Uu) Uua) Uub) Uuc) (tptp.aa_TPTP_ind_TPTP_ind (tptp.scratc1550011566bnd_if (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.scratc2035434666_image Uu Uua) Uub) Uuc) (tptp.aa_TPTP_ind_TPTP_ind (tptp.scratc1933877819d_soft Uu Uua Uub) Uuc)) tptp.scratc1745451206ptyset))) (forall ((Uu $$unsorted) (Uua $$unsorted) (Uub $$unsorted) (Uuc $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.aa_TPT60673477d_bool (tptp.aTP_Lamm_ct Uu) Uua) Uub) Uuc)) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.scratc1564950462d_e_is Uu) (tptp.aa_TPTP_ind_TPTP_ind (tptp.scratc2078076735_first Uu Uua) (tptp.aa_TPTP_ind_TPTP_ind (tptp.aa_TPT1424761345TP_ind (tptp.scratc1949829805d_pair Uu Uua) Uub) Uuc))) Uub)))) (forall ((Uu $$unsorted) (Uua $$unsorted) (Uub $$unsorted) (Uuc $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.aa_TPT60673477d_bool (tptp.aTP_Lamm_cr Uu) Uua) Uub) Uuc)) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.scratc1564950462d_e_is Uua) (tptp.aa_TPTP_ind_TPTP_ind (tptp.scratc1061739109second Uu Uua) (tptp.aa_TPTP_ind_TPTP_ind (tptp.aa_TPT1424761345TP_ind (tptp.scratc1949829805d_pair Uu Uua) Uub) Uuc))) Uuc)))) (forall ((Uu $$unsorted) (Uua $$unsorted) (Uub $$unsorted) (Uuc $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.aa_TPT60673477d_bool (tptp.aTP_Lamm_dg Uu) Uua) Uub) Uuc)) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.scratc1564950462d_e_is Uu) (tptp.aa_TPTP_ind_TPTP_ind (tptp.aa_TPT1424761345TP_ind tptp.scratc1549486784bnd_ap Uua) Uuc)) (tptp.aa_TPTP_ind_TPTP_ind (tptp.aa_TPT1424761345TP_ind tptp.scratc1549486784bnd_ap Uub) Uuc))))) (forall ((Uu $$unsorted) (Uua $$unsorted) (Uub $$unsorted) (Uuc $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.aa_TPT60673477d_bool (tptp.aTP_Lamm_ap Uu) Uua) Uub) Uuc)) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.scratc1777039668d_esti Uu) Uub) (tptp.aa_TPTP_ind_TPTP_ind (tptp.aa_TPT1424761345TP_ind tptp.scratc1549486784bnd_ap Uua) Uuc))))) (forall ((Uu $$unsorted) (Uua $$unsorted) (Uub $$unsorted) (Uuc $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.aa_TPT60673477d_bool (tptp.aTP_Lamm_ax Uu) Uua) Uub) Uuc)) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.scratc1564950462d_e_is Uu) Uub) (tptp.aa_TPTP_ind_TPTP_ind (tptp.aa_TPT1424761345TP_ind tptp.scratc1549486784bnd_ap Uua) Uuc))))) (forall ((Uu $$unsorted) (Uua $$unsorted) (Uub $$unsorted) (Uuc $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.aa_TPT60673477d_bool (tptp.aTP_Lamm_cz Uu) Uua) Uub) Uuc)) (tptp.scratc1451164978_is_of (tptp.aa_TPTP_ind_TPTP_ind (tptp.aa_TPT1424761345TP_ind (tptp.scratc1949829805d_pair Uu Uua) Uub) Uuc) (tptp.aa_TPT43085870d_bool (tptp.aTP_Lamm_cv Uu) Uua)))) (forall ((Uu $$unsorted) (Uua $$unsorted) (Uub $$unsorted) (Uuc $$unsorted)) (let ((_let_1 (tptp.aa_TPT43085870d_bool (tptp.scratc1777039668d_esti Uu) Uuc))) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.aa_TPT60673477d_bool (tptp.aTP_Lamm_ar Uu) Uua) Uub) Uuc)) (tptp.pp (tptp.scratc951703481d_l_ec (tptp.aa_TPTP_ind_bool _let_1 Uua) (tptp.aa_TPTP_ind_bool _let_1 Uub)))))) (forall ((Uu $$unsorted) (Uua $$unsorted) (Uub $$unsorted) (Uuc $$unsorted)) (let ((_let_1 (tptp.aa_TPT43085870d_bool (tptp.scratc1777039668d_esti