TSTP Solution File: SWW470+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWW470+1 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 1 00:20:55 EDT 2023
% Result : Theorem 0.58s 0.78s
% Output : Proof 0.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SWW470+1 : TPTP v8.1.2. Released v5.3.0.
% 0.10/0.13 % Command : do_cvc5 %s %d
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Aug 27 19:40:55 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.49 %----Proving TF0_NAR, FOF, or CNF
% 0.58/0.78 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.5FNrNbM1K3/cvc5---1.0.5_21873.p...
% 0.58/0.78 ------- get file name : TPTP file name is SWW470+1
% 0.58/0.78 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_21873.smt2...
% 0.58/0.78 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.58/0.78 % SZS status Theorem for SWW470+1
% 0.58/0.78 % SZS output start Proof for SWW470+1
% 0.58/0.78 (
% 0.58/0.78 (let ((_let_1 (tptp.hAPP_f762886889e_bool (tptp.hAPP_f1261923407e_bool tptp.cOMBC_892787026e_bool (tptp.hAPP_f963367678e_bool (tptp.cOMBB_145932198bool_a tptp.cOMBS_1378840469l_bool) (tptp.hAPP_f1509969235l_bool (tptp.cOMBB_1355796797bool_a (tptp.cOMBB_188601460_state tptp.fconj)) tptp.p))) (tptp.hAPP_f1759915619e_bool (tptp.cOMBB_160679318_state tptp.fNot) tptp.b)))) (let ((_let_2 (tptp.cOMBK_bool_state tptp.fFalse))) (let ((_let_3 (tptp.cOMBK_1458035955bool_a _let_2))) (let ((_let_4 (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a (tptp.hoare_1050552211iple_a _let_3 tptp.c _let_1)) tptp.bot_bo1687970473a_bool))) (let ((_let_5 (tptp.hoare_472868247rivs_a tptp.g))) (let ((_let_6 (tptp.hAPP_f1753944735l_bool _let_5 _let_4))) (let ((_let_7 (tptp.hBOOL _let_6))) (let ((_let_8 (not _let_7))) (let ((_let_9 (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.hAPP_a2036067514e_bool (tptp.cOMBK_1458035955bool_a P) Q) P)))) (let ((_let_10 (forall ((P $$unsorted) (Q $$unsorted)) (=> (tptp.is_bool P) (= (tptp.hAPP_state_bool (tptp.cOMBK_bool_state P) Q) P))))) (let ((_let_11 (forall ((P $$unsorted)) (=> (tptp.is_bool P) (or (= P tptp.fTrue) (= P tptp.fFalse)))))) (let ((_let_12 (tptp.hBOOL tptp.fFalse))) (let ((_let_13 (not _let_12))) (let ((_let_14 (tptp.hAPP_f1753944735l_bool tptp.finite506133020iple_a tptp.bot_bo1687970473a_bool))) (let ((_let_15 (tptp.hBOOL _let_14))) (let ((_let_16 (forall ((Ga $$unsorted) (Ca $$unsorted) (Q_1 $$unsorted) (Pa $$unsorted)) (=> (forall ((Z_1 $$unsorted) (S $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_a2036067514e_bool Pa Z_1) S)) (tptp.hBOOL (tptp.hAPP_f1753944735l_bool (tptp.hoare_472868247rivs_a Ga) (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a (tptp.hoare_1050552211iple_a (tptp.cOMBK_1458035955bool_a (tptp.hAPP_s1806633685e_bool (tptp.hAPP_f817621513e_bool tptp.cOMBC_2027030106e_bool tptp.fequal_state) S)) Ca (tptp.cOMBK_1458035955bool_a (tptp.hAPP_a2036067514e_bool Q_1 Z_1)))) tptp.bot_bo1687970473a_bool))))) (tptp.hBOOL (tptp.hAPP_f1753944735l_bool (tptp.hoare_472868247rivs_a Ga) (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a (tptp.hoare_1050552211iple_a Pa Ca Q_1)) tptp.bot_bo1687970473a_bool))))))) (let ((_let_17 (forall ((B_1_1 $$unsorted) (B_2 $$unsorted)) (tptp.is_bool (tptp.hAPP_f1753944735l_bool B_1_1 B_2))))) (let ((_let_18 (tptp.is_bool tptp.fFalse))) (let ((_let_19 (tptp.hAPP_a2036067514e_bool _let_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_20 (tptp.hBOOL (tptp.hAPP_state_bool _let_19 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12)))) (let ((_let_21 (= _let_2 _let_19))) (let ((_let_22 (= tptp.fFalse _let_6))) (let ((_let_23 (= tptp.fFalse (tptp.hAPP_state_bool _let_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12)))) (let ((_let_24 (ASSUME :args (_let_8)))) (let ((_let_25 (not _let_20))) (let ((_let_26 (or _let_25 (tptp.hBOOL (tptp.hAPP_f1753944735l_bool _let_5 (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a (tptp.hoare_1050552211iple_a (tptp.cOMBK_1458035955bool_a (tptp.hAPP_s1806633685e_bool (tptp.hAPP_f817621513e_bool tptp.cOMBC_2027030106e_bool tptp.fequal_state) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12)) tptp.c (tptp.cOMBK_1458035955bool_a (tptp.hAPP_a2036067514e_bool _let_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11)))) tptp.bot_bo1687970473a_bool)))))) (let ((_let_27 (forall ((Z_1 $$unsorted) (S $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_a2036067514e_bool (tptp.cOMBK_1458035955bool_a (tptp.cOMBK_bool_state tptp.fFalse)) Z_1) S))) (tptp.hBOOL (tptp.hAPP_f1753944735l_bool (tptp.hoare_472868247rivs_a tptp.g) (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a (tptp.hoare_1050552211iple_a (tptp.cOMBK_1458035955bool_a (tptp.hAPP_s1806633685e_bool (tptp.hAPP_f817621513e_bool tptp.cOMBC_2027030106e_bool tptp.fequal_state) S)) tptp.c (tptp.cOMBK_1458035955bool_a (tptp.hAPP_a2036067514e_bool (tptp.hAPP_f762886889e_bool (tptp.hAPP_f1261923407e_bool tptp.cOMBC_892787026e_bool (tptp.hAPP_f963367678e_bool (tptp.cOMBB_145932198bool_a tptp.cOMBS_1378840469l_bool) (tptp.hAPP_f1509969235l_bool (tptp.cOMBB_1355796797bool_a (tptp.cOMBB_188601460_state tptp.fconj)) tptp.p))) (tptp.hAPP_f1759915619e_bool (tptp.cOMBB_160679318_state tptp.fNot) tptp.b)) Z_1)))) tptp.bot_bo1687970473a_bool))))))) (let ((_let_28 (not _let_26))) (let ((_let_29 (not _let_27))) (let ((_let_30 (or _let_29 _let_7))) (let ((_let_31 (forall ((Ga $$unsorted) (Ca $$unsorted) (Q_1 $$unsorted) (Pa $$unsorted)) (or (not (forall ((Z_1 $$unsorted) (S $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_a2036067514e_bool Pa Z_1) S))) (tptp.hBOOL (tptp.hAPP_f1753944735l_bool (tptp.hoare_472868247rivs_a Ga) (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a (tptp.hoare_1050552211iple_a (tptp.cOMBK_1458035955bool_a (tptp.hAPP_s1806633685e_bool (tptp.hAPP_f817621513e_bool tptp.cOMBC_2027030106e_bool tptp.fequal_state) S)) Ca (tptp.cOMBK_1458035955bool_a (tptp.hAPP_a2036067514e_bool Q_1 Z_1)))) tptp.bot_bo1687970473a_bool)))))) (tptp.hBOOL (tptp.hAPP_f1753944735l_bool (tptp.hoare_472868247rivs_a Ga) (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a (tptp.hoare_1050552211iple_a Pa Ca Q_1)) tptp.bot_bo1687970473a_bool))))))) (let ((_let_32 (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_33 (or))) (let ((_let_34 (_let_29))) (let ((_let_35 (forall ((P $$unsorted) (Q $$unsorted)) (= P (tptp.hAPP_a2036067514e_bool (tptp.cOMBK_1458035955bool_a P) Q))))) (let ((_let_36 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_37 (= tptp.fTrue _let_6))) (let ((_let_38 (tptp.is_bool _let_6))) (let ((_let_39 (not _let_38))) (let ((_let_40 (or _let_39 _let_37 _let_22))) (let ((_let_41 (forall ((P $$unsorted)) (or (not (tptp.is_bool P)) (= tptp.fTrue P) (= tptp.fFalse P))))) (let ((_let_42 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_43 (_let_41))) (let ((_let_44 ((not (= (tptp.is_bool P) false))))) (let ((_let_45 (= tptp.fTrue _let_14))) (let ((_let_46 (not _let_37))) (let ((_let_47 (= tptp.fFalse _let_14))) (let ((_let_48 (tptp.is_bool _let_14))) (let ((_let_49 (not _let_48))) (let ((_let_50 (or _let_49 _let_45 _let_47))) (let ((_let_51 (not _let_47))) (let ((_let_52 (ASSUME :args (_let_15)))) (let ((_let_53 (ASSUME :args (_let_13)))) (let ((_let_54 (not _let_15))) (let ((_let_55 (REFL :args (_let_54)))) (let ((_let_56 (APPLY_UF tptp.hBOOL))) (let ((_let_57 (ASSUME :args (_let_47)))) (let ((_let_58 (SYMM (TRUE_INTRO _let_52)))) (let ((_let_59 (_let_17))) (let ((_let_60 (ASSUME :args _let_59))) (let ((_let_61 ((tptp.hAPP_f1753944735l_bool B_1_1 B_2)))) (let ((_let_62 (not _let_45))) (let ((_let_63 (MACRO_SR_PRED_INTRO :args ((= (not _let_8) _let_7))))) (let ((_let_64 (FALSE_INTRO _let_24))) (let ((_let_65 (ASSUME :args (_let_37)))) (let ((_let_66 (ASSUME :args (_let_45)))) (let ((_let_67 (not _let_18))) (let ((_let_68 (or _let_67 _let_23))) (let ((_let_69 (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.is_bool P)) (= P (tptp.hAPP_state_bool (tptp.cOMBK_bool_state P) Q)))))) (let ((_let_70 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_71 (ASSUME :args (_let_22)))) (let ((_let_72 (ASSUME :args (_let_23)))) (let ((_let_73 (ASSUME :args (_let_21)))) (let ((_let_74 (ASSUME :args (_let_20)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_24 _let_71 _let_72 _let_73 _let_74) :args (_let_8 _let_20 _let_22 _let_21 _let_23)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_74)) (CONG (TRANS (CONG (SYMM _let_73) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12)) :args (APPLY_UF tptp.hAPP_state_bool)) (SYMM _let_72) (SYMM (SYMM _let_71))) :args _let_56) _let_64)) :args (_let_8 _let_22 _let_23 _let_21 _let_20)) :args ((not (and _let_8 _let_20 _let_22 _let_21 _let_23)) SB_LITERAL))) (CONG _let_63 (REFL :args (_let_25)) (REFL :args ((not _let_22))) (REFL :args ((not _let_21))) (REFL :args ((not _let_23))) :args _let_33)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_68)) :args ((or _let_67 _let_23 (not _let_68)))) (ASSUME :args (_let_18)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_70 :args (tptp.fFalse SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP_state_bool (tptp.cOMBK_bool_state P) Q)))) :args (_let_69))) _let_70 :args (_let_68 false _let_69)) :args (_let_23 false _let_18 false _let_68)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_40)) :args ((or _let_39 _let_37 _let_22 (not _let_40)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_60 :args (_let_5 _let_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_61)) :args _let_59)) _let_60 :args (_let_38 false _let_17)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_24 _let_65 _let_66 _let_52) :args (_let_15 _let_8 _let_45 _let_37)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS _let_58 (CONG (TRANS (SYMM _let_66) (SYMM (SYMM _let_65))) :args _let_56) _let_64)) :args (_let_8 _let_37 _let_45 _let_15)) :args ((not (and _let_15 _let_8 _let_45 _let_37)) SB_LITERAL))) (CONG _let_55 _let_63 (REFL :args (_let_62)) (REFL :args (_let_46)) :args _let_33)) :args ((or _let_7 _let_54 _let_62 _let_46))) _let_24 _let_52 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_50)) :args ((or _let_49 _let_45 _let_47 (not _let_50)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_60 :args (tptp.finite506133020iple_a tptp.bot_bo1687970473a_bool QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_61)) :args _let_59)) _let_60 :args (_let_48 false _let_17)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_53 _let_57 _let_52) :args (_let_15 _let_13 _let_47)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS _let_58 (CONG (SYMM _let_57) :args _let_56) (FALSE_INTRO _let_53))) :args (_let_13 _let_47 _let_15)) :args ((not (and _let_15 _let_13 _let_47)) SB_LITERAL))) (CONG _let_55 (MACRO_SR_PRED_INTRO :args ((= (not _let_13) _let_12))) (REFL :args (_let_51)) :args _let_33)) :args ((or _let_12 _let_54 _let_51))) _let_53 _let_52 :args (_let_51 true _let_12 false _let_15)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_42 :args (_let_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_44)) :args _let_43)) _let_42 :args (_let_50 false _let_41)) :args (_let_45 false _let_48 true _let_47 false _let_50)) :args (_let_46 true _let_7 false _let_15 false _let_45)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_42 :args (_let_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_44)) :args _let_43)) _let_42 :args (_let_40 false _let_41)) :args (_let_22 false _let_38 true _let_37 false _let_40)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_36 :args (_let_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP_a2036067514e_bool (tptp.cOMBK_1458035955bool_a P) Q)))) :args (_let_35))) _let_36 :args (_let_21 false _let_35)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_26 0)) (CONG (REFL :args (_let_26)) (MACRO_SR_PRED_INTRO :args ((= (not _let_25) _let_20))) :args _let_33)) :args ((or _let_20 _let_26))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_34)) :args _let_34)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_29) _let_27))) (REFL :args (_let_28)) :args _let_33)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_30)) :args ((or _let_7 _let_29 (not _let_30)))) _let_24 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_32 :args (tptp.g tptp.c _let_1 _let_3 QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP_f1753944735l_bool (tptp.hoare_472868247rivs_a Ga) (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a (tptp.hoare_1050552211iple_a Pa Ca Q_1)) tptp.bot_bo1687970473a_bool))))) :args (_let_31))) _let_32 :args (_let_30 false _let_31)) :args (_let_29 true _let_7 false _let_30)) :args (_let_28 true _let_27)) :args (_let_20 true _let_26)) _let_24 :args (false false _let_23 false _let_22 false _let_21 false _let_20 true _let_7)) :args ((forall ((B_1_1 $$unsorted) (B_2 $$unsorted)) (tptp.is_bool (tptp.finite520909254iple_a B_1_1 B_2))) (forall ((B_1_1 $$unsorted) (B_2 $$unsorted)) (tptp.is_bool (tptp.finite1948426435iple_a B_1_1 B_2))) (tptp.is_bool tptp.bot_bot_bool) _let_18 (tptp.is_bool tptp.fTrue) (forall ((B_1_1 $$unsorted) (B_2 $$unsorted)) (tptp.is_bool (tptp.hAPP_state_bool B_1_1 B_2))) (forall ((B_1_1 $$unsorted) (B_2 $$unsorted)) (=> (tptp.is_bool B_2) (tptp.is_bool (tptp.hAPP_bool_bool B_1_1 B_2)))) (forall ((B_1_1 $$unsorted) (B_2 $$unsorted)) (tptp.is_bool (tptp.hAPP_H1927961489a_bool B_1_1 B_2))) _let_17 (forall ((Ga $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1753944735l_bool (tptp.hoare_472868247rivs_a Ga) tptp.bot_bo1687970473a_bool))) (forall ((Fun1_2 $$unsorted) (Com_2 $$unsorted) (Fun2_2 $$unsorted) (Fun1_1 $$unsorted) (Com_1 $$unsorted) (Fun2_1 $$unsorted)) (= (= (tptp.hoare_1050552211iple_a Fun1_2 Com_2 Fun2_2) (tptp.hoare_1050552211iple_a Fun1_1 Com_1 Fun2_1)) (and (= Fun1_2 Fun1_1) (= Com_2 Com_1) (= Fun2_2 Fun2_1)))) (forall ((Ga $$unsorted) (G_1 $$unsorted) (Ts $$unsorted)) (let ((_let_1 (tptp.hoare_472868247rivs_a Ga))) (=> (tptp.hBOOL (tptp.hAPP_f1753944735l_bool (tptp.hoare_472868247rivs_a G_1) Ts)) (=> (tptp.hBOOL (tptp.hAPP_f1753944735l_bool _let_1 G_1)) (tptp.hBOOL (tptp.hAPP_f1753944735l_bool _let_1 Ts)))))) (forall ((Ts $$unsorted) (Ga $$unsorted) (T $$unsorted)) (let ((_let_1 (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a T))) (let ((_let_2 (tptp.hoare_472868247rivs_a Ga))) (=> (tptp.hBOOL (tptp.hAPP_f1753944735l_bool _let_2 (tptp.hAPP_f1400872321a_bool _let_1 tptp.bot_bo1687970473a_bool))) (=> (tptp.hBOOL (tptp.hAPP_f1753944735l_bool _let_2 Ts)) (tptp.hBOOL (tptp.hAPP_f1753944735l_bool _let_2 (tptp.hAPP_f1400872321a_bool _let_1 Ts)))))))) (forall ((Ga $$unsorted) (Pa $$unsorted) (Ca $$unsorted) (Q_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.hoare_472868247rivs_a Ga))) (=> (=> (tptp.hBOOL C) (tptp.hBOOL (tptp.hAPP_f1753944735l_bool _let_1 (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a (tptp.hoare_1050552211iple_a Pa Ca Q_1)) tptp.bot_bo1687970473a_bool)))) (tptp.hBOOL (tptp.hAPP_f1753944735l_bool _let_1 (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a (tptp.hoare_1050552211iple_a (tptp.hAPP_b540892988e_bool (tptp.hAPP_f1824947087e_bool tptp.cOMBC_41962815e_bool (tptp.hAPP_f340725611e_bool (tptp.cOMBB_1348041619bool_a tptp.cOMBC_231445413l_bool) (tptp.hAPP_f1509969235l_bool (tptp.cOMBB_1355796797bool_a (tptp.cOMBB_188601460_state tptp.fconj)) Pa))) C) Ca Q_1)) tptp.bot_bo1687970473a_bool)))))) _let_16 (forall ((Q_1 $$unsorted) (Ga $$unsorted) (Pa $$unsorted) (Ca $$unsorted) (Q_3 $$unsorted)) (let ((_let_1 (tptp.hoare_472868247rivs_a Ga))) (=> (tptp.hBOOL (tptp.hAPP_f1753944735l_bool _let_1 (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a (tptp.hoare_1050552211iple_a Pa Ca Q_3)) tptp.bot_bo1687970473a_bool))) (=> (forall ((Z_1 $$unsorted) (S $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_a2036067514e_bool Q_3 Z_1) S)) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_a2036067514e_bool Q_1 Z_1) S)))) (tptp.hBOOL (tptp.hAPP_f1753944735l_bool _let_1 (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a (tptp.hoare_1050552211iple_a Pa Ca Q_1)) tptp.bot_bo1687970473a_bool))))))) (forall ((Pa $$unsorted) (Ga $$unsorted) (P_2 $$unsorted) (Ca $$unsorted) (Q_1 $$unsorted)) (let ((_let_1 (tptp.hoare_472868247rivs_a Ga))) (=> (tptp.hBOOL (tptp.hAPP_f1753944735l_bool _let_1 (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a (tptp.hoare_1050552211iple_a P_2 Ca Q_1)) tptp.bot_bo1687970473a_bool))) (=> (forall ((Z_1 $$unsorted) (S $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_a2036067514e_bool Pa Z_1) S)) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_a2036067514e_bool P_2 Z_1) S)))) (tptp.hBOOL (tptp.hAPP_f1753944735l_bool _let_1 (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a (tptp.hoare_1050552211iple_a Pa Ca Q_1)) tptp.bot_bo1687970473a_bool))))))) (forall ((Q_1 $$unsorted) (Pa $$unsorted) (Ga $$unsorted) (P_2 $$unsorted) (Ca $$unsorted) (Q_3 $$unsorted)) (let ((_let_1 (tptp.hoare_472868247rivs_a Ga))) (=> (tptp.hBOOL (tptp.hAPP_f1753944735l_bool _let_1 (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a (tptp.hoare_1050552211iple_a P_2 Ca Q_3)) tptp.bot_bo1687970473a_bool))) (=> (forall ((Z_1 $$unsorted) (S $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_a2036067514e_bool Pa Z_1) S)) (forall ((S_1 $$unsorted)) (=> (forall ((Z_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_a2036067514e_bool P_2 Z_2) S)) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_a2036067514e_bool Q_3 Z_2) S_1)))) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_a2036067514e_bool Q_1 Z_1) S_1)))))) (tptp.hBOOL (tptp.hAPP_f1753944735l_bool _let_1 (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a (tptp.hoare_1050552211iple_a Pa Ca Q_1)) tptp.bot_bo1687970473a_bool))))))) (forall ((A_3 $$unsorted) (Ba $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_H1926610125l_bool tptp.member564727580iple_a A_3))) (=> (tptp.hBOOL (tptp.hAPP_f1753944735l_bool _let_1 (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a Ba) A))) (=> (not (= A_3 Ba)) (tptp.hBOOL (tptp.hAPP_f1753944735l_bool _let_1 A)))))) (forall ((Ba $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_H1926610125l_bool tptp.member564727580iple_a A_3))) (=> (=> (not (tptp.hBOOL (tptp.hAPP_f1753944735l_bool _let_1 B_1))) (= A_3 Ba)) (tptp.hBOOL (tptp.hAPP_f1753944735l_bool _let_1 (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a Ba) B_1)))))) (forall ((A_3 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f1753944735l_bool (tptp.hAPP_H1926610125l_bool tptp.member564727580iple_a A_3) tptp.bot_bo1687970473a_bool)))) (forall ((A_3 $$unsorted)) (= (tptp.collec1266446174iple_a (tptp.hAPP_H562195827a_bool tptp.fequal1878252616iple_a A_3)) (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a A_3) tptp.bot_bo1687970473a_bool))) (forall ((A_3 $$unsorted)) (= (tptp.collec1266446174iple_a (tptp.hAPP_H562195827a_bool (tptp.hAPP_f1915402821a_bool tptp.cOMBC_2049287834a_bool tptp.fequal1878252616iple_a) A_3)) (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a A_3) tptp.bot_bo1687970473a_bool))) (forall ((Pa $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.collec1266446174iple_a (tptp.hAPP_f1400872321a_bool (tptp.hAPP_f1104866853a_bool tptp.cOMBS_213702372l_bool (tptp.hAPP_f13210641l_bool (tptp.cOMBB_633860163iple_a tptp.fconj) (tptp.hAPP_H562195827a_bool tptp.fequal1878252616iple_a A_3))) Pa)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_H1927961489a_bool