TSTP Solution File: SWW474+2 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWW474+2 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n009.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 00:21:09 EDT 2023
% Result : Theorem 5.61s 5.83s
% Output : Proof 5.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.19 % Problem : SWW474+2 : TPTP v8.1.2. Released v5.3.0.
% 0.09/0.20 % Command : do_cvc5 %s %d
% 0.19/0.40 % Computer : n009.cluster.edu
% 0.19/0.40 % Model : x86_64 x86_64
% 0.19/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.40 % Memory : 8042.1875MB
% 0.19/0.40 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.40 % CPULimit : 300
% 0.19/0.40 % WCLimit : 300
% 0.19/0.40 % DateTime : Sun Aug 27 20:39:50 EDT 2023
% 0.19/0.40 % CPUTime :
% 0.42/0.60 %----Proving TF0_NAR, FOF, or CNF
% 5.61/5.83 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.nwHJ340ZGh/cvc5---1.0.5_4871.p...
% 5.61/5.83 ------- get file name : TPTP file name is SWW474+2
% 5.61/5.83 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_4871.smt2...
% 5.61/5.83 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 5.61/5.83 % SZS status Theorem for SWW474+2
% 5.61/5.83 % SZS output start Proof for SWW474+2
% 5.61/5.83 (
% 5.61/5.83 (let ((_let_1 (tptp.hAPP_c1546227244_state tptp.hoare_Mirabelle_MGT tptp.y))) (let ((_let_2 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state _let_1) tptp.bot_bo1055319631e_bool))) (let ((_let_3 (tptp.dom_pname_com tptp.body))) (let ((_let_4 (tptp.cOMBB_422605457_pname tptp.hoare_Mirabelle_MGT))) (let ((_let_5 (tptp.hAPP_f631639356e_bool (tptp.image_275883510_state (tptp.hAPP_f1758910594_state _let_4 tptp.body_1)) _let_3))) (let ((_let_6 (tptp.hoare_659004819_state _let_5))) (let ((_let_7 (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_6 _let_2)))) (let ((_let_8 (not _let_7))) (let ((_let_9 (= (tptp.hAPP_p799580910on_com tptp.body tptp.pn) (tptp.some_com tptp.y)))) (let ((_let_10 (tptp.hBOOL tptp.wT_bodies))) (let ((_let_11 (tptp.hBOOL tptp.hoare_298929751gleton))) (let ((_let_12 (forall ((Pn $$unsorted) (B_4 $$unsorted)) (=> (tptp.hBOOL tptp.wT_bodies) (=> (= (tptp.hAPP_p799580910on_com tptp.body Pn) (tptp.some_com B_4)) (tptp.hBOOL (tptp.hAPP_com_bool tptp.wt B_4))))))) (let ((_let_13 (forall ((C $$unsorted)) (=> (tptp.hBOOL tptp.hoare_298929751gleton) (=> (tptp.hBOOL tptp.wT_bodies) (=> (tptp.hBOOL (tptp.hAPP_com_bool tptp.wt C)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hoare_659004819_state tptp.bot_bo1055319631e_bool) (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state (tptp.hAPP_c1546227244_state tptp.hoare_Mirabelle_MGT C)) tptp.bot_bo1055319631e_bool))))))))) (let ((_let_14 (forall ((G_1 $$unsorted) (G_2 $$unsorted) (Ts $$unsorted)) (let ((_let_1 (tptp.hoare_659004819_state G_1))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hoare_659004819_state G_2) Ts)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 G_2)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 Ts)))))))) (let ((_let_15 (forall ((G_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hoare_659004819_state G_1) tptp.bot_bo1055319631e_bool))))) (let ((_let_16 (tptp.fun tptp.pname tptp.bool))) (let ((_let_17 (forall ((G_1 $$unsorted) (G_2 $$unsorted) (Ts $$unsorted)) (let ((_let_1 (tptp.hoare_659004819_state G_1))) (or (not (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hoare_659004819_state G_2) Ts))) (not (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 G_2))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 Ts))))))) (let ((_let_18 (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_6 tptp.bot_bo1055319631e_bool)))) (let ((_let_19 (not _let_18))) (let ((_let_20 (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hoare_659004819_state tptp.bot_bo1055319631e_bool) _let_2)))) (let ((_let_21 (not _let_20))) (let ((_let_22 (or _let_21 _let_19 _let_7))) (let ((_let_23 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_24 (not _let_22))) (let ((_let_25 (tptp.hBOOL (tptp.hAPP_com_bool tptp.wt tptp.y)))) (let ((_let_26 (not _let_25))) (let ((_let_27 (or _let_26 _let_20))) (let ((_let_28 (forall ((C $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP_com_bool tptp.wt C))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hoare_659004819_state tptp.bot_bo1055319631e_bool) (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state (tptp.hAPP_c1546227244_state tptp.hoare_Mirabelle_MGT C)) tptp.bot_bo1055319631e_bool))))))) (let ((_let_29 (ASSUME :args (_let_10)))) (let ((_let_30 (_let_28))) (let ((_let_31 (not _let_9))) (let ((_let_32 (or _let_31 _let_25))) (let ((_let_33 (forall ((Pn $$unsorted) (B_4 $$unsorted)) (or (not (= (tptp.hAPP_p799580910on_com tptp.body Pn) (tptp.some_com B_4))) (tptp.hBOOL (tptp.hAPP_com_bool tptp.wt B_4)))))) (let ((_let_34 (_let_33))) (let ((_let_35 (_let_15))) (let ((_let_36 (ASSUME :args _let_35))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_23 :args (_let_5 tptp.bot_bo1055319631e_bool _let_2 QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP_f1760790145l_bool (tptp.hoare_659004819_state G_2) Ts) (tptp.hoare_659004819_state G_1)))) :args (_let_17))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_22)) :args ((or _let_7 _let_19 _let_21 _let_24))) (ASSUME :args (_let_8)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_36 :args (_let_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.hoare_659004819_state G_1)))) :args _let_35)) _let_36 :args (_let_18 false _let_15)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_27)) :args ((or _let_26 _let_20 (not _let_27)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_32)) :args ((or _let_31 _let_25 (not _let_32)))) (ASSUME :args (_let_9)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_34) :args (tptp.pn tptp.y QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP_p799580910on_com tptp.body Pn) (tptp.some_com B_4)))) :args _let_34)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))) _let_29 :args (_let_33 false _let_10)) :args (_let_32 false _let_33)) :args (_let_25 false _let_9 false _let_32)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_30) :args (tptp.y QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.hAPP_c1546227244_state tptp.hoare_Mirabelle_MGT C)))) :args _let_30)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))) (ASSUME :args (_let_11)) _let_29 :args (_let_28 false _let_11 false _let_10)) :args (_let_27 false _let_28)) :args (_let_20 false _let_25 false _let_27)) :args (_let_24 true _let_7 false _let_18 false _let_20)) _let_23 :args (false true _let_22 false _let_17)) :args ((forall ((B_1_1 $$unsorted)) (=> (tptp.is_bool B_1_1) (tptp.is_fun_pname_bool (tptp.cOMBK_bool_pname B_1_1)))) (forall ((B_1_1 $$unsorted)) (=> (tptp.is_bool B_1_1) (tptp.is_fun1661590463l_bool (tptp.cOMBK_1857069011e_bool B_1_1)))) (tptp.is_bool tptp.wT_bodies) (tptp.is_fun1661590463l_bool tptp.finite_finite_pname) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.finite1282449217_pname B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.finite774711482_state B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.finite1626890877e_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.finite132673334e_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.finite89670078_pname B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.finite506823037_state B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.finite1268145088e_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.finite959343283e_bool B_1_1 B_2_1))) (tptp.is_pname (tptp.undefined_pname tptp.pname)) (tptp.is_fun_pname_bool (tptp.undefi17486888e_bool _let_16)) (tptp.is_fun1661590463l_bool (tptp.undefi64961550l_bool (tptp.fun _let_16 tptp.bool))) (tptp.is_bool tptp.hoare_298929751gleton) (forall ((B_1_1 $$unsorted)) (tptp.is_fun_pname_bool (tptp.dom_pname_com B_1_1))) (forall ((B_1_1 $$unsorted)) (=> (tptp.is_pname B_1_1) (tptp.is_option_pname (tptp.some_pname B_1_1)))) (forall ((B_1_1 $$unsorted)) (=> (tptp.is_option_pname B_1_1) (tptp.is_fun_pname_bool (tptp.set_pname B_1_1)))) (tptp.is_bool tptp.bot_bot_bool) (tptp.is_fun_pname_bool tptp.bot_bo844097828e_bool) (tptp.is_fun1661590463l_bool tptp.bot_bo1649642514l_bool) (tptp.is_bool tptp.fFalse) (tptp.is_bool tptp.fTrue) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.hAPP_com_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_pname B_2_1) (tptp.is_pname (tptp.hAPP_pname_pname B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (and (tptp.is_fun_pname_bool B_1_1) (tptp.is_pname B_2_1)) (tptp.is_bool (tptp.hAPP_pname_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_pname B_2_1) (tptp.is_fun_pname_bool (tptp.hAPP_p61793385e_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_pname B_2_1) (tptp.is_fun1661590463l_bool (tptp.hAPP_p338031245l_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.hAPP_state_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_bool B_2_1) (tptp.is_bool (tptp.hAPP_bool_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_pname (tptp.hAPP_H1344248906_pname B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.hAPP_H513860823e_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_fun_pname_bool (tptp.hAPP_H1632039476e_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_fun1661590463l_bool (tptp.hAPP_H737849090l_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.hAPP_f990396704l_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_fun_pname_bool B_2_1) (tptp.is_pname (tptp.hAPP_f1297739591_pname B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (and (tptp.is_fun1661590463l_bool B_1_1) (tptp.is_fun_pname_bool B_2_1)) (tptp.is_bool (tptp.hAPP_f1664156314l_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_fun_pname_bool B_2_1) (tptp.is_fun_pname_bool (tptp.hAPP_f759274231e_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_fun_pname_bool B_2_1) (tptp.is_fun1661590463l_bool (tptp.hAPP_f434788991l_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_fun_pname_bool (tptp.hAPP_f42430548e_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.hAPP_f327114704l_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_pname (tptp.hAPP_f1008690464_pname B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.hAPP_f1760790145l_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_fun_pname_bool (tptp.hAPP_f1745235422e_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_fun1661590463l_bool (tptp.hAPP_f748867288l_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_fun1661590463l_bool B_2_1) (tptp.is_bool (tptp.hAPP_f1935102916l_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_fun1661590463l_bool B_2_1) (tptp.is_fun_pname_bool (tptp.hAPP_f674760225e_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_fun1661590463l_bool B_2_1) (tptp.is_fun1661590463l_bool (tptp.hAPP_f559147733l_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.hAPP_f239102607l_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_fun_pname_bool (tptp.hAPP_f280588268e_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.hAPP_f389811538l_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.hAPP_f1904669497l_bool B_1_1 B_2_1))) (tptp.is_pname tptp.pn) _let_15 (forall ((Ts $$unsorted) (G_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool Ts) G_1)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hoare_659004819_state G_1) Ts)))) (forall ((Ts $$unsorted) (G_1 $$unsorted) (Ts_1 $$unsorted)) (let ((_let_1 (tptp.hoare_659004819_state G_1))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 Ts_1)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool Ts) Ts_1)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 Ts)))))) (forall ((G_1 $$unsorted) (G_2 $$unsorted) (Ts $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hoare_659004819_state G_2) Ts)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool G_2) G_1)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hoare_659004819_state G_1) Ts))))) _let_14 (forall ((Ts $$unsorted) (G_1 $$unsorted) (T $$unsorted)) (let ((_let_1 (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state T))) (let ((_let_2 (tptp.hoare_659004819_state G_1))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_2 (tptp.hAPP_f921536533e_bool _let_1 tptp.bot_bo1055319631e_bool))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_2 Ts)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_2 (tptp.hAPP_f921536533e_bool _let_1 Ts)))))))) (forall ((G_1 $$unsorted) (T $$unsorted) (Ts $$unsorted)) (let ((_let_1 (tptp.hoare_659004819_state G_1))) (let ((_let_2 (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state T))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 (tptp.hAPP_f921536533e_bool _let_2 Ts))) (and (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 (tptp.hAPP_f921536533e_bool _let_2 tptp.bot_bo1055319631e_bool))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 Ts))))))) (forall ((Pn_1 $$unsorted) (G_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state (tptp.hAPP_c1546227244_state tptp.hoare_Mirabelle_MGT (tptp.hAPP_pname_com tptp.body_1 Pn_1))))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hoare_659004819_state (tptp.hAPP_f921536533e_bool _let_1 G_1)) (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state (tptp.hAPP_c1546227244_state tptp.hoare_Mirabelle_MGT (tptp.hAPP_option_com_com tptp.the_com (tptp.hAPP_p799580910on_com tptp.body Pn_1)))) tptp.bot_bo1055319631e_bool))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hoare_659004819_state G_1) (tptp.hAPP_f921536533e_bool _let_1 tptp.bot_bo1055319631e_bool)))))) (forall ((A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A_1)) (tptp.hBOOL (tptp.hAPP_f389811538l_bool tptp.finite786885583l_bool (tptp.hAPP_f783502055l_bool tptp.collec1613912337l_bool (tptp.hAPP_f510955609l_bool (tptp.hAPP_f1879335953l_bool tptp.cOMBC_7971162l_bool tptp.ord_le675606854l_bool) A_1)))))) (forall ((A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool A_1)) (tptp.hBOOL (tptp.hAPP_f1904669497l_bool tptp.finite1586217244l_bool (tptp.hAPP_f1987093l_bool tptp.collec1277803610l_bool (tptp.hAPP_f1269496639l_bool (tptp.hAPP_f1508257257l_bool tptp.cOMBC_1084925030l_bool tptp.ord_le1076702565l_bool) A_1)))))) (forall ((A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state A_1)) (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool (tptp.hAPP_f1970439265l_bool tptp.collec111528142e_bool (tptp.hAPP_f854625363l_bool (tptp.hAPP_f2119687429l_bool tptp.cOMBC_1018307482l_bool tptp.ord_le1720872323e_bool) A_1)))))) (forall ((A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A_1)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool (tptp.hAPP_f434788991l_bool (tptp.hAPP_f1297925993l_bool tptp.cOMBC_1284144636l_bool tptp.ord_le313189616e_bool) A_1)))))) (forall ((H $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state Fa)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.hAPP_f748867288l_bool (tptp.image_1259634916e_bool H) Fa))))) (forall ((H $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state Fa)) (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool (tptp.hAPP_f854625363l_bool (tptp.image_277167759e_bool H) Fa))))) (forall ((H $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname Fa)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.hAPP_f434788991l_bool (tptp.image_47868345e_bool H) Fa))))) (forall ((H $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname Fa)) (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool (tptp.hAPP_f1874607724l_bool (tptp.image_505480954e_bool H) Fa))))) (forall ((H $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool Fa)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state (tptp.hAPP_f780887186e_bool (tptp.image_936554724_state H) Fa))))) (forall ((H $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool Fa)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state (tptp.hAPP_f772567431e_bool (tptp.image_774712299_state H) Fa))))) (forall ((H $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool Fa)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f674760225e_bool (tptp.image_1283814551_pname H) Fa))))) (forall ((H $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool Fa)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f280588268e_bool (tptp.image_636285904_pname H) Fa))))) (forall ((H $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname Fa)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state (tptp.hAPP_f631639356e_bool (tptp.image_275883510_state H) Fa))))) (forall ((A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool tptp.bot_bo844097828e_bool) A_1))) (forall ((A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool tptp.bot_bo1055319631e_bool) A_1))) (forall ((A $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A_1)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool A) A_1))))) (forall ((A $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool A_1)) (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool (tptp.hAPP_f1970439265l_bool (tptp.hAPP_f601642911l_bool tptp.insert1991711667e_bool A) A_1))))) (forall ((A $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A) A_1))))) (forall ((A $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state A_1)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A) A_1))))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool tptp.bot_bo1649642514l_bool)) (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool tptp.bot_bo1325454745l_bool)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state tptp.bot_bo1055319631e_bool)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname tptp.bot_bo844097828e_bool)) (forall ((Q_1 $$unsorted) (P_1 $$unsorted)) (=> (or (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool P_1))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool Q_1)))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f624840228l_bool tptp.cOMBS_350070575l_bool (tptp.hAPP_f143162813l_bool (tptp.cOMBB_2095475776e_bool tptp.fconj) P_1)) Q_1)))))) (forall ((Q_1 $$unsorted) (P_1 $$unsorted)) (=> (or (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool (tptp.hAPP_f1970439265l_bool tptp.collec111528142e_bool P_1))) (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool (tptp.hAPP_f1970439265l_bool tptp.collec111528142e_bool Q_1)))) (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool (tptp.hAPP_f1970439265l_bool tptp.collec111528142e_bool (tptp.hAPP_f1970439265l_bool (tptp.hAPP_f1850463605l_bool tptp.cOMBS_2138645332l_bool (tptp.hAPP_f482022705l_bool (tptp.cOMBB_2020112947e_bool tptp.fconj) P_1)) Q_1)))))) (forall ((Q_1 $$unsorted) (P_1 $$unsorted)) (=> (or (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state (tptp.hAPP_f921536533e_bool tptp.collec727977250_state P_1))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state (tptp.hAPP_f921536533e_bool tptp.collec727977250_state Q_1)))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state (tptp.hAPP_f921536533e_bool tptp.collec727977250_state (tptp.hAPP_f921536533e_bool (tptp.hAPP_f760664097e_bool tptp.cOMBS_1248383340l_bool (tptp.hAPP_f1558728829l_bool (tptp.cOMBB_1382207997_state tptp.fconj) P_1)) Q_1)))))) (forall ((Q_1 $$unsorted) (P_1 $$unsorted)) (=> (or (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f759274231e_bool tptp.collect_pname P_1))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f759274231e_bool tptp.collect_pname Q_1)))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f759274231e_bool tptp.collect_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_f649174806e_bool tptp.cOMBS_568398431l_bool (tptp.hAPP_f1402196763l_bool (tptp.cOMBB_675860798_pname tptp.fconj) P_1)) Q_1)))))) (forall ((C $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1745235422e_bool (tptp.image_1925245338_pname (tptp.cOMBK_588224941_state C)) A_1))) (let ((_let_2 (= A_1 tptp.bot_bo1055319631e_bool))) (and (=> _let_2 (= _let_1 tptp.bot_bo844097828e_bool)) (=> (not _let_2) (= _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname C) tptp.bot_bo844097828e_bool))))))) (forall ((C $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f631639356e_bool (tptp.image_275883510_state (tptp.cOMBK_90103121_pname C)) A_1))) (let ((_let_2 (= A_1 tptp.bot_bo844097828e_bool))) (=> (tptp.is_fun_pname_bool A_1) (and (=> _let_2 (= _let_1 tptp.bot_bo1055319631e_bool)) (=> (not _let_2) (= _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state C) tptp.bot_bo1055319631e_bool)))))))) (forall ((C $$unsorted) (X_1 $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_1) A_1)) (= (tptp.hAPP_f1745235422e_bool (tptp.image_1925245338_pname (tptp.cOMBK_588224941_state C)) A_1) (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname C) tptp.bot_bo844097828e_bool)))) (forall ((C $$unsorted) (X_1 $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A_1)) (= (tptp.hAPP_f631639356e_bool (tptp.image_275883510_state (tptp.cOMBK_90103121_pname C)) A_1) (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state C) tptp.bot_bo1055319631e_bool)))) (forall ((F $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.dom_pname_com F))) (=> (= (tptp.hAPP_p799580910on_com F X_1) (tptp.some_com Y_1)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1) _let_1) _let_1)))) (forall ((B $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state A_1)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool B) (tptp.hAPP_f748867288l_bool (tptp.image_1259634916e_bool F) A_1))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool B))))) (forall ((B $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state A_1)) (=> (tptp.hBOOL (tptp.hAPP_f239102607l_bool (tptp.hAPP_f1269496639l_bool tptp.ord_le1076702565l_bool B) (tptp.hAPP_f854625363l_bool (tptp.image_277167759e_bool F) A_1))) (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool B))))) (forall ((B $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state A_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) (tptp.hAPP_f1745235422e_bool (tptp.image_1925245338_pname F) A_1))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B))))) (forall ((B $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A_1)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool B) (tptp.hAPP_f434788991l_bool (tptp.image_47868345e_bool F) A_1))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool B))))) (forall ((B $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A_1)) (=> (tptp.hBOOL (tptp.hAPP_f239102607l_bool (tptp.hAPP_f1269496639l_bool tptp.ord_le1076702565l_bool B) (tptp.hAPP_f1874607724l_bool (tptp.image_505480954e_bool F) A_1))) (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool B))))) (forall ((B $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) (tptp.hAPP_f759274231e_bool (tptp.image_pname_pname F) A_1))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B))))) (forall ((B $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A_1)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool B) (tptp.hAPP_f780887186e_bool (tptp.image_936554724_state F) A_1))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state B))))) (forall ((B $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool A_1)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool B) (tptp.hAPP_f772567431e_bool (tptp.image_774712299_state F) A_1))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state B))))) (forall ((B $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) (tptp.hAPP_f674760225e_bool (tptp.image_1283814551_pname F) A_1))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B))))) (forall ((B $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool A_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) (tptp.hAPP_f280588268e_bool (tptp.image_636285904_pname F) A_1))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B))))) (forall ((B $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A_1)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool B) (tptp.hAPP_f631639356e_bool (tptp.image_275883510_state F) A_1))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state B))))) (forall ((A_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1) tptp.bot_bo844097828e_bool))) (=> (tptp.is_fun_pname_bool A_1) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_1) _let_1)) (or (= A_1 tptp.bot_bo844097828e_bool) (= A_1 _let_1)))))) (forall ((A_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state X_1) tptp.bot_bo1055319631e_bool))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool A_1) _let_1)) (or (= A_1 tptp.bot_bo1055319631e_bool) (= A_1 _let_1))))) _let_13 (forall ((A $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A) tptp.bot_bo844097828e_bool)))) (forall ((A $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state A) tptp.bot_bo1055319631e_bool)))) (forall ((B_1 $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname A))) (=> (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B))) (= A B_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname B_1) B)))))) (forall ((B_1 $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H248360617l_bool tptp.member1758697444_state A))) (=> (=> (not (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 B))) (= A B_1)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state B_1) B)))))) (forall ((A $$unsorted) (B_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname A))) (=> (and (tptp.is_pname A) (tptp.is_pname B_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname B_1) A_1))) (=> (not (= A B_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A_1))))))) (forall ((A $$unsorted) (B_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_H248360617l_bool tptp.member1758697444_state A))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state B_1) A_1))) (=> (not (= A B_1)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 A_1)))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (=> (and (tptp.is_fun_pname_bool A_1) (tptp.is_fun_pname_bool B)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_1) B)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) A_1)) (= A_1 B))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool A_1) B)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool B) A_1)) (= A_1 B)))) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname C))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_1) B)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B)))))) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H248360617l_bool tptp.member1758697444_state C))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool A_1) B)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 A_1)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 B)))))) (forall ((A_1 $$unsorted) (B_1 $$unsorted) (F $$unsorted) (X_1 $$unsorted)) (=> (= B_1 (tptp.hAPP_H1344248906_pname F X_1)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_1) A_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname B_1) (tptp.hAPP_f1745235422e_bool (tptp.image_1925245338_pname F) A_1)))))) (forall ((A_1 $$unsorted) (B_1 $$unsorted) (F $$unsorted) (X_1 $$unsorted)) (=> (= B_1 (tptp.hAPP_p1842370726_state F X_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A_1)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state B_1) (tptp.hAPP_f631639356e_bool (tptp.image_275883510_state F) A_1)))))) (forall ((A $$unsorted) (A_1 $$unsorted)) (=> (= A_1 tptp.bot_bo844097828e_bool) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A) A_1))))) (forall ((A $$unsorted) (A_1 $$unsorted)) (=> (= A_1 tptp.bot_bo1055319631e_bool) (not (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state A) A_1))))) (forall ((P_1 $$unsorted)) (= (= (tptp.hAPP_f759274231e_bool tptp.collect_pname P_1) tptp.bot_bo844097828e_bool) (forall ((X_2 $$unsorted)) (=> (tptp.is_pname X_2) (not (tptp.hBOOL (tptp.hAPP_pname_bool P_1 X_2))))))) (forall ((P_1 $$unsorted)) (= (= (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool P_1) tptp.bot_bo1649642514l_bool) (forall ((X_2 $$unsorted)) (=> (tptp.is_fun_pname_bool X_2) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 X_2))))))) (forall ((P_1 $$unsorted)) (= (= (tptp.hAPP_f1970439265l_bool tptp.collec111528142e_bool P_1) tptp.bot_bo1325454745l_bool) (forall ((X_2 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f1760790145l_bool P_1 X_2)))))) (forall ((P_1 $$unsorted)) (= (= (tptp.hAPP_f921536533e_bool tptp.collec727977250_state P_1) tptp.bot_bo1055319631e_bool) (forall ((X_2 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_H513860823e_bool P_1 X_2)))))) (forall ((C $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname C) tptp.bot_bo844097828e_bool)))) (forall ((C $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state C) tptp.bot_bo1055319631e_bool)))) (forall ((P_1 $$unsorted)) (= (= tptp.bot_bo844097828e_bool (tptp.hAPP_f759274231e_bool tptp.collect_pname P_1)) (forall ((X_2 $$unsorted)) (=> (tptp.is_pname X_2) (not (tptp.hBOOL (tptp.hAPP_pname_bool P_1 X_2))))))) (forall ((P_1 $$unsorted)) (= (= tptp.bot_bo1649642514l_bool (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool P_1)) (forall ((X_2 $$unsorted)) (=> (tptp.is_fun_pname_bool X_2) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 X_2))))))) (forall ((P_1 $$unsorted)) (= (= tptp.bot_bo1325454745l_bool (tptp.hAPP_f1970439265l_bool tptp.collec111528142e_bool P_1)) (forall ((X_2 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f1760790145l_bool P_1 X_2)))))) (forall ((P_1 $$unsorted)) (= (= tptp.bot_bo1055319631e_bool (tptp.hAPP_f921536533e_bool tptp.collec727977250_state P_1)) (forall ((X_2 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_H513860823e_bool P_1 X_2)))))) (forall ((A_1 $$unsorted)) (=> (tptp.is_fun_pname_bool A_1) (= (exists ((X_2 $$unsorted)) (and (tptp.is_pname X_2) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A_1)))) (not (= A_1 tptp.bot_bo844097828e_bool))))) (forall ((A_1 $$unsorted)) (= (exists ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_2) A_1))) (not (= A_1 tptp.bot_bo1055319631e_bool)))) (forall ((A_1 $$unsorted)) (=> (tptp.is_fun_pname_bool A_1) (= (forall ((X_2 $$unsorted)) (=> (tptp.is_pname X_2) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A_1))))) (= A_1 tptp.bot_bo844097828e_bool)))) (forall ((A_1 $$unsorted)) (= (forall ((X_2 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_2) A_1)))) (= A_1 tptp.bot_bo1055319631e_bool))) (= tptp.bot_bo844097828e_bool (tptp.hAPP_f759274231e_bool tptp.collect_pname (tptp.cOMBK_bool_pname tptp.fFalse))) (= tptp.bot_bo1649642514l_bool (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool (tptp.cOMBK_1857069011e_bool tptp.fFalse))) (= tptp.bot_bo1325454745l_bool (tptp.hAPP_f1970439265l_bool tptp.collec111528142e_bool (tptp.cOMBK_564432736e_bool tptp.fFalse))) (= tptp.bot_bo1055319631e_bool (tptp.hAPP_f921536533e_bool tptp.collec727977250_state (tptp.cOMBK_1079618832_state tptp.fFalse))) (forall ((A $$unsorted) (A_1 $$unsorted)) (=> (tptp.is_fun_pname_bool A_1) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A) A_1)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A) A_1) A_1)))) (forall ((A $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state A) A_1)) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A) A_1) A_1))) (forall ((B_1 $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname