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 : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 1 00:20:55 EDT 2023
% Result : Theorem 0.23s 0.82s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SWW470_1 : TPTP v8.1.2. Released v5.3.0.
% 0.00/0.16 % Command : do_cvc5 %s %d
% 0.16/0.36 % Computer : n014.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Sun Aug 27 22:35:46 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.23/0.52 %----Proving TF0_NAR, FOF, or CNF
% 0.23/0.82 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.9Nb3SIp7xv/cvc5---1.0.5_4435.p...
% 0.23/0.82 ------- get file name : TPTP file name is SWW470_1
% 0.23/0.82 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_4435.smt2...
% 0.23/0.82 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.23/0.82 % SZS status Theorem for SWW470_1
% 0.23/0.82 % SZS output start Proof for SWW470_1
% 0.23/0.82 (
% 0.23/0.82 (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.hoare_1617968510rivs_a tptp.g))) (let ((_let_5 (tptp.hBOOL (tptp.hAPP_f1454306822l_bool _let_4 (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a (tptp.hoare_1652181356iple_a _let_3 tptp.c _let_1)) tptp.bot_bo1208640912a_bool))))) (let ((_let_6 (not _let_5))) (let ((_let_7 (forall ((P tptp.fun_state_bool) (Q tptp.x_a)) (= (tptp.hAPP_a2036067514e_bool (tptp.cOMBK_1458035955bool_a P) Q) P)))) (let ((_let_8 (forall ((P tptp.bool) (Q tptp.state)) (= (tptp.hAPP_state_bool (tptp.cOMBK_bool_state P) Q) P)))) (let ((_let_9 (tptp.hBOOL tptp.fFalse))) (let ((_let_10 (not _let_9))) (let ((_let_11 (forall ((Ga tptp.fun_Ho1877127206a_bool) (Ca tptp.com) (Q_1 tptp.fun_a_fun_state_bool) (Pa tptp.fun_a_fun_state_bool)) (=> (forall ((Z_1 tptp.x_a) (S tptp.state)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_a2036067514e_bool Pa Z_1) S)) (tptp.hBOOL (tptp.hAPP_f1454306822l_bool (tptp.hoare_1617968510rivs_a Ga) (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a (tptp.hoare_1652181356iple_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_bo1208640912a_bool))))) (tptp.hBOOL (tptp.hAPP_f1454306822l_bool (tptp.hoare_1617968510rivs_a Ga) (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a (tptp.hoare_1652181356iple_a Pa Ca Q_1)) tptp.bot_bo1208640912a_bool))))))) (let ((_let_12 (tptp.hAPP_a2036067514e_bool _let_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_13 (tptp.hBOOL (tptp.hAPP_state_bool _let_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12)))) (let ((_let_14 (= _let_2 _let_12))) (let ((_let_15 (= tptp.fFalse (tptp.hAPP_state_bool _let_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12)))) (let ((_let_16 (ASSUME :args (_let_10)))) (let ((_let_17 (not _let_13))) (let ((_let_18 (or _let_17 (tptp.hBOOL (tptp.hAPP_f1454306822l_bool _let_4 (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a (tptp.hoare_1652181356iple_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_bo1208640912a_bool)))))) (let ((_let_19 (forall ((Z_1 tptp.x_a) (S tptp.state)) (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_f1454306822l_bool (tptp.hoare_1617968510rivs_a tptp.g) (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a (tptp.hoare_1652181356iple_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_bo1208640912a_bool))))))) (let ((_let_20 (not _let_18))) (let ((_let_21 (not _let_19))) (let ((_let_22 (or _let_21 _let_5))) (let ((_let_23 (forall ((Ga tptp.fun_Ho1877127206a_bool) (Ca tptp.com) (Q_1 tptp.fun_a_fun_state_bool) (Pa tptp.fun_a_fun_state_bool)) (or (not (forall ((Z_1 tptp.x_a) (S tptp.state)) (or (not (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_a2036067514e_bool Pa Z_1) S))) (tptp.hBOOL (tptp.hAPP_f1454306822l_bool (tptp.hoare_1617968510rivs_a Ga) (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a (tptp.hoare_1652181356iple_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_bo1208640912a_bool)))))) (tptp.hBOOL (tptp.hAPP_f1454306822l_bool (tptp.hoare_1617968510rivs_a Ga) (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a (tptp.hoare_1652181356iple_a Pa Ca Q_1)) tptp.bot_bo1208640912a_bool))))))) (let ((_let_24 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_25 (or))) (let ((_let_26 (_let_21))) (let ((_let_27 (forall ((P tptp.fun_state_bool) (Q tptp.x_a)) (= P (tptp.hAPP_a2036067514e_bool (tptp.cOMBK_1458035955bool_a P) Q))))) (let ((_let_28 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_29 (forall ((P tptp.bool) (Q tptp.state)) (= P (tptp.hAPP_state_bool (tptp.cOMBK_bool_state P) Q))))) (let ((_let_30 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_31 (ASSUME :args (_let_13)))) (let ((_let_32 (ASSUME :args (_let_14)))) (let ((_let_33 (ASSUME :args (_let_15)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_31 _let_32 _let_33 _let_16) :args (_let_10 _let_13 _let_14 _let_15)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_16)) (CONG (TRANS (SYMM (SYMM _let_33)) (CONG (SYMM (SYMM _let_32)) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12)) :args (APPLY_UF tptp.hAPP_state_bool))) :args (APPLY_UF tptp.hBOOL)) (TRUE_INTRO _let_31))) :args (_let_13 _let_14 _let_15 _let_10)) :args ((not (and _let_10 _let_13 _let_14 _let_15)) SB_LITERAL))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_10) _let_9))) (REFL :args (_let_17)) (REFL :args ((not _let_14))) (REFL :args ((not _let_15))) :args _let_25)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_30 :args (tptp.fFalse SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP_state_bool (tptp.cOMBK_bool_state P) Q)))) :args (_let_29))) _let_30 :args (_let_15 false _let_29)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_28 :args (_let_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP_a2036067514e_bool (tptp.cOMBK_1458035955bool_a P) Q)))) :args (_let_27))) _let_28 :args (_let_14 false _let_27)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_18 0)) (CONG (REFL :args (_let_18)) (MACRO_SR_PRED_INTRO :args ((= (not _let_17) _let_13))) :args _let_25)) :args ((or _let_13 _let_18))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_26)) :args _let_26)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_21) _let_19))) (REFL :args (_let_20)) :args _let_25)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_22)) :args ((or _let_5 _let_21 (not _let_22)))) (ASSUME :args (_let_6)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_24 :args (tptp.g tptp.c _let_1 _let_3 QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP_f1454306822l_bool (tptp.hoare_1617968510rivs_a Ga) (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a (tptp.hoare_1652181356iple_a Pa Ca Q_1)) tptp.bot_bo1208640912a_bool))))) :args (_let_23))) _let_24 :args (_let_22 false _let_23)) :args (_let_21 true _let_5 false _let_22)) :args (_let_20 true _let_19)) :args (_let_13 true _let_18)) _let_16 :args (false false _let_15 false _let_14 false _let_13 true _let_9)) :args ((forall ((Ga tptp.fun_Ho1877127206a_bool)) (tptp.hBOOL (tptp.hAPP_f1454306822l_bool (tptp.hoare_1617968510rivs_a Ga) tptp.bot_bo1208640912a_bool))) (forall ((Fun1_2 tptp.fun_a_fun_state_bool) (Com_2 tptp.com) (Fun2_2 tptp.fun_a_fun_state_bool) (Fun1_1 tptp.fun_a_fun_state_bool) (Com_1 tptp.com) (Fun2_1 tptp.fun_a_fun_state_bool)) (= (= (tptp.hoare_1652181356iple_a Fun1_2 Com_2 Fun2_2) (tptp.hoare_1652181356iple_a Fun1_1 Com_1 Fun2_1)) (and (= Fun1_2 Fun1_1) (= Com_2 Com_1) (= Fun2_2 Fun2_1)))) (forall ((Ga tptp.fun_Ho1877127206a_bool) (G_1 tptp.fun_Ho1877127206a_bool) (Ts tptp.fun_Ho1877127206a_bool)) (let ((_let_1 (tptp.hoare_1617968510rivs_a Ga))) (=> (tptp.hBOOL (tptp.hAPP_f1454306822l_bool (tptp.hoare_1617968510rivs_a G_1) Ts)) (=> (tptp.hBOOL (tptp.hAPP_f1454306822l_bool _let_1 G_1)) (tptp.hBOOL (tptp.hAPP_f1454306822l_bool _let_1 Ts)))))) (forall ((Ts tptp.fun_Ho1877127206a_bool) (Ga tptp.fun_Ho1877127206a_bool) (T tptp.hoare_1927711152iple_a)) (let ((_let_1 (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a T))) (let ((_let_2 (tptp.hoare_1617968510rivs_a Ga))) (=> (tptp.hBOOL (tptp.hAPP_f1454306822l_bool _let_2 (tptp.hAPP_f16502863a_bool _let_1 tptp.bot_bo1208640912a_bool))) (=> (tptp.hBOOL (tptp.hAPP_f1454306822l_bool _let_2 Ts)) (tptp.hBOOL (tptp.hAPP_f1454306822l_bool _let_2 (tptp.hAPP_f16502863a_bool _let_1 Ts)))))))) (forall ((Ga tptp.fun_Ho1877127206a_bool) (Pa tptp.fun_a_fun_state_bool) (Ca tptp.com) (Q_1 tptp.fun_a_fun_state_bool) (C tptp.bool)) (let ((_let_1 (tptp.hoare_1617968510rivs_a Ga))) (=> (=> (tptp.hBOOL C) (tptp.hBOOL (tptp.hAPP_f1454306822l_bool _let_1 (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a (tptp.hoare_1652181356iple_a Pa Ca Q_1)) tptp.bot_bo1208640912a_bool)))) (tptp.hBOOL (tptp.hAPP_f1454306822l_bool _let_1 (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a (tptp.hoare_1652181356iple_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_bo1208640912a_bool)))))) _let_11 (forall ((Q_1 tptp.fun_a_fun_state_bool) (Ga tptp.fun_Ho1877127206a_bool) (Pa tptp.fun_a_fun_state_bool) (Ca tptp.com) (Q_3 tptp.fun_a_fun_state_bool)) (let ((_let_1 (tptp.hoare_1617968510rivs_a Ga))) (=> (tptp.hBOOL (tptp.hAPP_f1454306822l_bool _let_1 (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a (tptp.hoare_1652181356iple_a Pa Ca Q_3)) tptp.bot_bo1208640912a_bool))) (=> (forall ((Z_1 tptp.x_a) (S tptp.state)) (=> (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_f1454306822l_bool _let_1 (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a (tptp.hoare_1652181356iple_a Pa Ca Q_1)) tptp.bot_bo1208640912a_bool))))))) (forall ((Pa tptp.fun_a_fun_state_bool) (Ga tptp.fun_Ho1877127206a_bool) (P_2 tptp.fun_a_fun_state_bool) (Ca tptp.com) (Q_1 tptp.fun_a_fun_state_bool)) (let ((_let_1 (tptp.hoare_1617968510rivs_a Ga))) (=> (tptp.hBOOL (tptp.hAPP_f1454306822l_bool _let_1 (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a (tptp.hoare_1652181356iple_a P_2 Ca Q_1)) tptp.bot_bo1208640912a_bool))) (=> (forall ((Z_1 tptp.x_a) (S tptp.state)) (=> (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_f1454306822l_bool _let_1 (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a (tptp.hoare_1652181356iple_a Pa Ca Q_1)) tptp.bot_bo1208640912a_bool))))))) (forall ((Q_1 tptp.fun_a_fun_state_bool) (Pa tptp.fun_a_fun_state_bool) (Ga tptp.fun_Ho1877127206a_bool) (P_2 tptp.fun_a_fun_state_bool) (Ca tptp.com) (Q_3 tptp.fun_a_fun_state_bool)) (let ((_let_1 (tptp.hoare_1617968510rivs_a Ga))) (=> (tptp.hBOOL (tptp.hAPP_f1454306822l_bool _let_1 (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a (tptp.hoare_1652181356iple_a P_2 Ca Q_3)) tptp.bot_bo1208640912a_bool))) (=> (forall ((Z_1 tptp.x_a) (S tptp.state)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_a2036067514e_bool Pa Z_1) S)) (forall ((S_1 tptp.state)) (=> (forall ((Z_2 tptp.x_a)) (=> (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_f1454306822l_bool _let_1 (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a (tptp.hoare_1652181356iple_a Pa Ca Q_1)) tptp.bot_bo1208640912a_bool))))))) (forall ((A_3 tptp.hoare_1927711152iple_a) (Ba tptp.hoare_1927711152iple_a) (A tptp.fun_Ho1877127206a_bool)) (let ((_let_1 (tptp.hAPP_H694056973l_bool tptp.member127332739iple_a A_3))) (=> (tptp.hBOOL (tptp.hAPP_f1454306822l_bool _let_1 (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a Ba) A))) (=> (not (= A_3 Ba)) (tptp.hBOOL (tptp.hAPP_f1454306822l_bool _let_1 A)))))) (forall ((Ba tptp.hoare_1927711152iple_a) (A_3 tptp.hoare_1927711152iple_a) (B_1 tptp.fun_Ho1877127206a_bool)) (let ((_let_1 (tptp.hAPP_H694056973l_bool tptp.member127332739iple_a A_3))) (=> (=> (not (tptp.hBOOL (tptp.hAPP_f1454306822l_bool _let_1 B_1))) (= A_3 Ba)) (tptp.hBOOL (tptp.hAPP_f1454306822l_bool _let_1 (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a Ba) B_1)))))) (forall ((A_3 tptp.hoare_1927711152iple_a)) (not (tptp.hBOOL (tptp.hAPP_f1454306822l_bool (tptp.hAPP_H694056973l_bool tptp.member127332739iple_a A_3) tptp.bot_bo1208640912a_bool)))) (forall ((A_3 tptp.hoare_1927711152iple_a)) (= (tptp.collec829051333iple_a (tptp.hAPP_H1027145665a_bool tptp.fequal1440857775iple_a A_3)) (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a A_3) tptp.bot_bo1208640912a_bool))) (forall ((A_3 tptp.hoare_1927711152iple_a)) (= (tptp.collec829051333iple_a (tptp.hAPP_H1027145665a_bool (tptp.hAPP_f1216137953a_bool tptp.cOMBC_671859290a_bool tptp.fequal1440857775iple_a) A_3)) (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a A_3) tptp.bot_bo1208640912a_bool))) (forall ((Pa tptp.fun_Ho1877127206a_bool) (A_3 tptp.hoare_1927711152iple_a)) (let ((_let_1 (tptp.collec829051333iple_a (tptp.hAPP_f16502863a_bool (tptp.hAPP_f2112551770a_bool tptp.cOMBS_2061548107l_bool (tptp.hAPP_f749678531l_bool (tptp.cOMBB_196465322iple_a tptp.fconj) (tptp.hAPP_H1027145665a_bool tptp.fequal1440857775iple_a A_3))) Pa)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_H1448631928a_bool Pa A_3)))) (and (=> _let_2 (= _let_1 (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a A_3) tptp.bot_bo1208640912a_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bo1208640912a_bool)))))) (forall ((Pa tptp.fun_Ho1877127206a_bool) (A_3 tptp.hoare_1927711152iple_a)) (let ((_let_1 (tptp.collec829051333iple_a (tptp.hAPP_f16502863a_bool (tptp.hAPP_f2112551770a_bool tptp.cOMBS_2061548107l_bool (tptp.hAPP_f749678531l_bool (tptp.cOMBB_196465322iple_a tptp.fconj) (tptp.hAPP_H1027145665a_bool (tptp.hAPP_f1216137953a_bool tptp.cOMBC_671859290a_bool tptp.fequal1440857775iple_a) A_3))) Pa)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_H1448631928a_bool Pa A_3)))) (and (=> _let_2 (= _let_1 (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a A_3) tptp.bot_bo1208640912a_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bo1208640912a_bool)))))) (forall ((A_3 tptp.hoare_1927711152iple_a) (A tptp.fun_Ho1877127206a_bool)) (=> (= A tptp.bot_bo1208640912a_bool) (not (tptp.hBOOL (tptp.hAPP_f1454306822l_bool (tptp.hAPP_H694056973l_bool tptp.member127332739iple_a A_3) A))))) (forall ((Pa tptp.fun_Ho1877127206a_bool)) (= (= (tptp.collec829051333iple_a Pa) tptp.bot_bo1208640912a_bool) (forall ((X_2 tptp.hoare_1927711152iple_a)) (not (tptp.hBOOL (tptp.hAPP_H1448631928a_bool Pa X_2)))))) (forall ((Ca tptp.hoare_1927711152iple_a)) (not (tptp.hBOOL (tptp.hAPP_f1454306822l_bool (tptp.hAPP_H694056973l_bool tptp.member127332739iple_a Ca) tptp.bot_bo1208640912a_bool)))) (forall ((Pa tptp.fun_Ho1877127206a_bool)) (= (= tptp.bot_bo1208640912a_bool (tptp.collec829051333iple_a Pa)) (forall ((X_2 tptp.hoare_1927711152iple_a)) (not (tptp.hBOOL (tptp.hAPP_H1448631928a_bool Pa X_2)))))) (forall ((A tptp.fun_Ho1877127206a_bool)) (= (exists ((X_2 tptp.hoare_1927711152iple_a)) (tptp.hBOOL (tptp.hAPP_f1454306822l_bool (tptp.hAPP_H694056973l_bool tptp.member127332739iple_a X_2) A))) (not (= A tptp.bot_bo1208640912a_bool)))) (forall ((A tptp.fun_Ho1877127206a_bool)) (= (forall ((X_2 tptp.hoare_1927711152iple_a)) (not (tptp.hBOOL (tptp.hAPP_f1454306822l_bool (tptp.hAPP_H694056973l_bool tptp.member127332739iple_a X_2) A)))) (= A tptp.bot_bo1208640912a_bool))) (= tptp.bot_bo1208640912a_bool (tptp.collec829051333iple_a (tptp.cOMBK_712844119iple_a tptp.fFalse))) (forall ((A_3 tptp.hoare_1927711152iple_a) (A tptp.fun_Ho1877127206a_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1454306822l_bool (tptp.hAPP_H694056973l_bool tptp.member127332739iple_a A_3) A)) (= (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a A_3) A) A))) (forall ((Ba tptp.hoare_1927711152iple_a) (A_3 tptp.hoare_1927711152iple_a) (B_1 tptp.fun_Ho1877127206a_bool)) (let ((_let_1 (tptp.hAPP_H694056973l_bool tptp.member127332739iple_a A_3))) (=> (tptp.hBOOL (tptp.hAPP_f1454306822l_bool _let_1 B_1)) (tptp.hBOOL (tptp.hAPP_f1454306822l_bool _let_1 (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a Ba) B_1)))))) (forall ((B_1 tptp.fun_Ho1877127206a_bool) (X_1 tptp.hoare_1927711152iple_a) (A tptp.fun_Ho1877127206a_bool)) (let ((_let_1 (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a X_1))) (let ((_let_2 (tptp.hAPP_H694056973l_bool tptp.member127332739iple_a X_1))) (=> (not (tptp.hBOOL (tptp.hAPP_f1454306822l_bool _let_2 A))) (=> (not (tptp.hBOOL (tptp.hAPP_f1454306822l_bool _let_2 B_1))) (= (= (tptp.hAPP_f16502863a_bool _let_1 A) (tptp.hAPP_f16502863a_bool _let_1 B_1)) (= A B_1))))))) (forall ((Y_2 tptp.hoare_1927711152iple_a) (A tptp.fun_Ho1877127206a_bool) (X_1 tptp.hoare_1927711152iple_a)) (= (tptp.hBOOL (tptp.hAPP_H1448631928a_bool (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a Y_2) A) X_1)) (or (= Y_2 X_1) (tptp.hBOOL (tptp.hAPP_H1448631928a_bool A X_1))))) (forall ((A_3 tptp.hoare_1927711152iple_a) (Ba tptp.hoare_1927711152iple_a) (A tptp.fun_Ho1877127206a_bool)) (let ((_let_1 (tptp.hAPP_H694056973l_bool tptp.member127332739iple_a A_3))) (= (tptp.hBOOL (tptp.hAPP_f1454306822l_bool _let_1 (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a Ba) A))) (or (= A_3 Ba) (tptp.hBOOL (tptp.hAPP_f1454306822l_bool _let_1 A)))))) (forall ((X_1 tptp.hoare_1927711152iple_a) (Y_2 tptp.hoare_1927711152iple_a) (A tptp.fun_Ho1877127206a_bool)) (let ((_let_1 (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a X_1))) (let ((_let_2 (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a Y_2))) (= (tptp.hAPP_f16502863a_bool _let_1 (tptp.hAPP_f16502863a_bool _let_2 A)) (tptp.hAPP_f16502863a_bool _let_2 (tptp.hAPP_f16502863a_bool _let_1 A)))))) (forall ((X_1 tptp.hoare_1927711152iple_a) (A tptp.fun_Ho1877127206a_bool)) (let ((_let_1 (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a X_1))) (let ((_let_2 (tptp.hAPP_f16502863a_bool _let_1 A))) (= (tptp.hAPP_f16502863a_bool _let_1 _let_2) _let_2)))) (forall ((A_3 tptp.hoare_1927711152iple_a) (Pa tptp.fun_Ho1877127206a_bool)) (= (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a A_3) (tptp.collec829051333iple_a Pa)) (tptp.collec829051333iple_a (tptp.hAPP_f16502863a_bool (tptp.hAPP_f2112551770a_bool tptp.cOMBS_2061548107l_bool (tptp.hAPP_f749678531l_bool (tptp.cOMBB_196465322iple_a tptp.fimplies) (tptp.hAPP_f16502863a_bool (tptp.cOMBB_213049548iple_a tptp.fNot) (tptp.hAPP_H1027145665a_bool (tptp.hAPP_f1216137953a_bool tptp.cOMBC_671859290a_bool tptp.fequal1440857775iple_a) A_3)))) Pa)))) (forall ((A_3 tptp.hoare_1927711152iple_a) (B_1 