Pa A_3)))) (and (=> _let_2 (= _let_1 (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a A_3) tptp.bot_bo1687970473a_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bo1687970473a_bool)))))) (forall ((Pa $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.collec1266446174iple_a (tptp.hAPP_f1400872321a_bool (tptp.hAPP_f1104866853a_bool tptp.cOMBS_213702372l_bool (tptp.hAPP_f13210641l_bool (tptp.cOMBB_633860163iple_a tptp.fconj) (tptp.hAPP_H562195827a_bool (tptp.hAPP_f1915402821a_bool tptp.cOMBC_2049287834a_bool tptp.fequal1878252616iple_a) A_3))) Pa)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_H1927961489a_bool Pa A_3)))) (and (=> _let_2 (= _let_1 (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a A_3) tptp.bot_bo1687970473a_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bo1687970473a_bool)))))) (forall ((A_3 $$unsorted) (A $$unsorted)) (=> (= A tptp.bot_bo1687970473a_bool) (not (tptp.hBOOL (tptp.hAPP_f1753944735l_bool (tptp.hAPP_H1926610125l_bool tptp.member564727580iple_a A_3) A))))) (forall ((Pa $$unsorted)) (= (= (tptp.collec1266446174iple_a Pa) tptp.bot_bo1687970473a_bool) (forall ((X_2 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_H1927961489a_bool Pa X_2)))))) (forall ((Ca $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f1753944735l_bool (tptp.hAPP_H1926610125l_bool tptp.member564727580iple_a Ca) tptp.bot_bo1687970473a_bool)))) (forall ((Pa $$unsorted)) (= (= tptp.bot_bo1687970473a_bool (tptp.collec1266446174iple_a Pa)) (forall ((X_2 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_H1927961489a_bool Pa X_2)))))) (forall ((A $$unsorted)) (= (exists ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1753944735l_bool (tptp.hAPP_H1926610125l_bool tptp.member564727580iple_a X_2) A))) (not (= A tptp.bot_bo1687970473a_bool)))) (forall ((A $$unsorted)) (= (forall ((X_2 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f1753944735l_bool (tptp.hAPP_H1926610125l_bool tptp.member564727580iple_a X_2) A)))) (= A tptp.bot_bo1687970473a_bool))) (= tptp.bot_bo1687970473a_bool (tptp.collec1266446174iple_a (tptp.cOMBK_1150238960iple_a tptp.fFalse))) (forall ((A_3 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1753944735l_bool (tptp.hAPP_H1926610125l_bool tptp.member564727580iple_a A_3) A)) (= (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a A_3) A) A))) (forall ((Ba $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_H1926610125l_bool tptp.member564727580iple_a A_3))) (=> (tptp.hBOOL (tptp.hAPP_f1753944735l_bool _let_1 B_1)) (tptp.hBOOL (tptp.hAPP_f1753944735l_bool _let_1 (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a Ba) B_1)))))) (forall ((B_1 $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a X_1))) (let ((_let_2 (tptp.hAPP_H1926610125l_bool tptp.member564727580iple_a X_1))) (=> (not (tptp.hBOOL (tptp.hAPP_f1753944735l_bool _let_2 A))) (=> (not (tptp.hBOOL (tptp.hAPP_f1753944735l_bool _let_2 B_1))) (= (= (tptp.hAPP_f1400872321a_bool _let_1 A) (tptp.hAPP_f1400872321a_bool _let_1 B_1)) (= A B_1))))))) (forall ((Y_2 $$unsorted) (A $$unsorted) (X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_H1927961489a_bool (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a Y_2) A) X_1)) (or (= Y_2 X_1) (tptp.hBOOL (tptp.hAPP_H1927961489a_bool A X_1))))) (forall ((A_3 $$unsorted) (Ba $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_H1926610125l_bool tptp.member564727580iple_a A_3))) (= (tptp.hBOOL (tptp.hAPP_f1753944735l_bool _let_1 (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a Ba) A))) (or (= A_3 Ba) (tptp.hBOOL (tptp.hAPP_f1753944735l_bool _let_1 A)))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a X_1))) (let ((_let_2 (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a Y_2))) (= (tptp.hAPP_f1400872321a_bool _let_1 (tptp.hAPP_f1400872321a_bool _let_2 A)) (tptp.hAPP_f1400872321a_bool _let_2 (tptp.hAPP_f1400872321a_bool _let_1 A)))))) (forall ((X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a X_1))) (let ((_let_2 (tptp.hAPP_f1400872321a_bool _let_1 A))) (= (tptp.hAPP_f1400872321a_bool _let_1 _let_2) _let_2)))) (forall ((A_3 $$unsorted) (Pa $$unsorted)) (= (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a A_3) (tptp.collec1266446174iple_a Pa)) (tptp.collec1266446174iple_a (tptp.hAPP_f1400872321a_bool (tptp.hAPP_f1104866853a_bool tptp.cOMBS_213702372l_bool (tptp.hAPP_f13210641l_bool (tptp.cOMBB_633860163iple_a tptp.fimplies) (tptp.hAPP_f1400872321a_bool (tptp.cOMBB_650444389iple_a tptp.fNot) (tptp.hAPP_H562195827a_bool (tptp.hAPP_f1915402821a_bool tptp.cOMBC_2049287834a_bool tptp.fequal1878252616iple_a) A_3)))) Pa)))) (forall ((A_3 $$unsorted) (B_1 $$unsorted)) (= (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a A_3) B_1) (tptp.collec1266446174iple_a (tptp.hAPP_f1400872321a_bool (tptp.hAPP_f1104866853a_bool tptp.cOMBS_213702372l_bool (tptp.hAPP_f13210641l_bool (tptp.cOMBB_633860163iple_a tptp.fdisj) (tptp.hAPP_H562195827a_bool (tptp.hAPP_f1915402821a_bool tptp.cOMBC_2049287834a_bool tptp.fequal1878252616iple_a) A_3))) (tptp.hAPP_f1400872321a_bool (tptp.hAPP_f945663555a_bool tptp.cOMBC_2067518550l_bool tptp.member564727580iple_a) B_1))))) (forall ((A_3 $$unsorted) (B_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1753944735l_bool (tptp.hAPP_H1926610125l_bool tptp.member564727580iple_a A_3) (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a A_3) B_1)))) (forall ((X_2 $$unsorted) (Xa $$unsorted)) (= (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a X_2) Xa) (tptp.collec1266446174iple_a (tptp.hAPP_f1400872321a_bool (tptp.hAPP_f1104866853a_bool tptp.cOMBS_213702372l_bool (tptp.hAPP_f13210641l_bool (tptp.cOMBB_633860163iple_a tptp.fdisj) (tptp.hAPP_H562195827a_bool (tptp.hAPP_f1915402821a_bool tptp.cOMBC_2049287834a_bool tptp.fequal1878252616iple_a) X_2))) (tptp.hAPP_f1400872321a_bool (tptp.hAPP_f945663555a_bool tptp.cOMBC_2067518550l_bool tptp.member564727580iple_a) Xa))))) (forall ((A_3 $$unsorted) (Ba $$unsorted)) (=> (= (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a A_3) tptp.bot_bo1687970473a_bool) (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a Ba) tptp.bot_bo1687970473a_bool)) (= A_3 Ba))) (forall ((Ba $$unsorted) (A_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1753944735l_bool (tptp.hAPP_H1926610125l_bool tptp.member564727580iple_a Ba) (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a A_3) tptp.bot_bo1687970473a_bool))) (= Ba A_3))) (forall ((A_3 $$unsorted) (Ba $$unsorted) (Ca $$unsorted) (D $$unsorted)) (= (= (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a A_3) (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a Ba) tptp.bot_bo1687970473a_bool)) (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a Ca) (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a D) tptp.bot_bo1687970473a_bool))) (or (and (= A_3 Ca) (= Ba D)) (and (= A_3 D) (= Ba Ca))))) (forall ((Ba $$unsorted) (A_3 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1753944735l_bool (tptp.hAPP_H1926610125l_bool tptp.member564727580iple_a Ba) (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a A_3) tptp.bot_bo1687970473a_bool))) (= Ba A_3))) (forall ((A_3 $$unsorted) (A $$unsorted)) (not (= (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a A_3) A) tptp.bot_bo1687970473a_bool))) (forall ((A_3 $$unsorted) (A $$unsorted)) (not (= tptp.bot_bo1687970473a_bool (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a A_3) A)))) (forall ((X_1 $$unsorted)) (= (tptp.hAPP_f1826273671iple_a tptp.the_el287271400iple_a (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a X_1) tptp.bot_bo1687970473a_bool)) X_1)) (forall ((X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_H1927961489a_bool tptp.bot_bo1687970473a_bool X_1)) (tptp.hBOOL tptp.bot_bot_bool))) (forall ((X_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_H1927961489a_bool tptp.bot_bo1687970473a_bool X_2)) (tptp.hBOOL tptp.bot_bot_bool))) (forall ((Ga $$unsorted) (Pa $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1753944735l_bool (tptp.hoare_472868247rivs_a Ga) (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a (tptp.hoare_1050552211iple_a Pa tptp.skip Pa)) tptp.bot_bo1687970473a_bool)))) (forall ((D $$unsorted) (R_1 $$unsorted) (Ga $$unsorted) (Pa $$unsorted) (Ca $$unsorted) (Q_1 $$unsorted)) (let ((_let_1 (tptp.hoare_472868247rivs_a Ga))) (=> (tptp.hBOOL (tptp.hAPP_f1753944735l_bool _let_1 (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a (tptp.hoare_1050552211iple_a Pa Ca Q_1)) tptp.bot_bo1687970473a_bool))) (=> (tptp.hBOOL (tptp.hAPP_f1753944735l_bool _let_1 (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a (tptp.hoare_1050552211iple_a Q_1 D R_1)) tptp.bot_bo1687970473a_bool))) (tptp.hBOOL (tptp.hAPP_f1753944735l_bool _let_1 (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a (tptp.hoare_1050552211iple_a Pa (tptp.semi Ca D) R_1)) tptp.bot_bo1687970473a_bool))))))) (forall ((Y_2 $$unsorted)) (not (forall ((Fun1 $$unsorted) (Com $$unsorted) (Fun2 $$unsorted)) (not (= Y_2 (tptp.hoare_1050552211iple_a Fun1 Com Fun2)))))) (forall ((X_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1753944735l_bool (tptp.hAPP_H1926610125l_bool tptp.member564727580iple_a X_1) A)) (not (forall ((B $$unsorted)) (=> (= A (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a X_1) B)) (tptp.hBOOL (tptp.hAPP_f1753944735l_bool (tptp.hAPP_H1926610125l_bool tptp.member564727580iple_a X_1) B))))))) (forall ((Com1_2 $$unsorted) (Com2_2 $$unsorted)) (not (= (tptp.semi Com1_2 Com2_2) tptp.skip))) (forall ((Com1_2 $$unsorted) (Com2_2 $$unsorted)) (not (= tptp.skip (tptp.semi Com1_2 Com2_2)))) (forall ((X_3 $$unsorted)) (= (tptp.hAPP_f1826273671iple_a tptp.the_el287271400iple_a X_3) (tptp.hAPP_f1826273671iple_a tptp.the_Ho1745054714iple_a (tptp.hAPP_f1447988451a_bool (tptp.cOMBB_545742339iple_a (tptp.hAPP_f1945881407l_bool tptp.fequal1765155200a_bool X_3)) (tptp.hAPP_f1170963427a_bool (tptp.hAPP_f1874567875a_bool tptp.cOMBC_1089176504a_bool tptp.insert1871499715iple_a) tptp.bot_bo1687970473a_bool))))) (forall ((A_3 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1753944735l_bool (tptp.hAPP_H1926610125l_bool tptp.member564727580iple_a A_3) A)) (exists ((B $$unsorted)) (and (= A (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a A_3) B)) (not (tptp.hBOOL (tptp.hAPP_f1753944735l_bool (tptp.hAPP_H1926610125l_bool tptp.member564727580iple_a A_3) B))))))) (forall ((Com1_1 $$unsorted) (Com2_1 $$unsorted) (Com1 $$unsorted) (Com2 $$unsorted)) (= (= (tptp.semi Com1_1 Com2_1) (tptp.semi Com1 Com2)) (and (= Com1_1 Com1) (= Com2_1 Com2)))) (forall ((X_1 $$unsorted)) (= (tptp.hAPP_f1826273671iple_a tptp.the_Ho1745054714iple_a (tptp.hAPP_H562195827a_bool tptp.fequal1878252616iple_a X_1)) X_1)) (forall ((A_3 $$unsorted)) (= (tptp.hAPP_f1826273671iple_a tptp.the_Ho1745054714iple_a (tptp.hAPP_H562195827a_bool (tptp.hAPP_f1915402821a_bool tptp.cOMBC_2049287834a_bool tptp.fequal1878252616iple_a) A_3)) A_3)) (forall ((X_1 $$unsorted) (Y_2 $$unsorted) (Pa $$unsorted)) (let ((_let_1 (tptp.hAPP_f1915402821a_bool tptp.cOMBC_2049287834a_bool tptp.fequal1878252616iple_a))) (let ((_let_2 (tptp.hAPP_f1826273671iple_a tptp.the_Ho1745054714iple_a (tptp.hAPP_f1400872321a_bool (tptp.hAPP_f1104866853a_bool tptp.cOMBS_213702372l_bool (tptp.hAPP_f13210641l_bool (tptp.cOMBB_633860163iple_a tptp.fconj) (tptp.hAPP_f1400872321a_bool (tptp.cOMBB_650444389iple_a (tptp.hAPP_b589554111l_bool tptp.fimplies Pa)) (tptp.hAPP_H562195827a_bool _let_1 X_1)))) (tptp.hAPP_f1400872321a_bool (tptp.cOMBB_650444389iple_a (tptp.hAPP_b589554111l_bool tptp.fimplies (tptp.hAPP_bool_bool tptp.fNot Pa))) (tptp.hAPP_H562195827a_bool _let_1 Y_2)))))) (let ((_let_3 (tptp.hBOOL Pa))) (and (=> _let_3 (= X_1 _let_2)) (=> (not _let_3) (= Y_2 _let_2))))))) (forall ((A $$unsorted)) (=> (forall ((Y_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f1753944735l_bool (tptp.hAPP_H1926610125l_bool tptp.member564727580iple_a Y_1) A)))) (= A tptp.bot_bo1687970473a_bool))) (forall ((Pa $$unsorted) (A_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_H1927961489a_bool Pa A_3)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_H1927961489a_bool Pa X_2)) (= X_2 A_3))) (= (tptp.hAPP_f1826273671iple_a tptp.the_Ho1745054714iple_a Pa) A_3)))) (forall ((Pa $$unsorted) (A_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_H1927961489a_bool Pa A_3)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_H1927961489a_bool Pa X_2)) (= X_2 A_3))) (tptp.hBOOL (tptp.hAPP_H1927961489a_bool Pa (tptp.hAPP_f1826273671iple_a tptp.the_Ho1745054714iple_a Pa)))))) (forall ((A_3 $$unsorted) (Pa $$unsorted)) (=> (exists ((X_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_H1927961489a_bool Pa X_2)) (forall ((Y_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_H1927961489a_bool Pa Y_1)) (= Y_1 X_2))))) (=> (tptp.hBOOL (tptp.hAPP_H1927961489a_bool Pa A_3)) (= (tptp.hAPP_f1826273671iple_a tptp.the_Ho1745054714iple_a