Uu) Uuc))) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.aa_TPT60673477d_bool (tptp.aTP_Lamm_as Uu) Uua) Uub) Uuc)) (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo1142376798l_bool tptp.scratc153411835nd_imp (tptp.aa_TPTP_ind_bool _let_1 Uua)) (tptp.aa_TPTP_ind_bool _let_1 Uub)))))) (forall ((Uu $$unsorted) (Uua $$unsorted) (Uub $$unsorted) (Uuc $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.aa_TPT60673477d_bool (tptp.aTP_Lamm_dh Uu) Uua) Uub) Uuc)) (=> (tptp.pp (tptp.aa_fun171081125l_bool (tptp.scratc1829701671all_of (tptp.aa_TPT43085870d_bool tptp.aTP_Lamm_ai Uu)) (tptp.aa_TPT43085870d_bool (tptp.aa_TPT60673477d_bool (tptp.aTP_Lamm_dg Uua) Uub) Uuc))) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.scratc1564950462d_e_is (tptp.aa_fun277296641TP_ind (tptp.aa_TPT494704832TP_ind tptp.scratc423746188d_d_Pi Uu) (tptp.aTP_Lamm_ah Uua))) Uub) Uuc))))) (forall ((Uu $$unsorted) (Uua $$unsorted) (Uub $$unsorted) (Uuc $$unsorted)) (let ((_let_1 (tptp.pp Uu))) (=> (and (tptp.gg_TPTP_ind Uua) (tptp.gg_TPTP_ind Uub) (tptp.gg_TPTP_ind Uuc)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.aa_TPT60673477d_bool (tptp.aTP_Lamm_bo Uu) Uua) Uub) Uuc)) (or (and _let_1 (= Uuc Uua)) (and (not _let_1) (= Uuc Uub))))))) (forall ((Uu $$unsorted) (Uua $$unsorted) (Uub $$unsorted) (Uuc $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.aa_fun1212484691d_bool (tptp.aTP_Lamm_dj Uu) Uua) Uub) Uuc)) (=> (tptp.pp (tptp.aa_TPTP_ind_bool Uua Uub)) (=> (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.scratc1564950462d_e_is Uu) Uub) Uuc)) (tptp.pp (tptp.aa_TPTP_ind_bool Uua Uuc)))))) (forall ((Uu $$unsorted) (Uua $$unsorted) (Uub $$unsorted) (Uuc $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.aa_fun1212484691d_bool (tptp.aTP_Lamm_bb Uu) Uua) Uub) Uuc)) (=> (tptp.pp (tptp.aa_TPTP_ind_bool Uua Uub)) (=> (tptp.pp (tptp.aa_TPTP_ind_bool Uua Uuc)) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.scratc1564950462d_e_is Uu) Uub) Uuc)))))) (forall ((Uu $$unsorted) (Uua $$unsorted) (Uub $$unsorted) (Uuc $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.aa_TPT60673477d_bool (tptp.aTP_Lamm_az Uu) Uua) Uub) Uuc)) (tptp.pp (tptp.aa_fun171081125l_bool (tptp.scratc87254192nd_all Uu) (tptp.aa_TPT43085870d_bool (tptp.aa_TPT60673477d_bool (tptp.aa_TPT1123896796d_bool (tptp.aTP_Lamm_ay Uu) Uua) Uub) Uuc))))) (forall ((Uu $$unsorted) (Uua $$unsorted) (Uub $$unsorted) (Uuc $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.aa_TPT60673477d_bool (tptp.aTP_Lamm_aq Uu) Uua) Uub) Uuc)) (tptp.pp (tptp.aa_fun171081125l_bool (tptp.scratc940362479l_some Uua) (tptp.aa_TPT43085870d_bool (tptp.aa_TPT60673477d_bool (tptp.aTP_Lamm_ap Uu) Uub) Uuc))))) (forall ((Uu $$unsorted) (Uua $$unsorted) (Uub $$unsorted) (Uuc $$unsorted) (Uud $$unsorted)) (let ((_let_1 (tptp.aa_TPT1424761345TP_ind tptp.scratc1549486784bnd_ap Uub))) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.aa_TPT60673477d_bool (tptp.aa_TPT1123896796d_bool (tptp.aTP_Lamm_ay Uu) Uua) Uub) Uuc) Uud)) (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo1142376798l_bool tptp.scratc153411835nd_imp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.scratc1564950462d_e_is