tptp.fun_Ho1877127206a_bool)) (= (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a A_3) B_1) (tptp.collec829051333iple_a (tptp.hAPP_f16502863a_bool (tptp.hAPP_f2112551770a_bool tptp.cOMBS_2061548107l_bool (tptp.hAPP_f749678531l_bool (tptp.cOMBB_196465322iple_a tptp.fdisj) (tptp.hAPP_H1027145665a_bool (tptp.hAPP_f1216137953a_bool tptp.cOMBC_671859290a_bool tptp.fequal1440857775iple_a) A_3))) (tptp.hAPP_f16502863a_bool (tptp.hAPP_f684479953a_bool tptp.cOMBC_862840740l_bool tptp.member127332739iple_a) B_1))))) (forall ((A_3 tptp.hoare_1927711152iple_a) (B_1 tptp.fun_Ho1877127206a_bool)) (tptp.hBOOL (tptp.hAPP_f1454306822l_bool (tptp.hAPP_H694056973l_bool tptp.member127332739iple_a A_3) (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a A_3) B_1)))) (forall ((X_2 tptp.hoare_1927711152iple_a) (Xa tptp.fun_Ho1877127206a_bool)) (= (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a X_2) Xa) (tptp.collec829051333iple_a (tptp.hAPP_f16502863a_bool (tptp.hAPP_f2112551770a_bool tptp.cOMBS_2061548107l_bool (tptp.hAPP_f749678531l_bool (tptp.cOMBB_196465322iple_a tptp.fdisj) (tptp.hAPP_H1027145665a_bool (tptp.hAPP_f1216137953a_bool tptp.cOMBC_671859290a_bool tptp.fequal1440857775iple_a) X_2))) (tptp.hAPP_f16502863a_bool (tptp.hAPP_f684479953a_bool tptp.cOMBC_862840740l_bool tptp.member127332739iple_a) Xa))))) (forall ((A_3 tptp.hoare_1927711152iple_a) (Ba tptp.hoare_1927711152iple_a)) (=> (= (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a A_3) tptp.bot_bo1208640912a_bool) (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a Ba) tptp.bot_bo1208640912a_bool)) (= A_3 Ba))) (forall ((Ba tptp.hoare_1927711152iple_a) (A_3 tptp.hoare_1927711152iple_a)) (=> (tptp.hBOOL (tptp.hAPP_f1454306822l_bool (tptp.hAPP_H694056973l_bool tptp.member127332739iple_a Ba) (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a A_3) tptp.bot_bo1208640912a_bool))) (= Ba A_3))) (forall ((A_3 tptp.hoare_1927711152iple_a) (Ba tptp.hoare_1927711152iple_a) (Ca tptp.hoare_1927711152iple_a) (D tptp.hoare_1927711152iple_a)) (= (= (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a A_3) (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a Ba) tptp.bot_bo1208640912a_bool)) (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a Ca) (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a D) tptp.bot_bo1208640912a_bool))) (or (and (= A_3 Ca) (= Ba D)) (and (= A_3 D) (= Ba Ca))))) (forall ((Ba tptp.hoare_1927711152iple_a) (A_3 tptp.hoare_1927711152iple_a)) (= (tptp.hBOOL (tptp.hAPP_f1454306822l_bool (tptp.hAPP_H694056973l_bool tptp.member127332739iple_a Ba) (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a A_3) tptp.bot_bo1208640912a_bool))) (= Ba A_3))) (forall ((A_3 tptp.hoare_1927711152iple_a) (A tptp.fun_Ho1877127206a_bool)) (not (= (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a A_3) A) tptp.bot_bo1208640912a_bool))) (forall ((A_3 tptp.hoare_1927711152iple_a) (A tptp.fun_Ho1877127206a_bool)) (not (= tptp.bot_bo1208640912a_bool (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a A_3) A)))) (forall ((X_1 tptp.hoare_1927711152iple_a)) (= (tptp.hAPP_f490779847iple_a tptp.the_el1997360207iple_a (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a X_1) tptp.bot_bo1208640912a_bool)) X_1)) (forall ((X_1 tptp.hoare_1927711152iple_a)) (= (tptp.hBOOL (tptp.hAPP_H1448631928a_bool tptp.bot_bo1208640912a_bool X_1)) (tptp.hBOOL tptp.bot_bot_bool))) (forall ((X_2 tptp.hoare_1927711152iple_a)) (= (tptp.hBOOL (tptp.hAPP_H1448631928a_bool tptp.bot_bo1208640912a_bool X_2)) (tptp.hBOOL tptp.bot_bot_bool))) (forall ((Ga tptp.fun_Ho1877127206a_bool) (Pa tptp.fun_a_fun_state_bool)) (tptp.hBOOL (tptp.hAPP_f1454306822l_bool (tptp.hoare_1617968510rivs_a Ga) (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a (tptp.hoare_1652181356iple_a Pa tptp.skip Pa)) tptp.bot_bo1208640912a_bool)))) (forall ((D tptp.com) (R_1 tptp.fun_a_fun_state_bool) (Ga tptp.fun_Ho1877127206a_bool) (Pa tptp.fun_a_fun_state_bool) (Ca tptp.com) (Q_1 tptp.fun_a_fun_state_bool)) (let ((_let_1 (tptp.hoare_1617968510rivs_a Ga))) (=> (tptp.hBOOL (tptp.hAPP_f1454306822l_bool _let_1 (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a (tptp.hoare_1652181356iple_a Pa Ca Q_1)) tptp.bot_bo1208640912a_bool))) (=> (tptp.hBOOL (tptp.hAPP_f1454306822l_bool _let_1 (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a (tptp.hoare_1652181356iple_a Q_1 D R_1)) tptp.bot_bo1208640912a_bool))) (tptp.hBOOL (tptp.hAPP_f1454306822l_bool _let_1 (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a (tptp.hoare_1652181356iple_a Pa (tptp.semi Ca D) R_1)) tptp.bot_bo1208640912a_bool))))))) (forall ((Y_2 tptp.hoare_1927711152iple_a)) (not (forall ((Fun1 tptp.fun_a_fun_state_bool) (Com tptp.com) (Fun2 tptp.fun_a_fun_state_bool)) (not (= Y_2 (tptp.hoare_1652181356iple_a Fun1 Com Fun2)))))) (forall ((X_1 tptp.hoare_1927711152iple_a) (A tptp.fun_Ho1877127206a_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1454306822l_bool (tptp.hAPP_H694056973l_bool tptp.member127332739iple_a X_1) A)) (not (forall ((B tptp.fun_Ho1877127206a_bool)) (=> (= A (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a X_1) B)) (tptp.hBOOL (tptp.hAPP_f1454306822l_bool (tptp.hAPP_H694056973l_bool tptp.member127332739iple_a X_1) B))))))) (forall ((Com1_2 tptp.com) (Com2_2 tptp.com)) (not (= (tptp.semi Com1_2 Com2_2) tptp.skip))) (forall ((Com1_2 tptp.com) (Com2_2 tptp.com)) (not (= tptp.skip (tptp.semi Com1_2 Com2_2)))) (forall ((X_3 tptp.fun_Ho1877127206a_bool)) (= (tptp.hAPP_f490779847iple_a tptp.the_el1997360207iple_a X_3) (tptp.hAPP_f490779847iple_a tptp.the_Ho1307659873iple_a (tptp.hAPP_f909473944a_bool (tptp.cOMBB_1083611331iple_a (tptp.hAPP_f625100287l_bool tptp.fequal1285825639a_bool X_3)) (tptp.hAPP_f993216280a_bool (tptp.hAPP_f1022403729a_bool tptp.cOMBC_825881325a_bool tptp.insert1434104874iple_a) tptp.bot_bo1208640912a_bool))))) (forall ((A_3 tptp.hoare_1927711152iple_a) (A tptp.fun_Ho1877127206a_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1454306822l_bool (tptp.hAPP_H694056973l_bool