Pa) A_3)))) (forall ((Pa $$unsorted)) (=> (exists ((X_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_H1927961489a_bool Pa X_2)) (forall ((Y_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_H1927961489a_bool Pa Y_1)) (= Y_1 X_2))))) (tptp.hBOOL (tptp.hAPP_H1927961489a_bool Pa (tptp.hAPP_f1826273671iple_a tptp.the_Ho1745054714iple_a Pa))))) (forall ((Q_1 $$unsorted) (Ga $$unsorted) (Ca $$unsorted) (Pa $$unsorted)) (=> (forall ((Z_1 $$unsorted) (S $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_a2036067514e_bool Pa Z_1) S)) (exists ((P_1 $$unsorted) (Q_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f1753944735l_bool (tptp.hoare_472868247rivs_a Ga) (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a (tptp.hoare_1050552211iple_a P_1 Ca Q_2)) tptp.bot_bo1687970473a_bool))) (forall ((S_1 $$unsorted)) (=> (forall ((Z_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_a2036067514e_bool P_1 Z_2) S)) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_a2036067514e_bool Q_2 Z_2) S_1)))) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_a2036067514e_bool Q_1 Z_1) S_1)))))))) (tptp.hBOOL (tptp.hAPP_f1753944735l_bool (tptp.hoare_472868247rivs_a Ga) (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a (tptp.hoare_1050552211iple_a Pa Ca Q_1)) tptp.bot_bo1687970473a_bool))))) (forall ((A $$unsorted)) (= (not (= A tptp.bot_bo1687970473a_bool)) (exists ((X_2 $$unsorted) (B $$unsorted)) (and (= A (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a X_2) B)) (not (tptp.hBOOL (tptp.hAPP_f1753944735l_bool (tptp.hAPP_H1926610125l_bool tptp.member564727580iple_a X_2) B))))))) (forall ((F_1 $$unsorted) (A_3 $$unsorted) (Ba $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_H1927961489a_bool (tptp.finite388748825iple_a F_1 (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a A_3) tptp.bot_bo1687970473a_bool)) Ba)) (= A_3 Ba))) (forall ((X_1 $$unsorted) (F_1 $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.finite520909254iple_a F_1 F)) (= (tptp.hAPP_f1826273671iple_a F (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a X_1) tptp.bot_bo1687970473a_bool)) X_1))) (forall ((X_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_H1927961489a_bool tptp.bot_bo1687970473a_bool X_2)) (tptp.hBOOL (tptp.hAPP_f1753944735l_bool (tptp.hAPP_H1926610125l_bool tptp.member564727580iple_a X_2) tptp.bot_bo1687970473a_bool)))) (forall ((F_1 $$unsorted) (X_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_H1927961489a_bool (tptp.finite388748825iple_a F_1 tptp.bot_bo1687970473a_bool) X_1)))) (forall ((F_1 $$unsorted) (A $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_H1927961489a_bool (tptp.finite388748825iple_a F_1 A) X_1)) (not (= A tptp.bot_bo1687970473a_bool)))) (forall ((F_1 $$unsorted) (A_3 $$unsorted) (A $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_H1927961489a_bool (tptp.finite1734202118iple_a F_1 A_3 A) X_1)) (=> (not (tptp.hBOOL (tptp.hAPP_f1753944735l_bool (tptp.hAPP_H1926610125l_bool tptp.member564727580iple_a A_3) A))) (tptp.hBOOL (tptp.hAPP_H1927961489a_bool (tptp.finite388748825iple_a F_1 (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a A_3) A)) X_1))))) (forall ((X_1 $$unsorted) (A $$unsorted) (F_1 $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.finite520909254iple_a F_1 F)) (=> (tptp.hBOOL (tptp.hAPP_f1753944735l_bool tptp.finite506133020iple_a A)) (=> (not (tptp.hBOOL (tptp.hAPP_f1753944735l_bool (tptp.hAPP_H1926610125l_bool tptp.member564727580iple_a X_1) A))) (=> (not (= A tptp.bot_bo1687970473a_bool)) (= (tptp.hAPP_f1826273671iple_a F (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a X_1) A)) (tptp.hAPP_H401672213iple_a (tptp.hAPP_H568064713iple_a F_1 X_1) (tptp.hAPP_f1826273671iple_a F A)))))))) (forall ((F_1 $$unsorted) (A $$unsorted)) (= (tptp.hAPP_f1826273671iple_a (tptp.finite233325225iple_a F_1) A) (tptp.hAPP_f1826273671iple_a tptp.the_Ho1745054714iple_a (tptp.finite388748825iple_a F_1 A)))) (forall ((Q_1 $$unsorted) (Pa $$unsorted)) (=> (or (tptp.hBOOL (tptp.hAPP_f1753944735l_bool tptp.finite506133020iple_a (tptp.collec1266446174iple_a Pa))) (tptp.hBOOL (tptp.hAPP_f1753944735l_bool tptp.finite506133020iple_a (tptp.collec1266446174iple_a Q_1)))) (tptp.hBOOL (tptp.hAPP_f1753944735l_bool tptp.finite506133020iple_a (tptp.collec1266446174iple_a (tptp.hAPP_f1400872321a_bool (tptp.hAPP_f1104866853a_bool tptp.cOMBS_213702372l_bool (tptp.hAPP_f13210641l_bool (tptp.cOMBB_633860163iple_a tptp.fconj) Pa)) Q_1)))))) _let_15 (forall ((A_3 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1753944735l_bool tptp.finite506133020iple_a A)) (tptp.hBOOL (tptp.hAPP_f1753944735l_bool tptp.finite506133020iple_a (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a A_3) A))))) (forall ((X_1 $$unsorted) (A $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1753944735l_bool (tptp.hAPP_H1926610125l_bool tptp.member564727580iple_a X_1) A)) (tptp.hBOOL (tptp.hAPP_H1927961489a_bool A X_1)))) (forall ((Pa $$unsorted)) (= (tptp.collec1266446174iple_a Pa) Pa)) (forall ((A $$unsorted) (F_1 $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.finite520909254iple_a F_1 F)) (=> (tptp.hBOOL (tptp.hAPP_f1753944735l_bool tptp.finite506133020iple_a A)) (= (tptp.hAPP_f1826273671iple_a F A) (tptp.hAPP_f1826273671iple_a (tptp.finite233325225iple_a F_1) A))))) (forall ((F_1 $$unsorted) (Z $$unsorted)) (tptp.hBOOL (tptp.hAPP_H1927961489a_bool (tptp.finite1734202118iple_a F_1 Z tptp.bot_bo1687970473a_bool) Z))) (forall ((F_1 $$unsorted) (Z $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_H1927961489a_bool (tptp.finite1734202118iple_a F_1 Z tptp.bot_bo1687970473a_bool) X_1)) (= X_1 Z))) (forall ((F_1 $$unsorted) (Z $$unsorted) (Y_2 $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_f1753944735l_bool (tptp.hAPP_H1926610125l_bool tptp.member564727580iple_a X_1) A))) (=> (tptp.hBOOL (tptp.hAPP_H1927961489a_bool (tptp.finite1734202118iple_a F_1 Z A) Y_2)) (tptp.hBOOL (tptp.hAPP_H1927961489a_bool (tptp.finite1734202118iple_a F_1 Z (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a X_1) A)) (tptp.hAPP_H401672213iple_a (tptp.hAPP_H568064713iple_a F_1 X_1) Y_2)))))) (forall ((Pa $$unsorted) (Q_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1753944735l_bool tptp.finite506133020iple_a (tptp.collec1266446174iple_a (tptp.hAPP_f1400872321a_bool (tptp.hAPP_f1104866853a_bool tptp.cOMBS_213702372l_bool (tptp.hAPP_f13210641l_bool (tptp.cOMBB_633860163iple_a tptp.fdisj) Pa)) Q_1)))) (and (tptp.hBOOL (tptp.hAPP_f1753944735l_bool tptp.finite506133020iple_a (tptp.collec1266446174iple_a Pa))) (tptp.hBOOL (tptp.hAPP_f1753944735l_bool tptp.finite506133020iple_a (tptp.collec1266446174iple_a Q_1)))))) (forall ((A_3 $$unsorted) (A $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1753944735l_bool tptp.finite506133020iple_a (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a A_3) A))) (tptp.hBOOL (tptp.hAPP_f1753944735l_bool tptp.finite506133020iple_a A)))) (forall ((A_3 $$unsorted) (G $$unsorted) (F_1 $$unsorted)) (=> (= G (tptp.finite233325225iple_a F_1)) (= (tptp.hAPP_f1826273671iple_a G (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a A_3) tptp.bot_bo1687970473a_bool)) A_3))) (forall ((F_1 $$unsorted) (A_3 $$unsorted)) (= (tptp.hAPP_f1826273671iple_a (tptp.finite233325225iple_a F_1) (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a A_3) tptp.bot_bo1687970473a_bool)) A_3)) (forall ((A $$unsorted) (F_1 $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.finite520909254iple_a F_1 F)) (=> (tptp.hBOOL (tptp.hAPP_f1753944735l_bool tptp.finite506133020iple_a A)) (=> (not (= A tptp.bot_bo1687970473a_bool)) (=> (forall ((X_2 $$unsorted) (Y_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1753944735l_bool (tptp.hAPP_H1926610125l_bool tptp.member564727580iple_a (tptp.hAPP_H401672213iple_a (tptp.hAPP_H568064713iple_a F_1 X_2) Y_1)) (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a X_2) (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a Y_1) tptp.bot_bo1687970473a_bool))))) (tptp.hBOOL (tptp.hAPP_f1753944735l_bool (tptp.hAPP_H1926610125l_bool tptp.member564727580iple_a (tptp.hAPP_f1826273671iple_a F A)) A))))))) (forall ((F_1 $$unsorted) (A_3 $$unsorted) (X_3 $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_H1927961489a_bool (tptp.finite388748825iple_a F_1 (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a A_3) X_3)) X_1)) (not (forall ((A_2 $$unsorted) (A_1 $$unsorted)) (=> (= (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a A_3) X_3) (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a A_2) A_1)) (=> (tptp.hBOOL (tptp.hAPP_H1927961489a_bool (tptp.finite1734202118iple_a F_1 A_2 A_1) X_1)) (tptp.hBOOL (tptp.hAPP_f1753944735l_bool (tptp.hAPP_H1926610125l_bool tptp.member564727580iple_a A_2) A_1)))))))) (forall ((F_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1753944735l_bool tptp.finite506133020iple_a A)) (=> (not (= A tptp.bot_bo1687970473a_bool)) (exists ((X1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_H1927961489a_bool (tptp.finite388748825iple_a F_1 A) X1)))))) (forall ((Pa $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1753944735l_bool tptp.finite506133020iple_a F)) (=> (tptp.hBOOL (tptp.hAPP_f1753944735l_bool Pa tptp.bot_bo1687970473a_bool)) (=> (forall ((X_2 $$unsorted) (F_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1753944735l_bool tptp.finite506133020iple_a F_2)) (=> (not (tptp.hBOOL (tptp.hAPP_f1753944735l_bool (tptp.hAPP_H1926610125l_bool tptp.member564727580iple_a X_2) F_2))) (=> (tptp.hBOOL (tptp.hAPP_f1753944735l_bool Pa F_2)) (tptp.hBOOL (tptp.hAPP_f1753944735l_bool Pa (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a X_2) F_2))))))) (tptp.hBOOL (tptp.hAPP_f1753944735l_bool Pa F)))))) (forall ((A_3 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1753944735l_bool tptp.finite506133020iple_a A_3)) (or (= A_3 tptp.bot_bo1687970473a_bool) (exists ((A_1 $$unsorted) (A_2 $$unsorted)) (and (= A_3 (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a A_2) A_1)) (tptp.hBOOL (tptp.hAPP_f1753944735l_bool tptp.finite506133020iple_a A_1))))))) (forall ((F_1 $$unsorted) (Z $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1753944735l_bool tptp.finite506133020iple_a A)) (exists ((X1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_H1927961489a_bool (tptp.finite1734202118iple_a F_1 Z A) X1))))) (forall ((F_1 $$unsorted) (A1 $$unsorted) (A2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_H1927961489a_bool (tptp.finite388748825iple_a F_1 A1) A2)) (exists ((A_2 $$unsorted) (A_1 $$unsorted) (X_2 $$unsorted)) (and (= A1 (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a A_2) A_1)) (= A2 X_2) (tptp.hBOOL (tptp.hAPP_H1927961489a_bool (tptp.finite1734202118iple_a F_1 A_2 A_1) X_2)) (not (tptp.hBOOL (tptp.hAPP_f1753944735l_bool (tptp.hAPP_H1926610125l_bool tptp.member564727580iple_a A_2) A_1))))))) (forall ((F_1 $$unsorted) (Z $$unsorted) (A1 $$unsorted) (A2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_H1927961489a_bool (tptp.finite1734202118iple_a F_1 Z A1) A2)) (or (and (= A1 tptp.bot_bo1687970473a_bool) (= A2 Z)) (exists ((X_2 $$unsorted) (A_1 $$unsorted) (Y_1 $$unsorted)) (and (= A1 (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a X_2) A_1)) (= A2 (tptp.hAPP_H401672213iple_a (tptp.hAPP_H568064713iple_a F_1 X_2) Y_1)) (not (tptp.hBOOL (tptp.hAPP_f1753944735l_bool (tptp.hAPP_H1926610125l_bool tptp.member564727580iple_a X_2) A_1))) (tptp.hBOOL (tptp.hAPP_H1927961489a_bool (tptp.finite1734202118iple_a F_1 Z A_1) Y_1))))))) (forall ((X_1 $$unsorted) (A $$unsorted) (F_1 $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.finite1948426435iple_a F_1 F)) (=> (tptp.hBOOL (tptp.hAPP_f1753944735l_bool tptp.finite506133020iple_a A)) (=> (not (= A tptp.bot_bo1687970473a_bool)) (= (tptp.hAPP_f1826273671iple_a F (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a X_1) A)) (tptp.hAPP_H401672213iple_a (tptp.hAPP_H568064713iple_a F_1 X_1) (tptp.hAPP_f1826273671iple_a F A))))))) (forall ((Pa $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1753944735l_bool tptp.finite506133020iple_a F)) (=> (not (= F tptp.bot_bo1687970473a_bool)) (=> (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1753944735l_bool Pa (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a X_2) tptp.bot_bo1687970473a_bool)))) (=> (forall ((X_2 $$unsorted) (F_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1753944735l_bool tptp.finite506133020iple_a F_2)) (=> (not (= F_2 tptp.bot_bo1687970473a_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_f1753944735l_bool (tptp.hAPP_H1926610125l_bool tptp.member564727580iple_a X_2) F_2))) (=> (tptp.hBOOL (tptp.hAPP_f1753944735l_bool Pa F_2)) (tptp.hBOOL (tptp.hAPP_f1753944735l_bool Pa (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool tptp.insert1871499715iple_a X_2) F_2)))))))) (tptp.hBOOL (tptp.hAPP_f1753944735l_bool Pa F))))))) (forall ((X_1 $$unsorted) (F_1 $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.finite1948426435iple_a F_1 F)) (= (tptp.hAPP_H401672213iple_a (tptp.hAPP_H568064713iple_a F_1 X_1) X_1) X_1))) (forall ((X_1 $$unsorted) (A $$unsorted) (F_1 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.hAPP_f1826273671iple_a F A))) (=> (tptp.hBOOL (tptp.finite1948426435iple_a F_1 F)) (=> (tptp.hBOOL (tptp.hAPP_f1753944735l_bool tptp.finite506133020iple_a A)) (=> (tptp.hBOOL (tptp.hAPP_f1753944735l_bool (tptp.hAPP_H1926610125l_bool tptp.member564727580iple_a X_1) A)) (= (tptp.hAPP_H401672213iple_a (tptp.hAPP_H568064713iple_a F_1 X_1) _let_1) _let_1)))))) (forall ((P $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP_bool_bool tptp.fNot P))) (not (tptp.hBOOL P)))) (forall ((P $$unsorted)) (or (tptp.hBOOL P) (tptp.hBOOL (tptp.hAPP_bool_bool tptp.fNot P)))) (forall ((Q $$unsorted) (P $$unsorted)) (or (not (tptp.hBOOL P)) (not (tptp.hBOOL Q)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fconj P) Q)))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fconj P) Q))) (tptp.hBOOL P))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fconj P) Q))) (tptp.hBOOL Q))) (forall ((Q $$unsorted) (P $$unsorted)) (or (not (tptp.hBOOL P)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fdisj P) Q)))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL Q)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fdisj P) Q)))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fdisj P) Q))) (tptp.hBOOL P) (tptp.hBOOL Q))) _let_13 _let_11 (forall ((Q $$unsorted) (P $$unsorted)) (or (tptp.hBOOL P) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fimplies P) Q)))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL Q)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fimplies P) Q)))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fimplies P) Q))) (not (tptp.hBOOL P)) (tptp.hBOOL Q))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool tptp.fequal_state X) Y))) (= X Y))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool tptp.fequal_state X) Y)))) _let_10 _let_9 (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_state_bool (tptp.hAPP_f1759915619e_bool (tptp.cOMBB_160679318_state P) Q) R) (tptp.hAPP_bool_bool P (tptp.hAPP_state_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_state_bool (tptp.hAPP_b2019457360e_bool (tptp.hAPP_f167292325e_bool tptp.cOMBC_231445413l_bool P) Q) R) (tptp.hAPP_bool_bool (tptp.hAPP_s58564346l_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_state_bool (tptp.hAPP_f1759915619e_bool (tptp.hAPP_f644196280e_bool tptp.cOMBS_1378840469l_bool P) Q) R) (tptp.hAPP_bool_bool (tptp.hAPP_s58564346l_bool P R) (tptp.hAPP_state_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool (tptp.hAPP_f817621513e_bool tptp.cOMBC_2027030106e_bool P) Q) R) (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool P R) Q))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP_H1927961489a_bool (tptp.hAPP_H562195827a_bool tptp.fequal1878252616iple_a X) Y))) (= X Y))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_H1927961489a_bool (tptp.hAPP_H562195827a_bool tptp.fequal1878252616iple_a X) Y)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_a2036067514e_bool (tptp.hAPP_b540892988e_bool (tptp.hAPP_f1824947087e_bool tptp.cOMBC_41962815e_bool P) Q) R) (tptp.hAPP_b2019457360e_bool (tptp.hAPP_a723219176e_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted)) (=> (tptp.is_bool P) (= (tptp.hAPP_H1927961489a_bool (tptp.cOMBK_1150238960iple_a P) Q) P))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_s58564346l_bool (tptp.hAPP_f1259673775l_bool (tptp.cOMBB_188601460_state P) Q) R) (tptp.hAPP_b589554111l_bool P (tptp.hAPP_state_bool Q R)))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP_f1753944735l_bool (tptp.hAPP_f1945881407l_bool tptp.fequal1765155200a_bool X) Y))) (= X Y))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_f1753944735l_bool (tptp.hAPP_f1945881407l_bool tptp.fequal1765155200a_bool X) Y)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H1927961489a_bool (tptp.hAPP_f1400872321a_bool (tptp.cOMBB_650444389iple_a P) Q) R) (tptp.hAPP_bool_bool P (tptp.hAPP_H1927961489a_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H1927961489a_bool (tptp.hAPP_f1400872321a_bool (tptp.hAPP_f1104866853a_bool tptp.cOMBS_213702372l_bool P) Q) R) (tptp.hAPP_bool_bool (tptp.hAPP_H1877746411l_bool P R) (tptp.hAPP_H1927961489a_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_a2036067514e_bool (tptp.hAPP_f762886889e_bool (tptp.hAPP_f1261923407e_bool tptp.cOMBC_892787026e_bool P) Q) R) (tptp.hAPP_f1759915619e_bool (tptp.hAPP_a1200519163e_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H1877746411l_bool (tptp.hAPP_f13210641l_bool (tptp.cOMBB_633860163iple_a P) Q) R) (tptp.hAPP_b589554111l_bool P (tptp.hAPP_H1927961489a_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_a849909144l_bool (tptp.hAPP_f1509969235l_bool (tptp.cOMBB_1355796797bool_a P) Q) R) (tptp.hAPP_f1259673775l_bool P (tptp.hAPP_a2036067514e_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H1927961489a_bool (tptp.hAPP_H562195827a_bool (tptp.hAPP_f1915402821a_bool tptp.cOMBC_2049287834a_bool P) Q) R) (tptp.hAPP_H1927961489a_bool (tptp.hAPP_H562195827a_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_a723219176e_bool (tptp.hAPP_f340725611e_bool (tptp.cOMBB_1348041619bool_a P) Q) R) (tptp.hAPP_f167292325e_bool P (tptp.hAPP_a849909144l_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H1927961489a_bool (tptp.hAPP_f1447988451a_bool (tptp.cOMBB_545742339iple_a P) Q) R) (tptp.hAPP_f1753944735l_bool P (tptp.hAPP_H562195827a_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H1927961489a_bool (tptp.hAPP_f1400872321a_bool (tptp.hAPP_f945663555a_bool tptp.cOMBC_2067518550l_bool P) Q) R) (tptp.hAPP_f1753944735l_bool (tptp.hAPP_H1926610125l_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_a1200519163e_bool (tptp.hAPP_f963367678e_bool (tptp.cOMBB_145932198bool_a P) Q) R) (tptp.hAPP_f644196280e_bool P (tptp.hAPP_a849909144l_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H562195827a_bool (tptp.hAPP_f1170963427a_bool (tptp.hAPP_f1874567875a_bool tptp.cOMBC_1089176504a_bool P) Q) R) (tptp.hAPP_f1400872321a_bool (tptp.hAPP_H1816261935a_bool P R) Q))) _let_8 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.58/0.79 )
% 0.58/0.79 % SZS output end Proof for SWW470+1
% 0.58/0.79 % cvc5---1.0.5 exiting
% 0.58/0.79 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------