TSTP Solution File: SWW474_1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWW474_1 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 1 00:21:07 EDT 2023
% Result : Theorem 0.76s 0.95s
% Output : Proof 0.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.18 % Problem : SWW474_1 : TPTP v8.1.2. Released v5.3.0.
% 0.13/0.19 % Command : do_cvc5 %s %d
% 0.20/0.41 % Computer : n014.cluster.edu
% 0.20/0.41 % Model : x86_64 x86_64
% 0.20/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.41 % Memory : 8042.1875MB
% 0.20/0.41 % OS : Linux 3.10.0-693.el7.x86_64
% 0.20/0.41 % CPULimit : 300
% 0.20/0.41 % WCLimit : 300
% 0.20/0.41 % DateTime : Sun Aug 27 20:27:01 EDT 2023
% 0.20/0.41 % CPUTime :
% 0.27/0.60 %----Proving TF0_NAR, FOF, or CNF
% 0.76/0.95 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.uhD64Essca/cvc5---1.0.5_21284.p...
% 0.76/0.95 ------- get file name : TPTP file name is SWW474_1
% 0.76/0.95 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_21284.smt2...
% 0.76/0.95 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.76/0.95 % SZS status Theorem for SWW474_1
% 0.76/0.95 % SZS output start Proof for SWW474_1
% 0.76/0.95 (
% 0.76/0.95 (let ((_let_1 (tptp.hAPP_c379084956_state tptp.hoare_Mirabelle_MGT tptp.y))) (let ((_let_2 (tptp.insert668001005_state _let_1 tptp.bot_bo454148287e_bool))) (let ((_let_3 (tptp.dom_pname_com tptp.body))) (let ((_let_4 (tptp.image_1256224870_state (tptp.cOMBB_573322273_pname tptp.hoare_Mirabelle_MGT tptp.body_1) _let_3))) (let ((_let_5 (tptp.hoare_1193527299_state _let_4))) (let ((_let_6 (tptp.hBOOL (tptp.hAPP_f355887345l_bool _let_5 _let_2)))) (let ((_let_7 (not _let_6))) (let ((_let_8 (= (tptp.hAPP_p799580910on_com tptp.body tptp.pn) (tptp.some_com tptp.y)))) (let ((_let_9 (tptp.hBOOL tptp.wT_bodies))) (let ((_let_10 (tptp.hBOOL tptp.hoare_1310879719gleton))) (let ((_let_11 (forall ((Pn tptp.pname) (B_2 tptp.com)) (=> (tptp.hBOOL tptp.wT_bodies) (=> (= (tptp.hAPP_p799580910on_com tptp.body Pn) (tptp.some_com B_2)) (tptp.hBOOL (tptp.wt B_2))))))) (let ((_let_12 (forall ((C_1 tptp.com)) (=> (tptp.hBOOL tptp.hoare_1310879719gleton) (=> (tptp.hBOOL tptp.wT_bodies) (=> (tptp.hBOOL (tptp.wt C_1)) (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hoare_1193527299_state tptp.bot_bo454148287e_bool) (tptp.insert668001005_state (tptp.hAPP_c379084956_state tptp.hoare_Mirabelle_MGT C_1) tptp.bot_bo454148287e_bool))))))))) (let ((_let_13 (forall ((G tptp.fun_Ho734851753e_bool) (G_1 tptp.fun_Ho734851753e_bool) (Ts tptp.fun_Ho734851753e_bool)) (let ((_let_1 (tptp.hoare_1193527299_state G))) (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hoare_1193527299_state G_1) Ts)) (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool _let_1 G_1)) (tptp.hBOOL (tptp.hAPP_f355887345l_bool _let_1 Ts)))))))) (let ((_let_14 (forall ((G tptp.fun_Ho734851753e_bool)) (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hoare_1193527299_state G) tptp.bot_bo454148287e_bool))))) (let ((_let_15 (forall ((G tptp.fun_Ho734851753e_bool) (G_1 tptp.fun_Ho734851753e_bool) (Ts tptp.fun_Ho734851753e_bool)) (let ((_let_1 (tptp.hoare_1193527299_state G))) (or (not (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hoare_1193527299_state G_1) Ts))) (not (tptp.hBOOL (tptp.hAPP_f355887345l_bool _let_1 G_1))) (tptp.hBOOL (tptp.hAPP_f355887345l_bool _let_1 Ts))))))) (let ((_let_16 (tptp.hBOOL (tptp.hAPP_f355887345l_bool _let_5 tptp.bot_bo454148287e_bool)))) (let ((_let_17 (not _let_16))) (let ((_let_18 (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hoare_1193527299_state tptp.bot_bo454148287e_bool) _let_2)))) (let ((_let_19 (not _let_18))) (let ((_let_20 (or _let_19 _let_17 _let_6))) (let ((_let_21 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_22 (not _let_20))) (let ((_let_23 (tptp.hBOOL (tptp.wt tptp.y)))) (let ((_let_24 (not _let_23))) (let ((_let_25 (or _let_24 _let_18))) (let ((_let_26 (forall ((C_1 tptp.com)) (or (not (tptp.hBOOL (tptp.wt C_1))) (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hoare_1193527299_state tptp.bot_bo454148287e_bool) (tptp.insert668001005_state (tptp.hAPP_c379084956_state tptp.hoare_Mirabelle_MGT C_1) tptp.bot_bo454148287e_bool))))))) (let ((_let_27 (ASSUME :args (_let_9)))) (let ((_let_28 (_let_26))) (let ((_let_29 (not _let_8))) (let ((_let_30 (or _let_29 _let_23))) (let ((_let_31 (forall ((Pn tptp.pname) (B_2 tptp.com)) (or (not (= (tptp.hAPP_p799580910on_com tptp.body Pn) (tptp.some_com B_2))) (tptp.hBOOL (tptp.wt B_2)))))) (let ((_let_32 (_let_31))) (let ((_let_33 (_let_14))) (let ((_let_34 (ASSUME :args _let_33))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_21 :args (_let_4 tptp.bot_bo454148287e_bool _let_2 QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP_f355887345l_bool (tptp.hoare_1193527299_state G_1) Ts) (tptp.hoare_1193527299_state G)))) :args (_let_15))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_20)) :args ((or _let_6 _let_17 _let_19 _let_22))) (ASSUME :args (_let_7)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_34 :args (_let_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.hoare_1193527299_state G)))) :args _let_33)) _let_34 :args (_let_16 false _let_14)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_25)) :args ((or _let_24 _let_18 (not _let_25)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_30)) :args ((or _let_29 _let_23 (not _let_30)))) (ASSUME :args (_let_8)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_32) :args (tptp.pn tptp.y QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP_p799580910on_com tptp.body Pn) (tptp.some_com B_2)))) :args _let_32)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))) _let_27 :args (_let_31 false _let_9)) :args (_let_30 false _let_31)) :args (_let_23 false _let_8 false _let_30)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_28) :args (tptp.y QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.hAPP_c379084956_state tptp.hoare_Mirabelle_MGT C_1)))) :args _let_28)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))) (ASSUME :args (_let_10)) _let_27 :args (_let_26 false _let_10 false _let_9)) :args (_let_25 false _let_26)) :args (_let_18 false _let_23 false _let_25)) :args (_let_22 true _let_6 false _let_16 false _let_18)) _let_21 :args (false true _let_20 false _let_15)) :args (_let_14 (forall ((Ts tptp.fun_Ho734851753e_bool) (G tptp.fun_Ho734851753e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hAPP_f15397171l_bool tptp.ord_le1119700979e_bool Ts) G)) (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hoare_1193527299_state G) Ts)))) (forall ((Ts tptp.fun_Ho734851753e_bool) (G tptp.fun_Ho734851753e_bool) (Ts_1 tptp.fun_Ho734851753e_bool)) (let ((_let_1 (tptp.hoare_1193527299_state G))) (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool _let_1 Ts_1)) (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hAPP_f15397171l_bool tptp.ord_le1119700979e_bool Ts) Ts_1)) (tptp.hBOOL (tptp.hAPP_f355887345l_bool _let_1 Ts)))))) (forall ((G tptp.fun_Ho734851753e_bool) (G_1 tptp.fun_Ho734851753e_bool) (Ts tptp.fun_Ho734851753e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hoare_1193527299_state G_1) Ts)) (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hAPP_f15397171l_bool tptp.ord_le1119700979e_bool G_1) G)) (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hoare_1193527299_state G) Ts))))) _let_13 (forall ((Ts tptp.fun_Ho734851753e_bool) (G tptp.fun_Ho734851753e_bool) (T tptp.hoare_1848483303_state)) (let ((_let_1 (tptp.hoare_1193527299_state