Uua) (tptp.aa_TPTP_ind_TPTP_ind _let_1 Uuc)) (tptp.aa_TPTP_ind_TPTP_ind _let_1 Uud))) (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.scratc1564950462d_e_is Uu) Uuc) Uud)))))) (forall ((Uu $$unsorted) (Uua $$unsorted) (Uub $$unsorted) (Uuc $$unsorted) (Uud $$unsorted)) (let ((_let_1 (tptp.aa_TPT1424761345TP_ind tptp.scratc1549486784bnd_ap Uub))) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.aa_TPT60673477d_bool (tptp.aa_TPT1123896796d_bool (tptp.aTP_Lamm_an Uu) Uua) Uub) Uuc) Uud)) (=> (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool Uu Uuc) Uud)) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.scratc1564950462d_e_is Uua) (tptp.aa_TPTP_ind_TPTP_ind _let_1 Uuc)) (tptp.aa_TPTP_ind_TPTP_ind _let_1 Uud))))))) (forall ((Uu $$unsorted) (Uua $$unsorted) (Uub $$unsorted) (Uuc $$unsorted) (Uud $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.aa_TPT60673477d_bool (tptp.aa_fun987228051d_bool (tptp.aTP_Lamm_am Uu) Uua) Uub) Uuc) Uud)) (tptp.pp (tptp.aa_fun171081125l_bool (tptp.scratc1829701671all_of (tptp.aa_TPT43085870d_bool tptp.aTP_Lamm_ai Uu)) (tptp.aa_TPT43085870d_bool (tptp.aa_TPT60673477d_bool (tptp.aa_TPT1123896796d_bool (tptp.aa_fun845057962d_bool (tptp.aTP_Lamm_al Uu) Uua) Uub) Uuc) Uud))))) (forall ((Uu $$unsorted) (Uua $$unsorted) (Uub $$unsorted) (Uuc $$unsorted) (Uud $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.aa_TPT60673477d_bool (tptp.aa_fun987228051d_bool (tptp.aTP_Lamm_ao Uu) Uua) Uub) Uuc) Uud)) (tptp.pp (tptp.aa_fun171081125l_bool (tptp.scratc1829701671all_of (tptp.aa_TPT43085870d_bool tptp.aTP_Lamm_ai Uu)) (tptp.aa_TPT43085870d_bool (tptp.aa_TPT60673477d_bool (tptp.aa_TPT1123896796d_bool (tptp.aTP_Lamm_an Uua) Uub) Uuc) Uud))))) (forall ((Uu $$unsorted) (Uua $$unsorted) (Uub $$unsorted) (Uuc $$unsorted) (Uud $$unsorted)) (= (tptp.aa_TPTP_ind_TPTP_ind (tptp.aa_TPT1424761345TP_ind (tptp.aa_TPT1791839040TP_ind (tptp.aa_TPT1781712639TP_ind (tptp.aTP_Lamm_au Uu) Uua) Uub) Uuc) Uud) (tptp.aa_TPTP_ind_TPTP_ind (tptp.aa_TPT1424761345TP_ind tptp.scratc1549486784bnd_ap Uua) (tptp.aa_TPTP_ind_TPTP_ind (tptp.aa_TPT1424761345TP_ind tptp.scratc1549486784bnd_ap (tptp.aa_TPTP_ind_TPTP_ind (tptp.scratc302523178wissel Uu Uub) Uuc)) Uud)))) (forall ((Uu $$unsorted) (Uua $$unsorted) (Uub $$unsorted) (Uuc $$unsorted) (Uud $$unsorted) (Uue $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.aa_TPT60673477d_bool (tptp.aa_TPT1123896796d_bool (tptp.aa_fun845057962d_bool (tptp.aTP_Lamm_al Uu) Uua) Uub) Uuc) Uud) Uue)) (tptp.pp (tptp.aa_fun171081125l_bool (tptp.scratc1829701671all_of (tptp.aa_TPT43085870d_bool tptp.aTP_Lamm_ai Uu)) (tptp.aa_TPT43085870d_bool (tptp.aa_TPT60673477d_bool (tptp.aa_TPT1123896796d_bool (tptp.aa_TPT985247859d_bool (tptp.aa_fun1107270209d_bool (tptp.aTP_Lamm_ak Uu) Uua) Uub) Uuc) Uud) Uue))))) (forall ((Uu $$unsorted) (Uua $$unsorted) (Uub $$unsorted) (Uuc $$unsorted) (Uud $$unsorted) (Uue $$unsorted) (Uuf $$unsorted)) (let ((_let_1 (tptp.aa_TPT1424761345TP_ind tptp.scratc1549486784bnd_ap Uub))) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.aa_TPT60673477d_bool (tptp.aa_TPT1123896796d_bool (tptp.aa_TPT985247859d_bool (tptp.aa_TPT125613450d_bool (tptp.aTP_Lamm_aj