tptp.member127332739iple_a A_3) A)) (exists ((B tptp.fun_Ho1877127206a_bool)) (and (= A (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a A_3) B)) (not (tptp.hBOOL (tptp.hAPP_f1454306822l_bool (tptp.hAPP_H694056973l_bool tptp.member127332739iple_a A_3) B))))))) (forall ((Com1_1 tptp.com) (Com2_1 tptp.com) (Com1 tptp.com) (Com2 tptp.com)) (= (= (tptp.semi Com1_1 Com2_1) (tptp.semi Com1 Com2)) (and (= Com1_1 Com1) (= Com2_1 Com2)))) (forall ((X_1 tptp.hoare_1927711152iple_a)) (= (tptp.hAPP_f490779847iple_a tptp.the_Ho1307659873iple_a (tptp.hAPP_H1027145665a_bool tptp.fequal1440857775iple_a X_1)) X_1)) (forall ((A_3 tptp.hoare_1927711152iple_a)) (= (tptp.hAPP_f490779847iple_a tptp.the_Ho1307659873iple_a (tptp.hAPP_H1027145665a_bool (tptp.hAPP_f1216137953a_bool tptp.cOMBC_671859290a_bool tptp.fequal1440857775iple_a) A_3)) A_3)) (forall ((X_1 tptp.hoare_1927711152iple_a) (Y_2 tptp.hoare_1927711152iple_a) (Pa tptp.bool)) (let ((_let_1 (tptp.hAPP_f1216137953a_bool tptp.cOMBC_671859290a_bool tptp.fequal1440857775iple_a))) (let ((_let_2 (tptp.hAPP_f490779847iple_a tptp.the_Ho1307659873iple_a (tptp.hAPP_f16502863a_bool (tptp.hAPP_f2112551770a_bool tptp.cOMBS_2061548107l_bool (tptp.hAPP_f749678531l_bool (tptp.cOMBB_196465322iple_a tptp.fconj) (tptp.hAPP_f16502863a_bool (tptp.cOMBB_213049548iple_a (tptp.hAPP_b589554111l_bool tptp.fimplies Pa)) (tptp.hAPP_H1027145665a_bool _let_1 X_1)))) (tptp.hAPP_f16502863a_bool (tptp.cOMBB_213049548iple_a (tptp.hAPP_b589554111l_bool tptp.fimplies (tptp.hAPP_bool_bool tptp.fNot Pa))) (tptp.hAPP_H1027145665a_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 tptp.fun_Ho1877127206a_bool)) (=> (forall ((Y_1 tptp.hoare_1927711152iple_a)) (not (tptp.hBOOL (tptp.hAPP_f1454306822l_bool (tptp.hAPP_H694056973l_bool tptp.member127332739iple_a Y_1) A)))) (= A tptp.bot_bo1208640912a_bool))) (forall ((Pa tptp.fun_Ho1877127206a_bool) (A_3 tptp.hoare_1927711152iple_a)) (=> (tptp.hBOOL (tptp.hAPP_H1448631928a_bool Pa A_3)) (=> (forall ((X_2 tptp.hoare_1927711152iple_a)) (=> (tptp.hBOOL (tptp.hAPP_H1448631928a_bool Pa X_2)) (= X_2 A_3))) (= (tptp.hAPP_f490779847iple_a tptp.the_Ho1307659873iple_a Pa) A_3)))) (forall ((Pa tptp.fun_Ho1877127206a_bool) (A_3 tptp.hoare_1927711152iple_a)) (=> (tptp.hBOOL (tptp.hAPP_H1448631928a_bool Pa A_3)) (=> (forall ((X_2 tptp.hoare_1927711152iple_a)) (=> (tptp.hBOOL (tptp.hAPP_H1448631928a_bool Pa X_2)) (= X_2 A_3))) (tptp.hBOOL (tptp.hAPP_H1448631928a_bool Pa (tptp.hAPP_f490779847iple_a tptp.the_Ho1307659873iple_a Pa)))))) (forall ((A_3 tptp.hoare_1927711152iple_a) (Pa tptp.fun_Ho1877127206a_bool)) (=> (exists ((X_2 tptp.hoare_1927711152iple_a)) (and (tptp.hBOOL (tptp.hAPP_H1448631928a_bool Pa X_2)) (forall ((Y_1 tptp.hoare_1927711152iple_a)) (=> (tptp.hBOOL (tptp.hAPP_H1448631928a_bool Pa Y_1)) (= Y_1 X_2))))) (=> (tptp.hBOOL (tptp.hAPP_H1448631928a_bool Pa A_3)) (= (tptp.hAPP_f490779847iple_a tptp.the_Ho1307659873iple_a Pa) A_3)))) (forall ((Pa tptp.fun_Ho1877127206a_bool)) (=> (exists ((X_2 tptp.hoare_1927711152iple_a)) (and (tptp.hBOOL (tptp.hAPP_H1448631928a_bool Pa X_2)) (forall ((Y_1 tptp.hoare_1927711152iple_a)) (=> (tptp.hBOOL (tptp.hAPP_H1448631928a_bool Pa Y_1)) (= Y_1 X_2))))) (tptp.hBOOL (tptp.hAPP_H1448631928a_bool Pa (tptp.hAPP_f490779847iple_a tptp.the_Ho1307659873iple_a Pa))))) (forall ((Q_1 tptp.fun_a_fun_state_bool) (Ga tptp.fun_Ho1877127206a_bool) (Ca tptp.com) (Pa tptp.fun_a_fun_state_bool)) (=> (forall ((Z_1 tptp.x_a) (S tptp.state)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_a2036067514e_bool Pa Z_1) S)) (exists ((P_1 tptp.fun_a_fun_state_bool) (Q_2 tptp.fun_a_fun_state_bool)) (and (tptp.hBOOL (tptp.hAPP_f1454306822l_bool (tptp.hoare_1617968510rivs_a Ga) (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a (tptp.hoare_1652181356iple_a P_1 Ca Q_2)) tptp.bot_bo1208640912a_bool))) (forall ((S_1 tptp.state)) (=> (forall ((Z_2 tptp.x_a)) (=> (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_f1454306822l_bool (tptp.hoare_1617968510rivs_a Ga) (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a (tptp.hoare_1652181356iple_a Pa Ca Q_1)) tptp.bot_bo1208640912a_bool))))) (forall ((A tptp.fun_Ho1877127206a_bool)) (= (not (= A tptp.bot_bo1208640912a_bool)) (exists ((X_2 tptp.hoare_1927711152iple_a) (B tptp.fun_Ho1877127206a_bool)) (and (= A (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a X_2) B)) (not (tptp.hBOOL (tptp.hAPP_f1454306822l_bool (tptp.hAPP_H694056973l_bool tptp.member127332739iple_a X_2) B))))))) (forall ((F_1 tptp.fun_Ho333840202iple_a) (A_3 tptp.hoare_1927711152iple_a) (Ba tptp.hoare_1927711152iple_a)) (= (tptp.hBOOL (tptp.hAPP_H1448631928a_bool (tptp.finite2098837632iple_a F_1 (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a A_3) tptp.bot_bo1208640912a_bool)) Ba)) (= A_3 Ba))) (forall ((X_1 tptp.hoare_1927711152iple_a) (F_1 tptp.fun_Ho333840202iple_a) (F tptp.fun_fu1033095803iple_a)) (=> (tptp.hBOOL (tptp.finite83514413iple_a F_1 F)) (= (tptp.hAPP_f490779847iple_a F (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a X_1) tptp.bot_bo1208640912a_bool)) X_1))) (forall ((X_2 tptp.hoare_1927711152iple_a)) (= (tptp.hBOOL (tptp.hAPP_H1448631928a_bool tptp.bot_bo1208640912a_bool X_2)) (tptp.hBOOL (tptp.hAPP_f1454306822l_bool (tptp.hAPP_H694056973l_bool tptp.member127332739iple_a X_2) tptp.bot_bo1208640912a_bool)))) (forall ((F_1 tptp.fun_Ho333840202iple_a) (X_1 tptp.hoare_1927711152iple_a)) (not (tptp.hBOOL (tptp.hAPP_H1448631928a_bool (tptp.finite2098837632iple_a F_1 tptp.bot_bo1208640912a_bool) X_1)))) (forall ((F_1 tptp.fun_Ho333840202iple_a) (A tptp.fun_Ho1877127206a_bool) (X_1 tptp.hoare_1927711152iple_a)) (=> (tptp.hBOOL (tptp.hAPP_H1448631928a_bool (tptp.finite2098837632iple_a F_1 A) X_1)) (not (= A tptp.bot_bo1208640912a_bool)))) (forall ((F_1 tptp.fun_Ho333840202iple_a) (A_3 tptp.hoare_1927711152iple_a) (A tptp.fun_Ho1877127206a_bool) (X_1 tptp.hoare_1927711152iple_a)) (=> (tptp.hBOOL (tptp.hAPP_H1448631928a_bool (tptp.finite148164294iple_a F_1 A_3 A) X_1)) (=> (not (tptp.hBOOL (tptp.hAPP_f1454306822l_bool (tptp.hAPP_H694056973l_bool tptp.member127332739iple_a A_3) A))) (tptp.hBOOL (tptp.hAPP_H1448631928a_bool (tptp.finite2098837632iple_a F_1 (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a A_3) A)) X_1))))) (forall ((X_1 tptp.hoare_1927711152iple_a) (A tptp.fun_Ho1877127206a_bool) (F_1 tptp.fun_Ho333840202iple_a) (F tptp.fun_fu1033095803iple_a)) (=> (tptp.hBOOL (tptp.finite83514413iple_a F_1 F)) (=> (tptp.hBOOL (tptp.hAPP_f1454306822l_bool tptp.finite68738179iple_a A)) (=> (not (tptp.hBOOL (tptp.hAPP_f1454306822l_bool (tptp.hAPP_H694056973l_bool tptp.member127332739iple_a X_1) A))) (=> (not (= A tptp.bot_bo1208640912a_bool)) (= (tptp.hAPP_f490779847iple_a F (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a X_1) A)) (tptp.hAPP_H963118037iple_a (tptp.hAPP_H1700437986iple_a F_1 X_1) (tptp.hAPP_f490779847iple_a F A)))))))) (forall ((F_1 tptp.fun_Ho333840202iple_a) (A tptp.fun_Ho1877127206a_bool)) (= (tptp.hAPP_f490779847iple_a (tptp.finite1943414032iple_a F_1) A) (tptp.hAPP_f490779847iple_a tptp.the_Ho1307659873iple_a (tptp.finite2098837632iple_a F_1 A)))) (forall ((Q_1 tptp.fun_Ho1877127206a_bool) (Pa tptp.fun_Ho1877127206a_bool)) (=> (or (tptp.hBOOL (tptp.hAPP_f1454306822l_bool tptp.finite68738179iple_a (tptp.collec829051333iple_a Pa))) (tptp.hBOOL (tptp.hAPP_f1454306822l_bool tptp.finite68738179iple_a (tptp.collec829051333iple_a Q_1)))) (tptp.hBOOL (tptp.hAPP_f1454306822l_bool tptp.finite68738179iple_a (tptp.collec829051333iple_a (tptp.hAPP_f16502863a_bool (tptp.hAPP_f2112551770a_bool tptp.cOMBS_2061548107l_bool (tptp.hAPP_f749678531l_bool (tptp.cOMBB_196465322iple_a tptp.fconj) Pa)) Q_1)))))) (tptp.hBOOL (tptp.hAPP_f1454306822l_bool tptp.finite68738179iple_a tptp.bot_bo1208640912a_bool)) (forall ((A_3 tptp.hoare_1927711152iple_a) (A tptp.fun_Ho1877127206a_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1454306822l_bool tptp.finite68738179iple_a A)) (tptp.hBOOL (tptp.hAPP_f1454306822l_bool tptp.finite68738179iple_a (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a A_3) A))))) (forall ((X_1 tptp.hoare_1927711152iple_a) (A tptp.fun_Ho1877127206a_bool)) (= (tptp.hBOOL (tptp.hAPP_f1454306822l_bool (tptp.hAPP_H694056973l_bool tptp.member127332739iple_a X_1) A)) (tptp.hBOOL (tptp.hAPP_H1448631928a_bool A X_1)))) (forall ((Pa tptp.fun_Ho1877127206a_bool)) (= (tptp.collec829051333iple_a Pa) Pa)) (forall ((A tptp.fun_Ho1877127206a_bool) (F_1 tptp.fun_Ho333840202iple_a) (F tptp.fun_fu1033095803iple_a)) (=> (tptp.hBOOL (tptp.finite83514413iple_a F_1 F)) (=> (tptp.hBOOL (tptp.hAPP_f1454306822l_bool tptp.finite68738179iple_a A)) (= (tptp.hAPP_f490779847iple_a F A) (tptp.hAPP_f490779847iple_a (tptp.finite1943414032iple_a F_1) A))))) (forall ((F_1 tptp.fun_Ho333840202iple_a) (Z tptp.hoare_1927711152iple_a)) (tptp.hBOOL (tptp.hAPP_H1448631928a_bool (tptp.finite148164294iple_a F_1 Z tptp.bot_bo1208640912a_bool) Z))) (forall ((F_1 tptp.fun_Ho333840202iple_a) (Z tptp.hoare_1927711152iple_a) (X_1 tptp.hoare_1927711152iple_a)) (=> (tptp.hBOOL (tptp.hAPP_H1448631928a_bool (tptp.finite148164294iple_a F_1 Z tptp.bot_bo1208640912a_bool) X_1)) (= X_1 Z))) (forall ((F_1 tptp.fun_Ho333840202iple_a) (Z tptp.hoare_1927711152iple_a) (Y_2 tptp.hoare_1927711152iple_a) (X_1 tptp.hoare_1927711152iple_a) (A tptp.fun_Ho1877127206a_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_f1454306822l_bool (tptp.hAPP_H694056973l_bool tptp.member127332739iple_a X_1) A))) (=> (tptp.hBOOL (tptp.hAPP_H1448631928a_bool (tptp.finite148164294iple_a F_1 Z A) Y_2)) (tptp.hBOOL (tptp.hAPP_H1448631928a_bool (tptp.finite148164294iple_a F_1 Z (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a X_1) A)) (tptp.hAPP_H963118037iple_a (tptp.hAPP_H1700437986iple_a F_1 X_1) Y_2)))))) (forall ((Pa tptp.fun_Ho1877127206a_bool) (Q_1 tptp.fun_Ho1877127206a_bool)) (= (tptp.hBOOL (tptp.hAPP_f1454306822l_bool tptp.finite68738179iple_a (tptp.collec829051333iple_a (tptp.hAPP_f16502863a_bool (tptp.hAPP_f2112551770a_bool tptp.cOMBS_2061548107l_bool (tptp.hAPP_f749678531l_bool (tptp.cOMBB_196465322iple_a tptp.fdisj) Pa)) Q_1)))) (and (tptp.hBOOL (tptp.hAPP_f1454306822l_bool tptp.finite68738179iple_a (tptp.collec829051333iple_a Pa))) (tptp.hBOOL (tptp.hAPP_f1454306822l_bool tptp.finite68738179iple_a (tptp.collec829051333iple_a Q_1)))))) (forall ((A_3 tptp.hoare_1927711152iple_a) (A tptp.fun_Ho1877127206a_bool)) (= (tptp.hBOOL (tptp.hAPP_f1454306822l_bool tptp.finite68738179iple_a (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a A_3) A))) (tptp.hBOOL (tptp.hAPP_f1454306822l_bool tptp.finite68738179iple_a A)))) (forall ((A_3 tptp.hoare_1927711152iple_a) (G tptp.fun_fu1033095803iple_a) (F_1 tptp.fun_Ho333840202iple_a)) (=> (= G (tptp.finite1943414032iple_a F_1)) (= (tptp.hAPP_f490779847iple_a G (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a A_3) tptp.bot_bo1208640912a_bool)) A_3))) (forall ((F_1 tptp.fun_Ho333840202iple_a) (A_3 tptp.hoare_1927711152iple_a)) (= (tptp.hAPP_f490779847iple_a (tptp.finite1943414032iple_a F_1) (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a A_3) tptp.bot_bo1208640912a_bool)) A_3)) (forall ((A tptp.fun_Ho1877127206a_bool) (F_1 tptp.fun_Ho333840202iple_a) (F tptp.fun_fu1033095803iple_a)) (=> (tptp.hBOOL (tptp.finite83514413iple_a F_1 F)) (=> (tptp.hBOOL (tptp.hAPP_f1454306822l_bool tptp.finite68738179iple_a A)) (=> (not (= A tptp.bot_bo1208640912a_bool)) (=> (forall ((X_2 tptp.hoare_1927711152iple_a) (Y_1 tptp.hoare_1927711152iple_a)) (tptp.hBOOL (tptp.hAPP_f1454306822l_bool (tptp.hAPP_H694056973l_bool tptp.member127332739iple_a (tptp.hAPP_H963118037iple_a (tptp.hAPP_H1700437986iple_a F_1 X_2) Y_1)) (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a X_2) (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a Y_1) tptp.bot_bo1208640912a_bool))))) (tptp.hBOOL (tptp.hAPP_f1454306822l_bool (tptp.hAPP_H694056973l_bool tptp.member127332739iple_a (tptp.hAPP_f490779847iple_a F A)) A))))))) (forall ((F_1 tptp.fun_Ho333840202iple_a) (A_3 tptp.hoare_1927711152iple_a) (X_3 tptp.fun_Ho1877127206a_bool) (X_1 tptp.hoare_1927711152iple_a)) (=> (tptp.hBOOL (tptp.hAPP_H1448631928a_bool (tptp.finite2098837632iple_a F_1 (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a A_3) X_3)) X_1)) (not (forall ((A_2 tptp.hoare_1927711152iple_a) (A_1 tptp.fun_Ho1877127206a_bool)) (=> (= (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a A_3) X_3) (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a A_2) A_1)) (=> (tptp.hBOOL (tptp.hAPP_H1448631928a_bool (tptp.finite148164294iple_a F_1 A_2 A_1) X_1)) (tptp.hBOOL (tptp.hAPP_f1454306822l_bool (tptp.hAPP_H694056973l_bool tptp.member127332739iple_a A_2) A_1)))))))) (forall ((F_1 tptp.fun_Ho333840202iple_a) (A tptp.fun_Ho1877127206a_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1454306822l_bool tptp.finite68738179iple_a A)) (=> (not (= A tptp.bot_bo1208640912a_bool)) (exists ((X1 tptp.hoare_1927711152iple_a)) (tptp.hBOOL (tptp.hAPP_H1448631928a_bool (tptp.finite2098837632iple_a F_1 A) X1)))))) (forall ((Pa tptp.fun_fu832487784l_bool) (F tptp.fun_Ho1877127206a_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1454306822l_bool tptp.finite68738179iple_a F)) (=> (tptp.hBOOL (tptp.hAPP_f1454306822l_bool Pa tptp.bot_bo1208640912a_bool)) (=> (forall ((X_2 tptp.hoare_1927711152iple_a) (F_2 tptp.fun_Ho1877127206a_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1454306822l_bool tptp.finite68738179iple_a F_2)) (=> (not (tptp.hBOOL (tptp.hAPP_f1454306822l_bool (tptp.hAPP_H694056973l_bool tptp.member127332739iple_a X_2) F_2))) (=> (tptp.hBOOL (tptp.hAPP_f1454306822l_bool Pa F_2)) (tptp.hBOOL (tptp.hAPP_f1454306822l_bool Pa (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a X_2) F_2))))))) (tptp.hBOOL (tptp.hAPP_f1454306822l_bool Pa F)))))) (forall ((A_3 tptp.fun_Ho1877127206a_bool)) (= (tptp.hBOOL (tptp.hAPP_f1454306822l_bool tptp.finite68738179iple_a A_3)) (or (= A_3 tptp.bot_bo1208640912a_bool) (exists ((A_1 tptp.fun_Ho1877127206a_bool) (A_2 tptp.hoare_1927711152iple_a)) (and (= A_3 (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a A_2) A_1)) (tptp.hBOOL (tptp.hAPP_f1454306822l_bool tptp.finite68738179iple_a A_1))))))) (forall ((F_1 tptp.fun_Ho333840202iple_a) (Z tptp.hoare_1927711152iple_a) (A tptp.fun_Ho1877127206a_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1454306822l_bool tptp.finite68738179iple_a A)) (exists ((X1 tptp.hoare_1927711152iple_a)) (tptp.hBOOL (tptp.hAPP_H1448631928a_bool (tptp.finite148164294iple_a F_1 Z A) X1))))) (forall ((F_1 tptp.fun_Ho333840202iple_a) (A1 tptp.fun_Ho1877127206a_bool) (A2 tptp.hoare_1927711152iple_a)) (= (tptp.hBOOL (tptp.hAPP_H1448631928a_bool (tptp.finite2098837632iple_a F_1 A1) A2)) (exists ((A_2 tptp.hoare_1927711152iple_a) (A_1 tptp.fun_Ho1877127206a_bool) (X_2 tptp.hoare_1927711152iple_a)) (and (= A1 (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a A_2) A_1)) (= A2 X_2) (tptp.hBOOL (tptp.hAPP_H1448631928a_bool (tptp.finite148164294iple_a F_1 A_2 A_1) X_2)) (not (tptp.hBOOL (tptp.hAPP_f1454306822l_bool (tptp.hAPP_H694056973l_bool tptp.member127332739iple_a A_2) A_1))))))) (forall ((F_1 tptp.fun_Ho333840202iple_a) (Z tptp.hoare_1927711152iple_a) (A1 tptp.fun_Ho1877127206a_bool) (A2 tptp.hoare_1927711152iple_a)) (= (tptp.hBOOL (tptp.hAPP_H1448631928a_bool (tptp.finite148164294iple_a F_1 Z A1) A2)) (or (and (= A1 tptp.bot_bo1208640912a_bool) (= A2 Z)) (exists ((X_2 tptp.hoare_1927711152iple_a) (A_1 tptp.fun_Ho1877127206a_bool) (Y_1 tptp.hoare_1927711152iple_a)) (and (= A1 (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a X_2) A_1)) (= A2 (tptp.hAPP_H963118037iple_a (tptp.hAPP_H1700437986iple_a F_1 X_2) Y_1)) (not (tptp.hBOOL (tptp.hAPP_f1454306822l_bool (tptp.hAPP_H694056973l_bool tptp.member127332739iple_a X_2) A_1))) (tptp.hBOOL (tptp.hAPP_H1448631928a_bool (tptp.finite148164294iple_a F_1 Z A_1) Y_1))))))) (forall ((X_1 tptp.hoare_1927711152iple_a) (A tptp.fun_Ho1877127206a_bool) (F_1 tptp.fun_Ho333840202iple_a) (F tptp.fun_fu1033095803iple_a)) (=> (tptp.hBOOL (tptp.finite1511031594iple_a F_1 F)) (=> (tptp.hBOOL (tptp.hAPP_f1454306822l_bool tptp.finite68738179iple_a A)) (=> (not (= A tptp.bot_bo1208640912a_bool)) (= (tptp.hAPP_f490779847iple_a F (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a X_1) A)) (tptp.hAPP_H963118037iple_a (tptp.hAPP_H1700437986iple_a F_1 X_1) (tptp.hAPP_f490779847iple_a F A))))))) (forall ((Pa tptp.fun_fu832487784l_bool) (F tptp.fun_Ho1877127206a_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1454306822l_bool tptp.finite68738179iple_a F)) (=> (not (= F tptp.bot_bo1208640912a_bool)) (=> (forall ((X_2 tptp.hoare_1927711152iple_a)) (tptp.hBOOL (tptp.hAPP_f1454306822l_bool Pa (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a X_2) tptp.bot_bo1208640912a_bool)))) (=> (forall ((X_2 tptp.hoare_1927711152iple_a) (F_2 tptp.fun_Ho1877127206a_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1454306822l_bool tptp.finite68738179iple_a F_2)) (=> (not (= F_2 tptp.bot_bo1208640912a_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_f1454306822l_bool (tptp.hAPP_H694056973l_bool tptp.member127332739iple_a X_2) F_2))) (=> (tptp.hBOOL (tptp.hAPP_f1454306822l_bool Pa F_2)) (tptp.hBOOL (tptp.hAPP_f1454306822l_bool Pa (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool tptp.insert1434104874iple_a X_2) F_2)))))))) (tptp.hBOOL (tptp.hAPP_f1454306822l_bool Pa F))))))) (forall ((X_1 tptp.hoare_1927711152iple_a) (F_1 tptp.fun_Ho333840202iple_a) (F tptp.fun_fu1033095803iple_a)) (=> (tptp.hBOOL (tptp.finite1511031594iple_a F_1 F)) (= (tptp.hAPP_H963118037iple_a (tptp.hAPP_H1700437986iple_a F_1 X_1) X_1) X_1))) (forall ((X_1 tptp.hoare_1927711152iple_a) (A tptp.fun_Ho1877127206a_bool) (F_1 tptp.fun_Ho333840202iple_a) (F tptp.fun_fu1033095803iple_a)) (let ((_let_1 (tptp.hAPP_f490779847iple_a F A))) (=> (tptp.hBOOL (tptp.finite1511031594iple_a F_1 F)) (=> (tptp.hBOOL (tptp.hAPP_f1454306822l_bool tptp.finite68738179iple_a A)) (=> (tptp.hBOOL (tptp.hAPP_f1454306822l_bool (tptp.hAPP_H694056973l_bool tptp.member127332739iple_a X_1) A)) (= (tptp.hAPP_H963118037iple_a (tptp.hAPP_H1700437986iple_a F_1 X_1) _let_1) _let_1)))))) (forall ((P tptp.bool)) (or (not (tptp.hBOOL (tptp.hAPP_bool_bool tptp.fNot P))) (not (tptp.hBOOL P)))) (forall ((P tptp.bool)) (or (tptp.hBOOL P) (tptp.hBOOL (tptp.hAPP_bool_bool tptp.fNot P)))) (forall ((Q tptp.bool) (P tptp.bool)) (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 tptp.bool) (Q tptp.bool)) (or (not (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fconj P) Q))) (tptp.hBOOL P))) (forall ((P tptp.bool) (Q tptp.bool)) (or (not (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fconj P) Q))) (tptp.hBOOL Q))) (forall ((Q tptp.bool) (P tptp.bool)) (or (not (tptp.hBOOL P)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fdisj P) Q)))) (forall ((P tptp.bool) (Q tptp.bool)) (or (not (tptp.hBOOL Q)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fdisj P) Q)))) (forall ((P tptp.bool) (Q tptp.bool)) (or (not (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fdisj P) Q))) (tptp.hBOOL P) (tptp.hBOOL Q))) _let_10 (forall ((P tptp.bool)) (or (= P tptp.fTrue) (= P tptp.fFalse))) (forall ((Q tptp.bool) (P tptp.bool)) (or (tptp.hBOOL P) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fimplies P) Q)))) (forall ((P tptp.bool) (Q tptp.bool)) (or (not (tptp.hBOOL Q)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fimplies P) Q)))) (forall ((P tptp.bool) (Q tptp.bool)) (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 tptp.state) (Y tptp.state)) (or (not (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool tptp.fequal_state X) Y))) (= X Y))) (forall ((X tptp.state) (Y tptp.state)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool tptp.fequal_state X) Y)))) _let_8 _let_7 (forall ((P tptp.fun_bool_bool) (Q tptp.fun_state_bool) (R tptp.state)) (= (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 tptp.fun_st2063251938l_bool) (Q tptp.bool) (R tptp.state)) (= (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 tptp.fun_st2063251938l_bool) (Q tptp.fun_state_bool) (R tptp.state)) (= (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 tptp.fun_st1506752259e_bool) (Q tptp.state) (R tptp.state)) (= (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 tptp.hoare_1927711152iple_a) (Y tptp.hoare_1927711152iple_a)) (or (not (tptp.hBOOL (tptp.hAPP_H1448631928a_bool (tptp.hAPP_H1027145665a_bool tptp.fequal1440857775iple_a X) Y))) (= X Y))) (forall ((X tptp.hoare_1927711152iple_a) (Y tptp.hoare_1927711152iple_a)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_H1448631928a_bool (tptp.hAPP_H1027145665a_bool tptp.fequal1440857775iple_a X) Y)))) (forall ((P tptp.fun_a_998512028e_bool) (Q tptp.bool) (R tptp.x_a)) (= (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 tptp.bool) (Q tptp.hoare_1927711152iple_a)) (= (tptp.hAPP_H1448631928a_bool (tptp.cOMBK_712844119iple_a P) Q) P)) (forall ((P tptp.fun_bo1549164019l_bool) (Q tptp.fun_state_bool) (R tptp.state)) (= (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 tptp.fun_Ho1877127206a_bool) (Y tptp.fun_Ho1877127206a_bool)) (or (not (tptp.hBOOL (tptp.hAPP_f1454306822l_bool (tptp.hAPP_f625100287l_bool tptp.fequal1285825639a_bool X) Y))) (= X Y))) (forall ((X tptp.fun_Ho1877127206a_bool) (Y tptp.fun_Ho1877127206a_bool)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_f1454306822l_bool (tptp.hAPP_f625100287l_bool tptp.fequal1285825639a_bool X) Y)))) (forall ((P tptp.fun_bool_bool) (Q tptp.fun_Ho1877127206a_bool) (R tptp.hoare_1927711152iple_a)) (= (tptp.hAPP_H1448631928a_bool (tptp.hAPP_f16502863a_bool (tptp.cOMBB_213049548iple_a P) Q) R) (tptp.hAPP_bool_bool P (tptp.hAPP_H1448631928a_bool Q R)))) (forall ((P tptp.fun_Ho957066028l_bool) (Q tptp.fun_Ho1877127206a_bool) (R tptp.hoare_1927711152iple_a)) (= (tptp.hAPP_H1448631928a_bool (tptp.hAPP_f16502863a_bool (tptp.hAPP_f2112551770a_bool tptp.cOMBS_2061548107l_bool P) Q) R) (tptp.hAPP_bool_bool (tptp.hAPP_H1487873860l_bool P R) (tptp.hAPP_H1448631928a_bool Q R)))) (forall ((P tptp.fun_a_2117018159e_bool) (Q tptp.fun_state_bool) (R tptp.x_a)) (= (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 tptp.fun_bo1549164019l_bool) (Q tptp.fun_Ho1877127206a_bool) (R tptp.hoare_1927711152iple_a)) (= (tptp.hAPP_H1487873860l_bool (tptp.hAPP_f749678531l_bool (tptp.cOMBB_196465322iple_a P) Q) R) (tptp.hAPP_b589554111l_bool P (tptp.hAPP_H1448631928a_bool Q R)))) (forall ((P tptp.fun_fu1658206819l_bool) (Q tptp.fun_a_fun_state_bool) (R tptp.x_a)) (= (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 tptp.fun_Ho440810351a_bool) (Q tptp.hoare_1927711152iple_a) (R tptp.hoare_1927711152iple_a)) (= (tptp.hAPP_H1448631928a_bool (tptp.hAPP_H1027145665a_bool (tptp.hAPP_f1216137953a_bool tptp.cOMBC_671859290a_bool P) Q) R) (tptp.hAPP_H1448631928a_bool (tptp.hAPP_H1027145665a_bool P R) Q))) (forall ((P tptp.fun_fu1219323149e_bool) (Q tptp.fun_a_1632297036l_bool) (R tptp.x_a)) (= (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 tptp.fun_fu832487784l_bool) (Q tptp.fun_Ho440810351a_bool) (R tptp.hoare_1927711152iple_a)) (= (tptp.hAPP_H1448631928a_bool (tptp.hAPP_f909473944a_bool (tptp.cOMBB_1083611331iple_a P) Q) R) (tptp.hAPP_f1454306822l_bool P (tptp.hAPP_H1027145665a_bool Q R)))) (forall ((P tptp.fun_Ho525994229l_bool) (Q tptp.fun_Ho1877127206a_bool) (R tptp.hoare_1927711152iple_a)) (= (tptp.hAPP_H1448631928a_bool (tptp.hAPP_f16502863a_bool (tptp.hAPP_f684479953a_bool tptp.cOMBC_862840740l_bool P) Q) R) (tptp.hAPP_f1454306822l_bool (tptp.hAPP_H694056973l_bool P R) Q))) (forall ((P tptp.fun_fu1047394976e_bool) (Q tptp.fun_a_1632297036l_bool) (R tptp.x_a)) (= (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 tptp.fun_Ho1630563774a_bool) (Q tptp.fun_Ho1877127206a_bool) (R tptp.hoare_1927711152iple_a)) (= (tptp.hAPP_H1027145665a_bool (tptp.hAPP_f993216280a_bool (tptp.hAPP_f1022403729a_bool tptp.cOMBC_825881325a_bool P) Q) R) (tptp.hAPP_f16502863a_bool (tptp.hAPP_H1975128022a_bool P R) Q))) _let_6 true))))))))))))))))))))))))))))))))))))
% 0.23/0.82 )
% 0.23/0.82 % SZS output end Proof for SWW470_1
% 0.23/0.83 % cvc5---1.0.5 exiting
% 0.23/0.83 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------