A))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname B_1) B)))))) (forall ((B_1 $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H248360617l_bool tptp.member1758697444_state A))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 B)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state B_1) B)))))) (forall ((B $$unsorted) (X_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1))) (let ((_let_2 (tptp.hAPP_p338031245l_bool tptp.member_pname X_1))) (=> (and (tptp.is_fun_pname_bool B) (tptp.is_fun_pname_bool A_1)) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_2 A_1))) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_2 B))) (= (= (tptp.hAPP_f759274231e_bool _let_1 A_1) (tptp.hAPP_f759274231e_bool _let_1 B)) (= A_1 B)))))))) (forall ((B $$unsorted) (X_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state X_1))) (let ((_let_2 (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_1))) (=> (not (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_2 A_1))) (=> (not (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_2 B))) (= (= (tptp.hAPP_f921536533e_bool _let_1 A_1) (tptp.hAPP_f921536533e_bool _let_1 B)) (= A_1 B))))))) (forall ((Y_1 $$unsorted) (A_1 $$unsorted) (X_1 $$unsorted)) (=> (and (tptp.is_pname Y_1) (tptp.is_pname X_1)) (= (tptp.hBOOL (tptp.hAPP_pname_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname Y_1) A_1) X_1)) (or (= Y_1 X_1) (tptp.hBOOL (tptp.hAPP_pname_bool A_1 X_1)))))) (forall ((Y_1 $$unsorted) (A_1 $$unsorted) (X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_H513860823e_bool (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state Y_1) A_1) X_1)) (or (= Y_1 X_1) (tptp.hBOOL (tptp.hAPP_H513860823e_bool A_1 X_1))))) (forall ((A $$unsorted) (B_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname A))) (=> (and (tptp.is_pname A) (tptp.is_pname B_1)) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname B_1) A_1))) (or (= A B_1) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A_1))))))) (forall ((A $$unsorted) (B_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_H248360617l_bool tptp.member1758697444_state A))) (= (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state B_1) A_1))) (or (= A B_1) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 A_1)))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1))) (let ((_let_2 (tptp.hAPP_p905327722e_bool tptp.insert_pname Y_1))) (= (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool _let_2 A_1)) (tptp.hAPP_f759274231e_bool _let_2 (tptp.hAPP_f759274231e_bool _let_1 A_1)))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state X_1))) (let ((_let_2 (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state Y_1))) (= (tptp.hAPP_f921536533e_bool _let_1 (tptp.hAPP_f921536533e_bool _let_2 A_1)) (tptp.hAPP_f921536533e_bool _let_2 (tptp.hAPP_f921536533e_bool _let_1 A_1)))))) (forall ((X_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1))) (let ((_let_2 (tptp.hAPP_f759274231e_bool _let_1 A_1))) (= (tptp.hAPP_f759274231e_bool _let_1 _let_2) _let_2)))) (forall ((X_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state X_1))) (let ((_let_2 (tptp.hAPP_f921536533e_bool _let_1 A_1))) (= (tptp.hAPP_f921536533e_bool _let_1 _let_2) _let_2)))) (forall ((A $$unsorted) (P_1 $$unsorted)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A) (tptp.hAPP_f759274231e_bool tptp.collect_pname P_1)) (tptp.hAPP_f759274231e_bool tptp.collect_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_f649174806e_bool tptp.cOMBS_568398431l_bool (tptp.hAPP_f1402196763l_bool (tptp.cOMBB_675860798_pname tptp.fimplies) (tptp.hAPP_f759274231e_bool (tptp.cOMBB_647938656_pname tptp.fNot) (tptp.hAPP_p61793385e_bool (tptp.hAPP_f22061361e_bool tptp.cOMBC_1149511130e_bool tptp.fequal_pname) A)))) P_1)))) (forall ((A $$unsorted) (P_1 $$unsorted)) (= (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool A) (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool P_1)) (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f624840228l_bool tptp.cOMBS_350070575l_bool (tptp.hAPP_f143162813l_bool (tptp.cOMBB_2095475776e_bool tptp.fimplies) (tptp.hAPP_f559147733l_bool (tptp.cOMBB_307249310e_bool tptp.fNot) (tptp.hAPP_f434788991l_bool (tptp.hAPP_f1297925993l_bool tptp.cOMBC_1284144636l_bool tptp.fequal533582459e_bool) A)))) P_1)))) (forall ((A $$unsorted) (P_1 $$unsorted)) (= (tptp.hAPP_f1970439265l_bool (tptp.hAPP_f601642911l_bool tptp.insert1991711667e_bool A) (tptp.hAPP_f1970439265l_bool tptp.collec111528142e_bool P_1)) (tptp.hAPP_f1970439265l_bool tptp.collec111528142e_bool (tptp.hAPP_f1970439265l_bool (tptp.hAPP_f1850463605l_bool tptp.cOMBS_2138645332l_bool (tptp.hAPP_f482022705l_bool (tptp.cOMBB_2020112947e_bool tptp.fimplies) (tptp.hAPP_f1970439265l_bool (tptp.cOMBB_1957242197e_bool tptp.fNot) (tptp.hAPP_f854625363l_bool (tptp.hAPP_f2119687429l_bool tptp.cOMBC_1018307482l_bool tptp.fequal1746921144e_bool) A)))) P_1)))) (forall ((A $$unsorted) (P_1 $$unsorted)) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A) (tptp.hAPP_f921536533e_bool tptp.collec727977250_state P_1)) (tptp.hAPP_f921536533e_bool tptp.collec727977250_state (tptp.hAPP_f921536533e_bool (tptp.hAPP_f760664097e_bool tptp.cOMBS_1248383340l_bool (tptp.hAPP_f1558728829l_bool (tptp.cOMBB_1382207997_state tptp.fimplies) (tptp.hAPP_f921536533e_bool (tptp.cOMBB_416661851_state tptp.fNot) (tptp.hAPP_H1645666623e_bool (tptp.hAPP_f262880489e_bool tptp.cOMBC_1424981238e_bool tptp.fequal1531560888_state) A)))) P_1)))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A) B) (tptp.hAPP_f759274231e_bool tptp.collect_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_f649174806e_bool tptp.cOMBS_568398431l_bool (tptp.hAPP_f1402196763l_bool (tptp.cOMBB_675860798_pname tptp.fdisj) (tptp.hAPP_p61793385e_bool (tptp.hAPP_f22061361e_bool tptp.cOMBC_1149511130e_bool tptp.fequal_pname) A))) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f661147897e_bool tptp.cOMBC_1058051404l_bool tptp.member_pname) B))))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool A) B) (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f624840228l_bool tptp.cOMBS_350070575l_bool (tptp.hAPP_f143162813l_bool (tptp.cOMBB_2095475776e_bool tptp.fdisj) (tptp.hAPP_f434788991l_bool (tptp.hAPP_f1297925993l_bool tptp.cOMBC_1284144636l_bool tptp.fequal533582459e_bool) A))) (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1145991873l_bool tptp.cOMBC_1988546018l_bool tptp.member799430823e_bool) B))))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.hAPP_f1970439265l_bool (tptp.hAPP_f601642911l_bool tptp.insert1991711667e_bool A) B) (tptp.hAPP_f1970439265l_bool tptp.collec111528142e_bool (tptp.hAPP_f1970439265l_bool (tptp.hAPP_f1850463605l_bool tptp.cOMBS_2138645332l_bool (tptp.hAPP_f482022705l_bool (tptp.cOMBB_2020112947e_bool tptp.fdisj) (tptp.hAPP_f854625363l_bool (tptp.hAPP_f2119687429l_bool tptp.cOMBC_1018307482l_bool tptp.fequal1746921144e_bool) A))) (tptp.hAPP_f1970439265l_bool (tptp.hAPP_f517001763l_bool tptp.cOMBC_1166591542l_bool tptp.member402455436e_bool) B))))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A) B) (tptp.hAPP_f921536533e_bool tptp.collec727977250_state (tptp.hAPP_f921536533e_bool (tptp.hAPP_f760664097e_bool tptp.cOMBS_1248383340l_bool (tptp.hAPP_f1558728829l_bool (tptp.cOMBB_1382207997_state tptp.fdisj) (tptp.hAPP_H1645666623e_bool (tptp.hAPP_f262880489e_bool tptp.cOMBC_1424981238e_bool tptp.fequal1531560888_state) A))) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1262649863e_bool tptp.cOMBC_764456866l_bool tptp.member1758697444_state) B))))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A) (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A) B)))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state A) (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A) B)))) (forall ((A_1 $$unsorted) (B $$unsorted)) (=> (= A_1 B) (not (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_1) B)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) A_1))))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (=> (= A_1 B) (not (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool A_1) B)) (not (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool B) A_1))))))) (forall ((C_1 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_1))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) C_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 C_1)))))) (forall ((C_1 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool A_1))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 B)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool B) C_1)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 C_1)))))) (forall ((X_1 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname X_1))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_1) B)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B)))))) (forall ((X_1 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_1))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool A_1) B)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 A_1)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 B)))))) (forall ((B $$unsorted) (X_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname X_1))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_1) B)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B)))))) (forall ((B $$unsorted) (X_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_1))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 A_1)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool A_1) B)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 B)))))) (forall ((X_1 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname X_1))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_1) B)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B)))))) (forall ((X_1 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_1))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool A_1) B)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 A_1)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 B)))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (=> (= A_1 B) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) A_1)))) (forall ((A_1 $$unsorted) (B $$unsorted)) (=> (= A_1 B) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool B) A_1)))) (forall ((A_1 $$unsorted) (B $$unsorted)) (=> (= A_1 B) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_1) B)))) (forall ((A_1 $$unsorted) (B $$unsorted)) (=> (= A_1 B) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool A_1) B)))) (forall ((A_1 $$unsorted) (B $$unsorted)) (=> (and (tptp.is_fun_pname_bool A_1) (tptp.is_fun_pname_bool B)) (= (= A_1 B) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_1) B)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) A_1)))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (= (= A_1 B) (and (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool A_1) B)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool B) A_1))))) (forall ((A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_1) A_1))) (forall ((A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool A_1) A_1))) (forall ((B_1 $$unsorted) (F $$unsorted) (X_1 $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_1) A_1)) (=> (= B_1 (tptp.hAPP_H1344248906_pname F X_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname B_1) (tptp.hAPP_f1745235422e_bool (tptp.image_1925245338_pname F) A_1)))))) (forall ((B_1 $$unsorted) (F $$unsorted) (X_1 $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A_1)) (=> (= B_1 (tptp.hAPP_p1842370726_state F X_1)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state B_1) (tptp.hAPP_f631639356e_bool (tptp.image_275883510_state F) A_1)))))) (forall ((F $$unsorted) (X_1 $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_1) A_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname (tptp.hAPP_H1344248906_pname F X_1)) (tptp.hAPP_f1745235422e_bool (tptp.image_1925245338_pname F) A_1))))) (forall ((F $$unsorted) (X_1 $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A_1)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state (tptp.hAPP_p1842370726_state F X_1)) (tptp.hAPP_f631639356e_bool (tptp.image_275883510_state F) A_1))))) (forall ((Z $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state Z) (tptp.hAPP_f631639356e_bool (tptp.image_275883510_state F) A_1))) (exists ((X_2 $$unsorted)) (and (tptp.is_pname X_2) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A_1)) (= Z (tptp.hAPP_p1842370726_state F X_2)))))) (forall ((P_1 $$unsorted) (Q_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f624840228l_bool tptp.cOMBS_350070575l_bool (tptp.hAPP_f143162813l_bool (tptp.cOMBB_2095475776e_bool tptp.fdisj) P_1)) Q_1)))) (and (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool P_1))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool Q_1)))))) (forall ((P_1 $$unsorted) (Q_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool (tptp.hAPP_f1970439265l_bool tptp.collec111528142e_bool (tptp.hAPP_f1970439265l_bool (tptp.hAPP_f1850463605l_bool tptp.cOMBS_2138645332l_bool (tptp.hAPP_f482022705l_bool (tptp.cOMBB_2020112947e_bool tptp.fdisj) P_1)) Q_1)))) (and (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool (tptp.hAPP_f1970439265l_bool tptp.collec111528142e_bool P_1))) (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool (tptp.hAPP_f1970439265l_bool tptp.collec111528142e_bool Q_1)))))) (forall ((P_1 $$unsorted) (Q_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state (tptp.hAPP_f921536533e_bool tptp.collec727977250_state (tptp.hAPP_f921536533e_bool (tptp.hAPP_f760664097e_bool tptp.cOMBS_1248383340l_bool (tptp.hAPP_f1558728829l_bool (tptp.cOMBB_1382207997_state tptp.fdisj) P_1)) Q_1)))) (and (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state (tptp.hAPP_f921536533e_bool tptp.collec727977250_state P_1))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state (tptp.hAPP_f921536533e_bool tptp.collec727977250_state Q_1)))))) (forall ((P_1 $$unsorted) (Q_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f759274231e_bool tptp.collect_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_f649174806e_bool tptp.cOMBS_568398431l_bool (tptp.hAPP_f1402196763l_bool (tptp.cOMBB_675860798_pname tptp.fdisj) P_1)) Q_1)))) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f759274231e_bool tptp.collect_pname P_1))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f759274231e_bool tptp.collect_pname Q_1)))))) (forall ((X_2 $$unsorted) (Xa $$unsorted)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname X_2) Xa) (tptp.hAPP_f759274231e_bool tptp.collect_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_f649174806e_bool tptp.cOMBS_568398431l_bool (tptp.hAPP_f1402196763l_bool (tptp.cOMBB_675860798_pname tptp.fdisj) (tptp.hAPP_p61793385e_bool (tptp.hAPP_f22061361e_bool tptp.cOMBC_1149511130e_bool tptp.fequal_pname) X_2))) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f661147897e_bool tptp.cOMBC_1058051404l_bool tptp.member_pname) Xa))))) (forall ((X_2 $$unsorted) (Xa $$unsorted)) (= (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool X_2) Xa) (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f624840228l_bool tptp.cOMBS_350070575l_bool (tptp.hAPP_f143162813l_bool (tptp.cOMBB_2095475776e_bool tptp.fdisj) (tptp.hAPP_f434788991l_bool (tptp.hAPP_f1297925993l_bool tptp.cOMBC_1284144636l_bool tptp.fequal533582459e_bool) X_2))) (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1145991873l_bool tptp.cOMBC_1988546018l_bool tptp.member799430823e_bool) Xa))))) (forall ((X_2 $$unsorted) (Xa $$unsorted)) (= (tptp.hAPP_f1970439265l_bool (tptp.hAPP_f601642911l_bool tptp.insert1991711667e_bool X_2) Xa) (tptp.hAPP_f1970439265l_bool tptp.collec111528142e_bool (tptp.hAPP_f1970439265l_bool (tptp.hAPP_f1850463605l_bool tptp.cOMBS_2138645332l_bool (tptp.hAPP_f482022705l_bool (tptp.cOMBB_2020112947e_bool tptp.fdisj) (tptp.hAPP_f854625363l_bool (tptp.hAPP_f2119687429l_bool tptp.cOMBC_1018307482l_bool tptp.fequal1746921144e_bool) X_2))) (tptp.hAPP_f1970439265l_bool (tptp.hAPP_f517001763l_bool tptp.cOMBC_1166591542l_bool tptp.member402455436e_bool) Xa))))) (forall ((X_2 $$unsorted) (Xa $$unsorted)) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state X_2) Xa) (tptp.hAPP_f921536533e_bool tptp.collec727977250_state (tptp.hAPP_f921536533e_bool (tptp.hAPP_f760664097e_bool tptp.cOMBS_1248383340l_bool (tptp.hAPP_f1558728829l_bool (tptp.cOMBB_1382207997_state tptp.fdisj) (tptp.hAPP_H1645666623e_bool (tptp.hAPP_f262880489e_bool tptp.cOMBC_1424981238e_bool tptp.fequal1531560888_state) X_2))) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1262649863e_bool tptp.cOMBC_764456866l_bool tptp.member1758697444_state) Xa))))) (forall ((A $$unsorted) (B_1 $$unsorted)) (=> (and (tptp.is_pname A) (tptp.is_pname B_1)) (=> (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A) tptp.bot_bo844097828e_bool) (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname B_1) tptp.bot_bo844097828e_bool)) (= A B_1)))) (forall ((A $$unsorted) (B_1 $$unsorted)) (=> (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A) tptp.bot_bo1055319631e_bool) (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state B_1) tptp.bot_bo1055319631e_bool)) (= A B_1))) (forall ((B_1 $$unsorted) (A $$unsorted)) (=> (and (tptp.is_pname B_1) (tptp.is_pname A)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname B_1) (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A) tptp.bot_bo844097828e_bool))) (= B_1 A)))) (forall ((B_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state B_1) (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A) tptp.bot_bo1055319631e_bool))) (= B_1 A))) (forall ((A $$unsorted) (B_1 $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.is_pname A) (tptp.is_pname B_1) (tptp.is_pname C) (tptp.is_pname D)) (= (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A) (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname B_1) tptp.bot_bo844097828e_bool)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname C) (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname D) tptp.bot_bo844097828e_bool))) (or (and (= A C) (= B_1 D)) (and (= A D) (= B_1 C)))))) (forall ((A $$unsorted) (B_1 $$unsorted) (C $$unsorted) (D $$unsorted)) (= (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A) (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state B_1) tptp.bot_bo1055319631e_bool)) (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state C) (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state D) tptp.bot_bo1055319631e_bool))) (or (and (= A C) (= B_1 D)) (and (= A D) (= B_1 C))))) (forall ((B_1 $$unsorted) (A $$unsorted)) (=> (and (tptp.is_pname B_1) (tptp.is_pname A)) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname B_1) (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A) tptp.bot_bo844097828e_bool))) (= B_1 A)))) (forall ((B_1 $$unsorted) (A $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state B_1) (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A) tptp.bot_bo1055319631e_bool))) (= B_1 A))) (forall ((A $$unsorted) (A_1 $$unsorted)) (not (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A) A_1) tptp.bot_bo844097828e_bool))) (forall ((A $$unsorted) (A_1 $$unsorted)) (not (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A) A_1) tptp.bot_bo1055319631e_bool))) (forall ((A $$unsorted) (A_1 $$unsorted)) (not (= tptp.bot_bo844097828e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A) A_1)))) (forall ((A $$unsorted) (A_1 $$unsorted)) (not (= tptp.bot_bo1055319631e_bool (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A) A_1)))) (forall ((A $$unsorted) (A_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool A) A_1))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A_1)))) (forall ((A $$unsorted) (A_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool (tptp.hAPP_f1970439265l_bool (tptp.hAPP_f601642911l_bool tptp.insert1991711667e_bool A) A_1))) (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool A_1)))) (forall ((A $$unsorted) (A_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A) A_1))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A_1)))) (forall ((A $$unsorted) (A_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A) A_1))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state A_1)))) (forall ((A_1 $$unsorted)) (=> (tptp.is_fun_pname_bool A_1) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_1) tptp.bot_bo844097828e_bool)) (= A_1 tptp.bot_bo844097828e_bool)))) (forall ((A_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool A_1) tptp.bot_bo1055319631e_bool)) (= A_1 tptp.bot_bo1055319631e_bool))) (forall ((F $$unsorted) (A_1 $$unsorted)) (= (= (tptp.hAPP_f1745235422e_bool (tptp.image_1925245338_pname F) A_1) tptp.bot_bo844097828e_bool) (= A_1 tptp.bot_bo1055319631e_bool))) (forall ((F $$unsorted) (A_1 $$unsorted)) (=> (tptp.is_fun_pname_bool A_1) (= (= (tptp.hAPP_f631639356e_bool (tptp.image_275883510_state F) A_1) tptp.bot_bo1055319631e_bool) (= A_1 tptp.bot_bo844097828e_bool)))) (forall ((F $$unsorted)) (= (tptp.hAPP_f1745235422e_bool (tptp.image_1925245338_pname F) tptp.bot_bo1055319631e_bool) tptp.bot_bo844097828e_bool)) (forall ((F $$unsorted)) (= (tptp.hAPP_f631639356e_bool (tptp.image_275883510_state F) tptp.bot_bo844097828e_bool) tptp.bot_bo1055319631e_bool)) (forall ((F $$unsorted) (A_1 $$unsorted)) (= (= tptp.bot_bo844097828e_bool (tptp.hAPP_f1745235422e_bool (tptp.image_1925245338_pname F) A_1)) (= A_1 tptp.bot_bo1055319631e_bool))) (forall ((F $$unsorted) (A_1 $$unsorted)) (=> (tptp.is_fun_pname_bool A_1) (= (= tptp.bot_bo1055319631e_bool (tptp.hAPP_f631639356e_bool (tptp.image_275883510_state F) A_1)) (= A_1 tptp.bot_bo844097828e_bool)))) (forall ((A_1 $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool A_1) B)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool B)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A_1))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f239102607l_bool (tptp.hAPP_f1269496639l_bool tptp.ord_le1076702565l_bool A_1) B)) (=> (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool B)) (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool A_1))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool A_1) B)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state B)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state A_1))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_1) B)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A_1))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool B)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool A_1) B)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A_1))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool B)) (=> (tptp.hBOOL (tptp.hAPP_f239102607l_bool (tptp.hAPP_f1269496639l_bool tptp.ord_le1076702565l_bool A_1) B)) (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool A_1))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state B)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool A_1) B)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state A_1))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_1) B)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A_1))))) (forall ((A $$unsorted) (C_1 $$unsorted) (D_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_p905327722e_bool tptp.insert_pname A))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool C_1) D_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool _let_1 C_1)) (tptp.hAPP_f759274231e_bool _let_1 D_1)))))) (forall ((A $$unsorted) (C_1 $$unsorted) (D_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool C_1) D_1)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool (tptp.hAPP_f921536533e_bool _let_1 C_1)) (tptp.hAPP_f921536533e_bool _let_1 D_1)))))) (forall ((X_1 $$unsorted) (A_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A_1)) (tptp.hBOOL (tptp.hAPP_pname_bool A_1 X_1)))) (forall ((X_1 $$unsorted) (A_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_1) A_1)) (tptp.hBOOL (tptp.hAPP_H513860823e_bool A_1 X_1)))) (forall ((P_1 $$unsorted)) (= (tptp.hAPP_f921536533e_bool tptp.collec727977250_state P_1) P_1)) (forall ((P_1 $$unsorted)) (=> (tptp.is_fun_pname_bool P_1) (= (tptp.hAPP_f759274231e_bool tptp.collect_pname P_1) P_1))) (forall ((P_1 $$unsorted)) (=> (tptp.is_fun1661590463l_bool P_1) (= (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool P_1) P_1))) (forall ((P_1 $$unsorted)) (= (tptp.hAPP_f1970439265l_bool tptp.collec111528142e_bool P_1) P_1)) (forall ((B_1 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_1))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname B_1) B)))))) (forall ((B_1 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool A_1))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 B)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state B_1) B)))))) (forall ((B $$unsorted) (X_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_1))) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A_1))) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1) B))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B)))))) (forall ((B $$unsorted) (X_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool A_1))) (=> (not (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_1) A_1))) (= (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state X_1) B))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 B)))))) (forall ((X_1 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1) A_1)) B)) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) B)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_1) B))))) (forall ((X_1 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state X_1) A_1)) B)) (and (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_1) B)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool A_1) B))))) (forall ((B $$unsorted) (A $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A) B)))) (forall ((B $$unsorted) (A $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool B) (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A) B)))) (forall ((F $$unsorted) (X_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1745235422e_bool (tptp.image_1925245338_pname F) A_1))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_1) A_1)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname (tptp.hAPP_H1344248906_pname F X_1)) _let_1) _let_1)))) (forall ((F $$unsorted) (X_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f631639356e_bool (tptp.image_275883510_state F) A_1))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A_1)) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state (tptp.hAPP_p1842370726_state F X_1)) _let_1) _let_1)))) (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.image_1925245338_pname F))) (= (tptp.hAPP_f1745235422e_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A) B)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname (tptp.hAPP_H1344248906_pname F A)) (tptp.hAPP_f1745235422e_bool _let_1 B))))) (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.image_275883510_state F))) (= (tptp.hAPP_f631639356e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A) B)) (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state (tptp.hAPP_p1842370726_state F A)) (tptp.hAPP_f631639356e_bool _let_1 B))))) (forall ((F $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.image_1925245338_pname F))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool A_1) B)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f1745235422e_bool _let_1 A_1)) (tptp.hAPP_f1745235422e_bool _let_1 B)))))) (forall ((F $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.image_275883510_state F))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_1) B)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool (tptp.hAPP_f631639356e_bool _let_1 A_1)) (tptp.hAPP_f631639356e_bool _let_1 B)))))) (forall ((B $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (=> (tptp.is_fun_pname_bool B) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) (tptp.hAPP_f1745235422e_bool (tptp.image_1925245338_pname F) A_1))) (exists ((AA $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool AA) A_1)) (= B (tptp.hAPP_f1745235422e_bool (tptp.image_1925245338_pname F) AA))))))) (forall ((B $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool B) (tptp.hAPP_f631639356e_bool (tptp.image_275883510_state F) A_1))) (exists ((AA $$unsorted)) (and (tptp.is_fun_pname_bool AA) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool AA) A_1)) (= B (tptp.hAPP_f631639356e_bool (tptp.image_275883510_state F) AA)))))) (forall ((M_1 $$unsorted) (A $$unsorted) (B_1 $$unsorted)) (=> (= (tptp.hAPP_p799580910on_com M_1 A) (tptp.some_com B_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A) (tptp.dom_pname_com M_1))))) (forall ((P_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f759274231e_bool tptp.collect_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_f649174806e_bool tptp.cOMBS_568398431l_bool (tptp.hAPP_f1402196763l_bool (tptp.cOMBB_675860798_pname tptp.fconj) (tptp.hAPP_p61793385e_bool (tptp.hAPP_f22061361e_bool tptp.cOMBC_1149511130e_bool tptp.fequal_pname) A))) P_1)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_pname_bool P_1 A)))) (and (=> _let_2 (= _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A) tptp.bot_bo844097828e_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bo844097828e_bool)))))) (forall ((P_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f624840228l_bool tptp.cOMBS_350070575l_bool (tptp.hAPP_f143162813l_bool (tptp.cOMBB_2095475776e_bool tptp.fconj) (tptp.hAPP_f434788991l_bool (tptp.hAPP_f1297925993l_bool tptp.cOMBC_1284144636l_bool tptp.fequal533582459e_bool) A))) P_1)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 A)))) (and (=> _let_2 (= _let_1 (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool A) tptp.bot_bo1649642514l_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bo1649642514l_bool)))))) (forall ((P_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f1970439265l_bool tptp.collec111528142e_bool (tptp.hAPP_f1970439265l_bool (tptp.hAPP_f1850463605l_bool tptp.cOMBS_2138645332l_bool (tptp.hAPP_f482022705l_bool (tptp.cOMBB_2020112947e_bool tptp.fconj) (tptp.hAPP_f854625363l_bool (tptp.hAPP_f2119687429l_bool tptp.cOMBC_1018307482l_bool tptp.fequal1746921144e_bool) A))) P_1)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_f1760790145l_bool P_1 A)))) (and (=> _let_2 (= _let_1 (tptp.hAPP_f1970439265l_bool (tptp.hAPP_f601642911l_bool tptp.insert1991711667e_bool A) tptp.bot_bo1325454745l_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bo1325454745l_bool)))))) (forall ((P_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f921536533e_bool tptp.collec727977250_state (tptp.hAPP_f921536533e_bool (tptp.hAPP_f760664097e_bool tptp.cOMBS_1248383340l_bool (tptp.hAPP_f1558728829l_bool (tptp.cOMBB_1382207997_state tptp.fconj) (tptp.hAPP_H1645666623e_bool (tptp.hAPP_f262880489e_bool tptp.cOMBC_1424981238e_bool tptp.fequal1531560888_state) A))) P_1)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_H513860823e_bool P_1 A)))) (and (=> _let_2 (= _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A) tptp.bot_bo1055319631e_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bo1055319631e_bool)))))) (forall ((P_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f759274231e_bool tptp.collect_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_f649174806e_bool tptp.cOMBS_568398431l_bool (tptp.hAPP_f1402196763l_bool (tptp.cOMBB_675860798_pname tptp.fconj) (tptp.hAPP_p61793385e_bool tptp.fequal_pname A))) P_1)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_pname_bool P_1 A)))) (and (=> _let_2 (= _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A) tptp.bot_bo844097828e_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bo844097828e_bool)))))) (forall ((P_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f624840228l_bool tptp.cOMBS_350070575l_bool (tptp.hAPP_f143162813l_bool (tptp.cOMBB_2095475776e_bool tptp.fconj) (tptp.hAPP_f434788991l_bool tptp.fequal533582459e_bool A))) P_1)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 A)))) (and (=> _let_2 (= _let_1 (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool A) tptp.bot_bo1649642514l_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bo1649642514l_bool)))))) (forall ((P_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f1970439265l_bool tptp.collec111528142e_bool (tptp.hAPP_f1970439265l_bool (tptp.hAPP_f1850463605l_bool tptp.cOMBS_2138645332l_bool (tptp.hAPP_f482022705l_bool (tptp.cOMBB_2020112947e_bool tptp.fconj) (tptp.hAPP_f854625363l_bool tptp.fequal1746921144e_bool A))) P_1)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_f1760790145l_bool P_1 A)))) (and (=> _let_2 (= _let_1 (tptp.hAPP_f1970439265l_bool (tptp.hAPP_f601642911l_bool tptp.insert1991711667e_bool A) tptp.bot_bo1325454745l_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bo1325454745l_bool)))))) (forall ((P_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f921536533e_bool tptp.collec727977250_state (tptp.hAPP_f921536533e_bool (tptp.hAPP_f760664097e_bool tptp.cOMBS_1248383340l_bool (tptp.hAPP_f1558728829l_bool (tptp.cOMBB_1382207997_state tptp.fconj) (tptp.hAPP_H1645666623e_bool tptp.fequal1531560888_state A))) P_1)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_H513860823e_bool P_1 A)))) (and (=> _let_2 (= _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A) tptp.bot_bo1055319631e_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bo1055319631e_bool)))))) (forall ((A $$unsorted)) (= (tptp.hAPP_f759274231e_bool tptp.collect_pname (tptp.hAPP_p61793385e_bool (tptp.hAPP_f22061361e_bool tptp.cOMBC_1149511130e_bool tptp.fequal_pname) A)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A) tptp.bot_bo844097828e_bool))) (forall ((A $$unsorted)) (= (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool (tptp.hAPP_f434788991l_bool (tptp.hAPP_f1297925993l_bool tptp.cOMBC_1284144636l_bool tptp.fequal533582459e_bool) A)) (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool A) tptp.bot_bo1649642514l_bool))) (forall ((A $$unsorted)) (= (tptp.hAPP_f1970439265l_bool tptp.collec111528142e_bool (tptp.hAPP_f854625363l_bool (tptp.hAPP_f2119687429l_bool tptp.cOMBC_1018307482l_bool tptp.fequal1746921144e_bool) A)) (tptp.hAPP_f1970439265l_bool (tptp.hAPP_f601642911l_bool tptp.insert1991711667e_bool A) tptp.bot_bo1325454745l_bool))) (forall ((A $$unsorted)) (= (tptp.hAPP_f921536533e_bool tptp.collec727977250_state (tptp.hAPP_H1645666623e_bool (tptp.hAPP_f262880489e_bool tptp.cOMBC_1424981238e_bool tptp.fequal1531560888_state) A)) (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A) tptp.bot_bo1055319631e_bool))) (forall ((A $$unsorted)) (= (tptp.hAPP_f759274231e_bool tptp.collect_pname (tptp.hAPP_p61793385e_bool tptp.fequal_pname A)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A) tptp.bot_bo844097828e_bool))) (forall ((A $$unsorted)) (= (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool (tptp.hAPP_f434788991l_bool tptp.fequal533582459e_bool A)) (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool A) tptp.bot_bo1649642514l_bool))) (forall ((A $$unsorted)) (= (tptp.hAPP_f1970439265l_bool tptp.collec111528142e_bool (tptp.hAPP_f854625363l_bool tptp.fequal1746921144e_bool A)) (tptp.hAPP_f1970439265l_bool (tptp.hAPP_f601642911l_bool tptp.insert1991711667e_bool A) tptp.bot_bo1325454745l_bool))) (forall ((A $$unsorted)) (= (tptp.hAPP_f921536533e_bool tptp.collec727977250_state (tptp.hAPP_H1645666623e_bool tptp.fequal1531560888_state A)) (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A) tptp.bot_bo1055319631e_bool))) (forall ((C $$unsorted) (G_1 $$unsorted)) (=> (tptp.hBOOL tptp.hoare_298929751gleton) (=> (forall ((X_2 $$unsorted)) (=> (tptp.is_pname X_2) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) (tptp.dom_pname_com tptp.body))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hoare_659004819_state G_1) (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state (tptp.hAPP_c1546227244_state tptp.hoare_Mirabelle_MGT (tptp.hAPP_pname_com tptp.body_1 X_2))) tptp.bot_bo1055319631e_bool)))))) (=> (tptp.hBOOL (tptp.hAPP_com_bool tptp.wt C)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hoare_659004819_state G_1) (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state (tptp.hAPP_c1546227244_state tptp.hoare_Mirabelle_MGT C)) tptp.bot_bo1055319631e_bool))))))) _let_12 (forall ((B_1 $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (=> (tptp.is_pname B_1) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname B_1) (tptp.hAPP_f1745235422e_bool (tptp.image_1925245338_pname F) A_1))) (not (forall ((X_2 $$unsorted)) (=> (= B_1 (tptp.hAPP_H1344248906_pname F X_2)) (not (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_2) A_1))))))))) (forall ((B_1 $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state B_1) (tptp.hAPP_f631639356e_bool (tptp.image_275883510_state F) A_1))) (not (forall ((X_2 $$unsorted)) (=> (tptp.is_pname X_2) (=> (= B_1 (tptp.hAPP_p1842370726_state F X_2)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A_1))))))))) (forall ((P_1 $$unsorted) (A_1 $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool Fa) A_1)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool P_1 tptp.bot_bo1649642514l_bool)) (=> (forall ((A_3 $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool A_3))) (=> (and (tptp.is_fun_pname_bool A_3) (tptp.is_fun1661590463l_bool F_1)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool F_1)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool _let_1 A_1)) (=> (not (tptp.hBOOL (tptp.hAPP_f1935102916l_bool _let_1 F_1))) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool P_1 F_1)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool P_1 (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool A_3) F_1)))))))))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool P_1 Fa))))))) (forall ((P_1 $$unsorted) (A_1 $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool Fa)) (=> (tptp.hBOOL (tptp.hAPP_f239102607l_bool (tptp.hAPP_f1269496639l_bool tptp.ord_le1076702565l_bool Fa) A_1)) (=> (tptp.hBOOL (tptp.hAPP_f239102607l_bool P_1 tptp.bot_bo1325454745l_bool)) (=> (forall ((A_3 $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f105100493l_bool tptp.member402455436e_bool A_3))) (=> (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool F_1)) (=> (tptp.hBOOL (tptp.hAPP_f239102607l_bool _let_1 A_1)) (=> (not (tptp.hBOOL (tptp.hAPP_f239102607l_bool _let_1 F_1))) (=> (tptp.hBOOL (tptp.hAPP_f239102607l_bool P_1 F_1)) (tptp.hBOOL (tptp.hAPP_f239102607l_bool P_1 (tptp.hAPP_f1970439265l_bool (tptp.hAPP_f601642911l_bool tptp.insert1991711667e_bool A_3) F_1))))))))) (tptp.hBOOL (tptp.hAPP_f239102607l_bool P_1 Fa))))))) (forall ((P_1 $$unsorted) (A_1 $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool Fa) A_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 tptp.bot_bo844097828e_bool)) (=> (forall ((A_3 $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname A_3))) (=> (and (tptp.is_pname A_3) (tptp.is_fun_pname_bool F_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname F_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A_1)) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 F_1))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 F_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A_3) F_1)))))))))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 Fa))))))) (forall ((P_1 $$unsorted) (A_1 $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool Fa) A_1)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool P_1 tptp.bot_bo1055319631e_bool)) (=> (forall ((A_3 $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_H248360617l_bool tptp.member1758697444_state A_3))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state F_1)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 A_1)) (=> (not (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 F_1))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool P_1 F_1)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool P_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A_3) F_1))))))))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool P_1 Fa))))))) (forall ((P $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_com_bool tptp.wt (tptp.hAPP_pname_com tptp.body_1 P))) (not (forall ((Y_2 $$unsorted)) (not (= (tptp.hAPP_p799580910on_com tptp.body P) (tptp.some_com Y_2))))))) (forall ((B $$unsorted) (A_1 $$unsorted)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname X_2))) (=> (tptp.is_pname X_2) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B)))))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_1) B)))) (forall ((B $$unsorted) (A_1 $$unsorted)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_2))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 A_1)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 B))))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool A_1) B)))) (forall ((F $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state B)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool B) (tptp.hAPP_f780887186e_bool (tptp.image_936554724_state F) A_1))) (exists ((C_3 $$unsorted)) (and (tptp.is_fun1661590463l_bool C_3) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool C_3) A_1)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool C_3)) (= B (tptp.hAPP_f780887186e_bool (tptp.image_936554724_state F) C_3))))))) (forall ((F $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state B)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool B) (tptp.hAPP_f772567431e_bool (tptp.image_774712299_state F) A_1))) (exists ((C_3 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f239102607l_bool (tptp.hAPP_f1269496639l_bool tptp.ord_le1076702565l_bool C_3) A_1)) (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool C_3)) (= B (tptp.hAPP_f772567431e_bool (tptp.image_774712299_state F) C_3))))))) (forall ((F $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (=> (tptp.is_fun_pname_bool B) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) (tptp.hAPP_f674760225e_bool (tptp.image_1283814551_pname F) A_1))) (exists ((C_3 $$unsorted)) (and (tptp.is_fun1661590463l_bool C_3) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool C_3) A_1)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool C_3)) (= B (tptp.hAPP_f674760225e_bool (tptp.image_1283814551_pname F) C_3)))))))) (forall ((F $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (=> (tptp.is_fun_pname_bool B) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) (tptp.hAPP_f280588268e_bool (tptp.image_636285904_pname F) A_1))) (exists ((C_3 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f239102607l_bool (tptp.hAPP_f1269496639l_bool tptp.ord_le1076702565l_bool C_3) A_1)) (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool C_3)) (= B (tptp.hAPP_f280588268e_bool (tptp.image_636285904_pname F) C_3)))))))) (forall ((F $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (=> (tptp.is_fun1661590463l_bool B) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool B)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool B) (tptp.hAPP_f748867288l_bool (tptp.image_1259634916e_bool F) A_1))) (exists ((C_3 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool C_3) A_1)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state C_3)) (= B (tptp.hAPP_f748867288l_bool (tptp.image_1259634916e_bool F) C_3)))))))) (forall ((F $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool B)) (=> (tptp.hBOOL (tptp.hAPP_f239102607l_bool (tptp.hAPP_f1269496639l_bool tptp.ord_le1076702565l_bool B) (tptp.hAPP_f854625363l_bool (tptp.image_277167759e_bool F) A_1))) (exists ((C_3 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool C_3) A_1)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state C_3)) (= B (tptp.hAPP_f854625363l_bool (tptp.image_277167759e_bool F) C_3))))))) (forall ((F $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (=> (tptp.is_fun_pname_bool B) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) (tptp.hAPP_f1745235422e_bool (tptp.image_1925245338_pname F) A_1))) (exists ((C_3 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool C_3) A_1)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state C_3)) (= B (tptp.hAPP_f1745235422e_bool (tptp.image_1925245338_pname F) C_3)))))))) (forall ((F $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (=> (tptp.is_fun1661590463l_bool B) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool B)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool B) (tptp.hAPP_f434788991l_bool (tptp.image_47868345e_bool F) A_1))) (exists ((C_3 $$unsorted)) (and (tptp.is_fun_pname_bool C_3) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool C_3) A_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname C_3)) (= B (tptp.hAPP_f434788991l_bool (tptp.image_47868345e_bool F) C_3)))))))) (forall ((F $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool B)) (=> (tptp.hBOOL (tptp.hAPP_f239102607l_bool (tptp.hAPP_f1269496639l_bool tptp.ord_le1076702565l_bool B) (tptp.hAPP_f1874607724l_bool (tptp.image_505480954e_bool F) A_1))) (exists ((C_3 $$unsorted)) (and (tptp.is_fun_pname_bool C_3) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool C_3) A_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname C_3)) (= B (tptp.hAPP_f1874607724l_bool (tptp.image_505480954e_bool F) C_3))))))) (forall ((F $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (=> (tptp.is_fun_pname_bool B) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) (tptp.hAPP_f759274231e_bool (tptp.image_pname_pname F) A_1))) (exists ((C_3 $$unsorted)) (and (tptp.is_fun_pname_bool C_3) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool C_3) A_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname C_3)) (= B (tptp.hAPP_f759274231e_bool (tptp.image_pname_pname F) C_3)))))))) (forall ((F $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state B)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool B) (tptp.hAPP_f631639356e_bool (tptp.image_275883510_state F) A_1))) (exists ((C_3 $$unsorted)) (and (tptp.is_fun_pname_bool C_3) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool C_3) A_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname C_3)) (= B (tptp.hAPP_f631639356e_bool (tptp.image_275883510_state F) C_3))))))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname _let_3)) (forall ((P_1 $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool P_1 tptp.bot_bo1649642514l_bool)) (=> (forall ((X_2 $$unsorted) (F_1 $$unsorted)) (=> (and (tptp.is_fun_pname_bool X_2) (tptp.is_fun1661590463l_bool F_1)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool F_1)) (=> (not (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool X_2) F_1))) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool P_1 F_1)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool P_1 (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool X_2) F_1)))))))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool P_1 Fa)))))) (forall ((P_1 $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool Fa)) (=> (tptp.hBOOL (tptp.hAPP_f239102607l_bool P_1 tptp.bot_bo1325454745l_bool)) (=> (forall ((X_2 $$unsorted) (F_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool F_1)) (=> (not (tptp.hBOOL (tptp.hAPP_f239102607l_bool (tptp.hAPP_f105100493l_bool tptp.member402455436e_bool X_2) F_1))) (=> (tptp.hBOOL (tptp.hAPP_f239102607l_bool P_1 F_1)) (tptp.hBOOL (tptp.hAPP_f239102607l_bool P_1 (tptp.hAPP_f1970439265l_bool (tptp.hAPP_f601642911l_bool tptp.insert1991711667e_bool X_2) F_1))))))) (tptp.hBOOL (tptp.hAPP_f239102607l_bool P_1 Fa)))))) (forall ((P_1 $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 tptp.bot_bo844097828e_bool)) (=> (forall ((X_2 $$unsorted) (F_1 $$unsorted)) (=> (and (tptp.is_pname X_2) (tptp.is_fun_pname_bool F_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname F_1)) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) F_1))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 F_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname X_2) F_1)))))))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 Fa)))))) (forall ((P_1 $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool P_1 tptp.bot_bo1055319631e_bool)) (=> (forall ((X_2 $$unsorted) (F_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state F_1)) (=> (not (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_2) F_1))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool P_1 F_1)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool P_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state X_2) F_1))))))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool P_1 Fa)))))) (forall ((A $$unsorted)) (=> (tptp.is_fun1661590463l_bool A) (= (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)) (or (= A tptp.bot_bo1649642514l_bool) (exists ((A_4 $$unsorted) (A_3 $$unsorted)) (and (tptp.is_fun1661590463l_bool A_4) (tptp.is_fun_pname_bool A_3) (= A (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool A_3) A_4)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A_4)))))))) (forall ((A $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool A)) (or (= A tptp.bot_bo1325454745l_bool) (exists ((A_4 $$unsorted) (A_3 $$unsorted)) (and (= A (tptp.hAPP_f1970439265l_bool (tptp.hAPP_f601642911l_bool tptp.insert1991711667e_bool A_3) A_4)) (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool A_4))))))) (forall ((A $$unsorted)) (=> (tptp.is_fun_pname_bool A) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (or (= A tptp.bot_bo844097828e_bool) (exists ((A_4 $$unsorted) (A_3 $$unsorted)) (and (tptp.is_fun_pname_bool A_4) (tptp.is_pname A_3) (= A (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A_3) A_4)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A_4)))))))) (forall ((A $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state A)) (or (= A tptp.bot_bo1055319631e_bool) (exists ((A_4 $$unsorted) (A_3 $$unsorted)) (and (= A (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A_3) A_4)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state A_4))))))) (forall ((F $$unsorted) (A_1 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A_1))) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.hAPP_f434788991l_bool (tptp.image_47868345e_bool F) A_1))) (exists ((X_2 $$unsorted)) (and (tptp.is_pname X_2) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A_1)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f759274231e_bool tptp.collect_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_f649174806e_bool tptp.cOMBS_568398431l_bool (tptp.hAPP_f1402196763l_bool (tptp.cOMBB_675860798_pname tptp.fconj) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f661147897e_bool tptp.cOMBC_1058051404l_bool tptp.member_pname) A_1))) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f661147897e_bool tptp.cOMBC_1058051404l_bool (tptp.hAPP_f567934427l_bool (tptp.cOMBB_408569982_pname tptp.fequal533582459e_bool) F)) (tptp.hAPP_p61793385e_bool F X_2)))))))))))) (forall ((F $$unsorted) (A_1 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A_1))) (=> (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool (tptp.hAPP_f1874607724l_bool (tptp.image_505480954e_bool F) A_1))) (exists ((X_2 $$unsorted)) (and (tptp.is_pname X_2) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A_1)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f759274231e_bool tptp.collect_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_f649174806e_bool tptp.cOMBS_568398431l_bool (tptp.hAPP_f1402196763l_bool (tptp.cOMBB_675860798_pname tptp.fconj) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f661147897e_bool tptp.cOMBC_1058051404l_bool tptp.member_pname) A_1))) (tptp.hAPP_f1745235422e_bool (tptp.hAPP_f1558052123e_bool tptp.cOMBC_2140141647l_bool (tptp.hAPP_f2081555625l_bool (tptp.cOMBB_44445098_pname tptp.fequal1746921144e_bool) F)) (tptp.hAPP_p877885514e_bool F X_2)))))))))))) (forall ((F $$unsorted) (A_1 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state A_1))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state (tptp.hAPP_f921536533e_bool (tptp.image_650584225_state F) A_1))) (exists ((X_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_2) A_1)) (not (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state (tptp.hAPP_f921536533e_bool tptp.collec727977250_state (tptp.hAPP_f921536533e_bool (tptp.hAPP_f760664097e_bool tptp.cOMBS_1248383340l_bool (tptp.hAPP_f1558728829l_bool (tptp.cOMBB_1382207997_state tptp.fconj) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1262649863e_bool tptp.cOMBC_764456866l_bool tptp.member1758697444_state) A_1))) (tptp.hAPP_H1645666623e_bool (tptp.hAPP_f262880489e_bool tptp.cOMBC_1424981238e_bool (tptp.hAPP_f1844318385e_bool (tptp.cOMBB_291471741_state tptp.fequal1531560888_state) F)) (tptp.hAPP_H563960305_state F X_2)))))))))))) (forall ((F $$unsorted) (A_1 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A_1))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state (tptp.hAPP_f780887186e_bool (tptp.image_936554724_state F) A_1))) (exists ((X_2 $$unsorted)) (and (tptp.is_fun_pname_bool X_2) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool X_2) A_1)) (not (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f624840228l_bool tptp.cOMBS_350070575l_bool (tptp.hAPP_f143162813l_bool (tptp.cOMBB_2095475776e_bool tptp.fconj) (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1145991873l_bool tptp.cOMBC_1988546018l_bool tptp.member799430823e_bool) A_1))) (tptp.hAPP_H737849090l_bool (tptp.hAPP_f261382953l_bool tptp.cOMBC_2107548985e_bool (tptp.hAPP_f547518321e_bool (tptp.cOMBB_1170234304e_bool tptp.fequal1531560888_state) F)) (tptp.hAPP_f1308959284_state F X_2)))))))))))) (forall ((F $$unsorted) (A_1 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool A_1))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state (tptp.hAPP_f772567431e_bool (tptp.image_774712299_state F) A_1))) (exists ((X_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f239102607l_bool (tptp.hAPP_f105100493l_bool tptp.member402455436e_bool X_2) A_1)) (not (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool (tptp.hAPP_f1970439265l_bool tptp.collec111528142e_bool (tptp.hAPP_f1970439265l_bool (tptp.hAPP_f1850463605l_bool tptp.cOMBS_2138645332l_bool (tptp.hAPP_f482022705l_bool (tptp.cOMBB_2020112947e_bool tptp.fconj) (tptp.hAPP_f1970439265l_bool (tptp.hAPP_f517001763l_bool tptp.cOMBC_1166591542l_bool tptp.member402455436e_bool) A_1))) (tptp.hAPP_H248360617l_bool (tptp.hAPP_f492098723l_bool tptp.cOMBC_1305755390e_bool (tptp.hAPP_f481659057e_bool (tptp.cOMBB_1099197107e_bool tptp.fequal1531560888_state) F)) (tptp.hAPP_f2143211163_state F X_2)))))))))))) (forall ((F $$unsorted) (A_1 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A_1))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f759274231e_bool (tptp.image_pname_pname F) A_1))) (exists ((X_2 $$unsorted)) (and (tptp.is_pname X_2) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A_1)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f759274231e_bool tptp.collect_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_f649174806e_bool tptp.cOMBS_568398431l_bool (tptp.hAPP_f1402196763l_bool (tptp.cOMBB_675860798_pname tptp.fconj) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f661147897e_bool tptp.cOMBC_1058051404l_bool tptp.member_pname) A_1))) (tptp.hAPP_p61793385e_bool (tptp.hAPP_f22061361e_bool tptp.cOMBC_1149511130e_bool (tptp.hAPP_f1336811455e_bool (tptp.cOMBB_542850580_pname tptp.fequal_pname) F)) (tptp.hAPP_pname_pname F X_2)))))))))))) (forall ((F $$unsorted) (A_1 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state A_1))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f1745235422e_bool (tptp.image_1925245338_pname F) A_1))) (exists ((X_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_2) A_1)) (not (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state (tptp.hAPP_f921536533e_bool tptp.collec727977250_state (tptp.hAPP_f921536533e_bool (tptp.hAPP_f760664097e_bool tptp.cOMBS_1248383340l_bool (tptp.hAPP_f1558728829l_bool (tptp.cOMBB_1382207997_state tptp.fconj) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1262649863e_bool tptp.cOMBC_764456866l_bool tptp.member1758697444_state) A_1))) (tptp.hAPP_p877885514e_bool (tptp.hAPP_f294904177e_bool tptp.cOMBC_725526061e_bool (tptp.hAPP_f833390165e_bool (tptp.cOMBB_1456120487_state tptp.fequal_pname) F)) (tptp.hAPP_H1344248906_pname F X_2)))))))))))) (forall ((F $$unsorted) (A_1 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A_1))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f674760225e_bool (tptp.image_1283814551_pname F) A_1))) (exists ((X_2 $$unsorted)) (and (tptp.is_fun_pname_bool X_2) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool X_2) A_1)) (not (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f624840228l_bool tptp.cOMBS_350070575l_bool (tptp.hAPP_f143162813l_bool (tptp.cOMBB_2095475776e_bool tptp.fconj) (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1145991873l_bool tptp.cOMBC_1988546018l_bool tptp.member799430823e_bool) A_1))) (tptp.hAPP_p338031245l_bool (tptp.hAPP_f2082757169l_bool tptp.cOMBC_1004116266e_bool (tptp.hAPP_f1385420507e_bool (tptp.cOMBB_598082538e_bool tptp.fequal_pname) F)) (tptp.hAPP_f1297739591_pname F X_2)))))))))))) (forall ((F $$unsorted) (A_1 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool A_1))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f280588268e_bool (tptp.image_636285904_pname F) A_1))) (exists ((X_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f239102607l_bool (tptp.hAPP_f105100493l_bool tptp.member402455436e_bool X_2) A_1)) (not (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool (tptp.hAPP_f1970439265l_bool tptp.collec111528142e_bool (tptp.hAPP_f1970439265l_bool (tptp.hAPP_f1850463605l_bool tptp.cOMBS_2138645332l_bool (tptp.hAPP_f482022705l_bool (tptp.cOMBB_2020112947e_bool tptp.fconj) (tptp.hAPP_f1970439265l_bool (tptp.hAPP_f517001763l_bool tptp.cOMBC_1166591542l_bool tptp.member402455436e_bool) A_1))) (tptp.hAPP_p1617973726l_bool (tptp.hAPP_f2070658331l_bool tptp.cOMBC_367297061e_bool (tptp.hAPP_f1973135743e_bool (tptp.cOMBB_1671808265e_bool tptp.fequal_pname) F)) (tptp.hAPP_f1008690464_pname F X_2)))))))))))) (forall ((F $$unsorted) (A_1 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state A_1))) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.hAPP_f748867288l_bool (tptp.image_1259634916e_bool F) A_1))) (exists ((X_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_2) A_1)) (not (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state (tptp.hAPP_f921536533e_bool tptp.collec727977250_state (tptp.hAPP_f921536533e_bool (tptp.hAPP_f760664097e_bool tptp.cOMBS_1248383340l_bool (tptp.hAPP_f1558728829l_bool (tptp.cOMBB_1382207997_state tptp.fconj) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1262649863e_bool tptp.cOMBC_764456866l_bool tptp.member1758697444_state) A_1))) (tptp.hAPP_f631639356e_bool (tptp.hAPP_f1721106985e_bool tptp.cOMBC_498627897l_bool (tptp.hAPP_f376825399l_bool (tptp.cOMBB_1722165949_state tptp.fequal533582459e_bool) F)) (tptp.hAPP_H1632039476e_bool F X_2)))))))))))) (forall ((F $$unsorted) (A_1 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state A_1))) (=> (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool (tptp.hAPP_f854625363l_bool (tptp.image_277167759e_bool F) A_1))) (exists ((X_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_2) A_1)) (not (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state (tptp.hAPP_f921536533e_bool tptp.collec727977250_state (tptp.hAPP_f921536533e_bool (tptp.hAPP_f760664097e_bool tptp.cOMBS_1248383340l_bool (tptp.hAPP_f1558728829l_bool (tptp.cOMBB_1382207997_state tptp.fconj) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1262649863e_bool tptp.cOMBC_764456866l_bool tptp.member1758697444_state) A_1))) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1262649863e_bool tptp.cOMBC_764456866l_bool (tptp.hAPP_f1862834069l_bool (tptp.cOMBB_1239130257_state tptp.fequal1746921144e_bool) F)) (tptp.hAPP_H1645666623e_bool F X_2)))))))))))) (forall ((F $$unsorted) (A_1 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A_1))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state (tptp.hAPP_f631639356e_bool (tptp.image_275883510_state F) A_1))) (exists ((X_2 $$unsorted)) (and (tptp.is_pname X_2) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A_1)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f759274231e_bool tptp.collect_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_f649174806e_bool tptp.cOMBS_568398431l_bool (tptp.hAPP_f1402196763l_bool (tptp.cOMBB_675860798_pname tptp.fconj) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f661147897e_bool tptp.cOMBC_1058051404l_bool tptp.member_pname) A_1))) (tptp.hAPP_H1632039476e_bool (tptp.hAPP_f167506745e_bool tptp.cOMBC_290948233e_bool (tptp.hAPP_f998786331e_bool (tptp.cOMBB_799949246_pname tptp.fequal1531560888_state) F)) (tptp.hAPP_p1842370726_state F X_2)))))))))))) (forall ((Pname_2 $$unsorted) (Pname_1 $$unsorted)) (=> (and (tptp.is_pname Pname_2) (tptp.is_pname Pname_1)) (= (= (tptp.hAPP_pname_com tptp.body_1 Pname_2) (tptp.hAPP_pname_com tptp.body_1 Pname_1)) (= Pname_2 Pname_1)))) (forall ((G_1 $$unsorted) (Procs $$unsorted)) (let ((_let_1 (tptp.cOMBB_422605457_pname tptp.hoare_Mirabelle_MGT))) (let ((_let_2 (tptp.hAPP_f631639356e_bool (tptp.image_275883510_state (tptp.hAPP_f1758910594_state _let_1 tptp.body_1)) Procs))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hoare_659004819_state (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool G_1) _let_2)) (tptp.hAPP_f631639356e_bool (tptp.image_275883510_state (tptp.hAPP_f1758910594_state _let_1 (tptp.hAPP_f96342628me_com (tptp.cOMBB_923936821_pname tptp.the_com) tptp.body))) Procs))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname Procs)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hoare_659004819_state G_1) _let_2))))))) (forall ((A $$unsorted) (M_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A) (tptp.dom_pname_com M_1))) (exists ((B_3 $$unsorted)) (= (tptp.hAPP_p799580910on_com M_1 A) (tptp.some_com B_3))))) (forall ((X_1 $$unsorted)) (=> (tptp.is_pname X_1) (= (tptp.hAPP_f1297739591_pname tptp.the_elem_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1) tptp.bot_bo844097828e_bool)) X_1))) (forall ((X_1 $$unsorted)) (= (tptp.hAPP_f2143211163_state tptp.the_el23965208_state (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state