G))) (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool _let_1 (tptp.insert668001005_state T tptp.bot_bo454148287e_bool))) (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool _let_1 Ts)) (tptp.hBOOL (tptp.hAPP_f355887345l_bool _let_1 (tptp.insert668001005_state T Ts))))))) (forall ((G tptp.fun_Ho734851753e_bool) (T tptp.hoare_1848483303_state) (Ts tptp.fun_Ho734851753e_bool)) (let ((_let_1 (tptp.hoare_1193527299_state G))) (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool _let_1 (tptp.insert668001005_state T Ts))) (and (tptp.hBOOL (tptp.hAPP_f355887345l_bool _let_1 (tptp.insert668001005_state T tptp.bot_bo454148287e_bool))) (tptp.hBOOL (tptp.hAPP_f355887345l_bool _let_1 Ts)))))) (forall ((Pn_1 tptp.pname) (G tptp.fun_Ho734851753e_bool)) (let ((_let_1 (tptp.hAPP_c379084956_state tptp.hoare_Mirabelle_MGT (tptp.hAPP_pname_com tptp.body_1 Pn_1)))) (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hoare_1193527299_state (tptp.insert668001005_state _let_1 G)) (tptp.insert668001005_state (tptp.hAPP_c379084956_state tptp.hoare_Mirabelle_MGT (tptp.hAPP_option_com_com tptp.the_com (tptp.hAPP_p799580910on_com tptp.body Pn_1))) tptp.bot_bo454148287e_bool))) (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hoare_1193527299_state G) (tptp.insert668001005_state _let_1 tptp.bot_bo454148287e_bool)))))) (forall ((A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.collec1974731493e_bool (tptp.hAPP_f434788991l_bool (tptp.cOMBC_1284144636l_bool tptp.ord_le313189616e_bool) A)))))) (forall ((A tptp.fun_Ho734851753e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool tptp.finite1765195604_state A)) (tptp.hBOOL (tptp.hAPP_f1526158591l_bool tptp.finite297877756e_bool (tptp.collec1657840446e_bool (tptp.hAPP_f15397171l_bool (tptp.cOMBC_80545690l_bool tptp.ord_le1119700979e_bool) A)))))) (forall ((A tptp.fun_fu399576434l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f389811538l_bool tptp.finite786885583l_bool A)) (tptp.hBOOL (tptp.hAPP_f595608956l_bool tptp.finite1491191519l_bool (tptp.collec792590109l_bool (tptp.hAPP_f1759205631l_bool (tptp.cOMBC_336095980l_bool tptp.ord_le1375671464l_bool) A)))))) (forall ((A tptp.fun_fu64031073l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1359865257l_bool tptp.finite181314444l_bool A)) (tptp.hBOOL (tptp.hAPP_f844837559l_bool tptp.finite1393641268l_bool (tptp.collec1616186998l_bool (tptp.hAPP_f1607907235l_bool (tptp.cOMBC_1420373658l_bool tptp.ord_le101734315l_bool) A)))))) (forall ((A tptp.fun_fu1783763359l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1526158591l_bool tptp.finite297877756e_bool A)) (tptp.hBOOL (tptp.hAPP_f1359865257l_bool tptp.finite181314444l_bool (tptp.collec2020384458l_bool (tptp.hAPP_f511954751l_bool (tptp.cOMBC_1690116422l_bool tptp.ord_le1819283413l_bool) A)))))) (forall ((A tptp.fun_fu1430349052l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)) (tptp.hBOOL (tptp.hAPP_f389811538l_bool tptp.finite786885583l_bool (tptp.collec1613912337l_bool (tptp.hAPP_f510955609l_bool (tptp.cOMBC_7971162l_bool tptp.ord_le675606854l_bool) A)))))) (forall ((H tptp.fun_pn447269700_state) (Fa tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname Fa)) (tptp.hBOOL (tptp.hAPP_f355887345l_bool tptp.finite1765195604_state (tptp.image_1256224870_state H Fa))))) (forall ((H tptp.fun_fu1664106117_pname) (Fa tptp.fun_fu399576434l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f389811538l_bool tptp.finite786885583l_bool Fa)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.image_1705983821_pname H Fa))))) (forall ((H tptp.fun_fu1931361878_pname) (Fa tptp.fun_fu64031073l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1359865257l_bool tptp.finite181314444l_bool Fa)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.image_2036190066_pname H Fa))))) (forall ((H tptp.fun_fu891110808_pname) (Fa tptp.fun_fu1783763359l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1526158591l_bool tptp.finite297877756e_bool Fa)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.image_1825746272_pname H Fa))))) (forall ((H tptp.fun_fu1499449723_pname) (Fa tptp.fun_fu1430349052l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool Fa)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.image_1283814551_pname H Fa))))) (forall ((H tptp.fun_fu230733820_state) (Fa tptp.fun_fu399576434l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f389811538l_bool tptp.finite786885583l_bool Fa)) (tptp.hBOOL (tptp.hAPP_f355887345l_bool tptp.finite1765195604_state (tptp.image_2078273054_state H Fa))))) (forall ((H tptp.fun_fu1538259051_state) (Fa tptp.fun_fu64031073l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1359865257l_bool tptp.finite181314444l_bool Fa)) (tptp.hBOOL (tptp.hAPP_f355887345l_bool tptp.finite1765195604_state (tptp.image_71018297_state H Fa))))) (forall ((H tptp.fun_fu1404623273_state) (Fa tptp.fun_fu1783763359l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1526158591l_bool tptp.finite297877756e_bool Fa)) (tptp.hBOOL (tptp.hAPP_f355887345l_bool tptp.finite1765195604_state (tptp.image_730818763_state H Fa))))) (forall ((H tptp.fun_fu1387033222_state) (Fa tptp.fun_fu1430349052l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool Fa)) (tptp.hBOOL (tptp.hAPP_f355887345l_bool tptp.finite1765195604_state (tptp.image_1916896084_state H Fa))))) (forall ((H tptp.fun_pn422929397l_bool) (Fa tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname Fa)) (tptp.hBOOL (tptp.hAPP_f389811538l_bool tptp.finite786885583l_bool (tptp.image_1642285373l_bool H Fa))))) (forall ((H tptp.fun_pn1359388668l_bool) (Fa tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname Fa)) (tptp.hBOOL (tptp.hAPP_f1359865257l_bool tptp.finite181314444l_bool (tptp.image_1820576158l_bool H Fa))))) (forall ((H tptp.fun_pn2079317538e_bool) (Fa tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname Fa)) (tptp.hBOOL (tptp.hAPP_f1526158591l_bool tptp.finite297877756e_bool (tptp.image_2051793258e_bool H Fa))))) (forall ((H tptp.fun_pn800050071e_bool) (Fa tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname Fa)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.image_47868345e_bool H Fa))))) (forall ((H tptp.fun_Ho872578118l_bool) (Fa tptp.fun_Ho734851753e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool tptp.finite1765195604_state Fa)) (tptp.hBOOL (tptp.hAPP_f389811538l_bool tptp.finite786885583l_bool (tptp.image_7400930l_bool H Fa))))) (forall ((H tptp.fun_Ho1489168363l_bool) (Fa tptp.fun_Ho734851753e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool tptp.finite1765195604_state Fa)) (tptp.hBOOL (tptp.hAPP_f1359865257l_bool tptp.finite181314444l_bool (tptp.image_783059513l_bool H Fa))))) (forall ((H tptp.fun_Ho1480763635e_bool) (Fa tptp.fun_Ho734851753e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool tptp.finite1765195604_state Fa)) (tptp.hBOOL (tptp.hAPP_f1526158591l_bool tptp.finite297877756e_bool (tptp.image_249571983e_bool H Fa))))) (forall ((H tptp.fun_Ho585232518e_bool) (Fa tptp.fun_Ho734851753e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool tptp.finite1765195604_state Fa)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.image_983321428e_bool H Fa))))) (forall ((H tptp.fun_Ho862234382_pname) (Fa tptp.fun_Ho734851753e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool tptp.finite1765195604_state Fa)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.image_2075962154_pname H Fa))))) (forall ((H tptp.fun_pname_pname) (Fa tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname Fa)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.image_pname_pname H Fa))))) (forall ((A tptp.fun_Ho734851753e_bool)) (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hAPP_f15397171l_bool tptp.ord_le1119700979e_bool tptp.bot_bo454148287e_bool) A))) (forall ((A tptp.fun_fu1430349052l_bool)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool tptp.bot_bo1649642514l_bool) A))) (forall ((A tptp.fun_fu1783763359l_bool)) (tptp.hBOOL (tptp.hAPP_f1526158591l_bool (tptp.hAPP_f511954751l_bool tptp.ord_le1819283413l_bool tptp.bot_bo2068035593l_bool) A))) (forall ((A tptp.fun_pname_bool)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool tptp.bot_bo844097828e_bool) A))) (forall ((A_2 tptp.hoare_1848483303_state) (A tptp.fun_Ho734851753e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool tptp.finite1765195604_state A)) (tptp.hBOOL (tptp.hAPP_f355887345l_bool tptp.finite1765195604_state (tptp.insert668001005_state A_2 A))))) (forall ((A_2 tptp.pname) (A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.insert_pname A_2 A))))) (forall ((A_2 tptp.fun_fu1430349052l_bool) (A tptp.fun_fu399576434l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f389811538l_bool tptp.finite786885583l_bool A)) (tptp.hBOOL (tptp.hAPP_f389811538l_bool tptp.finite786885583l_bool (tptp.insert1117693814l_bool A_2 A))))) (forall ((A_2 tptp.fun_fu1783763359l_bool) (A tptp.fun_fu64031073l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1359865257l_bool tptp.finite181314444l_bool A)) (tptp.hBOOL (tptp.hAPP_f1359865257l_bool tptp.finite181314444l_bool (tptp.insert1735796133l_bool A_2 A))))) (forall ((A_2 tptp.fun_Ho734851753e_bool) (A tptp.fun_fu1783763359l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1526158591l_bool tptp.finite297877756e_bool A)) (tptp.hBOOL (tptp.hAPP_f1526158591l_bool tptp.finite297877756e_bool (tptp.insert1390540323e_bool A_2 A))))) (forall ((A_2 tptp.fun_pname_bool) (A tptp.fun_fu1430349052l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.insert1325755072e_bool A_2 A))))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname tptp.bot_bo844097828e_bool)) (tptp.hBOOL (tptp.hAPP_f355887345l_bool tptp.finite1765195604_state tptp.bot_bo454148287e_bool)) (tptp.hBOOL (tptp.hAPP_f389811538l_bool tptp.finite786885583l_bool tptp.bot_bo1537088220l_bool)) (tptp.hBOOL (tptp.hAPP_f1359865257l_bool tptp.finite181314444l_bool tptp.bot_bo973295223l_bool)) (tptp.hBOOL (tptp.hAPP_f1526158591l_bool tptp.finite297877756e_bool tptp.bot_bo2068035593l_bool)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool tptp.bot_bo1649642514l_bool)) (forall ((Q_1 tptp.fun_pname_bool) (P_1 tptp.fun_pname_bool)) (=> (or (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.collect_pname P_1))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.collect_pname Q_1)))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.collect_pname (tptp.cOMBS_568398431l_bool (tptp.cOMBB_675860798_pname tptp.fconj P_1) Q_1)))))) (forall ((Q_1 tptp.fun_Ho734851753e_bool) (P_1 tptp.fun_Ho734851753e_bool)) (=> (or (tptp.hBOOL (tptp.hAPP_f355887345l_bool tptp.finite1765195604_state (tptp.collec1708318610_state P_1))) (tptp.hBOOL (tptp.hAPP_f355887345l_bool tptp.finite1765195604_state (tptp.collec1708318610_state Q_1)))) (tptp.hBOOL (tptp.hAPP_f355887345l_bool tptp.finite1765195604_state (tptp.collec1708318610_state (tptp.cOMBS_1990964188l_bool (tptp.cOMBB_215065709_state tptp.fconj P_1) Q_1)))))) (forall ((Q_1 tptp.fun_fu399576434l_bool) (P_1 tptp.fun_fu399576434l_bool)) (=> (or (tptp.hBOOL (tptp.hAPP_f389811538l_bool tptp.finite786885583l_bool (tptp.collec1613912337l_bool P_1))) (tptp.hBOOL (tptp.hAPP_f389811538l_bool tptp.finite786885583l_bool (tptp.collec1613912337l_bool Q_1)))) (tptp.hBOOL (tptp.hAPP_f389811538l_bool tptp.finite786885583l_bool (tptp.collec1613912337l_bool (tptp.cOMBS_811933079l_bool (tptp.cOMBB_689948150l_bool tptp.fconj P_1) Q_1)))))) (forall ((Q_1 tptp.fun_fu64031073l_bool) (P_1 tptp.fun_fu64031073l_bool)) (=> (or (tptp.hBOOL (tptp.hAPP_f1359865257l_bool tptp.finite181314444l_bool (tptp.collec2020384458l_bool P_1))) (tptp.hBOOL (tptp.hAPP_f1359865257l_bool tptp.finite181314444l_bool (tptp.collec2020384458l_bool Q_1)))) (tptp.hBOOL (tptp.hAPP_f1359865257l_bool tptp.finite181314444l_bool (tptp.collec2020384458l_bool (tptp.cOMBS_101732372l_bool (tptp.cOMBB_1936369445l_bool tptp.fconj P_1) Q_1)))))) (forall ((Q_1 tptp.fun_fu1783763359l_bool) (P_1 tptp.fun_fu1783763359l_bool)) (=> (or (tptp.hBOOL (tptp.hAPP_f1526158591l_bool tptp.finite297877756e_bool (tptp.collec1657840446e_bool P_1))) (tptp.hBOOL (tptp.hAPP_f1526158591l_bool tptp.finite297877756e_bool (tptp.collec1657840446e_bool Q_1)))) (tptp.hBOOL (tptp.hAPP_f1526158591l_bool tptp.finite297877756e_bool (tptp.collec1657840446e_bool (tptp.cOMBS_1278217668l_bool (tptp.cOMBB_1418941603e_bool tptp.fconj P_1) Q_1)))))) (forall ((Q_1 tptp.fun_fu1430349052l_bool) (P_1 tptp.fun_fu1430349052l_bool)) (=> (or (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.collec1974731493e_bool P_1))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.collec1974731493e_bool Q_1)))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.collec1974731493e_bool (tptp.cOMBS_350070575l_bool (tptp.cOMBB_2095475776e_bool tptp.fconj P_1) Q_1)))))) (forall ((C_1 tptp.hoare_1848483303_state) (A tptp.fun_pname_bool)) (let ((_let_1 (tptp.image_1256224870_state (tptp.cOMBK_240819937_pname C_1) A))) (let ((_let_2 (= A tptp.bot_bo844097828e_bool))) (and (=> _let_2 (= _let_1 tptp.bot_bo454148287e_bool)) (=> (not _let_2) (= _let_1 (tptp.insert668001005_state C_1 tptp.bot_bo454148287e_bool))))))) (forall ((C_1 tptp.pname) (A tptp.fun_Ho734851753e_bool)) (let ((_let_1 (tptp.image_2075962154_pname (tptp.cOMBK_1568566301_state C_1) A))) (let ((_let_2 (= A tptp.bot_bo454148287e_bool))) (and (=> _let_2 (= _let_1 tptp.bot_bo844097828e_bool)) (=> (not _let_2) (= _let_1 (tptp.insert_pname C_1 tptp.bot_bo844097828e_bool))))))) (forall ((C_1 tptp.fun_pname_bool) (A tptp.fun_Ho734851753e_bool)) (let ((_let_1 (tptp.image_983321428e_bool (tptp.cOMBK_1288377053_state C_1) A))) (let ((_let_2 (= A tptp.bot_bo454148287e_bool))) (and (=> _let_2 (= _let_1 tptp.bot_bo1649642514l_bool)) (=> (not _let_2) (= _let_1 (tptp.insert1325755072e_bool C_1 tptp.bot_bo1649642514l_bool))))))) (forall ((C_1 tptp.fun_Ho734851753e_bool) (A tptp.fun_Ho734851753e_bool)) (let ((_let_1 (tptp.image_249571983e_bool (tptp.cOMBK_1751623554_state C_1) A))) (let ((_let_2 (= A tptp.bot_bo454148287e_bool))) (and (=> _let_2 (= _let_1 tptp.bot_bo2068035593l_bool)) (=> (not _let_2) (= _let_1 (tptp.insert1390540323e_bool C_1 tptp.bot_bo2068035593l_bool))))))) (forall ((C_1 tptp.fun_pname_bool) (A tptp.fun_pname_bool)) (let ((_let_1 (tptp.image_47868345e_bool (tptp.cOMBK_37193422_pname C_1) A))) (let ((_let_2 (= A tptp.bot_bo844097828e_bool))) (and (=> _let_2 (= _let_1 tptp.bot_bo1649642514l_bool)) (=> (not _let_2) (= _let_1 (tptp.insert1325755072e_bool C_1 tptp.bot_bo1649642514l_bool))))))) (forall ((C_1 tptp.fun_Ho734851753e_bool) (A tptp.fun_pname_bool)) (let ((_let_1 (tptp.image_2051793258e_bool (tptp.cOMBK_1197227241_pname C_1) A))) (let ((_let_2 (= A tptp.bot_bo844097828e_bool))) (and (=> _let_2 (= _let_1 tptp.bot_bo2068035593l_bool)) (=> (not _let_2) (= _let_1 (tptp.insert1390540323e_bool C_1 tptp.bot_bo2068035593l_bool))))))) (forall ((C_1 tptp.pname) (A tptp.fun_pname_bool)) (let ((_let_1 (tptp.image_pname_pname (tptp.cOMBK_pname_pname C_1) A))) (let ((_let_2 (= A tptp.bot_bo844097828e_bool))) (and (=> _let_2 (= _let_1 tptp.bot_bo844097828e_bool)) (=> (not _let_2) (= _let_1 (tptp.insert_pname C_1 tptp.bot_bo844097828e_bool))))))) (forall ((C_1 tptp.hoare_1848483303_state) (A tptp.fun_fu1430349052l_bool)) (let ((_let_1 (tptp.image_1916896084_state (tptp.cOMBK_354802397e_bool C_1) A))) (let ((_let_2 (= A tptp.bot_bo1649642514l_bool))) (and (=> _let_2 (= _let_1 tptp.bot_bo454148287e_bool)) (=> (not _let_2) (= _let_1 (tptp.insert668001005_state C_1 tptp.bot_bo454148287e_bool))))))) (forall ((C_1 tptp.hoare_1848483303_state) (A tptp.fun_fu1783763359l_bool)) (let ((_let_1 (tptp.image_730818763_state (tptp.cOMBK_1270376774e_bool C_1) A))) (let ((_let_2 (= A tptp.bot_bo2068035593l_bool))) (and (=> _let_2 (= _let_1 tptp.bot_bo454148287e_bool)) (=> (not _let_2) (= _let_1 (tptp.insert668001005_state C_1 tptp.bot_bo454148287e_bool))))))) (forall ((C_1 tptp.pname) (A tptp.fun_fu1430349052l_bool)) (let ((_let_1 (tptp.image_1283814551_pname (tptp.cOMBK_948730864e_bool C_1) A))) (let ((_let_2 (= A tptp.bot_bo1649642514l_bool))) (and (=> _let_2 (= _let_1 tptp.bot_bo844097828e_bool)) (=> (not _let_2) (= _let_1 (tptp.insert_pname C_1 tptp.bot_bo844097828e_bool))))))) (forall ((C_1 tptp.pname) (A tptp.fun_fu1783763359l_bool)) (let ((_let_1 (tptp.image_1825746272_pname (tptp.cOMBK_1423274227e_bool C_1) A))) (let ((_let_2 (= A tptp.bot_bo2068035593l_bool))) (and (=> _let_2 (= _let_1 tptp.bot_bo844097828e_bool)) (=> (not _let_2) (= _let_1 (tptp.insert_pname C_1 tptp.bot_bo844097828e_bool))))))) (forall ((C_1 tptp.hoare_1848483303_state) (X_2 tptp.pname) (A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A)) (= (tptp.image_1256224870_state (tptp.cOMBK_240819937_pname C_1) A) (tptp.insert668001005_state C_1 tptp.bot_bo454148287e_bool)))) (forall ((C_1 tptp.pname) (X_2 tptp.hoare_1848483303_state) (A tptp.fun_Ho734851753e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hAPP_H1199573897l_bool tptp.member591555156_state X_2) A)) (= (tptp.image_2075962154_pname (tptp.cOMBK_1568566301_state C_1) A) (tptp.insert_pname C_1 tptp.bot_bo844097828e_bool)))) (forall ((C_1 tptp.fun_pname_bool) (X_2 tptp.hoare_1848483303_state) (A tptp.fun_Ho734851753e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hAPP_H1199573897l_bool tptp.member591555156_state X_2) A)) (= (tptp.image_983321428e_bool (tptp.cOMBK_1288377053_state C_1) A) (tptp.insert1325755072e_bool C_1 tptp.bot_bo1649642514l_bool)))) (forall ((C_1 tptp.fun_Ho734851753e_bool) (X_2 tptp.hoare_1848483303_state) (A tptp.fun_Ho734851753e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hAPP_H1199573897l_bool tptp.member591555156_state X_2) A)) (= (tptp.image_249571983e_bool (tptp.cOMBK_1751623554_state C_1) A) (tptp.insert1390540323e_bool C_1 tptp.bot_bo2068035593l_bool)))) (forall ((C_1 tptp.fun_pname_bool) (X_2 tptp.pname) (A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A)) (= (tptp.image_47868345e_bool (tptp.cOMBK_37193422_pname C_1) A) (tptp.insert1325755072e_bool C_1 tptp.bot_bo1649642514l_bool)))) (forall ((C_1 tptp.fun_Ho734851753e_bool) (X_2 tptp.pname) (A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A)) (= (tptp.image_2051793258e_bool (tptp.cOMBK_1197227241_pname C_1) A) (tptp.insert1390540323e_bool C_1 tptp.bot_bo2068035593l_bool)))) (forall ((C_1 tptp.pname) (X_2 tptp.pname) (A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A)) (= (tptp.image_pname_pname (tptp.cOMBK_pname_pname C_1) A) (tptp.insert_pname C_1 tptp.bot_bo844097828e_bool)))) (forall ((C_1 tptp.hoare_1848483303_state) (X_2 tptp.fun_pname_bool) (A tptp.fun_fu1430349052l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool X_2) A)) (= (tptp.image_1916896084_state (tptp.cOMBK_354802397e_bool C_1) A) (tptp.insert668001005_state C_1 tptp.bot_bo454148287e_bool)))) (forall ((C_1 tptp.hoare_1848483303_state) (X_2 tptp.fun_Ho734851753e_bool) (A tptp.fun_fu1783763359l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1526158591l_bool (tptp.hAPP_f1258983629l_bool tptp.member1948767740e_bool X_2) A)) (= (tptp.image_730818763_state (tptp.cOMBK_1270376774e_bool C_1) A) (tptp.insert668001005_state C_1 tptp.bot_bo454148287e_bool)))) (forall ((C_1 tptp.pname) (X_2 tptp.fun_pname_bool) (A tptp.fun_fu1430349052l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool X_2) A)) (= (tptp.image_1283814551_pname (tptp.cOMBK_948730864e_bool C_1) A) (tptp.insert_pname C_1 tptp.bot_bo844097828e_bool)))) (forall ((C_1 tptp.pname) (X_2 tptp.fun_Ho734851753e_bool) (A tptp.fun_fu1783763359l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1526158591l_bool (tptp.hAPP_f1258983629l_bool tptp.member1948767740e_bool X_2) A)) (= (tptp.image_1825746272_pname (tptp.cOMBK_1423274227e_bool C_1) A) (tptp.insert_pname C_1 tptp.bot_bo844097828e_bool)))) (forall ((F tptp.fun_pname_option_com) (X_2 tptp.pname) (Y_2 tptp.com)) (let ((_let_1 (tptp.dom_pname_com F))) (=> (= (tptp.hAPP_p799580910on_com F X_2) (tptp.some_com Y_2)) (= (tptp.insert_pname X_2 _let_1) _let_1)))) (forall ((F tptp.fun_fu799392094on_com) (X_2 tptp.fun_pname_bool) (Y_2 tptp.com)) (let ((_let_1 (tptp.dom_fu2081503504ol_com F))) (=> (= (tptp.hAPP_f2138803836on_com F X_2) (tptp.some_com Y_2)) (= (tptp.insert1325755072e_bool X_2 _let_1) _let_1)))) (forall ((F tptp.fun_fu549469569on_com) (X_2 tptp.fun_Ho734851753e_bool) (Y_2 tptp.com)) (let ((_let_1 (tptp.dom_fu475558963ol_com F))) (=> (= (tptp.hAPP_f636233299on_com F X_2) (tptp.some_com Y_2)) (= (tptp.insert1390540323e_bool X_2 _let_1) _let_1)))) (forall ((B tptp.fun_Ho734851753e_bool) (F tptp.fun_pn447269700_state) (A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hAPP_f15397171l_bool tptp.ord_le1119700979e_bool B) (tptp.image_1256224870_state F A))) (tptp.hBOOL (tptp.hAPP_f355887345l_bool tptp.finite1765195604_state B))))) (forall ((B tptp.fun_pname_bool) (F tptp.fun_fu1664106117_pname) (A tptp.fun_fu399576434l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f389811538l_bool tptp.finite786885583l_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) (tptp.image_1705983821_pname F A))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B))))) (forall ((B tptp.fun_pname_bool) (F tptp.fun_fu1931361878_pname) (A tptp.fun_fu64031073l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1359865257l_bool tptp.finite181314444l_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) (tptp.image_2036190066_pname F A))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B))))) (forall ((B tptp.fun_pname_bool) (F tptp.fun_fu891110808_pname) (A tptp.fun_fu1783763359l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1526158591l_bool tptp.finite297877756e_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) (tptp.image_1825746272_pname F A))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B))))) (forall ((B tptp.fun_pname_bool) (F tptp.fun_fu1499449723_pname) (A tptp.fun_fu1430349052l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) (tptp.image_1283814551_pname F A))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B))))) (forall ((B tptp.fun_Ho734851753e_bool) (F tptp.fun_fu230733820_state) (A tptp.fun_fu399576434l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f389811538l_bool tptp.finite786885583l_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hAPP_f15397171l_bool tptp.ord_le1119700979e_bool B) (tptp.image_2078273054_state F A))) (tptp.hBOOL (tptp.hAPP_f355887345l_bool tptp.finite1765195604_state B))))) (forall ((B tptp.fun_Ho734851753e_bool) (F tptp.fun_fu1538259051_state) (A tptp.fun_fu64031073l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1359865257l_bool