Uu) Uua) Uub) Uuc) Uud) Uue) Uuf)) (=> (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool Uu Uuc) Uud)) (=> (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool Uu Uue) Uuf)) (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.scratc1564950462d_e_is Uua) (tptp.aa_TPTP_ind_TPTP_ind (tptp.aa_TPT1424761345TP_ind tptp.scratc1549486784bnd_ap (tptp.aa_TPTP_ind_TPTP_ind _let_1 Uuc)) Uue)) (tptp.aa_TPTP_ind_TPTP_ind (tptp.aa_TPT1424761345TP_ind tptp.scratc1549486784bnd_ap (tptp.aa_TPTP_ind_TPTP_ind _let_1 Uud)) Uuf)))))))) (forall ((Uu $$unsorted) (Uua $$unsorted) (Uub $$unsorted) (Uuc $$unsorted) (Uud $$unsorted) (Uue $$unsorted) (Uuf $$unsorted)) (= (tptp.pp (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.aa_TPT60673477d_bool (tptp.aa_TPT1123896796d_bool (tptp.aa_TPT985247859d_bool (tptp.aa_fun1107270209d_bool (tptp.aTP_Lamm_ak Uu) Uua) Uub) Uuc) Uud) Uue) Uuf)) (tptp.pp (tptp.aa_fun171081125l_bool (tptp.scratc1829701671all_of (tptp.aa_TPT43085870d_bool tptp.aTP_Lamm_ai Uu)) (tptp.aa_TPT43085870d_bool (tptp.aa_TPT60673477d_bool (tptp.aa_TPT1123896796d_bool (tptp.aa_TPT985247859d_bool (tptp.aa_TPT125613450d_bool (tptp.aTP_Lamm_aj Uua) Uub) Uuc) Uud) Uue) Uuf))))) (forall ((Uu $$unsorted) (Uua $$unsorted)) (=> (tptp.gg_TPTP_ind Uu) (= (tptp.aa_TPTP_ind_TPTP_ind (tptp.aTP_Lamm_ah Uu) Uua) Uu))) (forall ((Uu $$unsorted)) (= (tptp.aa_TPTP_ind_TPTP_ind tptp.aTP_Lamm_ab Uu) tptp.scratc193932176nd_nat)) (tptp.pp tptp.fTrue) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo1142376798l_bool tptp.fconj P) Q))) (tptp.pp Q))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo1142376798l_bool tptp.fconj P) Q))) (tptp.pp P))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.pp P)) (not (tptp.pp Q)) (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo1142376798l_bool tptp.fconj P) Q)))) (forall ((P $$unsorted)) (=> (tptp.gg_bool P) (or (= P tptp.fTrue) (= P tptp.fFalse)))) (not (tptp.pp tptp.fFalse)) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo1142376798l_bool tptp.fimplies P) Q))) (not (tptp.pp P)) (tptp.pp Q))) (forall ((Q $$unsorted) (P $$unsorted)) (or (not (tptp.pp Q)) (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo1142376798l_bool tptp.fimplies P) Q)))) (forall ((P $$unsorted) (Q $$unsorted)) (or (tptp.pp P) (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo1142376798l_bool tptp.fimplies P) Q)))) (forall ((P $$unsorted) (X7 $$unsorted)) (or (not (tptp.pp (tptp.aa_TPTP_ind_bool P X7))) (tptp.pp (tptp.fEx_TPTP_ind P)))) _let_5 _let_4 (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.aa_TPTP_ind_bool (tptp.cOMBS_2003118649l_bool P Q) R) (tptp.aa_bool_bool (tptp.aa_TPT2142672771l_bool P R) (tptp.aa_TPTP_ind_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool (tptp.cOMBC_1555011498d_bool P) Q) R) (tptp.aa_TPTP_ind_bool (tptp.aa_TPT43085870d_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.aa_TPT2142672771l_bool (tptp.cOMBB_658106424TP_ind P Q) R) (tptp.aa_boo1142376798l_bool P (tptp.aa_TPTP_ind_bool Q R)))) _let_3 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 82.42/82.71 )
% 82.42/82.71 % SZS output end Proof for NUM641+4
% 82.42/82.71 % cvc5---1.0.5 exiting
% 82.55/82.71 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------