X_1) tptp.bot_bo1055319631e_bool)) X_1)) (forall ((F $$unsorted) (B $$unsorted) (A_1 $$unsorted)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_2) A_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname (tptp.hAPP_H1344248906_pname F X_2)) B)))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f1745235422e_bool (tptp.image_1925245338_pname F) A_1)) B)))) (forall ((F $$unsorted) (B $$unsorted) (A_1 $$unsorted)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.is_pname X_2) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A_1)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state (tptp.hAPP_p1842370726_state F X_2)) B))))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool (tptp.hAPP_f631639356e_bool (tptp.image_275883510_state F) A_1)) B)))) (forall ((X_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool X_1) X_1))) (forall ((X_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool X_1) X_1))) (forall ((A_1 $$unsorted)) (=> (tptp.is_fun_pname_bool A_1) (= (not (= A_1 tptp.bot_bo844097828e_bool)) (exists ((X_2 $$unsorted) (B_2 $$unsorted)) (and (tptp.is_pname X_2) (tptp.is_fun_pname_bool B_2) (= A_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname X_2) B_2)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) B_2)))))))) (forall ((A_1 $$unsorted)) (= (not (= A_1 tptp.bot_bo1055319631e_bool)) (exists ((X_2 $$unsorted) (B_2 $$unsorted)) (and (= A_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state X_2) B_2)) (not (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_2) B_2))))))) (forall ((X_4 $$unsorted)) (= (tptp.hAPP_option_com_com tptp.the_com (tptp.some_com X_4)) X_4)) (forall ((G_1 $$unsorted) (P_1 $$unsorted) (Pn_1 $$unsorted) (Q_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1949912908_state tptp.hoare_1575745797_state P_1))) (let ((_let_2 (tptp.hoare_659004819_state G_1))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_2 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state (tptp.hAPP_f588507005_state (tptp.hAPP_c408625258_state _let_1 (tptp.hAPP_option_com_com tptp.the_com (tptp.hAPP_p799580910on_com tptp.body Pn_1))) Q_1)) tptp.bot_bo1055319631e_bool))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_2 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state (tptp.hAPP_f588507005_state (tptp.hAPP_c408625258_state _let_1 (tptp.hAPP_pname_com tptp.body_1 Pn_1)) Q_1)) tptp.bot_bo1055319631e_bool))))))) (forall ((A_1 $$unsorted) (C $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname C))) (=> (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A_1))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A_1) B)))))) (forall ((A_1 $$unsorted) (C $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H248360617l_bool tptp.member1758697444_state C))) (=> (=> (not (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 B))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 A_1))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool A_1) B)))))) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname C))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A_1) B))) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A_1))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B)))))) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H248360617l_bool tptp.member1758697444_state C))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool A_1) B))) (=> (not (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 A_1))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 B)))))) (forall ((P_1 $$unsorted) (Q_1 $$unsorted)) (= (tptp.hAPP_f759274231e_bool tptp.collect_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_f649174806e_bool tptp.cOMBS_568398431l_bool (tptp.hAPP_f1402196763l_bool (tptp.cOMBB_675860798_pname tptp.fdisj) P_1)) Q_1)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool (tptp.hAPP_f759274231e_bool tptp.collect_pname P_1)) (tptp.hAPP_f759274231e_bool tptp.collect_pname Q_1)))) (forall ((P_1 $$unsorted) (Q_1 $$unsorted)) (= (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f624840228l_bool tptp.cOMBS_350070575l_bool (tptp.hAPP_f143162813l_bool (tptp.cOMBB_2095475776e_bool tptp.fdisj) P_1)) Q_1)) (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.semila1782091504l_bool (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool P_1)) (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool Q_1)))) (forall ((P_1 $$unsorted) (Q_1 $$unsorted)) (= (tptp.hAPP_f1970439265l_bool tptp.collec111528142e_bool (tptp.hAPP_f1970439265l_bool (tptp.hAPP_f1850463605l_bool tptp.cOMBS_2138645332l_bool (tptp.hAPP_f482022705l_bool (tptp.cOMBB_2020112947e_bool tptp.fdisj) P_1)) Q_1)) (tptp.hAPP_f1970439265l_bool (tptp.hAPP_f1587382801l_bool tptp.semila2055205435l_bool (tptp.hAPP_f1970439265l_bool tptp.collec111528142e_bool P_1)) (tptp.hAPP_f1970439265l_bool tptp.collec111528142e_bool Q_1)))) (forall ((P_1 $$unsorted) (Q_1 $$unsorted)) (= (tptp.hAPP_f921536533e_bool tptp.collec727977250_state (tptp.hAPP_f921536533e_bool (tptp.hAPP_f760664097e_bool tptp.cOMBS_1248383340l_bool (tptp.hAPP_f1558728829l_bool (tptp.cOMBB_1382207997_state tptp.fdisj) P_1)) Q_1)) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool (tptp.hAPP_f921536533e_bool tptp.collec727977250_state P_1)) (tptp.hAPP_f921536533e_bool tptp.collec727977250_state Q_1)))) (forall ((Fun1_2 $$unsorted) (Com_2 $$unsorted) (Fun2_2 $$unsorted) (Fun1_1 $$unsorted) (Com_1 $$unsorted) (Fun2_1 $$unsorted)) (= (= (tptp.hAPP_f588507005_state (tptp.hAPP_c408625258_state (tptp.hAPP_f1949912908_state tptp.hoare_1575745797_state Fun1_2) Com_2) Fun2_2) (tptp.hAPP_f588507005_state (tptp.hAPP_c408625258_state (tptp.hAPP_f1949912908_state tptp.hoare_1575745797_state Fun1_1) Com_1) Fun2_1)) (and (= Fun1_2 Fun1_1) (= Com_2 Com_1) (= Fun2_2 Fun2_1)))) (forall ((A_1 $$unsorted) (C $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname C))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A_1) B)))))) (forall ((A_1 $$unsorted) (C $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H248360617l_bool tptp.member1758697444_state C))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 B)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool A_1) B)))))) (forall ((B $$unsorted) (C $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname C))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A_1) B)))))) (forall ((B $$unsorted) (C $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_H248360617l_bool tptp.member1758697444_state C))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 A_1)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool A_1) B)))))) (forall ((P_1 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (= (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_2) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool A_1) B))) (tptp.hBOOL (tptp.hAPP_H513860823e_bool P_1 X_2)))) (and (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_2) A_1)) (tptp.hBOOL (tptp.hAPP_H513860823e_bool P_1 X_2)))) (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_2) B)) (tptp.hBOOL (tptp.hAPP_H513860823e_bool P_1 X_2))))))) (forall ((P_1 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (= (exists ((X_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_2) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool A_1) B))) (tptp.hBOOL (tptp.hAPP_H513860823e_bool P_1 X_2)))) (or (exists ((X_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_2) A_1)) (tptp.hBOOL (tptp.hAPP_H513860823e_bool P_1 X_2)))) (exists ((X_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_2) B)) (tptp.hBOOL (tptp.hAPP_H513860823e_bool P_1 X_2))))))) (forall ((A_1 $$unsorted) (B $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool A_1))) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool (tptp.hAPP_f921536533e_bool _let_1 B)) C_1) (tptp.hAPP_f921536533e_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool B) C_1))))) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname C))) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A_1) B))) (or (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B)))))) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H248360617l_bool tptp.member1758697444_state C))) (= (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool A_1) B))) (or (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 A_1)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 B)))))) (forall ((A_1 $$unsorted) (B $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool A_1))) (let ((_let_2 (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool B))) (= (tptp.hAPP_f921536533e_bool _let_1 (tptp.hAPP_f921536533e_bool _let_2 C_1)) (tptp.hAPP_f921536533e_bool _let_2 (tptp.hAPP_f921536533e_bool _let_1 C_1)))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool A_1))) (let ((_let_2 (tptp.hAPP_f921536533e_bool _let_1 B))) (= (tptp.hAPP_f921536533e_bool _let_1 _let_2) _let_2)))) (forall ((A_1 $$unsorted) (B $$unsorted)) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool A_1) B) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool B) A_1))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f661147897e_bool tptp.cOMBC_1058051404l_bool tptp.member_pname))) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A_1) B) (tptp.hAPP_f759274231e_bool tptp.collect_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_f649174806e_bool tptp.cOMBS_568398431l_bool (tptp.hAPP_f1402196763l_bool (tptp.cOMBB_675860798_pname tptp.fdisj) (tptp.hAPP_f759274231e_bool _let_1 A_1))) (tptp.hAPP_f759274231e_bool _let_1 B)))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f1145991873l_bool tptp.cOMBC_1988546018l_bool tptp.member799430823e_bool))) (= (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.semila1782091504l_bool A_1) B) (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f624840228l_bool tptp.cOMBS_350070575l_bool (tptp.hAPP_f143162813l_bool (tptp.cOMBB_2095475776e_bool tptp.fdisj) (tptp.hAPP_f559147733l_bool _let_1 A_1))) (tptp.hAPP_f559147733l_bool _let_1 B)))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f517001763l_bool tptp.cOMBC_1166591542l_bool tptp.member402455436e_bool))) (= (tptp.hAPP_f1970439265l_bool (tptp.hAPP_f1587382801l_bool tptp.semila2055205435l_bool A_1) B) (tptp.hAPP_f1970439265l_bool tptp.collec111528142e_bool (tptp.hAPP_f1970439265l_bool (tptp.hAPP_f1850463605l_bool tptp.cOMBS_2138645332l_bool (tptp.hAPP_f482022705l_bool (tptp.cOMBB_2020112947e_bool tptp.fdisj) (tptp.hAPP_f1970439265l_bool _let_1 A_1))) (tptp.hAPP_f1970439265l_bool _let_1 B)))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f1262649863e_bool tptp.cOMBC_764456866l_bool tptp.member1758697444_state))) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool A_1) B) (tptp.hAPP_f921536533e_bool tptp.collec727977250_state (tptp.hAPP_f921536533e_bool (tptp.hAPP_f760664097e_bool tptp.cOMBS_1248383340l_bool (tptp.hAPP_f1558728829l_bool (tptp.cOMBB_1382207997_state tptp.fdisj) (tptp.hAPP_f921536533e_bool _let_1 A_1))) (tptp.hAPP_f921536533e_bool _let_1 B)))))) (forall ((A_1 $$unsorted)) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool A_1) A_1) A_1)) (forall ((A_1 $$unsorted) (B $$unsorted)) (=> (and (tptp.is_fun_pname_bool A_1) (tptp.is_fun_pname_bool B)) (= (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A_1) B) tptp.bot_bo844097828e_bool) (and (= A_1 tptp.bot_bo844097828e_bool) (= B tptp.bot_bo844097828e_bool))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (= (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool A_1) B) tptp.bot_bo1055319631e_bool) (and (= A_1 tptp.bot_bo1055319631e_bool) (= B tptp.bot_bo1055319631e_bool)))) (forall ((A_1 $$unsorted)) (=> (tptp.is_fun_pname_bool A_1) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A_1) tptp.bot_bo844097828e_bool) A_1))) (forall ((A_1 $$unsorted)) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool A_1) tptp.bot_bo1055319631e_bool) A_1)) (forall ((B $$unsorted)) (=> (tptp.is_fun_pname_bool B) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool tptp.bot_bo844097828e_bool) B) B))) (forall ((B $$unsorted)) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool tptp.bot_bo1055319631e_bool) B) B)) (forall ((G_1 $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool G_1)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.semila1782091504l_bool Fa) G_1)))))) (forall ((G_1 $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool Fa)) (=> (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool G_1)) (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool (tptp.hAPP_f1970439265l_bool (tptp.hAPP_f1587382801l_bool tptp.semila2055205435l_bool Fa) G_1)))))) (forall ((G_1 $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname G_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool Fa) G_1)))))) (forall ((G_1 $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state G_1)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool Fa) G_1)))))) (forall ((Fa $$unsorted) (G_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.semila1782091504l_bool Fa) G_1))) (and (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool Fa)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool G_1))))) (forall ((Fa $$unsorted) (G_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool (tptp.hAPP_f1970439265l_bool (tptp.hAPP_f1587382801l_bool tptp.semila2055205435l_bool Fa) G_1))) (and (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool Fa)) (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool G_1))))) (forall ((Fa $$unsorted) (G_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool Fa) G_1))) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname Fa)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname G_1))))) (forall ((Fa $$unsorted) (G_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool Fa) G_1))) (and (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state Fa)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state G_1))))) (forall ((A $$unsorted) (B $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_p905327722e_bool tptp.insert_pname A))) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool (tptp.hAPP_f759274231e_bool _let_1 B)) C_1) (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool B) C_1))))) (forall ((A $$unsorted) (B $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A))) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool (tptp.hAPP_f921536533e_bool _let_1 B)) C_1) (tptp.hAPP_f921536533e_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool B) C_1))))) (forall ((A_1 $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A_1))) (let ((_let_2 (tptp.hAPP_p905327722e_bool tptp.insert_pname A))) (= (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool _let_2 B)) (tptp.hAPP_f759274231e_bool _let_2 (tptp.hAPP_f759274231e_bool _let_1 B)))))) (forall ((A_1 $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool A_1))) (let ((_let_2 (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A))) (= (tptp.hAPP_f921536533e_bool _let_1 (tptp.hAPP_f921536533e_bool _let_2 B)) (tptp.hAPP_f921536533e_bool _let_2 (tptp.hAPP_f921536533e_bool _let_1 B)))))) (forall ((B $$unsorted) (D_1 $$unsorted) (A_1 $$unsorted) (C_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_1) C_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) D_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A_1) B)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool C_1) D_1)))))) (forall ((B $$unsorted) (D_1 $$unsorted) (A_1 $$unsorted) (C_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool A_1) C_1)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool B) D_1)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool A_1) B)) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool C_1) D_1)))))) (forall ((B $$unsorted) (A_1 $$unsorted) (C_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_1) C_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) C_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A_1) B)) C_1))))) (forall ((B $$unsorted) (A_1 $$unsorted) (C_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool A_1) C_1)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool B) C_1)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool A_1) B)) C_1))))) (forall ((B $$unsorted) (A_1 $$unsorted)) (=> (tptp.is_fun_pname_bool A_1) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) A_1)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A_1) B) A_1)))) (forall ((B $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool B) A_1)) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool A_1) B) A_1))) (forall ((A_1 $$unsorted) (B $$unsorted)) (=> (tptp.is_fun_pname_bool B) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_1) B)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A_1) B) B)))) (forall ((A_1 $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool A_1) B)) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool A_1) B) B))) (forall ((A_1 $$unsorted) (B $$unsorted)) (=> (tptp.is_fun_pname_bool B) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_1) B)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A_1) B) B)))) (forall ((A_1 $$unsorted) (B $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool A_1) B)) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool A_1) B) B))) (forall ((B $$unsorted) (A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A_1) B)))) (forall ((B $$unsorted) (A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool B) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool A_1) B)))) (forall ((A_1 $$unsorted) (B $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_1) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A_1) B)))) (forall ((A_1 $$unsorted) (B $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool A_1) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool A_1) B)))) (forall ((F $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.image_275883510_state F))) (= (tptp.hAPP_f631639356e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A_1) B)) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool (tptp.hAPP_f631639356e_bool _let_1 A_1)) (tptp.hAPP_f631639356e_bool _let_1 B))))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A) B) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool (tptp.hAPP_f759274231e_bool tptp.collect_pname (tptp.hAPP_p61793385e_bool (tptp.hAPP_f22061361e_bool tptp.cOMBC_1149511130e_bool tptp.fequal_pname) A))) B))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A) B) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool (tptp.hAPP_f921536533e_bool tptp.collec727977250_state (tptp.hAPP_H1645666623e_bool (tptp.hAPP_f262880489e_bool tptp.cOMBC_1424981238e_bool tptp.fequal1531560888_state) A))) B))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool A) B) (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.semila1782091504l_bool (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool (tptp.hAPP_f434788991l_bool (tptp.hAPP_f1297925993l_bool tptp.cOMBC_1284144636l_bool tptp.fequal533582459e_bool) A))) B))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.hAPP_f1970439265l_bool (tptp.hAPP_f601642911l_bool tptp.insert1991711667e_bool A) B) (tptp.hAPP_f1970439265l_bool (tptp.hAPP_f1587382801l_bool tptp.semila2055205435l_bool (tptp.hAPP_f1970439265l_bool tptp.collec111528142e_bool (tptp.hAPP_f854625363l_bool (tptp.hAPP_f2119687429l_bool tptp.cOMBC_1018307482l_bool tptp.fequal1746921144e_bool) A))) B))) (forall ((A $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_p905327722e_bool tptp.insert_pname A))) (= (tptp.hAPP_f759274231e_bool _let_1 A_1) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool (tptp.hAPP_f759274231e_bool _let_1 tptp.bot_bo844097828e_bool)) A_1)))) (forall ((A $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A))) (= (tptp.hAPP_f921536533e_bool _let_1 A_1) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool (tptp.hAPP_f921536533e_bool _let_1 tptp.bot_bo1055319631e_bool)) A_1)))) (forall ((G_1 $$unsorted) (P_1 $$unsorted) (Q_1 $$unsorted) (Procs $$unsorted)) (let ((_let_1 (tptp.hAPP_f1777033564_state tptp.cOMBS_1401555724_state (tptp.hAPP_f950918952_state (tptp.cOMBB_2123334001_pname tptp.hoare_1575745797_state) P_1)))) (let ((_let_2 (tptp.hAPP_f631639356e_bool (tptp.image_275883510_state (tptp.hAPP_f1296386871_state (tptp.hAPP_f358330902_state tptp.cOMBS_1615712031_state (tptp.hAPP_f2136041130_state _let_1 tptp.body_1)) Q_1)) Procs))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hoare_659004819_state (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool G_1) _let_2)) (tptp.hAPP_f631639356e_bool (tptp.image_275883510_state (tptp.hAPP_f1296386871_state (tptp.hAPP_f358330902_state tptp.cOMBS_1615712031_state (tptp.hAPP_f2136041130_state _let_1 (tptp.hAPP_f96342628me_com (tptp.cOMBB_923936821_pname tptp.the_com) tptp.body))) Q_1)) Procs))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hoare_659004819_state G_1) _let_2)))))) (forall ((Z $$unsorted) (Y_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool Z))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool Y_1) X_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 Y_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 X_1)))))) (forall ((Z $$unsorted) (Y_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool Z))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool Y_1) X_1)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 Y_1)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 X_1)))))) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (=> (and (tptp.is_fun_pname_bool Y_1) (tptp.is_fun_pname_bool X_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool Y_1) X_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool X_1) Y_1)) (= X_1 Y_1))))) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool Y_1) X_1)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool X_1) Y_1)) (= X_1 Y_1)))) (forall ((Z $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool X_1))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 Y_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool Y_1) Z)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 Z)))))) (forall ((Z $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool X_1))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 Y_1)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool Y_1) Z)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 Z)))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (=> (and (tptp.is_fun_pname_bool X_1) (tptp.is_fun_pname_bool Y_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool X_1) Y_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool Y_1) X_1)) (= X_1 Y_1))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool X_1) Y_1)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool Y_1) X_1)) (= X_1 Y_1)))) (forall ((C $$unsorted) (B_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B_1) A)) (=> (= B_1 C) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool C) A))))) (forall ((C $$unsorted) (B_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool B_1) A)) (=> (= B_1 C) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool C) A))))) (forall ((C $$unsorted) (A $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B_1)) (=> (= B_1 C) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 C)))))) (forall ((C $$unsorted) (A $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool A))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 B_1)) (=> (= B_1 C) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 C)))))) (forall ((C $$unsorted) (A $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool C))) (=> (= A B_1) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A)))))) (forall ((C $$unsorted) (A $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool C))) (=> (= A B_1) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 B_1)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 A)))))) (forall ((C $$unsorted) (A $$unsorted) (B_1 $$unsorted)) (=> (= A B_1) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B_1) C)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) C))))) (forall ((C $$unsorted) (A $$unsorted) (B_1 $$unsorted)) (=> (= A B_1) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool B_1) C)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool A) C))))) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (=> (and (tptp.is_fun_pname_bool Y_1) (tptp.is_fun_pname_bool X_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool Y_1) X_1)) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool X_1) Y_1)) (= X_1 Y_1))))) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool Y_1) X_1)) (= (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool X_1) Y_1)) (= X_1 Y_1)))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (=> (= X_1 Y_1) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool X_1) Y_1)))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (=> (= X_1 Y_1) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool X_1) Y_1)))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (=> (and (tptp.is_fun_pname_bool X_1) (tptp.is_fun_pname_bool Y_1)) (= (= X_1 Y_1) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool Y_1) X_1)))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (= (= X_1 Y_1) (and (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool Y_1) X_1))))) (forall ((A $$unsorted) (A_2 $$unsorted)) (= (= (tptp.some_com A) (tptp.some_com A_2)) (= A A_2))) (forall ((G_1 $$unsorted) (P_1 $$unsorted) (C $$unsorted) (Q_1 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.hoare_659004819_state G_1))) (=> (=> (tptp.hBOOL C_1) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state (tptp.hAPP_f588507005_state (tptp.hAPP_c408625258_state (tptp.hAPP_f1949912908_state tptp.hoare_1575745797_state P_1) C) Q_1)) tptp.bot_bo1055319631e_bool)))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state (tptp.hAPP_f588507005_state (tptp.hAPP_c408625258_state (tptp.hAPP_f1949912908_state tptp.hoare_1575745797_state (tptp.hAPP_b1095269219e_bool (tptp.hAPP_f701449317e_bool tptp.cOMBC_471052088e_bool (tptp.hAPP_f873506917e_bool (tptp.cOMBB_1757942702_state tptp.cOMBC_231445413l_bool) (tptp.hAPP_f1283379615l_bool (tptp.cOMBB_1759179140_state (tptp.cOMBB_188601460_state tptp.fconj)) P_1))) C_1)) C) Q_1)) tptp.bot_bo1055319631e_bool)))))) (forall ((Pn_1 $$unsorted) (G_1 $$unsorted) (P_1 $$unsorted) (Q_1 $$unsorted) (Procs $$unsorted)) (let ((_let_1 (tptp.hAPP_f1777033564_state tptp.cOMBS_1401555724_state (tptp.hAPP_f950918952_state (tptp.cOMBB_2123334001_pname tptp.hoare_1575745797_state) P_1)))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hoare_659004819_state (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool G_1) (tptp.hAPP_f631639356e_bool (tptp.image_275883510_state (tptp.hAPP_f1296386871_state (tptp.hAPP_f358330902_state tptp.cOMBS_1615712031_state (tptp.hAPP_f2136041130_state _let_1 tptp.body_1)) Q_1)) Procs))) (tptp.hAPP_f631639356e_bool (tptp.image_275883510_state (tptp.hAPP_f1296386871_state (tptp.hAPP_f358330902_state tptp.cOMBS_1615712031_state (tptp.hAPP_f2136041130_state _let_1 (tptp.hAPP_f96342628me_com (tptp.cOMBB_923936821_pname tptp.the_com) tptp.body))) Q_1)) Procs))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname Pn_1) Procs)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hoare_659004819_state G_1) (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state (tptp.hAPP_f588507005_state (tptp.hAPP_c408625258_state (tptp.hAPP_f1949912908_state tptp.hoare_1575745797_state (tptp.hAPP_p1637813682e_bool P_1 Pn_1)) (tptp.hAPP_pname_com tptp.body_1 Pn_1)) (tptp.hAPP_p1637813682e_bool Q_1 Pn_1))) tptp.bot_bo1055319631e_bool))))))) (forall ((A $$unsorted)) (=> (tptp.is_fun_pname_bool A) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) tptp.bot_bo844097828e_bool)) (= A tptp.bot_bo844097828e_bool)))) (forall ((A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool A) tptp.bot_bo1055319631e_bool)) (= A tptp.bot_bo1055319631e_bool))) (forall ((A $$unsorted)) (=> (tptp.is_fun_pname_bool A) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) tptp.bot_bo844097828e_bool)) (= A tptp.bot_bo844097828e_bool)))) (forall ((A $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool A) tptp.bot_bo1055319631e_bool)) (= A tptp.bot_bo1055319631e_bool))) (forall ((A $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool tptp.bot_bo844097828e_bool) A))) (forall ((A $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool tptp.bot_bo1055319631e_bool) A))) (forall ((X_1 $$unsorted) (F $$unsorted) (G $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool F) G)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_pname_bool F X_1)) (tptp.hAPP_pname_bool G X_1))))) (forall ((X_1 $$unsorted) (F $$unsorted) (G $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool F) G)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_H513860823e_bool F X_1)) (tptp.hAPP_H513860823e_bool G X_1))))) (forall ((X_1 $$unsorted) (F $$unsorted) (G $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool F) G)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_pname_bool F X_1)) (tptp.hAPP_pname_bool G X_1))))) (forall ((X_1 $$unsorted) (F $$unsorted) (G $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool F) G)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_H513860823e_bool F X_1)) (tptp.hAPP_H513860823e_bool G X_1))))) (forall ((F $$unsorted) (G $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool F) G)) (forall ((X_2 $$unsorted)) (=> (tptp.is_pname X_2) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_pname_bool F X_2)) (tptp.hAPP_pname_bool G X_2))))))) (forall ((F $$unsorted) (G $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool F) G)) (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_H513860823e_bool F X_2)) (tptp.hAPP_H513860823e_bool G X_2)))))) (forall ((X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_pname_bool tptp.bot_bo844097828e_bool X_1)) (tptp.hBOOL tptp.bot_bot_bool))) (forall ((X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_H513860823e_bool tptp.bot_bo1055319631e_bool X_1)) (tptp.hBOOL tptp.bot_bot_bool))) (forall ((X_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_pname_bool tptp.bot_bo844097828e_bool X_2)) (tptp.hBOOL tptp.bot_bot_bool))) (forall ((X_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_H513860823e_bool tptp.bot_bo1055319631e_bool X_2)) (tptp.hBOOL tptp.bot_bot_bool))) (forall ((P_1 $$unsorted) (Pn_1 $$unsorted) (Q_1 $$unsorted) (G_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1949912908_state tptp.hoare_1575745797_state P_1))) (let ((_let_2 (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state (tptp.hAPP_f588507005_state (tptp.hAPP_c408625258_state _let_1 (tptp.hAPP_pname_com tptp.body_1 Pn_1)) Q_1)))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hoare_659004819_state (tptp.hAPP_f921536533e_bool _let_2 G_1)) (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state (tptp.hAPP_f588507005_state (tptp.hAPP_c408625258_state _let_1 (tptp.hAPP_option_com_com tptp.the_com (tptp.hAPP_p799580910on_com tptp.body Pn_1))) Q_1)) tptp.bot_bo1055319631e_bool))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hoare_659004819_state G_1) (tptp.hAPP_f921536533e_bool _let_2 tptp.bot_bo1055319631e_bool))))))) (forall ((P_1 $$unsorted) (Q_1 $$unsorted) (G_1 $$unsorted) (P_2 $$unsorted) (C0_1 $$unsorted) (Q_2 $$unsorted) (U_1 $$unsorted)) (let ((_let_1 (tptp.cOMBB_2123334001_pname tptp.hoare_1575745797_state))) (let ((_let_2 (tptp.hoare_659004819_state G_1))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname U_1)) (=> (forall ((P_3 $$unsorted)) (let ((_let_1 (tptp.hAPP_pname_com C0_1 P_3))) (let ((_let_2 (tptp.hoare_659004819_state G_1))) (=> (tptp.is_pname P_3) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_2 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state (tptp.hAPP_f588507005_state (tptp.hAPP_c408625258_state (tptp.hAPP_f1949912908_state tptp.hoare_1575745797_state (tptp.hAPP_p1637813682e_bool P_2 P_3)) _let_1) (tptp.hAPP_p1637813682e_bool Q_2 P_3))) tptp.bot_bo1055319631e_bool))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_2 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state (tptp.hAPP_f588507005_state (tptp.hAPP_c408625258_state (tptp.hAPP_f1949912908_state tptp.hoare_1575745797_state (tptp.hAPP_p1637813682e_bool P_1 P_3)) _let_1) (tptp.hAPP_p1637813682e_bool Q_1 P_3))) tptp.bot_bo1055319631e_bool)))))))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_2 (tptp.hAPP_f631639356e_bool (tptp.image_275883510_state (tptp.hAPP_f1296386871_state (tptp.hAPP_f358330902_state tptp.cOMBS_1615712031_state (tptp.hAPP_f2136041130_state (tptp.hAPP_f1777033564_state tptp.cOMBS_1401555724_state (tptp.hAPP_f950918952_state _let_1 P_2)) C0_1)) Q_2)) U_1))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_2 (tptp.hAPP_f631639356e_bool (tptp.image_275883510_state (tptp.hAPP_f1296386871_state (tptp.hAPP_f358330902_state tptp.cOMBS_1615712031_state (tptp.hAPP_f2136041130_state (tptp.hAPP_f1777033564_state tptp.cOMBS_1401555724_state (tptp.hAPP_f950918952_state _let_1 P_1)) C0_1)) Q_1)) U_1))))))))) (forall ((G_1 $$unsorted) (C $$unsorted) (Q_1 $$unsorted) (P_1 $$unsorted)) (=> (forall ((Z_2 $$unsorted) (S_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool P_1 Z_2) S_3)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hoare_659004819_state G_1) (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state (tptp.hAPP_f588507005_state (tptp.hAPP_c408625258_state (tptp.hAPP_f1949912908_state tptp.hoare_1575745797_state (tptp.cOMBK_631994958_state (tptp.hAPP_s1806633685e_bool (tptp.hAPP_f817621513e_bool tptp.cOMBC_2027030106e_bool tptp.fequal_state) S_3))) C) (tptp.cOMBK_631994958_state (tptp.hAPP_s1806633685e_bool Q_1 Z_2)))) tptp.bot_bo1055319631e_bool))))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hoare_659004819_state G_1) (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state (tptp.hAPP_f588507005_state (tptp.hAPP_c408625258_state (tptp.hAPP_f1949912908_state tptp.hoare_1575745797_state P_1) C) Q_1)) tptp.bot_bo1055319631e_bool))))) (forall ((G_1 $$unsorted) (P_1 $$unsorted) (Q_1 $$unsorted) (Procs $$unsorted)) (let ((_let_1 (tptp.hAPP_f1777033564_state tptp.cOMBS_1401555724_state (tptp.hAPP_f950918952_state (tptp.cOMBB_2123334001_pname tptp.hoare_1575745797_state) P_1)))) (let ((_let_2 (tptp.hAPP_f631639356e_bool (tptp.image_275883510_state (tptp.hAPP_f1296386871_state (tptp.hAPP_f358330902_state tptp.cOMBS_1615712031_state (tptp.hAPP_f2136041130_state _let_1 tptp.body_1)) Q_1)) Procs))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hoare_1065416081_state (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool G_1) _let_2)) (tptp.hAPP_f631639356e_bool (tptp.image_275883510_state (tptp.hAPP_f1296386871_state (tptp.hAPP_f358330902_state tptp.cOMBS_1615712031_state (tptp.hAPP_f2136041130_state _let_1 (tptp.hAPP_f96342628me_com (tptp.cOMBB_923936821_pname tptp.the_com) tptp.body))) Q_1)) Procs))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hoare_1065416081_state G_1) _let_2)))))) (forall ((P_1 $$unsorted) (G_1 $$unsorted) (P_2 $$unsorted) (C $$unsorted) (Q_1 $$unsorted)) (let ((_let_1 (tptp.hoare_659004819_state G_1))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state (tptp.hAPP_f588507005_state (tptp.hAPP_c408625258_state (tptp.hAPP_f1949912908_state tptp.hoare_1575745797_state P_2) C) Q_1)) tptp.bot_bo1055319631e_bool))) (=> (forall ((Z_2 $$unsorted) (S_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool P_1 Z_2) S_3)) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool P_2 Z_2) S_3)))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state (tptp.hAPP_f588507005_state (tptp.hAPP_c408625258_state (tptp.hAPP_f1949912908_state tptp.hoare_1575745797_state P_1) C) Q_1)) tptp.bot_bo1055319631e_bool))))))) (forall ((Q_1 $$unsorted) (G_1 $$unsorted) (P_1 $$unsorted) (C $$unsorted) (Q_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_c408625258_state (tptp.hAPP_f1949912908_state tptp.hoare_1575745797_state P_1) C))) (let ((_let_2 (tptp.hoare_659004819_state G_1))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_2 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state (tptp.hAPP_f588507005_state _let_1 Q_2)) tptp.bot_bo1055319631e_bool))) (=> (forall ((Z_2 $$unsorted) (S_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool Q_2 Z_2) S_3)) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool Q_1 Z_2) S_3)))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_2 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state (tptp.hAPP_f588507005_state _let_1 Q_1)) tptp.bot_bo1055319631e_bool)))))))) (forall ((P_1 $$unsorted) (Q_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state (tptp.hAPP_f588507005_state (tptp.hAPP_c408625258_state (tptp.hAPP_f1949912908_state tptp.hoare_1575745797_state P_1) C) Q_1)) tptp.bot_bo1055319631e_bool))) (let ((_let_2 (tptp.hoare_659004819_state tptp.bot_bo1055319631e_bool))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_2 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state (tptp.hAPP_c1546227244_state tptp.hoare_Mirabelle_MGT C)) tptp.bot_bo1055319631e_bool))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hoare_1065416081_state tptp.bot_bo1055319631e_bool) _let_1)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_2 _let_1))))))) (forall ((A_1 $$unsorted) (B $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_H513860823e_bool (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool A_1) B) X_1)) (=> (not (tptp.hBOOL (tptp.hAPP_H513860823e_bool A_1 X_1))) (tptp.hBOOL (tptp.hAPP_H513860823e_bool B X_1))))) (forall ((A_1 $$unsorted) (B $$unsorted) (X_1 $$unsorted)) (=> (=> (not (tptp.hBOOL (tptp.hAPP_H513860823e_bool B X_1))) (tptp.hBOOL (tptp.hAPP_H513860823e_bool A_1 X_1))) (tptp.hBOOL (tptp.hAPP_H513860823e_bool (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool A_1) B) X_1)))) (forall ((G_1 $$unsorted) (Ts $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hoare_659004819_state G_1) Ts)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hoare_1065416081_state G_1) Ts)))) (forall ((X_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_pname_bool tptp.bot_bo844097828e_bool X_2)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) tptp.bot_bo844097828e_bool)))) (forall ((X_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_H513860823e_bool tptp.bot_bo1055319631e_bool X_2)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_2) tptp.bot_bo1055319631e_bool)))) (forall ((Q_1 $$unsorted) (P_1 $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_pname_bool P_1 X_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool P_1) Q_1)) (tptp.hBOOL (tptp.hAPP_pname_bool Q_1 X_1))))) (forall ((Q_1 $$unsorted) (P_1 $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_H513860823e_bool P_1 X_1)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool P_1) Q_1)) (tptp.hBOOL (tptp.hAPP_H513860823e_bool Q_1 X_1))))) (forall ((X_1 $$unsorted) (P_1 $$unsorted) (Q_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool P_1) Q_1)) (=> (tptp.hBOOL (tptp.hAPP_pname_bool P_1 X_1)) (tptp.hBOOL (tptp.hAPP_pname_bool Q_1 X_1))))) (forall ((X_1 $$unsorted) (P_1 $$unsorted) (Q_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool P_1) Q_1)) (=> (tptp.hBOOL (tptp.hAPP_H513860823e_bool P_1 X_1)) (tptp.hBOOL (tptp.hAPP_H513860823e_bool Q_1 X_1))))) (forall ((A_1 $$unsorted) (B $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_H513860823e_bool B X_1)) (tptp.hBOOL (tptp.hAPP_H513860823e_bool (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool A_1) B) X_1)))) (forall ((B $$unsorted) (A_1 $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_H513860823e_bool A_1 X_1)) (tptp.hBOOL (tptp.hAPP_H513860823e_bool (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool A_1) B) X_1)))) (forall ((R_1 $$unsorted) (S $$unsorted)) (let ((_let_1 (tptp.hAPP_f661147897e_bool tptp.cOMBC_1058051404l_bool tptp.member_pname))) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool _let_1 R_1)) (tptp.hAPP_f759274231e_bool _let_1 S))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool R_1) S))))) (forall ((R_1 $$unsorted) (S $$unsorted)) (let ((_let_1 (tptp.hAPP_f1262649863e_bool tptp.cOMBC_764456866l_bool tptp.member1758697444_state))) (= (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool (tptp.hAPP_f921536533e_bool _let_1 R_1)) (tptp.hAPP_f921536533e_bool _let_1 S))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool R_1) S))))) (forall ((R_1 $$unsorted) (S $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_f661147897e_bool tptp.cOMBC_1058051404l_bool tptp.member_pname))) (= (tptp.hBOOL (tptp.hAPP_pname_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool (tptp.hAPP_f759274231e_bool _let_1 R_1)) (tptp.hAPP_f759274231e_bool _let_1 S)) X_2)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool R_1) S)))))) (forall ((R_1 $$unsorted) (S $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1262649863e_bool tptp.cOMBC_764456866l_bool tptp.member1758697444_state))) (= (tptp.hBOOL (tptp.hAPP_H513860823e_bool (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool (tptp.hAPP_f921536533e_bool _let_1 R_1)) (tptp.hAPP_f921536533e_bool _let_1 S)) X_2)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_2) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool R_1) S)))))) (forall ((Q_1 $$unsorted) (P_1 $$unsorted) (G_1 $$unsorted) (P_2 $$unsorted) (C $$unsorted) (Q_2 $$unsorted)) (let ((_let_1 (tptp.hoare_659004819_state G_1))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state (tptp.hAPP_f588507005_state (tptp.hAPP_c408625258_state (tptp.hAPP_f1949912908_state tptp.hoare_1575745797_state P_2) C) Q_2)) tptp.bot_bo1055319631e_bool))) (=> (forall ((Z_2 $$unsorted) (S_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool P_1 Z_2) S_3)) (forall ((S_4 $$unsorted)) (=> (forall ((Z_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool P_2 Z_3) S_3)) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool Q_2 Z_3) S_4)))) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool Q_1 Z_2) S_4)))))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state (tptp.hAPP_f588507005_state (tptp.hAPP_c408625258_state (tptp.hAPP_f1949912908_state tptp.hoare_1575745797_state P_1) C) Q_1)) tptp.bot_bo1055319631e_bool))))))) (forall ((F $$unsorted) (G $$unsorted)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.is_pname X_2) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_pname_bool F X_2)) (tptp.hAPP_pname_bool G X_2))))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool F) G)))) (forall ((F $$unsorted) (G $$unsorted)) (=> (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_H513860823e_bool F X_2)) (tptp.hAPP_H513860823e_bool G X_2)))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool F) G)))) (forall ((X_1 $$unsorted)) (= (tptp.set_pname (tptp.some_pname X_1)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1) tptp.bot_bo844097828e_bool))) (forall ((X_1 $$unsorted)) (= (tptp.set_Ho1831989999_state (tptp.some_H1133819688_state X_1)) (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state X_1) tptp.bot_bo1055319631e_bool))) (forall ((X_1 $$unsorted)) (= (tptp.set_com (tptp.some_com X_1)) (tptp.hAPP_f1682609283m_bool (tptp.hAPP_c566651504m_bool tptp.insert_com X_1) tptp.bot_bot_fun_com_bool))) (forall ((X_1 $$unsorted) (Xo $$unsorted)) (=> (tptp.is_option_pname Xo) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) (tptp.set_pname Xo))) (= Xo (tptp.some_pname X_1))))) (forall ((X_1 $$unsorted) (Xo $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_1) (tptp.set_Ho1831989999_state Xo))) (= Xo (tptp.some_H1133819688_state X_1)))) (forall ((X_1 $$unsorted) (Xo $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_1) (tptp.set_com Xo))) (= Xo (tptp.some_com X_1)))) (forall ((X_1 $$unsorted) (P_1 $$unsorted) (A_1 $$unsorted)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f990396704l_bool (tptp.hAPP_c667411853l_bool tptp.member_com X_2) (tptp.set_com A_1))) (tptp.hBOOL (tptp.hAPP_com_bool P_1 X_2)))) (=> (= A_1 (tptp.some_com X_1)) (tptp.hBOOL (tptp.hAPP_com_bool P_1 X_1))))) (forall ((F $$unsorted) (G $$unsorted) (X_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_H513860823e_bool (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool F) G) X_2)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool (tptp.hAPP_H513860823e_bool F X_2)) (tptp.hAPP_H513860823e_bool G X_2))))) (forall ((F $$unsorted) (G $$unsorted) (X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_H513860823e_bool (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool F) G) X_1)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.semila1168014441p_bool (tptp.hAPP_H513860823e_bool F X_1)) (tptp.hAPP_H513860823e_bool G X_1))))) (=> _let_11 (forall ((T_2 $$unsorted)) (not (forall ((S_3 $$unsorted)) (= S_3 T_2))))) (= _let_11 (exists ((S_3 $$unsorted) (T_2 $$unsorted)) (not (= S_3 T_2)))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool X_1))) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool (tptp.hAPP_f921536533e_bool _let_1 Y_1)) Z) (tptp.hAPP_f921536533e_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool Y_1) Z))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool X_1))) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool (tptp.hAPP_f921536533e_bool _let_1 Y_1)) Z) (tptp.hAPP_f921536533e_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool Y_1) Z))))) (forall ((A $$unsorted) (B_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool A))) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool (tptp.hAPP_f921536533e_bool _let_1 B_1)) C) (tptp.hAPP_f921536533e_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool B_1) C))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool X_1))) (let ((_let_2 (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool Y_1))) (= (tptp.hAPP_f921536533e_bool _let_1 (tptp.hAPP_f921536533e_bool _let_2 Z)) (tptp.hAPP_f921536533e_bool _let_2 (tptp.hAPP_f921536533e_bool _let_1 Z)))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool X_1))) (let ((_let_2 (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool Y_1))) (= (tptp.hAPP_f921536533e_bool _let_1 (tptp.hAPP_f921536533e_bool _let_2 Z)) (tptp.hAPP_f921536533e_bool _let_2 (tptp.hAPP_f921536533e_bool _let_1 Z)))))) (forall ((B_1 $$unsorted) (A $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool B_1))) (let ((_let_2 (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool A))) (= (tptp.hAPP_f921536533e_bool _let_1 (tptp.hAPP_f921536533e_bool _let_2 C)) (tptp.hAPP_f921536533e_bool _let_2 (tptp.hAPP_f921536533e_bool _let_1 C)))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool X_1))) (let ((_let_2 (tptp.hAPP_f921536533e_bool _let_1 Y_1))) (= (tptp.hAPP_f921536533e_bool _let_1 _let_2) _let_2)))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool X_1))) (let ((_let_2 (tptp.hAPP_f921536533e_bool _let_1 Y_1))) (= (tptp.hAPP_f921536533e_bool _let_1 _let_2) _let_2)))) (forall ((A $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool A))) (let ((_let_2 (tptp.hAPP_f921536533e_bool _let_1 B_1))) (= (tptp.hAPP_f921536533e_bool _let_1 _let_2) _let_2)))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool X_1) Y_1) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool Y_1) X_1))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool X_1) Y_1) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool Y_1) X_1))) (forall ((A $$unsorted) (B_1 $$unsorted)) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool A) B_1) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool B_1) A))) (forall ((X_1 $$unsorted)) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool X_1) X_1) X_1)) (forall ((A $$unsorted)) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool A) A) A)) (forall ((A $$unsorted) (B_1 $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A) B_1)) X_1)) (not (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) X_1)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B_1) X_1))))))) (forall ((A $$unsorted) (B_1 $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool A) B_1)) X_1)) (not (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool A) X_1)) (not (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool B_1) X_1))))))) (forall ((B_1 $$unsorted) (D $$unsorted) (A $$unsorted) (C $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) C)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B_1) D)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A) B_1)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool C) D)))))) (forall ((B_1 $$unsorted) (D $$unsorted) (A $$unsorted) (C $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool A) C)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool B_1) D)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool A) B_1)) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool C) D)))))) (forall ((Z $$unsorted) (Y_1 $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool Y_1) X_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool Z) X_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool Y_1) Z)) X_1))))) (forall ((Z $$unsorted) (Y_1 $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool Y_1) X_1)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool Z) X_1)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool Y_1) Z)) X_1))))) (forall ((B_1 $$unsorted) (A $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) X_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B_1) X_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A) B_1)) X_1))))) (forall ((B_1 $$unsorted) (A $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool A) X_1)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool B_1) X_1)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool A) B_1)) X_1))))) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (=> (tptp.is_fun_pname_bool X_1) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool Y_1) X_1)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool X_1) Y_1) X_1)))) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool Y_1) X_1)) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool X_1) Y_1) X_1))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (=> (tptp.is_fun_pname_bool Y_1) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool X_1) Y_1)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool X_1) Y_1) Y_1)))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool X_1) Y_1)) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool X_1) Y_1) Y_1))) (forall ((A $$unsorted) (X_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool X_1))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A) B_1)))))) (forall ((A $$unsorted) (X_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool X_1))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 B_1)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool A) B_1)))))) (forall ((B_1 $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool X_1))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A) B_1)))))) (forall ((B_1 $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool X_1))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool A) B_1)))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (Z $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool X_1) Y_1)) Z)) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool X_1) Z)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool Y_1) Z))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (Z $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool X_1) Y_1)) Z)) (and (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool X_1) Z)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool Y_1) Z))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (=> (tptp.is_fun_pname_bool Y_1) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool X_1) Y_1)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool X_1) Y_1) Y_1)))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool X_1) Y_1)) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool X_1) Y_1) Y_1))) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool Y_1) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool X_1) Y_1)))) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool Y_1) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool X_1) Y_1)))) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool Y_1) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool X_1) Y_1)))) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool Y_1) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool X_1) Y_1)))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool X_1) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool X_1) Y_1)))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool X_1) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool X_1) Y_1)))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool X_1) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool X_1) Y_1)))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool X_1) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool X_1) Y_1)))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (=> (and (tptp.is_fun_pname_bool X_1) (tptp.is_fun_pname_bool Y_1)) (= (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool X_1) Y_1) tptp.bot_bo844097828e_bool) (and (= X_1 tptp.bot_bo844097828e_bool) (= Y_1 tptp.bot_bo844097828e_bool))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (= (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool X_1) Y_1) tptp.bot_bo1055319631e_bool) (and (= X_1 tptp.bot_bo1055319631e_bool) (= Y_1 tptp.bot_bo1055319631e_bool)))) (forall ((X_1 $$unsorted)) (=> (tptp.is_fun_pname_bool X_1) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool X_1) tptp.bot_bo844097828e_bool) X_1))) (forall ((X_1 $$unsorted)) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool X_1) tptp.bot_bo1055319631e_bool) X_1)) (forall ((X_1 $$unsorted)) (=> (tptp.is_fun_pname_bool X_1) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool tptp.bot_bo844097828e_bool) X_1) X_1))) (forall ((X_1 $$unsorted)) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool tptp.bot_bo1055319631e_bool) X_1) X_1)) (forall ((B $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (and (tptp.is_fun1661590463l_bool B) (tptp.is_fun1661590463l_bool A_1)) (=> (tptp.hBOOL (tptp.finite1268145088e_bool F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A_1)) (=> (not (= A_1 tptp.bot_bo1649642514l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool B)) (=> (not (= B tptp.bot_bo1649642514l_bool)) (= (tptp.hAPP_f674760225e_bool Fa (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.semila1782091504l_bool A_1) B)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool F (tptp.hAPP_f674760225e_bool Fa A_1)) (tptp.hAPP_f674760225e_bool Fa B)))))))))) (forall ((B $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.finite959343283e_bool F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool A_1)) (=> (not (= A_1 tptp.bot_bo1325454745l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool B)) (=> (not (= B tptp.bot_bo1325454745l_bool)) (= (tptp.hAPP_f772567431e_bool Fa (tptp.hAPP_f1970439265l_bool (tptp.hAPP_f1587382801l_bool tptp.semila2055205435l_bool A_1) B)) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool F (tptp.hAPP_f772567431e_bool Fa A_1)) (tptp.hAPP_f772567431e_bool Fa B))))))))) (forall ((B $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (and (tptp.is_fun_pname_bool B) (tptp.is_fun_pname_bool A_1)) (=> (tptp.hBOOL (tptp.finite89670078_pname F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A_1)) (=> (not (= A_1 tptp.bot_bo844097828e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B)) (=> (not (= B tptp.bot_bo844097828e_bool)) (= (tptp.hAPP_f1297739591_pname Fa (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A_1) B)) (tptp.hAPP_pname_pname (tptp.hAPP_p1170154830_pname F (tptp.hAPP_f1297739591_pname Fa A_1)) (tptp.hAPP_f1297739591_pname Fa B)))))))))) (forall ((B $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.finite506823037_state F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state A_1)) (=> (not (= A_1 tptp.bot_bo1055319631e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state B)) (=> (not (= B tptp.bot_bo1055319631e_bool)) (= (tptp.hAPP_f2143211163_state Fa (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool A_1) B)) (tptp.hAPP_H563960305_state (tptp.hAPP_H521649881_state F (tptp.hAPP_f2143211163_state Fa A_1)) (tptp.hAPP_f2143211163_state Fa B))))))))) (forall ((B $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.hAPP_f674760225e_bool Fa A_1))) (=> (tptp.is_fun1661590463l_bool B) (=> (tptp.hBOOL (tptp.finite1268145088e_bool F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A_1)) (=> (not (= B tptp.bot_bo1649642514l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool B) A_1)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool F (tptp.hAPP_f674760225e_bool Fa B)) _let_1) _let_1)))))))) (forall ((B $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.hAPP_f772567431e_bool Fa A_1))) (=> (tptp.hBOOL (tptp.finite959343283e_bool F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool A_1)) (=> (not (= B tptp.bot_bo1325454745l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f239102607l_bool (tptp.hAPP_f1269496639l_bool tptp.ord_le1076702565l_bool B) A_1)) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool F (tptp.hAPP_f772567431e_bool Fa B)) _let_1) _let_1))))))) (forall ((B $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.hAPP_f1297739591_pname Fa A_1))) (=> (tptp.is_fun_pname_bool B) (=> (tptp.hBOOL (tptp.finite89670078_pname F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A_1)) (=> (not (= B tptp.bot_bo844097828e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) A_1)) (= (tptp.hAPP_pname_pname (tptp.hAPP_p1170154830_pname F (tptp.hAPP_f1297739591_pname Fa B)) _let_1) _let_1)))))))) (forall ((B $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.hAPP_f2143211163_state Fa A_1))) (=> (tptp.hBOOL (tptp.finite506823037_state F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state A_1)) (=> (not (= B tptp.bot_bo1055319631e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool B) A_1)) (= (tptp.hAPP_H563960305_state (tptp.hAPP_H521649881_state F (tptp.hAPP_f2143211163_state Fa B)) _let_1) _let_1))))))) (forall ((G_1 $$unsorted) (P_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hoare_659004819_state G_1) (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state (tptp.hAPP_f588507005_state (tptp.hAPP_c408625258_state (tptp.hAPP_f1949912908_state tptp.hoare_1575745797_state P_1) tptp.skip) P_1)) tptp.bot_bo1055319631e_bool)))) (forall ((X_1 $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (tptp.is_fun_pname_bool A_1) (=> (tptp.hBOOL (tptp.finite89670078_pname F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A_1)) (=> (not (= A_1 tptp.bot_bo844097828e_bool)) (= (tptp.hAPP_f1297739591_pname Fa (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1) A_1)) (tptp.hAPP_pname_pname (tptp.hAPP_p1170154830_pname F X_1) (tptp.hAPP_f1297739591_pname Fa A_1)))))))) (forall ((X_1 $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.finite506823037_state F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state A_1)) (=> (not (= A_1 tptp.bot_bo1055319631e_bool)) (= (tptp.hAPP_f2143211163_state Fa (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state X_1) A_1)) (tptp.hAPP_H563960305_state (tptp.hAPP_H521649881_state F X_1) (tptp.hAPP_f2143211163_state Fa A_1))))))) (forall ((X_1 $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (tptp.is_fun1661590463l_bool A_1) (=> (tptp.hBOOL (tptp.finite1268145088e_bool F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A_1)) (=> (not (= A_1 tptp.bot_bo1649642514l_bool)) (= (tptp.hAPP_f674760225e_bool Fa (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool X_1) A_1)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool F X_1) (tptp.hAPP_f674760225e_bool Fa A_1)))))))) (forall ((X_1 $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.finite959343283e_bool F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool A_1)) (=> (not (= A_1 tptp.bot_bo1325454745l_bool)) (= (tptp.hAPP_f772567431e_bool Fa (tptp.hAPP_f1970439265l_bool (tptp.hAPP_f601642911l_bool tptp.insert1991711667e_bool X_1) A_1)) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool F X_1) (tptp.hAPP_f772567431e_bool Fa A_1))))))) (forall ((P_1 $$unsorted) (Fa $$unsorted)) (=> (tptp.is_fun_pname_bool Fa) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname Fa)) (=> (not (= Fa tptp.bot_bo844097828e_bool)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.is_pname X_2) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname X_2) tptp.bot_bo844097828e_bool))))) (=> (forall ((X_2 $$unsorted) (F_1 $$unsorted)) (=> (and (tptp.is_pname X_2) (tptp.is_fun_pname_bool F_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname F_1)) (=> (not (= F_1 tptp.bot_bo844097828e_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) F_1))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 F_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname X_2) F_1))))))))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 Fa)))))))) (forall ((P_1 $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state Fa)) (=> (not (= Fa tptp.bot_bo1055319631e_bool)) (=> (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool P_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state X_2) tptp.bot_bo1055319631e_bool)))) (=> (forall ((X_2 $$unsorted) (F_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state F_1)) (=> (not (= F_1 tptp.bot_bo1055319631e_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_2) F_1))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool P_1 F_1)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool P_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state X_2) F_1)))))))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool P_1 Fa))))))) (forall ((P_1 $$unsorted) (Fa $$unsorted)) (=> (tptp.is_fun1661590463l_bool Fa) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool Fa)) (=> (not (= Fa tptp.bot_bo1649642514l_bool)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.is_fun_pname_bool X_2) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool P_1 (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool X_2) tptp.bot_bo1649642514l_bool))))) (=> (forall ((X_2 $$unsorted) (F_1 $$unsorted)) (=> (and (tptp.is_fun_pname_bool X_2) (tptp.is_fun1661590463l_bool F_1)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool F_1)) (=> (not (= F_1 tptp.bot_bo1649642514l_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool X_2) F_1))) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool P_1 F_1)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool P_1 (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool X_2) F_1))))))))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool P_1 Fa)))))))) (forall ((P_1 $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool Fa)) (=> (not (= Fa tptp.bot_bo1325454745l_bool)) (=> (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f239102607l_bool P_1 (tptp.hAPP_f1970439265l_bool (tptp.hAPP_f601642911l_bool tptp.insert1991711667e_bool X_2) tptp.bot_bo1325454745l_bool)))) (=> (forall ((X_2 $$unsorted) (F_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool F_1)) (=> (not (= F_1 tptp.bot_bo1325454745l_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_f239102607l_bool (tptp.hAPP_f105100493l_bool tptp.member402455436e_bool X_2) F_1))) (=> (tptp.hBOOL (tptp.hAPP_f239102607l_bool P_1 F_1)) (tptp.hBOOL (tptp.hAPP_f239102607l_bool P_1 (tptp.hAPP_f1970439265l_bool (tptp.hAPP_f601642911l_bool tptp.insert1991711667e_bool X_2) F_1)))))))) (tptp.hBOOL (tptp.hAPP_f239102607l_bool P_1 Fa))))))) (forall ((Pname $$unsorted)) (not (= (tptp.hAPP_pname_com tptp.body_1 Pname) tptp.skip))) (forall ((Pname $$unsorted)) (not (= tptp.skip (tptp.hAPP_pname_com tptp.body_1 Pname)))) (tptp.hBOOL (tptp.hAPP_com_bool tptp.wt tptp.skip)) (forall ((X_1 $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.hAPP_f1297739591_pname Fa A_1))) (=> (tptp.hBOOL (tptp.finite89670078_pname F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A_1)) (= (tptp.hAPP_pname_pname (tptp.hAPP_p1170154830_pname F X_1) _let_1) _let_1)))))) (forall ((X_1 $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.hAPP_f2143211163_state Fa A_1))) (=> (tptp.hBOOL (tptp.finite506823037_state F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state A_1)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_1) A_1)) (= (tptp.hAPP_H563960305_state (tptp.hAPP_H521649881_state F X_1) _let_1) _let_1)))))) (forall ((X_1 $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.hAPP_f674760225e_bool Fa A_1))) (=> (tptp.hBOOL (tptp.finite1268145088e_bool F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A_1)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool X_1) A_1)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool F X_1) _let_1) _let_1)))))) (forall ((X_1 $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.hAPP_f772567431e_bool Fa A_1))) (=> (tptp.hBOOL (tptp.finite959343283e_bool F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool A_1)) (=> (tptp.hBOOL (tptp.hAPP_f239102607l_bool (tptp.hAPP_f105100493l_bool tptp.member402455436e_bool X_1) A_1)) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool F X_1) _let_1) _let_1)))))) (forall ((N $$unsorted) (H $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (tptp.is_fun1661590463l_bool N) (=> (tptp.hBOOL (tptp.finite1268145088e_bool F Fa)) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (=> (and (tptp.is_fun_pname_bool X_2) (tptp.is_fun_pname_bool Y_2)) (= (tptp.hAPP_f759274231e_bool H (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool F X_2) Y_2)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool F (tptp.hAPP_f759274231e_bool H X_2)) (tptp.hAPP_f759274231e_bool H Y_2))))) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool N)) (=> (not (= N tptp.bot_bo1649642514l_bool)) (= (tptp.hAPP_f759274231e_bool H (tptp.hAPP_f674760225e_bool Fa N)) (tptp.hAPP_f674760225e_bool Fa (tptp.hAPP_f559147733l_bool (tptp.image_2063528359e_bool H) N))))))))) (forall ((N $$unsorted) (H $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.finite959343283e_bool F Fa)) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (= (tptp.hAPP_f921536533e_bool H (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool F X_2) Y_2)) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool F (tptp.hAPP_f921536533e_bool H X_2)) (tptp.hAPP_f921536533e_bool H Y_2)))) (=> (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool N)) (=> (not (= N tptp.bot_bo1325454745l_bool)) (= (tptp.hAPP_f921536533e_bool H (tptp.hAPP_f772567431e_bool Fa N)) (tptp.hAPP_f772567431e_bool Fa (tptp.hAPP_f1970439265l_bool (tptp.image_505022149e_bool H) N)))))))) (forall ((N $$unsorted) (H $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (tptp.is_fun_pname_bool N) (=> (tptp.hBOOL (tptp.finite89670078_pname F Fa)) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (=> (and (tptp.is_pname X_2) (tptp.is_pname Y_2)) (= (tptp.hAPP_pname_pname H (tptp.hAPP_pname_pname (tptp.hAPP_p1170154830_pname F X_2) Y_2)) (tptp.hAPP_pname_pname (tptp.hAPP_p1170154830_pname F (tptp.hAPP_pname_pname H X_2)) (tptp.hAPP_pname_pname H Y_2))))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname N)) (=> (not (= N tptp.bot_bo844097828e_bool)) (= (tptp.hAPP_pname_pname H (tptp.hAPP_f1297739591_pname Fa N)) (tptp.hAPP_f1297739591_pname Fa (tptp.hAPP_f759274231e_bool (tptp.image_pname_pname H) N))))))))) (forall ((N $$unsorted) (H $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.finite506823037_state F Fa)) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (= (tptp.hAPP_H563960305_state H (tptp.hAPP_H563960305_state (tptp.hAPP_H521649881_state F X_2) Y_2)) (tptp.hAPP_H563960305_state (tptp.hAPP_H521649881_state F (tptp.hAPP_H563960305_state H X_2)) (tptp.hAPP_H563960305_state H Y_2)))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state N)) (=> (not (= N tptp.bot_bo1055319631e_bool)) (= (tptp.hAPP_H563960305_state H (tptp.hAPP_f2143211163_state Fa N)) (tptp.hAPP_f2143211163_state Fa (tptp.hAPP_f921536533e_bool (tptp.image_650584225_state H) N)))))))) (forall ((G_1 $$unsorted) (P_1 $$unsorted) (B_1 $$unsorted) (C $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hoare_659004819_state G_1) (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state (tptp.hAPP_f588507005_state (tptp.hAPP_c408625258_state (tptp.hAPP_f1949912908_state tptp.hoare_1575745797_state (tptp.hAPP_f1863945078e_bool (tptp.hAPP_f915354021e_bool tptp.cOMBC_952831051e_bool (tptp.hAPP_f1138284024e_bool (tptp.cOMBB_20296667_state tptp.cOMBS_1378840469l_bool) (tptp.hAPP_f1283379615l_bool (tptp.cOMBB_1759179140_state (tptp.cOMBB_188601460_state tptp.fconj)) P_1))) (tptp.hAPP_f1759915619e_bool (tptp.cOMBB_160679318_state tptp.fNot) B_1))) (tptp.while B_1 C)) P_1)) tptp.bot_bo1055319631e_bool)))) (forall ((D $$unsorted) (R_1 $$unsorted) (G_1 $$unsorted) (P_1 $$unsorted) (C $$unsorted) (Q_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1949912908_state tptp.hoare_1575745797_state P_1))) (let ((_let_2 (tptp.hoare_659004819_state G_1))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_2 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state (tptp.hAPP_f588507005_state (tptp.hAPP_c408625258_state _let_1 C) Q_1)) tptp.bot_bo1055319631e_bool))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_2 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state (tptp.hAPP_f588507005_state (tptp.hAPP_c408625258_state (tptp.hAPP_f1949912908_state tptp.hoare_1575745797_state Q_1) D) R_1)) tptp.bot_bo1055319631e_bool))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_2 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state (tptp.hAPP_f588507005_state (tptp.hAPP_c408625258_state _let_1 (tptp.semi C D)) R_1)) tptp.bot_bo1055319631e_bool)))))))) (forall ((X_3 $$unsorted)) (= (tptp.hAPP_f1297739591_pname tptp.the_elem_pname X_3) (tptp.hAPP_f1297739591_pname tptp.the_pname (tptp.hAPP_f42430548e_bool (tptp.cOMBB_530759491_pname (tptp.hAPP_f434788991l_bool tptp.fequal533582459e_bool X_3)) (tptp.hAPP_f180827860e_bool (tptp.hAPP_f698292281e_bool tptp.cOMBC_1123258281e_bool tptp.insert_pname) tptp.bot_bo844097828e_bool))))) (forall ((X_3 $$unsorted)) (= (tptp.hAPP_f2143211163_state tptp.the_el23965208_state X_3) (tptp.hAPP_f2143211163_state tptp.the_Ho10452358_state (tptp.hAPP_f1456107715e_bool (tptp.cOMBB_1653402815_state (tptp.hAPP_f854625363l_bool tptp.fequal1746921144e_bool X_3)) (tptp.hAPP_f762269719e_bool (tptp.hAPP_f964290431e_bool tptp.cOMBC_488258100e_bool tptp.insert1835143293_state) tptp.bot_bo1055319631e_bool))))) (forall ((B_1 $$unsorted) (C $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_com_bool tptp.wt (tptp.while B_1 C))) (tptp.hBOOL (tptp.hAPP_com_bool tptp.wt C)))) (forall ((C1 $$unsorted) (C2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_com_bool tptp.wt (tptp.semi C1 C2))) (not (=> (tptp.hBOOL (tptp.hAPP_com_bool tptp.wt C1)) (not (tptp.hBOOL (tptp.hAPP_com_bool tptp.wt C2))))))) (forall ((Com1_3 $$unsorted) (Com2_3 $$unsorted) (Fun $$unsorted) (Com_1 $$unsorted)) (not (= (tptp.semi Com1_3 Com2_3) (tptp.while Fun Com_1)))) (forall ((Fun $$unsorted) (Com_1 $$unsorted) (Com1_3 $$unsorted) (Com2_3 $$unsorted)) (not (= (tptp.while Fun Com_1) (tptp.semi Com1_3 Com2_3)))) (forall ((Com1_3 $$unsorted) (Com2_3 $$unsorted) (Com1_2 $$unsorted) (Com2_2 $$unsorted)) (= (= (tptp.semi Com1_3 Com2_3) (tptp.semi Com1_2 Com2_2)) (and (= Com1_3 Com1_2) (= Com2_3 Com2_2)))) (forall ((Fun_1 $$unsorted) (Com_2 $$unsorted) (Fun $$unsorted) (Com_1 $$unsorted)) (= (= (tptp.while Fun_1 Com_2) (tptp.while Fun Com_1)) (and (= Fun_1 Fun) (= Com_2 Com_1)))) (forall ((Pname_1 $$unsorted) (Fun_1 $$unsorted) (Com_2 $$unsorted)) (not (= (tptp.hAPP_pname_com tptp.body_1 Pname_1) (tptp.while Fun_1 Com_2)))) (forall ((Fun_1 $$unsorted) (Com_2 $$unsorted) (Pname_1 $$unsorted)) (not (= (tptp.while Fun_1 Com_2) (tptp.hAPP_pname_com tptp.body_1 Pname_1)))) (forall ((B_1 $$unsorted) (C $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_com_bool tptp.wt C)) (tptp.hBOOL (tptp.hAPP_com_bool tptp.wt (tptp.while B_1 C))))) (forall ((Fun $$unsorted) (Com_1 $$unsorted)) (not (= tptp.skip (tptp.while Fun Com_1)))) (forall ((Fun $$unsorted) (Com_1 $$unsorted)) (not (= (tptp.while Fun Com_1) tptp.skip))) (forall ((Pname $$unsorted) (Com1_1 $$unsorted) (Com2_1 $$unsorted)) (not (= (tptp.hAPP_pname_com tptp.body_1 Pname) (tptp.semi Com1_1 Com2_1)))) (forall ((Com1_1 $$unsorted) (Com2_1 $$unsorted) (Pname $$unsorted)) (not (= (tptp.semi Com1_1 Com2_1) (tptp.hAPP_pname_com tptp.body_1 Pname)))) (forall ((C1 $$unsorted) (C0 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_com_bool tptp.wt C0)) (=> (tptp.hBOOL (tptp.hAPP_com_bool tptp.wt C1)) (tptp.hBOOL (tptp.hAPP_com_bool tptp.wt (tptp.semi C0 C1)))))) (forall ((Com1 $$unsorted) (Com2 $$unsorted)) (not (= tptp.skip (tptp.semi Com1 Com2)))) (forall ((Com1 $$unsorted) (Com2 $$unsorted)) (not (= (tptp.semi Com1 Com2) tptp.skip))) (forall ((X_1 $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (tptp.is_fun_pname_bool A_1) (=> (tptp.hBOOL (tptp.finite1282449217_pname F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A_1)) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A_1))) (=> (not (= A_1 tptp.bot_bo844097828e_bool)) (= (tptp.hAPP_f1297739591_pname Fa (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1) A_1)) (tptp.hAPP_pname_pname (tptp.hAPP_p1170154830_pname F X_1) (tptp.hAPP_f1297739591_pname Fa A_1))))))))) (forall ((X_1 $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.finite774711482_state F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state A_1)) (=> (not (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_1) A_1))) (=> (not (= A_1 tptp.bot_bo1055319631e_bool)) (= (tptp.hAPP_f2143211163_state Fa (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state X_1) A_1)) (tptp.hAPP_H563960305_state (tptp.hAPP_H521649881_state F X_1) (tptp.hAPP_f2143211163_state Fa A_1)))))))) (forall ((X_1 $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (tptp.is_fun1661590463l_bool A_1) (=> (tptp.hBOOL (tptp.finite1626890877e_bool F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A_1)) (=> (not (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool X_1) A_1))) (=> (not (= A_1 tptp.bot_bo1649642514l_bool)) (= (tptp.hAPP_f674760225e_bool Fa (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool X_1) A_1)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool F X_1) (tptp.hAPP_f674760225e_bool Fa A_1))))))))) (forall ((X_1 $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.finite132673334e_bool F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool A_1)) (=> (not (tptp.hBOOL (tptp.hAPP_f239102607l_bool (tptp.hAPP_f105100493l_bool tptp.member402455436e_bool X_1) A_1))) (=> (not (= A_1 tptp.bot_bo1325454745l_bool)) (= (tptp.hAPP_f772567431e_bool Fa (tptp.hAPP_f1970439265l_bool (tptp.hAPP_f601642911l_bool tptp.insert1991711667e_bool X_1) A_1)) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool F X_1) (tptp.hAPP_f772567431e_bool Fa A_1)))))))) (forall ((X_1 $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (tptp.is_pname X_1) (=> (tptp.hBOOL (tptp.finite1282449217_pname F Fa)) (= (tptp.hAPP_f1297739591_pname Fa (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1) tptp.bot_bo844097828e_bool)) X_1)))) (forall ((X_1 $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.finite774711482_state F Fa)) (= (tptp.hAPP_f2143211163_state Fa (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state X_1) tptp.bot_bo1055319631e_bool)) X_1))) (forall ((A_1 $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (tptp.is_fun_pname_bool A_1) (=> (tptp.hBOOL (tptp.finite1282449217_pname F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A_1)) (=> (not (= A_1 tptp.bot_bo844097828e_bool)) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (=> (and (tptp.is_pname X_2) (tptp.is_pname Y_2)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname (tptp.hAPP_pname_pname (tptp.hAPP_p1170154830_pname F X_2) Y_2)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname X_2) (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname Y_2) tptp.bot_bo844097828e_bool)))))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname (tptp.hAPP_f1297739591_pname Fa A_1)) A_1)))))))) (forall ((A_1 $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.finite774711482_state F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state A_1)) (=> (not (= A_1 tptp.bot_bo1055319631e_bool)) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state (tptp.hAPP_H563960305_state (tptp.hAPP_H521649881_state F X_2) Y_2)) (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state X_2) (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state Y_2) tptp.bot_bo1055319631e_bool))))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state (tptp.hAPP_f2143211163_state Fa A_1)) A_1))))))) (forall ((A_1 $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (tptp.is_fun1661590463l_bool A_1) (=> (tptp.hBOOL (tptp.finite1626890877e_bool F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A_1)) (=> (not (= A_1 tptp.bot_bo1649642514l_bool)) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (=> (and (tptp.is_fun_pname_bool X_2) (tptp.is_fun_pname_bool Y_2)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool F X_2) Y_2)) (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool X_2) (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool Y_2) tptp.bot_bo1649642514l_bool)))))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool (tptp.hAPP_f674760225e_bool Fa A_1)) A_1)))))))) (forall ((A_1 $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.finite132673334e_bool F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool A_1)) (=> (not (= A_1 tptp.bot_bo1325454745l_bool)) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f239102607l_bool (tptp.hAPP_f105100493l_bool tptp.member402455436e_bool (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool F X_2) Y_2)) (tptp.hAPP_f1970439265l_bool (tptp.hAPP_f601642911l_bool tptp.insert1991711667e_bool X_2) (tptp.hAPP_f1970439265l_bool (tptp.hAPP_f601642911l_bool tptp.insert1991711667e_bool Y_2) tptp.bot_bo1325454745l_bool))))) (tptp.hBOOL (tptp.hAPP_f239102607l_bool (tptp.hAPP_f105100493l_bool tptp.member402455436e_bool (tptp.hAPP_f772567431e_bool Fa A_1)) A_1))))))) (forall ((Y_1 $$unsorted)) (not (forall ((Fun1 $$unsorted) (Com $$unsorted) (Fun2 $$unsorted)) (not (= Y_1 (tptp.hAPP_f588507005_state (tptp.hAPP_c408625258_state (tptp.hAPP_f1949912908_state tptp.hoare_1575745797_state Fun1) Com) Fun2)))))) (forall ((F $$unsorted) (G $$unsorted) (M $$unsorted) (N $$unsorted)) (=> (= M N) (=> (forall ((X_2 $$unsorted)) (=> (tptp.is_pname X_2) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) N)) (= (tptp.hAPP_p1842370726_state F X_2) (tptp.hAPP_p1842370726_state G X_2))))) (= (tptp.hAPP_f631639356e_bool (tptp.image_275883510_state F) M) (tptp.hAPP_f631639356e_bool (tptp.image_275883510_state G) N))))) (forall ((Q_1 $$unsorted) (P_1 $$unsorted)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_H513860823e_bool P_1 X_2)) (tptp.hBOOL (tptp.hAPP_H513860823e_bool Q_1 X_2)))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool (tptp.hAPP_f921536533e_bool tptp.collec727977250_state P_1)) (tptp.hAPP_f921536533e_bool tptp.collec727977250_state Q_1))))) (forall ((Q_1 $$unsorted) (P_1 $$unsorted)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.is_pname X_2) (=> (tptp.hBOOL (tptp.hAPP_pname_bool P_1 X_2)) (tptp.hBOOL (tptp.hAPP_pname_bool Q_1 X_2))))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool tptp.collect_pname P_1)) (tptp.hAPP_f759274231e_bool tptp.collect_pname Q_1))))) (forall ((Q_1 $$unsorted) (P_1 $$unsorted)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.is_fun_pname_bool X_2) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 X_2)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool Q_1 X_2))))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool P_1)) (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool Q_1))))) (forall ((Q_1 $$unsorted) (P_1 $$unsorted)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool P_1 X_2)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool Q_1 X_2)))) (tptp.hBOOL (tptp.hAPP_f239102607l_bool (tptp.hAPP_f1269496639l_bool tptp.ord_le1076702565l_bool (tptp.hAPP_f1970439265l_bool tptp.collec111528142e_bool P_1)) (tptp.hAPP_f1970439265l_bool tptp.collec111528142e_bool Q_1))))) (forall ((Q_1 $$unsorted) (P_1 $$unsorted)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.is_pname X_2) (=> (tptp.hBOOL (tptp.hAPP_pname_bool P_1 X_2)) (tptp.hBOOL (tptp.hAPP_pname_bool Q_1 X_2))))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool P_1) Q_1)))) (forall ((Q_1 $$unsorted) (P_1 $$unsorted)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_H513860823e_bool P_1 X_2)) (tptp.hBOOL (tptp.hAPP_H513860823e_bool Q_1 X_2)))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool P_1) Q_1)))) (forall ((A $$unsorted) (A_1 $$unsorted)) (=> (tptp.is_fun_pname_bool A_1) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A) A_1)) (exists ((B_2 $$unsorted)) (and (tptp.is_fun_pname_bool B_2) (= A_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A) B_2)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A) B_2)))))))) (forall ((A $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state A) A_1)) (exists ((B_2 $$unsorted)) (and (= A_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A) B_2)) (not (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state A) B_2))))))) (forall ((X_1 $$unsorted) (A_1 $$unsorted)) (=> (tptp.is_fun_pname_bool A_1) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A_1)) (not (forall ((B_2 $$unsorted)) (=> (tptp.is_fun_pname_bool B_2) (=> (= A_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1) B_2)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) B_2))))))))) (forall ((X_1 $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_1) A_1)) (not (forall ((B_2 $$unsorted)) (=> (= A_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state X_1) B_2)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_1) B_2))))))) (forall ((A_1 $$unsorted)) (=> (tptp.is_fun_pname_bool A_1) (=> (forall ((Y_2 $$unsorted)) (=> (tptp.is_pname Y_2) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname Y_2) A_1))))) (= A_1 tptp.bot_bo844097828e_bool)))) (forall ((A_1 $$unsorted)) (=> (forall ((Y_2 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state Y_2) A_1)))) (= A_1 tptp.bot_bo1055319631e_bool))) (forall ((G_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.hoare_659004819_state G_1))) (=> (tptp.hBOOL tptp.hoare_298929751gleton) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state (tptp.hAPP_f588507005_state (tptp.hAPP_c408625258_state (tptp.hAPP_f1949912908_state tptp.hoare_1575745797_state (tptp.hAPP_f1935169308e_bool (tptp.cOMBB_1036740637_state (tptp.cOMBB_1911358915_state tptp.fAll_state)) (tptp.hAPP_f249262236e_bool (tptp.cOMBB_1476898461_state (tptp.hAPP_f915354021e_bool tptp.cOMBC_952831051e_bool (tptp.hAPP_f1138284024e_bool (tptp.cOMBB_20296667_state tptp.cOMBS_1378840469l_bool) (tptp.hAPP_f1283379615l_bool (tptp.cOMBB_1759179140_state (tptp.cOMBB_188601460_state tptp.fimplies)) (tptp.evalc C))))) tptp.fequal_state))) C) tptp.fequal_state)) tptp.bot_bo1055319631e_bool))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state (tptp.hAPP_c1546227244_state tptp.hoare_Mirabelle_MGT C)) tptp.bot_bo1055319631e_bool))))))) (forall ((G_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.hoare_659004819_state G_1))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state (tptp.hAPP_c1546227244_state tptp.hoare_Mirabelle_MGT C)) tptp.bot_bo1055319631e_bool))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state (tptp.hAPP_f588507005_state (tptp.hAPP_c408625258_state (tptp.hAPP_f1949912908_state tptp.hoare_1575745797_state (tptp.hAPP_f1935169308e_bool (tptp.cOMBB_1036740637_state (tptp.cOMBB_1911358915_state tptp.fAll_state)) (tptp.hAPP_f249262236e_bool (tptp.cOMBB_1476898461_state (tptp.hAPP_f915354021e_bool tptp.cOMBC_952831051e_bool (tptp.hAPP_f1138284024e_bool (tptp.cOMBB_20296667_state tptp.cOMBS_1378840469l_bool) (tptp.hAPP_f1283379615l_bool (tptp.cOMBB_1759179140_state (tptp.cOMBB_188601460_state tptp.fimplies)) (tptp.evalc C))))) tptp.fequal_state))) C) tptp.fequal_state)) tptp.bot_bo1055319631e_bool)))))) (forall ((C $$unsorted)) (= (tptp.hAPP_c1546227244_state tptp.hoare_Mirabelle_MGT C) (tptp.hAPP_f588507005_state (tptp.hAPP_c408625258_state (tptp.hAPP_f1949912908_state tptp.hoare_1575745797_state tptp.fequal_state) C) (tptp.evalc C)))) (forall ((Pn $$unsorted) (S0 $$unsorted) (S1_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool (tptp.evalc (tptp.hAPP_option_com_com tptp.the_com (tptp.hAPP_p799580910on_com tptp.body Pn))) S0) S1_1)) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool (tptp.evalc (tptp.hAPP_pname_com tptp.body_1 Pn)) S0) S1_1)))) (forall ((P $$unsorted) (S_2 $$unsorted) (S1_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool (tptp.evalc (tptp.hAPP_pname_com tptp.body_1 P)) S_2) S1_1)) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool (tptp.evalc (tptp.hAPP_option_com_com tptp.the_com (tptp.hAPP_p799580910on_com tptp.body P))) S_2) S1_1)))) (forall ((S_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool (tptp.evalc tptp.skip) S_2) T_1)) (= T_1 S_2))) (forall ((C $$unsorted) (B_1 $$unsorted) (S_1 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_state_bool B_1 S_1))) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool (tptp.evalc (tptp.while B_1 C)) S_1) S_1)))) (forall ((S2_1 $$unsorted) (C $$unsorted) (S1_2 $$unsorted) (B_1 $$unsorted) (S0_1 $$unsorted)) (let ((_let_1 (tptp.evalc (tptp.while B_1 C)))) (=> (tptp.hBOOL (tptp.hAPP_state_bool B_1 S0_1)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool (tptp.evalc C) S0_1) S1_2)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool _let_1 S1_2) S2_1)) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool _let_1 S0_1) S2_1))))))) (forall ((C1 $$unsorted) (S2 $$unsorted) (C0 $$unsorted) (S0 $$unsorted) (S1_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool (tptp.evalc C0) S0) S1_1)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool (tptp.evalc C1) S1_1) S2)) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool (tptp.evalc (tptp.semi C0 C1)) S0) S2))))) (forall ((S_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool (tptp.evalc tptp.skip) S_2) S_2))) (forall ((U $$unsorted) (C_2 $$unsorted) (S_2 $$unsorted) (T_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_s1806633685e_bool (tptp.evalc C_2) S_2))) (=> (tptp.hBOOL (tptp.hAPP_state_bool _let_1 T_1)) (=> (tptp.hBOOL (tptp.hAPP_state_bool _let_1 U)) (= U T_1))))) (forall ((C1 $$unsorted) (C2 $$unsorted) (S_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool (tptp.evalc (tptp.semi C1 C2)) S_2) T_1)) (not (forall ((S1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool (tptp.evalc C1) S_2) S1)) (not (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool (tptp.evalc C2) S1) T_1)))))))) (forall ((B_1 $$unsorted) (C $$unsorted) (S_1 $$unsorted) (T $$unsorted)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_state_bool B_1 S_1)))) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool (tptp.evalc (tptp.while B_1 C)) S_1) T)) (=> (=> (= T S_1) _let_1) (not (=> _let_1 (forall ((S1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool (tptp.evalc C) S_1) S1)) (not (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool (tptp.evalc (tptp.while B_1 C)) S1) T))))))))))) (forall ((C $$unsorted) (A $$unsorted) (F $$unsorted) (B_1 $$unsorted)) (=> (= A (tptp.hAPP_f759274231e_bool F B_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool C) B_1)) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (=> (and (tptp.is_fun_pname_bool X_2) (tptp.is_fun_pname_bool Y_2)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool Y_2) X_2)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool F Y_2)) (tptp.hAPP_f759274231e_bool F X_2)))))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool F C)) A)))))) (forall ((C $$unsorted) (A $$unsorted) (F $$unsorted) (B_1 $$unsorted)) (=> (= A (tptp.hAPP_f921536533e_bool F B_1)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool C) B_1)) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool Y_2) X_2)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool (tptp.hAPP_f921536533e_bool F Y_2)) (tptp.hAPP_f921536533e_bool F X_2))))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool (tptp.hAPP_f921536533e_bool F C)) A)))))) (forall ((F $$unsorted) (C $$unsorted) (B_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B_1) A)) (=> (= (tptp.hAPP_f759274231e_bool F B_1) C) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (=> (and (tptp.is_fun_pname_bool X_2) (tptp.is_fun_pname_bool Y_2)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool Y_2) X_2)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool F Y_2)) (tptp.hAPP_f759274231e_bool F X_2)))))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool C) (tptp.hAPP_f759274231e_bool F A))))))) (forall ((F $$unsorted) (C $$unsorted) (B_1 $$unsorted) (A $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool B_1) A)) (=> (= (tptp.hAPP_f921536533e_bool F B_1) C) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool Y_2) X_2)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool (tptp.hAPP_f921536533e_bool F Y_2)) (tptp.hAPP_f921536533e_bool F X_2))))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool C) (tptp.hAPP_f921536533e_bool F A))))))) (forall ((B $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.semila1130628874l_bool A_1) B))) (=> (tptp.hBOOL (tptp.finite1626890877e_bool F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A_1)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool B)) (=> (not (= _let_1 tptp.bot_bo1649642514l_bool)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool F (tptp.hAPP_f674760225e_bool Fa (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.semila1782091504l_bool A_1) B))) (tptp.hAPP_f674760225e_bool Fa _let_1)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool F (tptp.hAPP_f674760225e_bool Fa A_1)) (tptp.hAPP_f674760225e_bool Fa B))))))))) (forall ((B $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.hAPP_f1970439265l_bool (tptp.hAPP_f1587382801l_bool tptp.semila1410775201l_bool A_1) B))) (=> (tptp.hBOOL (tptp.finite132673334e_bool F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool A_1)) (=> (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool B)) (=> (not (= _let_1 tptp.bot_bo1325454745l_bool)) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool F (tptp.hAPP_f772567431e_bool Fa (tptp.hAPP_f1970439265l_bool (tptp.hAPP_f1587382801l_bool tptp.semila2055205435l_bool A_1) B))) (tptp.hAPP_f772567431e_bool Fa _let_1)) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool F (tptp.hAPP_f772567431e_bool Fa A_1)) (tptp.hAPP_f772567431e_bool Fa B))))))))) (forall ((B $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A_1) B))) (=> (tptp.hBOOL (tptp.finite1282449217_pname F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B)) (=> (not (= _let_1 tptp.bot_bo844097828e_bool)) (= (tptp.hAPP_pname_pname (tptp.hAPP_p1170154830_pname F (tptp.hAPP_f1297739591_pname Fa (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A_1) B))) (tptp.hAPP_f1297739591_pname Fa _let_1)) (tptp.hAPP_pname_pname (tptp.hAPP_p1170154830_pname F (tptp.hAPP_f1297739591_pname Fa A_1)) (tptp.hAPP_f1297739591_pname Fa B))))))))) (forall ((B $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool A_1) B))) (=> (tptp.hBOOL (tptp.finite774711482_state F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state A_1)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state B)) (=> (not (= _let_1 tptp.bot_bo1055319631e_bool)) (= (tptp.hAPP_H563960305_state (tptp.hAPP_H521649881_state F (tptp.hAPP_f2143211163_state Fa (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool A_1) B))) (tptp.hAPP_f2143211163_state Fa _let_1)) (tptp.hAPP_H563960305_state (tptp.hAPP_H521649881_state F (tptp.hAPP_f2143211163_state Fa A_1)) (tptp.hAPP_f2143211163_state Fa B))))))))) (forall ((B $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (and (tptp.is_fun1661590463l_bool B) (tptp.is_fun1661590463l_bool A_1)) (=> (tptp.hBOOL (tptp.finite1626890877e_bool F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A_1)) (=> (not (= A_1 tptp.bot_bo1649642514l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool B)) (=> (not (= B tptp.bot_bo1649642514l_bool)) (=> (= (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.semila1130628874l_bool A_1) B) tptp.bot_bo1649642514l_bool) (= (tptp.hAPP_f674760225e_bool Fa (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.semila1782091504l_bool A_1) B)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool F (tptp.hAPP_f674760225e_bool Fa A_1)) (tptp.hAPP_f674760225e_bool Fa B))))))))))) (forall ((B $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.finite132673334e_bool F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool A_1)) (=> (not (= A_1 tptp.bot_bo1325454745l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool B)) (=> (not (= B tptp.bot_bo1325454745l_bool)) (=> (= (tptp.hAPP_f1970439265l_bool (tptp.hAPP_f1587382801l_bool tptp.semila1410775201l_bool A_1) B) tptp.bot_bo1325454745l_bool) (= (tptp.hAPP_f772567431e_bool Fa (tptp.hAPP_f1970439265l_bool (tptp.hAPP_f1587382801l_bool