tptp.finite181314444l_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hAPP_f15397171l_bool tptp.ord_le1119700979e_bool B) (tptp.image_71018297_state F A))) (tptp.hBOOL (tptp.hAPP_f355887345l_bool tptp.finite1765195604_state B))))) (forall ((B tptp.fun_Ho734851753e_bool) (F tptp.fun_fu1404623273_state) (A tptp.fun_fu1783763359l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1526158591l_bool tptp.finite297877756e_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hAPP_f15397171l_bool tptp.ord_le1119700979e_bool B) (tptp.image_730818763_state F A))) (tptp.hBOOL (tptp.hAPP_f355887345l_bool tptp.finite1765195604_state B))))) (forall ((B tptp.fun_Ho734851753e_bool) (F tptp.fun_fu1387033222_state) (A tptp.fun_fu1430349052l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)) (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hAPP_f15397171l_bool tptp.ord_le1119700979e_bool B) (tptp.image_1916896084_state F A))) (tptp.hBOOL (tptp.hAPP_f355887345l_bool tptp.finite1765195604_state B))))) (forall ((B tptp.fun_fu399576434l_bool) (F tptp.fun_pn422929397l_bool) (A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (=> (tptp.hBOOL (tptp.hAPP_f389811538l_bool (tptp.hAPP_f1759205631l_bool tptp.ord_le1375671464l_bool B) (tptp.image_1642285373l_bool F A))) (tptp.hBOOL (tptp.hAPP_f389811538l_bool tptp.finite786885583l_bool B))))) (forall ((B tptp.fun_fu64031073l_bool) (F tptp.fun_pn1359388668l_bool) (A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (=> (tptp.hBOOL (tptp.hAPP_f1359865257l_bool (tptp.hAPP_f1607907235l_bool tptp.ord_le101734315l_bool B) (tptp.image_1820576158l_bool F A))) (tptp.hBOOL (tptp.hAPP_f1359865257l_bool tptp.finite181314444l_bool B))))) (forall ((B tptp.fun_pname_bool) (F tptp.fun_pname_pname) (A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) (tptp.image_pname_pname F A))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B))))) (forall ((B tptp.fun_fu1783763359l_bool) (F tptp.fun_pn2079317538e_bool) (A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (=> (tptp.hBOOL (tptp.hAPP_f1526158591l_bool (tptp.hAPP_f511954751l_bool tptp.ord_le1819283413l_bool B) (tptp.image_2051793258e_bool F A))) (tptp.hBOOL (tptp.hAPP_f1526158591l_bool tptp.finite297877756e_bool B))))) (forall ((B tptp.fun_fu1430349052l_bool) (F tptp.fun_pn800050071e_bool) (A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool B) (tptp.image_47868345e_bool F A))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool B))))) (forall ((B tptp.fun_fu399576434l_bool) (F tptp.fun_Ho872578118l_bool) (A tptp.fun_Ho734851753e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool tptp.finite1765195604_state A)) (=> (tptp.hBOOL (tptp.hAPP_f389811538l_bool (tptp.hAPP_f1759205631l_bool tptp.ord_le1375671464l_bool B) (tptp.image_7400930l_bool F A))) (tptp.hBOOL (tptp.hAPP_f389811538l_bool tptp.finite786885583l_bool B))))) (forall ((B tptp.fun_fu64031073l_bool) (F tptp.fun_Ho1489168363l_bool) (A tptp.fun_Ho734851753e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool tptp.finite1765195604_state A)) (=> (tptp.hBOOL (tptp.hAPP_f1359865257l_bool (tptp.hAPP_f1607907235l_bool tptp.ord_le101734315l_bool B) (tptp.image_783059513l_bool F A))) (tptp.hBOOL (tptp.hAPP_f1359865257l_bool tptp.finite181314444l_bool B))))) (forall ((B tptp.fun_pname_bool) (F tptp.fun_Ho862234382_pname) (A tptp.fun_Ho734851753e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool tptp.finite1765195604_state A)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) (tptp.image_2075962154_pname F A))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B))))) (forall ((B tptp.fun_fu1783763359l_bool) (F tptp.fun_Ho1480763635e_bool) (A tptp.fun_Ho734851753e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool tptp.finite1765195604_state A)) (=> (tptp.hBOOL (tptp.hAPP_f1526158591l_bool (tptp.hAPP_f511954751l_bool tptp.ord_le1819283413l_bool B) (tptp.image_249571983e_bool F A))) (tptp.hBOOL (tptp.hAPP_f1526158591l_bool tptp.finite297877756e_bool B))))) (forall ((B tptp.fun_fu1430349052l_bool) (F tptp.fun_Ho585232518e_bool) (A tptp.fun_Ho734851753e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool tptp.finite1765195604_state A)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool B) (tptp.image_983321428e_bool F A))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool B))))) (forall ((A tptp.fun_Ho734851753e_bool) (X_2 tptp.hoare_1848483303_state)) (let ((_let_1 (tptp.insert668001005_state X_2 tptp.bot_bo454148287e_bool))) (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hAPP_f15397171l_bool tptp.ord_le1119700979e_bool A) _let_1)) (or (= A tptp.bot_bo454148287e_bool) (= A _let_1))))) (forall ((A tptp.fun_fu1430349052l_bool) (X_2 tptp.fun_pname_bool)) (let ((_let_1 (tptp.insert1325755072e_bool X_2 tptp.bot_bo1649642514l_bool))) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool A) _let_1)) (or (= A tptp.bot_bo1649642514l_bool) (= A _let_1))))) (forall ((A tptp.fun_fu1783763359l_bool) (X_2 tptp.fun_Ho734851753e_bool)) (let ((_let_1 (tptp.insert1390540323e_bool X_2 tptp.bot_bo2068035593l_bool))) (=> (tptp.hBOOL (tptp.hAPP_f1526158591l_bool (tptp.hAPP_f511954751l_bool tptp.ord_le1819283413l_bool A) _let_1)) (or (= A tptp.bot_bo2068035593l_bool) (= A _let_1))))) (forall ((A tptp.fun_pname_bool) (X_2 tptp.pname)) (let ((_let_1 (tptp.insert_pname X_2 tptp.bot_bo844097828e_bool))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) _let_1)) (or (= A tptp.bot_bo844097828e_bool) (= A _let_1))))) _let_12 (forall ((A_2 tptp.hoare_1848483303_state)) (not (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hAPP_H1199573897l_bool tptp.member591555156_state A_2) tptp.bot_bo454148287e_bool)))) (forall ((A_2 tptp.fun_pname_bool)) (not (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool A_2) tptp.bot_bo1649642514l_bool)))) (forall ((A_2 tptp.fun_Ho734851753e_bool)) (not (tptp.hBOOL (tptp.hAPP_f1526158591l_bool (tptp.hAPP_f1258983629l_bool tptp.member1948767740e_bool A_2) tptp.bot_bo2068035593l_bool)))) (forall ((A_2 tptp.pname)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A_2) tptp.bot_bo844097828e_bool)))) (forall ((B_1 tptp.hoare_1848483303_state) (A_2 tptp.hoare_1848483303_state) (B tptp.fun_Ho734851753e_bool)) (let ((_let_1 (tptp.hAPP_H1199573897l_bool tptp.member591555156_state A_2))) (=> (=> (not (tptp.hBOOL (tptp.hAPP_f355887345l_bool _let_1 B))) (= A_2 B_1)) (tptp.hBOOL (tptp.hAPP_f355887345l_bool _let_1 (tptp.insert668001005_state B_1 B)))))) (forall ((B_1 tptp.fun_pname_bool) (A_2 tptp.fun_pname_bool) (B tptp.fun_fu1430349052l_bool)) (let ((_let_1 (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool A_2))) (=> (=> (not (tptp.hBOOL (tptp.hAPP_f1935102916l_bool _let_1 B))) (= A_2 B_1)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool _let_1 (tptp.insert1325755072e_bool B_1 B)))))) (forall ((B_1 tptp.fun_Ho734851753e_bool) (A_2 tptp.fun_Ho734851753e_bool) (B tptp.fun_fu1783763359l_bool)) (let ((_let_1 (tptp.hAPP_f1258983629l_bool tptp.member1948767740e_bool A_2))) (=> (=> (not (tptp.hBOOL (tptp.hAPP_f1526158591l_bool _let_1 B))) (= A_2 B_1)) (tptp.hBOOL (tptp.hAPP_f1526158591l_bool _let_1 (tptp.insert1390540323e_bool B_1 B)))))) (forall ((B_1 tptp.pname) (A_2 tptp.pname) (B tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname A_2))) (=> (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B))) (= A_2 B_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.insert_pname B_1 B)))))) (forall ((A_2 tptp.hoare_1848483303_state) (B_1 