tptp.semila2055205435l_bool A_1) B)) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool F (tptp.hAPP_f772567431e_bool Fa A_1)) (tptp.hAPP_f772567431e_bool Fa B)))))))))) (forall ((B $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (and (tptp.is_fun_pname_bool B) (tptp.is_fun_pname_bool A_1)) (=> (tptp.hBOOL (tptp.finite1282449217_pname F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A_1)) (=> (not (= A_1 tptp.bot_bo844097828e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B)) (=> (not (= B tptp.bot_bo844097828e_bool)) (=> (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A_1) B) tptp.bot_bo844097828e_bool) (= (tptp.hAPP_f1297739591_pname Fa (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool A_1) B)) (tptp.hAPP_pname_pname (tptp.hAPP_p1170154830_pname F (tptp.hAPP_f1297739591_pname Fa A_1)) (tptp.hAPP_f1297739591_pname Fa B))))))))))) (forall ((B $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.finite774711482_state F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state A_1)) (=> (not (= A_1 tptp.bot_bo1055319631e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state B)) (=> (not (= B tptp.bot_bo1055319631e_bool)) (=> (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool A_1) B) tptp.bot_bo1055319631e_bool) (= (tptp.hAPP_f2143211163_state Fa (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool A_1) B)) (tptp.hAPP_H563960305_state (tptp.hAPP_H521649881_state F (tptp.hAPP_f2143211163_state Fa A_1)) (tptp.hAPP_f2143211163_state Fa B)))))))))) (forall ((B $$unsorted) (C $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname C))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A_1) B))))))) (forall ((B $$unsorted) (C $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_H248360617l_bool tptp.member1758697444_state C))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 A_1)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 B)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool A_1) B))))))) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname C))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A_1) B))) (not (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A_1)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B)))))))) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H248360617l_bool tptp.member1758697444_state C))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool A_1) B))) (not (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 A_1)) (not (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 B)))))))) (forall ((G_1 $$unsorted) (Fa $$unsorted)) (=> (or (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool Fa)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool G_1))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.semila1130628874l_bool Fa) G_1))))) (forall ((G_1 $$unsorted) (Fa $$unsorted)) (=> (or (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool Fa)) (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool G_1))) (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool (tptp.hAPP_f1970439265l_bool (tptp.hAPP_f1587382801l_bool tptp.semila1410775201l_bool Fa) G_1))))) (forall ((G_1 $$unsorted) (Fa $$unsorted)) (=> (or (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname Fa)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname G_1))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool Fa) G_1))))) (forall ((G_1 $$unsorted) (Fa $$unsorted)) (=> (or (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state Fa)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state G_1))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool Fa) G_1))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (= (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A_1) B) tptp.bot_bo844097828e_bool) (forall ((X_2 $$unsorted)) (=> (tptp.is_pname X_2) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A_1)) (forall ((Xa $$unsorted)) (=> (tptp.is_pname Xa) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname Xa) B)) (not (= X_2 Xa)))))))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (= (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool A_1) B) tptp.bot_bo1055319631e_bool) (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_2) A_1)) (forall ((Xa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state Xa) B)) (not (= X_2 Xa)))))))) (forall ((A_1 $$unsorted)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A_1) tptp.bot_bo844097828e_bool) tptp.bot_bo844097828e_bool)) (forall ((A_1 $$unsorted)) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool A_1) tptp.bot_bo1055319631e_bool) tptp.bot_bo1055319631e_bool)) (forall ((B $$unsorted)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool tptp.bot_bo844097828e_bool) B) tptp.bot_bo844097828e_bool)) (forall ((B $$unsorted)) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool tptp.bot_bo1055319631e_bool) B) tptp.bot_bo1055319631e_bool)) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f661147897e_bool tptp.cOMBC_1058051404l_bool tptp.member_pname))) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A_1) B) (tptp.hAPP_f759274231e_bool tptp.collect_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_f649174806e_bool tptp.cOMBS_568398431l_bool (tptp.hAPP_f1402196763l_bool (tptp.cOMBB_675860798_pname tptp.fconj) (tptp.hAPP_f759274231e_bool _let_1 A_1))) (tptp.hAPP_f759274231e_bool _let_1 B)))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f1262649863e_bool tptp.cOMBC_764456866l_bool tptp.member1758697444_state))) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool A_1) B) (tptp.hAPP_f921536533e_bool tptp.collec727977250_state (tptp.hAPP_f921536533e_bool (tptp.hAPP_f760664097e_bool tptp.cOMBS_1248383340l_bool (tptp.hAPP_f1558728829l_bool (tptp.cOMBB_1382207997_state tptp.fconj) (tptp.hAPP_f921536533e_bool _let_1 A_1))) (tptp.hAPP_f921536533e_bool _let_1 B)))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f1145991873l_bool tptp.cOMBC_1988546018l_bool tptp.member799430823e_bool))) (= (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.semila1130628874l_bool A_1) B) (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f624840228l_bool tptp.cOMBS_350070575l_bool (tptp.hAPP_f143162813l_bool (tptp.cOMBB_2095475776e_bool tptp.fconj) (tptp.hAPP_f559147733l_bool _let_1 A_1))) (tptp.hAPP_f559147733l_bool _let_1 B)))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_f517001763l_bool tptp.cOMBC_1166591542l_bool tptp.member402455436e_bool))) (= (tptp.hAPP_f1970439265l_bool (tptp.hAPP_f1587382801l_bool tptp.semila1410775201l_bool A_1) B) (tptp.hAPP_f1970439265l_bool tptp.collec111528142e_bool (tptp.hAPP_f1970439265l_bool (tptp.hAPP_f1850463605l_bool tptp.cOMBS_2138645332l_bool (tptp.hAPP_f482022705l_bool (tptp.cOMBB_2020112947e_bool tptp.fconj) (tptp.hAPP_f1970439265l_bool _let_1 A_1))) (tptp.hAPP_f1970439265l_bool _let_1 B)))))) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname C))) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A_1) B))) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B)))))) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H248360617l_bool tptp.member1758697444_state C))) (= (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool A_1) B))) (and (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 A_1)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 B)))))) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname C))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A_1) B))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A_1))))) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H248360617l_bool tptp.member1758697444_state C))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool A_1) B))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 A_1))))) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname C))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A_1) B))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B))))) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H248360617l_bool tptp.member1758697444_state C))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool A_1) B))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 B))))) (forall ((P_1 $$unsorted) (Q_1 $$unsorted)) (= (tptp.hAPP_f921536533e_bool tptp.collec727977250_state (tptp.hAPP_f921536533e_bool (tptp.hAPP_f760664097e_bool tptp.cOMBS_1248383340l_bool (tptp.hAPP_f1558728829l_bool (tptp.cOMBB_1382207997_state tptp.fconj) P_1)) Q_1)) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool (tptp.hAPP_f921536533e_bool tptp.collec727977250_state P_1)) (tptp.hAPP_f921536533e_bool tptp.collec727977250_state Q_1)))) (forall ((P_1 $$unsorted) (Q_1 $$unsorted)) (= (tptp.hAPP_f759274231e_bool tptp.collect_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_f649174806e_bool tptp.cOMBS_568398431l_bool (tptp.hAPP_f1402196763l_bool (tptp.cOMBB_675860798_pname tptp.fconj) P_1)) Q_1)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool (tptp.hAPP_f759274231e_bool tptp.collect_pname P_1)) (tptp.hAPP_f759274231e_bool tptp.collect_pname Q_1)))) (forall ((P_1 $$unsorted) (Q_1 $$unsorted)) (= (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f624840228l_bool tptp.cOMBS_350070575l_bool (tptp.hAPP_f143162813l_bool (tptp.cOMBB_2095475776e_bool tptp.fconj) P_1)) Q_1)) (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.semila1130628874l_bool (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool P_1)) (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool Q_1)))) (forall ((P_1 $$unsorted) (Q_1 $$unsorted)) (= (tptp.hAPP_f1970439265l_bool tptp.collec111528142e_bool (tptp.hAPP_f1970439265l_bool (tptp.hAPP_f1850463605l_bool tptp.cOMBS_2138645332l_bool (tptp.hAPP_f482022705l_bool (tptp.cOMBB_2020112947e_bool tptp.fconj) P_1)) Q_1)) (tptp.hAPP_f1970439265l_bool (tptp.hAPP_f1587382801l_bool tptp.semila1410775201l_bool (tptp.hAPP_f1970439265l_bool tptp.collec111528142e_bool P_1)) (tptp.hAPP_f1970439265l_bool tptp.collec111528142e_bool Q_1)))) (forall ((X_1 $$unsorted) (A_1 $$unsorted) (P_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname X_1))) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A_1) (tptp.hAPP_f759274231e_bool tptp.collect_pname P_1)))) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A_1)) (tptp.hBOOL (tptp.hAPP_pname_bool P_1 X_1)))))) (forall ((X_1 $$unsorted) (A_1 $$unsorted) (P_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_1))) (= (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool A_1) (tptp.hAPP_f921536533e_bool tptp.collec727977250_state P_1)))) (and (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 A_1)) (tptp.hBOOL (tptp.hAPP_H513860823e_bool P_1 X_1)))))) (forall ((X_1 $$unsorted) (A_1 $$unsorted) (P_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool X_1))) (= (tptp.hBOOL (tptp.hAPP_f1935102916l_bool _let_1 (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.semila1130628874l_bool A_1) (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool P_1)))) (and (tptp.hBOOL (tptp.hAPP_f1935102916l_bool _let_1 A_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 X_1)))))) (forall ((X_1 $$unsorted) (A_1 $$unsorted) (P_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f105100493l_bool tptp.member402455436e_bool X_1))) (= (tptp.hBOOL (tptp.hAPP_f239102607l_bool _let_1 (tptp.hAPP_f1970439265l_bool (tptp.hAPP_f1587382801l_bool tptp.semila1410775201l_bool A_1) (tptp.hAPP_f1970439265l_bool tptp.collec111528142e_bool P_1)))) (and (tptp.hBOOL (tptp.hAPP_f239102607l_bool _let_1 A_1)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool P_1 X_1)))))) (forall ((R_1 $$unsorted) (S $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_f661147897e_bool tptp.cOMBC_1058051404l_bool tptp.member_pname))) (= (tptp.hBOOL (tptp.hAPP_pname_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool (tptp.hAPP_f759274231e_bool _let_1 R_1)) (tptp.hAPP_f759274231e_bool _let_1 S)) X_2)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool R_1) S)))))) (forall ((R_1 $$unsorted) (S $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1262649863e_bool tptp.cOMBC_764456866l_bool tptp.member1758697444_state))) (= (tptp.hBOOL (tptp.hAPP_H513860823e_bool (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool (tptp.hAPP_f921536533e_bool _let_1 R_1)) (tptp.hAPP_f921536533e_bool _let_1 S)) X_2)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_2) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool R_1) S)))))) (forall ((A_1 $$unsorted) (B $$unsorted) (C_1 $$unsorted)) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool A_1) B)) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool B) C_1))) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool C_1) A_1)) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool A_1) B)) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool B) C_1))) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool C_1) A_1)))) (forall ((B $$unsorted) (C_1 $$unsorted) (A_1 $$unsorted)) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool B) C_1)) A_1) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool B) A_1)) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool C_1) A_1)))) (forall ((B $$unsorted) (C_1 $$unsorted) (A_1 $$unsorted)) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool B) C_1)) A_1) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool B) A_1)) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool C_1) A_1)))) (forall ((A_1 $$unsorted) (B $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool A_1))) (= (tptp.hAPP_f921536533e_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool B) C_1)) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool (tptp.hAPP_f921536533e_bool _let_1 B)) (tptp.hAPP_f921536533e_bool _let_1 C_1))))) (forall ((A_1 $$unsorted) (B $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool A_1))) (= (tptp.hAPP_f921536533e_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool B) C_1)) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool (tptp.hAPP_f921536533e_bool _let_1 B)) (tptp.hAPP_f921536533e_bool _let_1 C_1))))) (forall ((B $$unsorted) (D_1 $$unsorted) (A_1 $$unsorted) (C_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_1) C_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) D_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A_1) B)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool C_1) D_1)))))) (forall ((B $$unsorted) (D_1 $$unsorted) (A_1 $$unsorted) (C_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool A_1) C_1)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool B) D_1)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool A_1) B)) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool C_1) D_1)))))) (forall ((B $$unsorted) (C_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool C_1))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A_1) B))))))) (forall ((B $$unsorted) (C_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool C_1))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 A_1)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 B)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool A_1) B))))))) (forall ((B $$unsorted) (A_1 $$unsorted)) (=> (tptp.is_fun_pname_bool B) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) A_1)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A_1) B) B)))) (forall ((B $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool B) A_1)) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool A_1) B) B))) (forall ((A_1 $$unsorted) (B $$unsorted)) (=> (tptp.is_fun_pname_bool A_1) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_1) B)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A_1) B) A_1)))) (forall ((A_1 $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool A_1) B)) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool A_1) B) A_1))) (forall ((A_1 $$unsorted) (B $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A_1) B)) B))) (forall ((A_1 $$unsorted) (B $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool A_1) B)) B))) (forall ((A_1 $$unsorted) (B $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A_1) B)) A_1))) (forall ((A_1 $$unsorted) (B $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool A_1) B)) A_1))) (forall ((B $$unsorted) (A $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_p905327722e_bool tptp.insert_pname A))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A) C_1)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool (tptp.hAPP_f759274231e_bool _let_1 B)) C_1) (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool B) C_1)))))) (forall ((B $$unsorted) (A $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state A) C_1)) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool (tptp.hAPP_f921536533e_bool _let_1 B)) C_1) (tptp.hAPP_f921536533e_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool B) C_1)))))) (forall ((B $$unsorted) (A $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A_1))) (let ((_let_2 (tptp.hAPP_p905327722e_bool tptp.insert_pname A))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A) A_1)) (= (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool _let_2 B)) (tptp.hAPP_f759274231e_bool _let_2 (tptp.hAPP_f759274231e_bool _let_1 B))))))) (forall ((B $$unsorted) (A $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool A_1))) (let ((_let_2 (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state A) A_1)) (= (tptp.hAPP_f921536533e_bool _let_1 (tptp.hAPP_f921536533e_bool _let_2 B)) (tptp.hAPP_f921536533e_bool _let_2 (tptp.hAPP_f921536533e_bool _let_1 B))))))) (forall ((B $$unsorted) (A $$unsorted) (C_1 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A) C_1))) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A) B)) C_1) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool B) C_1)))) (forall ((B $$unsorted) (A $$unsorted) (C_1 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state A) C_1))) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A) B)) C_1) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool B) C_1)))) (forall ((B $$unsorted) (A $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A_1))) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A) A_1))) (= (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname A) B)) (tptp.hAPP_f759274231e_bool _let_1 B))))) (forall ((B $$unsorted) (A $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool A_1))) (=> (not (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state A) A_1))) (= (tptp.hAPP_f921536533e_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A) B)) (tptp.hAPP_f921536533e_bool _let_1 B))))) (forall ((A $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_p905327722e_bool tptp.insert_pname A))) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool (tptp.hAPP_f759274231e_bool _let_1 A_1)) (tptp.hAPP_f759274231e_bool _let_1 B)) (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A_1) B))))) (forall ((A $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A))) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool (tptp.hAPP_f921536533e_bool _let_1 A_1)) (tptp.hAPP_f921536533e_bool _let_1 B)) (tptp.hAPP_f921536533e_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool A_1) B))))) (forall ((B $$unsorted) (A $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool B) C_1))) (let ((_let_2 (tptp.hAPP_p905327722e_bool tptp.insert_pname A))) (let ((_let_3 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool (tptp.hAPP_f759274231e_bool _let_2 B)) C_1))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A) C_1)))) (and (=> _let_4 (= _let_3 (tptp.hAPP_f759274231e_bool _let_2 _let_1))) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((B $$unsorted) (A $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool B) C_1))) (let ((_let_2 (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A))) (let ((_let_3 (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool (tptp.hAPP_f921536533e_bool _let_2 B)) C_1))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state A) C_1)))) (and (=> _let_4 (= _let_3 (tptp.hAPP_f921536533e_bool _let_2 _let_1))) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((B $$unsorted) (A $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A_1))) (let ((_let_2 (tptp.hAPP_f759274231e_bool _let_1 B))) (let ((_let_3 (tptp.hAPP_p905327722e_bool tptp.insert_pname A))) (let ((_let_4 (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool _let_3 B)))) (let ((_let_5 (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A) A_1)))) (and (=> _let_5 (= _let_4 (tptp.hAPP_f759274231e_bool _let_3 _let_2))) (=> (not _let_5) (= _let_4 _let_2))))))))) (forall ((B $$unsorted) (A $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool A_1))) (let ((_let_2 (tptp.hAPP_f921536533e_bool _let_1 B))) (let ((_let_3 (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A))) (let ((_let_4 (tptp.hAPP_f921536533e_bool _let_1 (tptp.hAPP_f921536533e_bool _let_3 B)))) (let ((_let_5 (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state A) A_1)))) (and (=> _let_5 (= _let_4 (tptp.hAPP_f921536533e_bool _let_3 _let_2))) (=> (not _let_5) (= _let_4 _let_2))))))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool X_1) Y_1)) X_1))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool X_1) Y_1)) X_1))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool X_1) Y_1)) X_1))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool X_1) Y_1)) X_1))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool X_1) Y_1)) Y_1))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool X_1) Y_1)) Y_1))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool X_1) Y_1)) Y_1))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool X_1) Y_1)) Y_1))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (=> (tptp.is_fun_pname_bool X_1) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool X_1) Y_1)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool X_1) Y_1) X_1)))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool X_1) Y_1)) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool X_1) Y_1) X_1))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool X_1))) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool Y_1) Z))) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 Y_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 Z)))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool X_1))) (= (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool Y_1) Z))) (and (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 Y_1)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 Z)))))) (forall ((B_1 $$unsorted) (A $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) X_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A) B_1)) X_1)))) (forall ((B_1 $$unsorted) (A $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool A) X_1)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool A) B_1)) X_1)))) (forall ((A $$unsorted) (B_1 $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B_1) X_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A) B_1)) X_1)))) (forall ((A $$unsorted) (B_1 $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool B_1) X_1)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool A) B_1)) X_1)))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (=> (tptp.is_fun_pname_bool X_1) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool X_1) Y_1)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool X_1) Y_1) X_1)))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool X_1) Y_1)) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool X_1) Y_1) X_1))) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (=> (tptp.is_fun_pname_bool Y_1) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool Y_1) X_1)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool X_1) Y_1) Y_1)))) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool Y_1) X_1)) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool X_1) Y_1) Y_1))) (forall ((B_1 $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool X_1))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A) B_1))))))) (forall ((B_1 $$unsorted) (X_1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool X_1))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 A)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 B_1)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool A) B_1))))))) (forall ((Z $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool X_1))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 Y_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 Z)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool Y_1) Z))))))) (forall ((Z $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool X_1))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 Y_1)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 Z)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool Y_1) Z))))))) (forall ((B_1 $$unsorted) (D $$unsorted) (A $$unsorted) (C $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) C)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B_1) D)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A) B_1)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool C) D)))))) (forall ((B_1 $$unsorted) (D $$unsorted) (A $$unsorted) (C $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool A) C)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool B_1) D)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool A) B_1)) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool C) D)))))) (forall ((X_1 $$unsorted) (A $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool X_1))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A) B_1))) (not (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B_1)))))))) (forall ((X_1 $$unsorted) (A $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool X_1))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool A) B_1))) (not (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 A)) (not (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 B_1)))))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool X_1) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool X_1) Y_1)) X_1)) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool X_1) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool X_1) Y_1)) X_1)) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool X_1))) (= (tptp.hAPP_f921536533e_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool Y_1) Z)) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool (tptp.hAPP_f921536533e_bool _let_1 Y_1)) (tptp.hAPP_f921536533e_bool _let_1 Z))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool X_1))) (= (tptp.hAPP_f921536533e_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool Y_1) Z)) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool (tptp.hAPP_f921536533e_bool _let_1 Y_1)) (tptp.hAPP_f921536533e_bool _let_1 Z))))) (forall ((Y_1 $$unsorted) (Z $$unsorted) (X_1 $$unsorted)) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool Y_1) Z)) X_1) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool Y_1) X_1)) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool Z) X_1)))) (forall ((Y_1 $$unsorted) (Z $$unsorted) (X_1 $$unsorted)) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool Y_1) Z)) X_1) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool Y_1) X_1)) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool Z) X_1)))) (forall ((X_1 $$unsorted)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool X_1) tptp.bot_bo844097828e_bool) tptp.bot_bo844097828e_bool)) (forall ((X_1 $$unsorted)) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool X_1) tptp.bot_bo1055319631e_bool) tptp.bot_bo1055319631e_bool)) (forall ((X_1 $$unsorted)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool tptp.bot_bo844097828e_bool) X_1) tptp.bot_bo844097828e_bool)) (forall ((X_1 $$unsorted)) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool tptp.bot_bo1055319631e_bool) X_1) tptp.bot_bo1055319631e_bool)) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool X_1))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool Y_1) Z))) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool (tptp.hAPP_f759274231e_bool _let_1 Y_1)) (tptp.hAPP_f759274231e_bool _let_1 Z)))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool X_1))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool (tptp.hAPP_f921536533e_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool Y_1) Z))) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool (tptp.hAPP_f921536533e_bool _let_1 Y_1)) (tptp.hAPP_f921536533e_bool _let_1 Z)))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool X_1))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool (tptp.hAPP_f759274231e_bool _let_1 Y_1)) (tptp.hAPP_f759274231e_bool _let_1 Z))) (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool Y_1) Z)))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool X_1))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool (tptp.hAPP_f921536533e_bool _let_1 Y_1)) (tptp.hAPP_f921536533e_bool _let_1 Z))) (tptp.hAPP_f921536533e_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool Y_1) Z)))))) (forall ((F $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.image_275883510_state F))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool (tptp.hAPP_f631639356e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A_1) B))) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool (tptp.hAPP_f631639356e_bool _let_1 A_1)) (tptp.hAPP_f631639356e_bool _let_1 B)))))) (forall ((A_1 $$unsorted) (B $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A_1))) (= (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool (tptp.hAPP_f759274231e_bool _let_1 B)) C_1) (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool B) C_1))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool C_1) A_1))))) (forall ((A_1 $$unsorted) (B $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool A_1))) (= (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool (tptp.hAPP_f921536533e_bool _let_1 B)) C_1) (tptp.hAPP_f921536533e_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool B) C_1))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool C_1) A_1))))) (forall ((P_1 $$unsorted) (F $$unsorted) (G $$unsorted) (S $$unsorted)) (let ((_let_1 (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool S))) (= (tptp.hAPP_f631639356e_bool (tptp.image_275883510_state (tptp.hAPP_f1661207211_state (tptp.hAPP_f137248406_state tptp.cOMBS_843273363_state (tptp.hAPP_f2101567797_state (tptp.hAPP_f939130838_state tptp.cOMBS_381334199_state (tptp.hAPP_f1405979047_state (tptp.cOMBB_707293872_pname tptp.if_Hoa533980679_state) P_1)) F)) G)) S) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool (tptp.hAPP_f631639356e_bool (tptp.image_275883510_state F) (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool tptp.collect_pname P_1)))) (tptp.hAPP_f631639356e_bool (tptp.image_275883510_state G) (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool tptp.collect_pname (tptp.hAPP_f759274231e_bool (tptp.cOMBB_647938656_pname tptp.fNot) P_1)))))))) (forall ((P_1 $$unsorted) (F $$unsorted) (G $$unsorted)) (= (tptp.dom_pname_com (tptp.hAPP_f2123220539on_com (tptp.hAPP_f1673966486on_com tptp.cOMBS_904531235on_com (tptp.hAPP_f648377725on_com (tptp.hAPP_f2093196134on_com tptp.cOMBS_1529518335on_com (tptp.hAPP_f755519727on_com (tptp.cOMBB_1394247784_pname tptp.if_option_com) P_1)) F)) G)) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila278973382e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool (tptp.dom_pname_com F)) (tptp.hAPP_f759274231e_bool tptp.collect_pname P_1))) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool (tptp.dom_pname_com G)) (tptp.hAPP_f759274231e_bool tptp.collect_pname (tptp.hAPP_f759274231e_bool (tptp.cOMBB_647938656_pname tptp.fNot) P_1)))))) (forall ((Q_1 $$unsorted) (P_1 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_1) B)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.is_pname X_2) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A_1)) (=> (tptp.hBOOL (tptp.hAPP_pname_bool P_1 X_2)) (tptp.hBOOL (tptp.hAPP_pname_bool Q_1 X_2)))))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool A_1) (tptp.hAPP_f759274231e_bool tptp.collect_pname P_1))) (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.semila1635148844e_bool B) (tptp.hAPP_f759274231e_bool tptp.collect_pname Q_1))))))) (forall ((Q_1 $$unsorted) (P_1 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool A_1) B)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_2) A_1)) (=> (tptp.hBOOL (tptp.hAPP_H513860823e_bool P_1 X_2)) (tptp.hBOOL (tptp.hAPP_H513860823e_bool Q_1 X_2))))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool A_1) (tptp.hAPP_f921536533e_bool tptp.collec727977250_state P_1))) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool B) (tptp.hAPP_f921536533e_bool tptp.collec727977250_state Q_1))))))) (forall ((Q_1 $$unsorted) (P_1 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool A_1) B)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.is_fun_pname_bool X_2) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool X_2) A_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 X_2)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool Q_1 X_2)))))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.semila1130628874l_bool A_1) (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool P_1))) (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.semila1130628874l_bool B) (tptp.hAPP_f559147733l_bool tptp.collec1974731493e_bool Q_1))))))) (forall ((Q_1 $$unsorted) (P_1 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f239102607l_bool (tptp.hAPP_f1269496639l_bool tptp.ord_le1076702565l_bool A_1) B)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f239102607l_bool (tptp.hAPP_f105100493l_bool tptp.member402455436e_bool X_2) A_1)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool P_1 X_2)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool Q_1 X_2))))) (tptp.hBOOL (tptp.hAPP_f239102607l_bool (tptp.hAPP_f1269496639l_bool tptp.ord_le1076702565l_bool (tptp.hAPP_f1970439265l_bool (tptp.hAPP_f1587382801l_bool tptp.semila1410775201l_bool A_1) (tptp.hAPP_f1970439265l_bool tptp.collec111528142e_bool P_1))) (tptp.hAPP_f1970439265l_bool (tptp.hAPP_f1587382801l_bool tptp.semila1410775201l_bool B) (tptp.hAPP_f1970439265l_bool tptp.collec111528142e_bool Q_1))))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool X_1))) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool X_2))) (= (tptp.hAPP_f921536533e_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool Y_2) Z_1)) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool (tptp.hAPP_f921536533e_bool _let_1 Y_2)) (tptp.hAPP_f921536533e_bool _let_1 Z_1))))) (= (tptp.hAPP_f921536533e_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool Y_1) Z)) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool (tptp.hAPP_f921536533e_bool _let_1 Y_1)) (tptp.hAPP_f921536533e_bool _let_1 Z)))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool X_1))) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool X_2))) (= (tptp.hAPP_f921536533e_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool Y_2) Z_1)) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila2145357127e_bool (tptp.hAPP_f921536533e_bool _let_1 Y_2)) (tptp.hAPP_f921536533e_bool _let_1 Z_1))))) (= (tptp.hAPP_f921536533e_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool Y_1) Z)) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.semila447562797e_bool (tptp.hAPP_f921536533e_bool _let_1 Y_1)) (tptp.hAPP_f921536533e_bool _let_1 Z)))))) (forall ((X_1 $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A_1) (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1) tptp.bot_bo844097828e_bool)))) (let ((_let_2 (tptp.hAPP_f1297739591_pname Fa A_1))) (let ((_let_3 (= _let_1 tptp.bot_bo844097828e_bool))) (=> (tptp.is_pname X_1) (=> (tptp.hBOOL (tptp.finite1282449217_pname F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A_1)) (and (=> _let_3 (= _let_2 X_1)) (=> (not _let_3) (= _let_2 (tptp.hAPP_pname_pname (tptp.hAPP_p1170154830_pname F X_1) (tptp.hAPP_f1297739591_pname Fa _let_1))))))))))))) (forall ((X_1 $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.minus_2076558538e_bool A_1) (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state X_1) tptp.bot_bo1055319631e_bool)))) (let ((_let_2 (tptp.hAPP_f2143211163_state Fa A_1))) (let ((_let_3 (= _let_1 tptp.bot_bo1055319631e_bool))) (=> (tptp.hBOOL (tptp.finite774711482_state F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state A_1)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_1) A_1)) (and (=> _let_3 (= _let_2 X_1)) (=> (not _let_3) (= _let_2 (tptp.hAPP_H563960305_state (tptp.hAPP_H521649881_state F X_1) (tptp.hAPP_f2143211163_state Fa _let_1)))))))))))) (forall ((X_1 $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.minus_1290075917l_bool A_1) (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool X_1) tptp.bot_bo1649642514l_bool)))) (let ((_let_2 (tptp.hAPP_f674760225e_bool Fa A_1))) (let ((_let_3 (= _let_1 tptp.bot_bo1649642514l_bool))) (=> (tptp.is_fun_pname_bool X_1) (=> (tptp.hBOOL (tptp.finite1626890877e_bool F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A_1)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool X_1) A_1)) (and (=> _let_3 (= _let_2 X_1)) (=> (not _let_3) (= _let_2 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool F X_1) (tptp.hAPP_f674760225e_bool Fa _let_1))))))))))))) (forall ((X_1 $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.hAPP_f1970439265l_bool (tptp.hAPP_f1587382801l_bool tptp.minus_164259166l_bool A_1) (tptp.hAPP_f1970439265l_bool (tptp.hAPP_f601642911l_bool tptp.insert1991711667e_bool X_1) tptp.bot_bo1325454745l_bool)))) (let ((_let_2 (tptp.hAPP_f772567431e_bool Fa A_1))) (let ((_let_3 (= _let_1 tptp.bot_bo1325454745l_bool))) (=> (tptp.hBOOL (tptp.finite132673334e_bool F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool A_1)) (=> (tptp.hBOOL (tptp.hAPP_f239102607l_bool (tptp.hAPP_f105100493l_bool tptp.member402455436e_bool X_1) A_1)) (and (=> _let_3 (= _let_2 X_1)) (=> (not _let_3) (= _let_2 (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool F X_1) (tptp.hAPP_f772567431e_bool Fa _let_1)))))))))))) (forall ((X_1 $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1))) (let ((_let_2 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A_1) (tptp.hAPP_f759274231e_bool _let_1 tptp.bot_bo844097828e_bool)))) (let ((_let_3 (tptp.hAPP_f1297739591_pname Fa (tptp.hAPP_f759274231e_bool _let_1 A_1)))) (let ((_let_4 (= _let_2 tptp.bot_bo844097828e_bool))) (=> (tptp.is_pname X_1) (=> (tptp.hBOOL (tptp.finite1282449217_pname F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A_1)) (and (=> _let_4 (= _let_3 X_1)) (=> (not _let_4) (= _let_3 (tptp.hAPP_pname_pname (tptp.hAPP_p1170154830_pname F X_1) (tptp.hAPP_f1297739591_pname Fa _let_2))))))))))))) (forall ((X_1 $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state X_1))) (let ((_let_2 (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.minus_2076558538e_bool A_1) (tptp.hAPP_f921536533e_bool _let_1 tptp.bot_bo1055319631e_bool)))) (let ((_let_3 (tptp.hAPP_f2143211163_state Fa (tptp.hAPP_f921536533e_bool _let_1 A_1)))) (let ((_let_4 (= _let_2 tptp.bot_bo1055319631e_bool))) (=> (tptp.hBOOL (tptp.finite774711482_state F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state A_1)) (and (=> _let_4 (= _let_3 X_1)) (=> (not _let_4) (= _let_3 (tptp.hAPP_H563960305_state (tptp.hAPP_H521649881_state F X_1) (tptp.hAPP_f2143211163_state Fa _let_2)))))))))))) (forall ((X_1 $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.hAPP_f1320879424l_bool tptp.insert1325755072e_bool X_1))) (let ((_let_2 (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.minus_1290075917l_bool A_1) (tptp.hAPP_f559147733l_bool _let_1 tptp.bot_bo1649642514l_bool)))) (let ((_let_3 (tptp.hAPP_f674760225e_bool Fa (tptp.hAPP_f559147733l_bool _let_1 A_1)))) (let ((_let_4 (= _let_2 tptp.bot_bo1649642514l_bool))) (=> (tptp.is_fun_pname_bool X_1) (=> (tptp.hBOOL (tptp.finite1626890877e_bool F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A_1)) (and (=> _let_4 (= _let_3 X_1)) (=> (not _let_4) (= _let_3 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool F X_1) (tptp.hAPP_f674760225e_bool Fa _let_2))))))))))))) (forall ((X_1 $$unsorted) (A_1 $$unsorted) (F $$unsorted) (Fa $$unsorted)) (let ((_let_1 (tptp.hAPP_f601642911l_bool tptp.insert1991711667e_bool X_1))) (let ((_let_2 (tptp.hAPP_f1970439265l_bool (tptp.hAPP_f1587382801l_bool tptp.minus_164259166l_bool A_1) (tptp.hAPP_f1970439265l_bool _let_1 tptp.bot_bo1325454745l_bool)))) (let ((_let_3 (tptp.hAPP_f772567431e_bool Fa (tptp.hAPP_f1970439265l_bool _let_1 A_1)))) (let ((_let_4 (= _let_2 tptp.bot_bo1325454745l_bool))) (=> (tptp.hBOOL (tptp.finite132673334e_bool F Fa)) (=> (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool A_1)) (and (=> _let_4 (= _let_3 X_1)) (=> (not _let_4) (= _let_3 (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool F X_1) (tptp.hAPP_f772567431e_bool Fa _let_2)))))))))))) (forall ((B $$unsorted) (C $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname C))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A_1)) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A_1) B))))))) (forall ((B $$unsorted) (C $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_H248360617l_bool tptp.member1758697444_state C))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 A_1)) (=> (not (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 B))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.minus_2076558538e_bool A_1) B))))))) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname C))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A_1) B))) (not (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B))))))) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H248360617l_bool tptp.member1758697444_state C))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.minus_2076558538e_bool A_1) B))) (not (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 A_1)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_1 B))))))) (forall ((B $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A_1)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f230953622l_bool tptp.minus_1290075917l_bool A_1) B))))) (forall ((B $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool A_1)) (tptp.hBOOL (tptp.hAPP_f239102607l_bool tptp.finite899049100e_bool (tptp.hAPP_f1970439265l_bool (tptp.hAPP_f1587382801l_bool tptp.minus_164259166l_bool A_1) B))))) (forall ((B $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A_1) B))))) (forall ((B $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state A_1)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.minus_2076558538e_bool A_1) B))))) (forall ((A $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_p905327722e_bool tptp.insert_pname A))) (=> (tptp.is_fun_pname_bool A_1) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A) A_1)) (= (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A_1) (tptp.hAPP_f759274231e_bool _let_1 tptp.bot_bo844097828e_bool))) A_1))))) (forall ((A $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A))) (=> (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state A) A_1)) (= (tptp.hAPP_f921536533e_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.minus_2076558538e_bool A_1) (tptp.hAPP_f921536533e_bool _let_1 tptp.bot_bo1055319631e_bool))) A_1)))) (forall ((X_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_p905327722e_bool tptp.insert_pname X_1))) (=> (tptp.is_fun_pname_bool A_1) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A_1))) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool (tptp.hAPP_f759274231e_bool _let_1 A_1)) (tptp.hAPP_f759274231e_bool _let_1 tptp.bot_bo844097828e_bool)) A_1))))) (forall ((X_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state X_1))) (=> (not (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state X_1) A_1))) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.minus_2076558538e_bool (tptp.hAPP_f921536533e_bool _let_1 A_1)) (tptp.hAPP_f921536533e_bool _let_1 tptp.bot_bo1055319631e_bool)) A_1)))) (forall ((A $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_p905327722e_bool tptp.insert_pname A))) (= (tptp.hAPP_f759274231e_bool _let_1 (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1388330588e_bool tptp.minus_1015773161e_bool A_1) (tptp.hAPP_f759274231e_bool _let_1 tptp.bot_bo844097828e_bool))) (tptp.hAPP_f759274231e_bool _let_1 A_1)))) (forall ((A $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A))) (= (tptp.hAPP_f921536533e_bool _let_1 (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.minus_2076558538e_bool A_1) (tptp.hAPP_f921536533e_bool _let_1 tptp.bot_bo1055319631e_bool))) (tptp.hAPP_f921536533e_bool _let_1 A_1)))) (forall ((A_1 $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP_H727730819e_bool tptp.insert1835143293_state A))) (let ((_let_2 (tptp.hAPP_f1583986009e_bool tptp.minus_2076558538e_bool A_1))) (= (tptp.hAPP_f921536533e_bool _let_2 (tptp.hAPP_f921536533e_bool _let_1 B)) (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1583986009e_bool tptp.minus_2076558538e_bool (tptp.hAPP_f921536533e_bool _let_2 (tptp.hAPP_f921536533e_bool _let_1 tptp.bot_bo1055319631e_bool))) B))))) (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))) (not (tptp.hBOOL tptp.fFalse)) (forall ((P $$unsorted)) (=> (tptp.is_bool P) (or (= P tptp.fTrue) (= P tptp.fFalse)))) (forall ((Q $$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) (P $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP_f327114704l_bool tptp.fAll_state P))) (tptp.hBOOL (tptp.hAPP_state_bool P X)))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (and (tptp.is_pname X) (tptp.is_pname Y)) (or (not (tptp.hBOOL (tptp.hAPP_pname_bool (tptp.hAPP_p61793385e_bool tptp.fequal_pname X) Y))) (= X Y)))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_pname_bool (tptp.hAPP_p61793385e_bool tptp.fequal_pname X) Y)))) (forall ((X $$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 $$unsorted)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool tptp.fequal_state X) Y)))) (forall ((P $$unsorted) (Q $$unsorted)) (=> (tptp.is_bool P) (= (tptp.hAPP_pname_bool (tptp.cOMBK_bool_pname P) Q) P))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.hAPP_o356497025on_com (tptp.hAPP_o334540577on_com (tptp.hAPP_b1679505845on_com tptp.if_option_com tptp.fTrue) X) Y) X)) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.hAPP_o356497025on_com (tptp.hAPP_o334540577on_com (tptp.hAPP_b1679505845on_com tptp.if_option_com tptp.fFalse) X) Y) Y)) (forall ((P $$unsorted)) (=> (tptp.is_bool P) (or (= P tptp.fTrue) (= P tptp.fFalse)))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (and (tptp.is_fun_pname_bool X) (tptp.is_fun_pname_bool Y)) (or (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.fequal533582459e_bool X) Y))) (= X Y)))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.fequal533582459e_bool X) Y)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_pname_bool (tptp.hAPP_f759274231e_bool (tptp.cOMBB_647938656_pname P) Q) R) (tptp.hAPP_bool_bool P (tptp.hAPP_pname_bool Q R)))) (forall ((P $$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_pname_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f649174806e_bool tptp.cOMBS_568398431l_bool P) Q) R) (tptp.hAPP_bool_bool (tptp.hAPP_p393069232l_bool P R) (tptp.hAPP_pname_bool Q R)))) (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_pname_bool (tptp.hAPP_p61793385e_bool (tptp.hAPP_f22061361e_bool tptp.cOMBC_1149511130e_bool P) Q) R) (tptp.hAPP_pname_bool (tptp.hAPP_p61793385e_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool (tptp.hAPP_f817621513e_bool tptp.cOMBC_2027030106e_bool P) Q) R) (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted)) (=> (tptp.is_bool P) (= (tptp.hAPP_f1664156314l_bool (tptp.cOMBK_1857069011e_bool P) Q) P))) (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.hAPP_s1806633685e_bool (tptp.cOMBK_631994958_state P) Q) P)) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.hAPP_H563960305_state (tptp.hAPP_H521649881_state (tptp.hAPP_b798484845_state tptp.if_Hoa533980679_state tptp.fTrue) X) Y) X)) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.hAPP_H563960305_state (tptp.hAPP_H521649881_state (tptp.hAPP_b798484845_state tptp.if_Hoa533980679_state tptp.fFalse) X) Y) Y)) (forall ((P $$unsorted)) (=> (tptp.is_bool P) (or (= P tptp.fTrue) (= P tptp.fFalse)))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP_H513860823e_bool (tptp.hAPP_H1645666623e_bool tptp.fequal1531560888_state X) Y))) (= X Y))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_H513860823e_bool (tptp.hAPP_H1645666623e_bool tptp.fequal1531560888_state X) Y)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_pname_com (tptp.hAPP_f96342628me_com (tptp.cOMBB_923936821_pname P) Q) R) (tptp.hAPP_option_com_com P (tptp.hAPP_p799580910on_com Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f559147733l_bool (tptp.cOMBB_307249310e_bool P) Q) R) (tptp.hAPP_bool_bool P (tptp.hAPP_f1664156314l_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_p393069232l_bool (tptp.hAPP_f1402196763l_bool (tptp.cOMBB_675860798_pname P) Q) R) (tptp.hAPP_b589554111l_bool P (tptp.hAPP_pname_bool Q R)))) (forall ((P $$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 ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f624840228l_bool tptp.cOMBS_350070575l_bool P) Q) R) (tptp.hAPP_bool_bool (tptp.hAPP_f1476298914l_bool P R) (tptp.hAPP_f1664156314l_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_pname_bool (tptp.hAPP_f42430548e_bool (tptp.cOMBB_530759491_pname P) Q) R) (tptp.hAPP_f1664156314l_bool P (tptp.hAPP_p61793385e_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_state_bool (tptp.hAPP_f1012183542e_bool (tptp.cOMBB_1911358915_state P) Q) R) (tptp.hAPP_f327114704l_bool P (tptp.hAPP_s1806633685e_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_pname_bool (tptp.hAPP_f759274231e_bool (tptp.hAPP_f661147897e_bool tptp.cOMBC_1058051404l_bool P) Q) R) (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_s1806633685e_bool (tptp.hAPP_b1095269219e_bool (tptp.hAPP_f701449317e_bool tptp.cOMBC_471052088e_bool P) Q) R) (tptp.hAPP_b2019457360e_bool (tptp.hAPP_s1874344717e_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool (tptp.hAPP_f2082757169l_bool tptp.cOMBC_1004116266e_bool P) Q) R) (tptp.hAPP_pname_bool (tptp.hAPP_f759274231e_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_p61793385e_bool (tptp.hAPP_f1336811455e_bool (tptp.cOMBB_542850580_pname P) Q) R) (tptp.hAPP_p61793385e_bool P (tptp.hAPP_pname_pname Q R)))) (forall ((P $$unsorted) (Q $$unsorted)) (=> (tptp.is_bool P) (= (tptp.hAPP_H513860823e_bool (tptp.cOMBK_1079618832_state P) Q) P))) (forall ((P $$unsorted) (Q $$unsorted)) (=> (tptp.is_pname P) (= (tptp.hAPP_H1344248906_pname (tptp.cOMBK_588224941_state P) Q) P))) (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.hAPP_p1842370726_state (tptp.cOMBK_90103121_pname P) Q) P)) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.fequal1746921144e_bool X) Y))) (= X Y))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.fequal1746921144e_bool X) Y)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_p799580910on_com (tptp.hAPP_f2123220539on_com (tptp.hAPP_f1673966486on_com tptp.cOMBS_904531235on_com P) Q) R) (tptp.hAPP_o356497025on_com (tptp.hAPP_p1086945780on_com P R) (tptp.hAPP_p799580910on_com Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_p1842370726_state (tptp.hAPP_f1758910594_state (tptp.cOMBB_422605457_pname P) Q) R) (tptp.hAPP_c1546227244_state P (tptp.hAPP_pname_com Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H513860823e_bool (tptp.hAPP_f921536533e_bool (tptp.cOMBB_416661851_state P) Q) R) (tptp.hAPP_bool_bool P (tptp.hAPP_H513860823e_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H513860823e_bool (tptp.hAPP_f921536533e_bool (tptp.hAPP_f760664097e_bool tptp.cOMBS_1248383340l_bool P) Q) R) (tptp.hAPP_bool_bool (tptp.hAPP_H226398757l_bool P R) (tptp.hAPP_H513860823e_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_pname_bool (tptp.hAPP_H1632039476e_bool (tptp.hAPP_f167506745e_bool tptp.cOMBC_290948233e_bool P) Q) R) (tptp.hAPP_H513860823e_bool (tptp.hAPP_p877885514e_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H513860823e_bool (tptp.hAPP_p877885514e_bool (tptp.hAPP_f294904177e_bool tptp.cOMBC_725526061e_bool P) Q) R) (tptp.hAPP_pname_bool (tptp.hAPP_H1632039476e_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f1476298914l_bool (tptp.hAPP_f143162813l_bool (tptp.cOMBB_2095475776e_bool P) Q) R) (tptp.hAPP_b589554111l_bool P (tptp.hAPP_f1664156314l_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool (tptp.hAPP_f1297925993l_bool tptp.cOMBC_1284144636l_bool P) Q) R) (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f759274231e_bool (tptp.hAPP_f1385420507e_bool (tptp.cOMBB_598082538e_bool P) Q) R) (tptp.hAPP_p61793385e_bool P (tptp.hAPP_f1297739591_pname Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_p61793385e_bool (tptp.hAPP_f180827860e_bool (tptp.hAPP_f698292281e_bool tptp.cOMBC_1123258281e_bool P) Q) R) (tptp.hAPP_f759274231e_bool (tptp.hAPP_p905327722e_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_s1806633685e_bool (tptp.hAPP_f1863945078e_bool (tptp.hAPP_f915354021e_bool tptp.cOMBC_952831051e_bool P) Q) R) (tptp.hAPP_f1759915619e_bool (tptp.hAPP_s1226857760e_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted)) (=> (tptp.is_bool P) (= (tptp.hAPP_f1760790145l_bool (tptp.cOMBK_564432736e_bool P) Q) P))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f1970439265l_bool (tptp.cOMBB_1957242197e_bool P) Q) R) (tptp.hAPP_bool_bool P (tptp.hAPP_f1760790145l_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H226398757l_bool (tptp.hAPP_f1558728829l_bool (tptp.cOMBB_1382207997_state P) Q) R) (tptp.hAPP_b589554111l_bool P (tptp.hAPP_H513860823e_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f1970439265l_bool (tptp.hAPP_f1850463605l_bool tptp.cOMBS_2138645332l_bool P) Q) R) (tptp.hAPP_bool_bool (tptp.hAPP_f1508101115l_bool P R) (tptp.hAPP_f1760790145l_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_pname_bool (tptp.hAPP_f1745235422e_bool (tptp.hAPP_f1558052123e_bool tptp.cOMBC_2140141647l_bool P) Q) R) (tptp.hAPP_f1760790145l_bool (tptp.hAPP_p1617973726l_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H513860823e_bool (tptp.hAPP_f631639356e_bool (tptp.hAPP_f1721106985e_bool tptp.cOMBC_498627897l_bool P) Q) R) (tptp.hAPP_f1664156314l_bool (tptp.hAPP_H737849090l_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f1664156314l_bool (tptp.hAPP_H737849090l_bool (tptp.hAPP_f261382953l_bool tptp.cOMBC_2107548985e_bool P) Q) R) (tptp.hAPP_H513860823e_bool (tptp.hAPP_f631639356e_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f1760790145l_bool (tptp.hAPP_p1617973726l_bool (tptp.hAPP_f2070658331l_bool tptp.cOMBC_367297061e_bool P) Q) R) (tptp.hAPP_pname_bool (tptp.hAPP_f1745235422e_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H1632039476e_bool (tptp.hAPP_f833390165e_bool (tptp.cOMBB_1456120487_state P) Q) R) (tptp.hAPP_p61793385e_bool P (tptp.hAPP_H1344248906_pname Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f559147733l_bool (tptp.hAPP_f1145991873l_bool tptp.cOMBC_1988546018l_bool P) Q) R) (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_p338031245l_bool (tptp.hAPP_f567934427l_bool (tptp.cOMBB_408569982_pname P) Q) R) (tptp.hAPP_f434788991l_bool P (tptp.hAPP_p61793385e_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_s2001034685l_bool (tptp.hAPP_f1283379615l_bool (tptp.cOMBB_1759179140_state P) Q) R) (tptp.hAPP_f1259673775l_bool P (tptp.hAPP_s1806633685e_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_s336103912e_bool (tptp.hAPP_f249262236e_bool (tptp.cOMBB_1476898461_state P) Q) R) (tptp.hAPP_f1863945078e_bool P (tptp.hAPP_s1806633685e_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_s1806633685e_bool (tptp.hAPP_f1935169308e_bool (tptp.cOMBB_1036740637_state P) Q) R) (tptp.hAPP_f1012183542e_bool P (tptp.hAPP_s336103912e_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_p1086945780on_com (tptp.hAPP_f648377725on_com (tptp.hAPP_f2093196134on_com tptp.cOMBS_1529518335on_com P) Q) R) (tptp.hAPP_o334540577on_com (tptp.hAPP_p1164893188on_com P R) (tptp.hAPP_p799580910on_com Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H513860823e_bool (tptp.hAPP_H1645666623e_bool (tptp.hAPP_f262880489e_bool tptp.cOMBC_1424981238e_bool P) Q) R) (tptp.hAPP_H513860823e_bool (tptp.hAPP_H1645666623e_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_p1842370726_state (tptp.hAPP_f1661207211_state (tptp.hAPP_f137248406_state tptp.cOMBS_843273363_state P) Q) R) (tptp.hAPP_H563960305_state (tptp.hAPP_p80247908_state P R) (tptp.hAPP_p1842370726_state Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f1508101115l_bool (tptp.hAPP_f482022705l_bool (tptp.cOMBB_2020112947e_bool P) Q) R) (tptp.hAPP_b589554111l_bool P (tptp.hAPP_f1760790145l_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f1745235422e_bool (tptp.hAPP_f1973135743e_bool (tptp.cOMBB_1671808265e_bool P) Q) R) (tptp.hAPP_p61793385e_bool P (tptp.hAPP_f1008690464_pname Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_p1842370726_state (tptp.hAPP_f1296386871_state (tptp.hAPP_f358330902_state tptp.cOMBS_1615712031_state P) Q) R) (tptp.hAPP_f588507005_state (tptp.hAPP_p1712839024_state P R) (tptp.hAPP_p1637813682e_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool (tptp.hAPP_f1879335953l_bool tptp.cOMBC_7971162l_bool P) Q) R) (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_s1874344717e_bool (tptp.hAPP_f873506917e_bool (tptp.cOMBB_1757942702_state P) Q) R) (tptp.hAPP_f167292325e_bool P (tptp.hAPP_s2001034685l_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_p1164893188on_com (tptp.hAPP_f755519727on_com (tptp.cOMBB_1394247784_pname P) Q) R) (tptp.hAPP_b1679505845on_com P (tptp.hAPP_pname_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H513860823e_bool (tptp.hAPP_f1456107715e_bool (tptp.cOMBB_1653402815_state P) Q) R) (tptp.hAPP_f1760790145l_bool P (tptp.hAPP_H1645666623e_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H513860823e_bool (tptp.hAPP_f921536533e_bool (tptp.hAPP_f1262649863e_bool tptp.cOMBC_764456866l_bool P) Q) R) (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool (tptp.hAPP_f492098723l_bool tptp.cOMBC_1305755390e_bool P) Q) R) (tptp.hAPP_H513860823e_bool (tptp.hAPP_f921536533e_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_p877885514e_bool (tptp.hAPP_f998786331e_bool (tptp.cOMBB_799949246_pname P) Q) R) (tptp.hAPP_H1645666623e_bool P (tptp.hAPP_p1842370726_state Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H737849090l_bool (tptp.hAPP_f376825399l_bool (tptp.cOMBB_1722165949_state P) Q) R) (tptp.hAPP_f434788991l_bool P (tptp.hAPP_H1632039476e_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_p1712839024_state (tptp.hAPP_f2136041130_state (tptp.hAPP_f1777033564_state tptp.cOMBS_1401555724_state P) Q) R) (tptp.hAPP_c408625258_state (tptp.hAPP_p2032835427_state P R) (tptp.hAPP_pname_com Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_s1226857760e_bool (tptp.hAPP_f1138284024e_bool (tptp.cOMBB_20296667_state P) Q) R) (tptp.hAPP_f644196280e_bool P (tptp.hAPP_s2001034685l_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool (tptp.hAPP_f2119687429l_bool tptp.cOMBC_1018307482l_bool P) Q) R) (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f631639356e_bool (tptp.hAPP_f547518321e_bool (tptp.cOMBB_1170234304e_bool P) Q) R) (tptp.hAPP_H1645666623e_bool P (tptp.hAPP_f1308959284_state Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H1645666623e_bool (tptp.hAPP_f1844318385e_bool (tptp.cOMBB_291471741_state P) Q) R) (tptp.hAPP_H1645666623e_bool P (tptp.hAPP_H563960305_state Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_p80247908_state (tptp.hAPP_f2101567797_state (tptp.hAPP_f939130838_state tptp.cOMBS_381334199_state P) Q) R) (tptp.hAPP_H521649881_state (tptp.hAPP_p964374716_state P R) (tptp.hAPP_p1842370726_state Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f1970439265l_bool (tptp.hAPP_f517001763l_bool tptp.cOMBC_1166591542l_bool P) Q) R) (tptp.hAPP_f239102607l_bool (tptp.hAPP_f105100493l_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_p1617973726l_bool (tptp.hAPP_f2081555625l_bool (tptp.cOMBB_44445098_pname P) Q) R) (tptp.hAPP_f854625363l_bool P (tptp.hAPP_p877885514e_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f921536533e_bool (tptp.hAPP_f481659057e_bool (tptp.cOMBB_1099197107e_bool P) Q) R) (tptp.hAPP_H1645666623e_bool P (tptp.hAPP_f2143211163_state Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H1645666623e_bool (tptp.hAPP_f762269719e_bool (tptp.hAPP_f964290431e_bool tptp.cOMBC_488258100e_bool P) Q) R) (tptp.hAPP_f921536533e_bool (tptp.hAPP_H727730819e_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_p964374716_state (tptp.hAPP_f1405979047_state (tptp.cOMBB_707293872_pname P) Q) R) (tptp.hAPP_b798484845_state P (tptp.hAPP_pname_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f239102607l_bool (tptp.hAPP_f1269496639l_bool (tptp.hAPP_f1508257257l_bool tptp.cOMBC_1084925030l_bool P) Q) R) (tptp.hAPP_f239102607l_bool (tptp.hAPP_f1269496639l_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_p2032835427_state (tptp.hAPP_f950918952_state (tptp.cOMBB_2123334001_pname P) Q) R) (tptp.hAPP_f1949912908_state P (tptp.hAPP_p1637813682e_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_H248360617l_bool (tptp.hAPP_f1862834069l_bool (tptp.cOMBB_1239130257_state P) Q) R) (tptp.hAPP_f854625363l_bool P (tptp.hAPP_H1645666623e_bool Q R)))) _let_11 _let_10 (tptp.hBOOL (tptp.hAPP_f1760790145l_bool tptp.finite784854244_state tptp.fa)) (not (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_H248360617l_bool tptp.member1758697444_state _let_1) tptp.fa))) (tptp.hBOOL (tptp.hAPP_f1760790145l_bool (tptp.hAPP_f854625363l_bool tptp.ord_le1720872323e_bool tptp.fa) (tptp.hAPP_f631639356e_bool (tptp.image_275883510_state (tptp.hAPP_f1758910594_state _let_4 (tptp.hAPP_f96342628me_com (tptp.cOMBB_923936821_pname tptp.the_com) tptp.body))) _let_3))) _let_9 (tptp.hBOOL (tptp.hAPP_f1760790145l_bool _let_6 tptp.fa)) _let_8 true)))))))))))))))))))))))))))))))))))))))
% 5.61/5.85 )
% 5.61/5.85 % SZS output end Proof for SWW474+2
% 5.61/5.85 % cvc5---1.0.5 exiting
% 5.61/5.85 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------