tptp.hoare_1848483303_state) (A tptp.fun_Ho734851753e_bool)) (let ((_let_1 (tptp.hAPP_H1199573897l_bool tptp.member591555156_state A_2))) (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool _let_1 (tptp.insert668001005_state B_1 A))) (=> (not (= A_2 B_1)) (tptp.hBOOL (tptp.hAPP_f355887345l_bool _let_1 A)))))) (forall ((A_2 tptp.fun_pname_bool) (B_1 tptp.fun_pname_bool) (A tptp.fun_fu1430349052l_bool)) (let ((_let_1 (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool A_2))) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool _let_1 (tptp.insert1325755072e_bool B_1 A))) (=> (not (= A_2 B_1)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool _let_1 A)))))) (forall ((A_2 tptp.fun_Ho734851753e_bool) (B_1 tptp.fun_Ho734851753e_bool) (A tptp.fun_fu1783763359l_bool)) (let ((_let_1 (tptp.hAPP_f1258983629l_bool tptp.member1948767740e_bool A_2))) (=> (tptp.hBOOL (tptp.hAPP_f1526158591l_bool _let_1 (tptp.insert1390540323e_bool B_1 A))) (=> (not (= A_2 B_1)) (tptp.hBOOL (tptp.hAPP_f1526158591l_bool _let_1 A)))))) (forall ((A_2 tptp.pname) (B_1 tptp.pname) (A tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname A_2))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.insert_pname B_1 A))) (=> (not (= A_2 B_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A)))))) (forall ((A tptp.fun_Ho734851753e_bool) (B tptp.fun_Ho734851753e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hAPP_f15397171l_bool tptp.ord_le1119700979e_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hAPP_f15397171l_bool tptp.ord_le1119700979e_bool B) A)) (= A B)))) (forall ((A tptp.fun_fu1430349052l_bool) (B tptp.fun_fu1430349052l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool B) A)) (= A B)))) (forall ((A tptp.fun_fu1783763359l_bool) (B tptp.fun_fu1783763359l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1526158591l_bool (tptp.hAPP_f511954751l_bool tptp.ord_le1819283413l_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f1526158591l_bool (tptp.hAPP_f511954751l_bool tptp.ord_le1819283413l_bool B) A)) (= A B)))) (forall ((A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) A)) (= A B)))) (forall ((C_1 tptp.hoare_1848483303_state) (A tptp.fun_Ho734851753e_bool) (B tptp.fun_Ho734851753e_bool)) (let ((_let_1 (tptp.hAPP_H1199573897l_bool tptp.member591555156_state C_1))) (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hAPP_f15397171l_bool tptp.ord_le1119700979e_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f355887345l_bool _let_1 B)))))) (forall ((C_1 tptp.fun_pname_bool) (A tptp.fun_fu1430349052l_bool) (B tptp.fun_fu1430349052l_bool)) (let ((_let_1 (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool C_1))) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool _let_1 B)))))) (forall ((C_1 tptp.fun_Ho734851753e_bool) (A tptp.fun_fu1783763359l_bool) (B tptp.fun_fu1783763359l_bool)) (let ((_let_1 (tptp.hAPP_f1258983629l_bool tptp.member1948767740e_bool C_1))) (=> (tptp.hBOOL (tptp.hAPP_f1526158591l_bool (tptp.hAPP_f511954751l_bool tptp.ord_le1819283413l_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f1526158591l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f1526158591l_bool _let_1 B)))))) (forall ((C_1 tptp.pname) (A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname C_1))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B)))))) (forall ((A tptp.fun_Ho734851753e_bool) (B_1 tptp.fun_pname_bool) (F tptp.fun_Ho585232518e_bool) (X_2 tptp.hoare_1848483303_state)) (=> (= B_1 (tptp.hAPP_H1355725988e_bool F X_2)) (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hAPP_H1199573897l_bool tptp.member591555156_state X_2) A)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool B_1) (tptp.image_983321428e_bool F A)))))) (forall ((A tptp.fun_Ho734851753e_bool) (B_1 tptp.fun_Ho734851753e_bool) (F tptp.fun_Ho1480763635e_bool) (X_2 tptp.hoare_1848483303_state)) (=> (= B_1 (tptp.hAPP_H1618070847e_bool F X_2)) (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hAPP_H1199573897l_bool tptp.member591555156_state X_2) A)) (tptp.hBOOL (tptp.hAPP_f1526158591l_bool (tptp.hAPP_f1258983629l_bool tptp.member1948767740e_bool B_1) (tptp.image_249571983e_bool F A)))))) (forall ((A tptp.fun_pname_bool) (B_1 tptp.fun_pname_bool) (F tptp.fun_pn800050071e_bool) (X_2 tptp.pname)) (=> (= B_1 (tptp.hAPP_p61793385e_bool F X_2)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool B_1) (tptp.image_47868345e_bool F A)))))) (forall ((A tptp.fun_pname_bool) (B_1 tptp.fun_Ho734851753e_bool) (F tptp.fun_pn2079317538e_bool) (X_2 tptp.pname)) (=> (= B_1 (tptp.hAPP_p276714170e_bool F X_2)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A)) (tptp.hBOOL (tptp.hAPP_f1526158591l_bool (tptp.hAPP_f1258983629l_bool tptp.member1948767740e_bool B_1) (tptp.image_2051793258e_bool F A)))))) (forall ((A tptp.fun_fu1430349052l_bool) (B_1 tptp.hoare_1848483303_state) (F tptp.fun_fu1387033222_state) (X_2 tptp.fun_pname_bool)) (=> (= B_1 (tptp.hAPP_f141816996_state F X_2)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hAPP_H1199573897l_bool tptp.member591555156_state B_1) (tptp.image_1916896084_state F A)))))) (forall ((A tptp.fun_fu1783763359l_bool) (B_1 tptp.hoare_1848483303_state) (F tptp.fun_fu1404623273_state) (X_2 tptp.fun_Ho734851753e_bool)) (=> (= B_1 (tptp.hAPP_f2099317627_state F X_2)) (=> (tptp.hBOOL (tptp.hAPP_f1526158591l_bool (tptp.hAPP_f1258983629l_bool tptp.member1948767740e_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hAPP_H1199573897l_bool tptp.member591555156_state B_1) (tptp.image_730818763_state F A)))))) (forall ((A tptp.fun_Ho734851753e_bool) (B_1 tptp.pname) (F tptp.fun_Ho862234382_pname) (X_2 tptp.hoare_1848483303_state)) (=> (= B_1 (tptp.hAPP_H1494965722_pname F X_2)) (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hAPP_H1199573897l_bool tptp.member591555156_state X_2) A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname B_1) (tptp.image_2075962154_pname F A)))))) (forall ((A tptp.fun_pname_bool) (B_1 tptp.pname) (F tptp.fun_pname_pname) (X_2 tptp.pname)) (=> (= B_1 (tptp.hAPP_pname_pname F X_2)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname B_1) (tptp.image_pname_pname F A)))))) (forall ((A tptp.fun_fu1430349052l_bool) (B_1 tptp.pname) (F tptp.fun_fu1499449723_pname) (X_2 tptp.fun_pname_bool)) (=> (= B_1 (tptp.hAPP_f1297739591_pname F X_2)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname B_1) (tptp.image_1283814551_pname F A)))))) (forall ((A tptp.fun_fu1783763359l_bool) (B_1 tptp.pname) (F tptp.fun_fu891110808_pname) (X_2 tptp.fun_Ho734851753e_bool)) (=> (= B_1 (tptp.hAPP_f50667184_pname F X_2)) (=> (tptp.hBOOL (tptp.hAPP_f1526158591l_bool (tptp.hAPP_f1258983629l_bool tptp.member1948767740e_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname B_1) (tptp.image_1825746272_pname F A)))))) (forall ((A tptp.fun_pname_bool) (B_1 tptp.hoare_1848483303_state) (F tptp.fun_pn447269700_state) (X_2 tptp.pname)) (=> (= B_1 (tptp.hAPP_p675228438_state F X_2)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A)) (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hAPP_H1199573897l_bool tptp.member591555156_state B_1) (tptp.image_1256224870_state F A)))))) (forall ((A_2 tptp.fun_pname_bool) (A tptp.fun_fu1430349052l_bool)) (=> (= A tptp.bot_bo1649642514l_bool) (not (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool A_2) A))))) (forall ((A_2 tptp.fun_Ho734851753e_bool) (A tptp.fun_fu1783763359l_bool)) (=> (= A tptp.bot_bo2068035593l_bool) (not (tptp.hBOOL (tptp.hAPP_f1526158591l_bool (tptp.hAPP_f1258983629l_bool tptp.member1948767740e_bool A_2) A))))) (forall ((A_2 tptp.hoare_1848483303_state) (A tptp.fun_Ho734851753e_bool)) (=> (= A tptp.bot_bo454148287e_bool) (not (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hAPP_H1199573897l_bool tptp.member591555156_state A_2) A))))) (forall ((A_2 tptp.pname) (A tptp.fun_pname_bool)) (=> (= A tptp.bot_bo844097828e_bool) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A_2) A))))) (forall ((P_1 tptp.fun_fu399576434l_bool)) (= (= (tptp.collec1613912337l_bool P_1) tptp.bot_bo1537088220l_bool) (forall ((X_1 tptp.fun_fu1430349052l_bool)) (not (tptp.hBOOL (tptp.hAPP_f1935102916l_bool P_1 X_1)))))) (forall ((P_1 tptp.fun_fu64031073l_bool)) (= (= (tptp.collec2020384458l_bool P_1) tptp.bot_bo973295223l_bool) (forall ((X_1 tptp.fun_fu1783763359l_bool)) (not (tptp.hBOOL (tptp.hAPP_f1526158591l_bool P_1 X_1)))))) (forall ((P_1 tptp.fun_fu1783763359l_bool)) (= (= (tptp.collec1657840446e_bool P_1) tptp.bot_bo2068035593l_bool) (forall ((X_1 tptp.fun_Ho734851753e_bool)) (not (tptp.hBOOL (tptp.hAPP_f355887345l_bool P_1 X_1)))))) (forall ((P_1 tptp.fun_fu1430349052l_bool)) (= (= (tptp.collec1974731493e_bool P_1) tptp.bot_bo1649642514l_bool) (forall ((X_1 tptp.fun_pname_bool)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 X_1)))))) (forall ((P_1 tptp.fun_Ho734851753e_bool)) (= (= (tptp.collec1708318610_state P_1) tptp.bot_bo454148287e_bool) (forall ((X_1 tptp.hoare_1848483303_state)) (not (tptp.hBOOL (tptp.hAPP_H2060173127e_bool P_1 X_1)))))) (forall ((P_1 tptp.fun_pname_bool)) (= (= (tptp.collect_pname P_1) tptp.bot_bo844097828e_bool) (forall ((X_1 tptp.pname)) (not (tptp.hBOOL (tptp.hAPP_pname_bool P_1 X_1)))))) (forall ((C_1 tptp.fun_pname_bool)) (not (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool C_1) tptp.bot_bo1649642514l_bool)))) (forall ((C_1 tptp.fun_Ho734851753e_bool)) (not (tptp.hBOOL (tptp.hAPP_f1526158591l_bool (tptp.hAPP_f1258983629l_bool tptp.member1948767740e_bool C_1) tptp.bot_bo2068035593l_bool)))) (forall ((C_1 tptp.hoare_1848483303_state)) (not (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hAPP_H1199573897l_bool tptp.member591555156_state C_1) tptp.bot_bo454148287e_bool)))) (forall ((C_1 tptp.pname)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname C_1) tptp.bot_bo844097828e_bool)))) (forall ((P_1 tptp.fun_fu399576434l_bool)) (= (= tptp.bot_bo1537088220l_bool (tptp.collec1613912337l_bool P_1)) (forall ((X_1 tptp.fun_fu1430349052l_bool)) (not (tptp.hBOOL (tptp.hAPP_f1935102916l_bool P_1 X_1)))))) (forall ((P_1 tptp.fun_fu64031073l_bool)) (= (= tptp.bot_bo973295223l_bool (tptp.collec2020384458l_bool P_1)) (forall ((X_1 tptp.fun_fu1783763359l_bool)) (not (tptp.hBOOL (tptp.hAPP_f1526158591l_bool P_1 X_1)))))) (forall ((P_1 tptp.fun_fu1783763359l_bool)) (= (= tptp.bot_bo2068035593l_bool (tptp.collec1657840446e_bool P_1)) (forall ((X_1 tptp.fun_Ho734851753e_bool)) (not (tptp.hBOOL (tptp.hAPP_f355887345l_bool P_1 X_1)))))) (forall ((P_1 tptp.fun_fu1430349052l_bool)) (= (= tptp.bot_bo1649642514l_bool (tptp.collec1974731493e_bool P_1)) (forall ((X_1 tptp.fun_pname_bool)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 X_1)))))) (forall ((P_1 tptp.fun_Ho734851753e_bool)) (= (= tptp.bot_bo454148287e_bool (tptp.collec1708318610_state P_1)) (forall ((X_1 tptp.hoare_1848483303_state)) (not (tptp.hBOOL (tptp.hAPP_H2060173127e_bool P_1 X_1)))))) (forall ((P_1 tptp.fun_pname_bool)) (= (= tptp.bot_bo844097828e_bool (tptp.collect_pname P_1)) (forall ((X_1 tptp.pname)) (not (tptp.hBOOL (tptp.hAPP_pname_bool P_1 X_1)))))) (forall ((A tptp.fun_fu1430349052l_bool)) (= (exists ((X_1 tptp.fun_pname_bool)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool X_1) A))) (not (= A tptp.bot_bo1649642514l_bool)))) (forall ((A tptp.fun_fu1783763359l_bool)) (= (exists ((X_1 tptp.fun_Ho734851753e_bool)) (tptp.hBOOL (tptp.hAPP_f1526158591l_bool (tptp.hAPP_f1258983629l_bool tptp.member1948767740e_bool X_1) A))) (not (= A tptp.bot_bo2068035593l_bool)))) (forall ((A tptp.fun_Ho734851753e_bool)) (= (exists ((X_1 tptp.hoare_1848483303_state)) (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hAPP_H1199573897l_bool tptp.member591555156_state X_1) A))) (not (= A tptp.bot_bo454148287e_bool)))) (forall ((A tptp.fun_pname_bool)) (= (exists ((X_1 tptp.pname)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A))) (not (= A tptp.bot_bo844097828e_bool)))) (forall ((A tptp.fun_fu1430349052l_bool)) (= (forall ((X_1 tptp.fun_pname_bool)) (not (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool X_1) A)))) (= A tptp.bot_bo1649642514l_bool))) (forall ((A tptp.fun_fu1783763359l_bool)) (= (forall ((X_1 tptp.fun_Ho734851753e_bool)) (not (tptp.hBOOL (tptp.hAPP_f1526158591l_bool (tptp.hAPP_f1258983629l_bool tptp.member1948767740e_bool X_1) A)))) (= A tptp.bot_bo2068035593l_bool))) (forall ((A tptp.fun_Ho734851753e_bool)) (= (forall ((X_1 tptp.hoare_1848483303_state)) (not (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hAPP_H1199573897l_bool tptp.member591555156_state X_1) A)))) (= A tptp.bot_bo454148287e_bool))) (forall ((A tptp.fun_pname_bool)) (= (forall ((X_1 tptp.pname)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A)))) (= A tptp.bot_bo844097828e_bool))) (= tptp.bot_bo973295223l_bool (tptp.collec2020384458l_bool (tptp.cOMBK_2014663096l_bool tptp.fFalse))) (= tptp.bot_bo2068035593l_bool (tptp.collec1657840446e_bool (tptp.cOMBK_2110745040e_bool tptp.fFalse))) (= tptp.bot_bo1649642514l_bool (tptp.collec1974731493e_bool (tptp.cOMBK_1857069011e_bool tptp.fFalse))) (= tptp.bot_bo454148287e_bool (tptp.collec1708318610_state (tptp.cOMBK_2059960192_state tptp.fFalse))) (= tptp.bot_bo844097828e_bool (tptp.collect_pname (tptp.cOMBK_bool_pname tptp.fFalse))) (forall ((A_2 tptp.pname) (A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A_2) A)) (= (tptp.insert_pname A_2 A) A))) (forall ((A_2 tptp.hoare_1848483303_state) (A tptp.fun_Ho734851753e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hAPP_H1199573897l_bool tptp.member591555156_state A_2) A)) (= (tptp.insert668001005_state A_2 A) A))) (forall ((B_1 tptp.pname) (A_2 tptp.pname) (B tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname A_2))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.insert_pname B_1 B)))))) (forall ((B_1 tptp.hoare_1848483303_state) (A_2 tptp.hoare_1848483303_state) (B tptp.fun_Ho734851753e_bool)) (let ((_let_1 (tptp.hAPP_H1199573897l_bool tptp.member591555156_state A_2))) (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool _let_1 B)) (tptp.hBOOL (tptp.hAPP_f355887345l_bool _let_1 (tptp.insert668001005_state B_1 B)))))) (forall ((B tptp.fun_pname_bool) (X_2 tptp.pname) (A tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname X_2))) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A))) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B))) (= (= (tptp.insert_pname X_2 A) (tptp.insert_pname X_2 B)) (= A B)))))) (forall ((B tptp.fun_Ho734851753e_bool) (X_2 tptp.hoare_1848483303_state) (A tptp.fun_Ho734851753e_bool)) (let ((_let_1 (tptp.hAPP_H1199573897l_bool tptp.member591555156_state X_2))) (=> (not (tptp.hBOOL (tptp.hAPP_f355887345l_bool _let_1 A))) (=> (not (tptp.hBOOL (tptp.hAPP_f355887345l_bool _let_1 B))) (= (= (tptp.insert668001005_state X_2 A) (tptp.insert668001005_state X_2 B)) (= A B)))))) (forall ((Y_2 tptp.pname) (A tptp.fun_pname_bool) (X_2 tptp.pname)) (= (tptp.hBOOL (tptp.hAPP_pname_bool (tptp.insert_pname Y_2 A) X_2)) (or (= Y_2 X_2) (tptp.hBOOL (tptp.hAPP_pname_bool A X_2))))) (forall ((Y_2 tptp.hoare_1848483303_state) (A tptp.fun_Ho734851753e_bool) (X_2 tptp.hoare_1848483303_state)) (= (tptp.hBOOL (tptp.hAPP_H2060173127e_bool (tptp.insert668001005_state Y_2 A) X_2)) (or (= Y_2 X_2) (tptp.hBOOL (tptp.hAPP_H2060173127e_bool A X_2))))) (forall ((A_2 tptp.pname) (B_1 tptp.pname) (A tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname A_2))) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.insert_pname B_1 A))) (or (= A_2 B_1) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A)))))) (forall ((A_2 tptp.hoare_1848483303_state) (B_1 tptp.hoare_1848483303_state) (A tptp.fun_Ho734851753e_bool)) (let ((_let_1 (tptp.hAPP_H1199573897l_bool tptp.member591555156_state A_2))) (= (tptp.hBOOL (tptp.hAPP_f355887345l_bool _let_1 (tptp.insert668001005_state B_1 A))) (or (= A_2 B_1) (tptp.hBOOL (tptp.hAPP_f355887345l_bool _let_1 A)))))) (forall ((X_2 tptp.pname) (Y_2 tptp.pname) (A tptp.fun_pname_bool)) (= (tptp.insert_pname X_2 (tptp.insert_pname Y_2 A)) (tptp.insert_pname Y_2 (tptp.insert_pname X_2 A)))) (forall ((X_2 tptp.hoare_1848483303_state) (Y_2 tptp.hoare_1848483303_state) (A tptp.fun_Ho734851753e_bool)) (= (tptp.insert668001005_state X_2 (tptp.insert668001005_state Y_2 A)) (tptp.insert668001005_state Y_2 (tptp.insert668001005_state X_2 A)))) (forall ((X_2 tptp.pname) (A tptp.fun_pname_bool)) (let ((_let_1 (tptp.insert_pname X_2 A))) (= (tptp.insert_pname X_2 _let_1) _let_1))) (forall ((X_2 tptp.hoare_1848483303_state) (A tptp.fun_Ho734851753e_bool)) (let ((_let_1 (tptp.insert668001005_state X_2 A))) (= (tptp.insert668001005_state X_2 _let_1) _let_1))) (forall ((A_2 tptp.pname) (P_1 tptp.fun_pname_bool)) (= (tptp.insert_pname A_2 (tptp.collect_pname P_1)) (tptp.collect_pname (tptp.cOMBS_568398431l_bool (tptp.cOMBB_675860798_pname tptp.fimplies (tptp.cOMBB_647938656_pname tptp.fNot (tptp.hAPP_p61793385e_bool (tptp.cOMBC_1149511130e_bool tptp.fequal_pname) A_2))) P_1)))) (forall ((A_2 tptp.hoare_1848483303_state) (P_1 tptp.fun_Ho734851753e_bool)) (= (tptp.insert668001005_state A_2 (tptp.collec1708318610_state P_1)) (tptp.collec1708318610_state (tptp.cOMBS_1990964188l_bool (tptp.cOMBB_215065709_state tptp.fimplies (tptp.cOMBB_1397003211_state tptp.fNot (tptp.hAPP_H1618070847e_bool (tptp.cOMBC_1947058646e_bool tptp.fequal364418600_state) A_2))) P_1)))) (forall ((A_2 tptp.fun_pname_bool) (P_1 tptp.fun_fu1430349052l_bool)) (= (tptp.insert1325755072e_bool A_2 (tptp.collec1974731493e_bool P_1)) (tptp.collec1974731493e_bool (tptp.cOMBS_350070575l_bool (tptp.cOMBB_2095475776e_bool tptp.fimplies (tptp.cOMBB_307249310e_bool tptp.fNot (tptp.hAPP_f434788991l_bool (tptp.cOMBC_1284144636l_bool tptp.fequal533582459e_bool) A_2))) P_1)))) (forall ((A_2 tptp.fun_Ho734851753e_bool) (P_1 tptp.fun_fu1783763359l_bool)) (= (tptp.insert1390540323e_bool A_2 (tptp.collec1657840446e_bool P_1)) (tptp.collec1657840446e_bool (tptp.cOMBS_1278217668l_bool (tptp.cOMBB_1418941603e_bool tptp.fimplies (tptp.cOMBB_1356070853e_bool tptp.fNot (tptp.hAPP_f15397171l_bool (tptp.cOMBC_80545690l_bool tptp.fequal1145749800e_bool) A_2))) P_1)))) (forall ((A_2 tptp.pname) (B tptp.fun_pname_bool)) (= (tptp.insert_pname A_2 B) (tptp.collect_pname (tptp.cOMBS_568398431l_bool (tptp.cOMBB_675860798_pname tptp.fdisj (tptp.hAPP_p61793385e_bool (tptp.cOMBC_1149511130e_bool tptp.fequal_pname) A_2)) (tptp.hAPP_f759274231e_bool (tptp.cOMBC_1058051404l_bool tptp.member_pname) B))))) (forall ((A_2 tptp.hoare_1848483303_state) (B tptp.fun_Ho734851753e_bool)) (= (tptp.insert668001005_state A_2 B) (tptp.collec1708318610_state (tptp.cOMBS_1990964188l_bool (tptp.cOMBB_215065709_state tptp.fdisj (tptp.hAPP_H1618070847e_bool (tptp.cOMBC_1947058646e_bool tptp.fequal364418600_state) A_2)) (tptp.hAPP_f617245717e_bool (tptp.cOMBC_1803918242l_bool tptp.member591555156_state) B))))) (forall ((A_2 tptp.fun_pname_bool) (B tptp.fun_fu1430349052l_bool)) (= (tptp.insert1325755072e_bool A_2 B) (tptp.collec1974731493e_bool (tptp.cOMBS_350070575l_bool (tptp.cOMBB_2095475776e_bool tptp.fdisj (tptp.hAPP_f434788991l_bool (tptp.cOMBC_1284144636l_bool tptp.fequal533582459e_bool) A_2)) (tptp.hAPP_f559147733l_bool (tptp.cOMBC_1988546018l_bool tptp.member799430823e_bool) B))))) (forall ((A_2 tptp.fun_Ho734851753e_bool) (B tptp.fun_fu1783763359l_bool)) (= (tptp.insert1390540323e_bool A_2 B) (tptp.collec1657840446e_bool (tptp.cOMBS_1278217668l_bool (tptp.cOMBB_1418941603e_bool tptp.fdisj (tptp.hAPP_f15397171l_bool (tptp.cOMBC_80545690l_bool tptp.fequal1145749800e_bool) A_2)) (tptp.hAPP_f1360064833l_bool (tptp.cOMBC_1100692246l_bool tptp.member1948767740e_bool) B))))) (forall ((A_2 tptp.pname) (B tptp.fun_pname_bool)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A_2) (tptp.insert_pname A_2 B)))) (forall ((A_2 tptp.hoare_1848483303_state) (B tptp.fun_Ho734851753e_bool)) (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hAPP_H1199573897l_bool tptp.member591555156_state A_2) (tptp.insert668001005_state A_2 B)))) (forall ((A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (=> (= A B) (not (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) B)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) A))))))) (forall ((A tptp.fun_Ho734851753e_bool) (B tptp.fun_Ho734851753e_bool)) (=> (= A B) (not (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hAPP_f15397171l_bool tptp.ord_le1119700979e_bool A) B)) (not (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hAPP_f15397171l_bool tptp.ord_le1119700979e_bool B) A))))))) (forall ((C_2 tptp.fun_pname_bool) (A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A))) (=> (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_2)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 C_2)))))) (forall ((C_2 tptp.fun_Ho734851753e_bool) (A tptp.fun_Ho734851753e_bool) (B tptp.fun_Ho734851753e_bool)) (let ((_let_1 (tptp.hAPP_f15397171l_bool tptp.ord_le1119700979e_bool A))) (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool _let_1 B)) (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hAPP_f15397171l_bool tptp.ord_le1119700979e_bool B) C_2)) (tptp.hBOOL (tptp.hAPP_f355887345l_bool _let_1 C_2)))))) (forall ((X_2 tptp.pname) (A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname X_2))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B)))))) (forall ((X_2 tptp.hoare_1848483303_state) (A tptp.fun_Ho734851753e_bool) (B tptp.fun_Ho734851753e_bool)) (let ((_let_1 (tptp.hAPP_H1199573897l_bool tptp.member591555156_state X_2))) (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hAPP_f15397171l_bool tptp.ord_le1119700979e_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f355887345l_bool _let_1 B)))))) (forall ((B tptp.fun_pname_bool) (X_2 tptp.pname) (A tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname X_2))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) B)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B)))))) (forall ((B tptp.fun_Ho734851753e_bool) (X_2 tptp.hoare_1848483303_state) (A tptp.fun_Ho734851753e_bool)) (let ((_let_1 (tptp.hAPP_H1199573897l_bool tptp.member591555156_state X_2))) (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool _let_1 A)) (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hAPP_f15397171l_bool tptp.ord_le1119700979e_bool A) B)) (tptp.hBOOL (tptp.hAPP_f355887345l_bool _let_1 B)))))) (forall ((X_2 tptp.pname) (A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname X_2))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B)))))) (forall ((X_2 tptp.hoare_1848483303_state) (A tptp.fun_Ho734851753e_bool) (B tptp.fun_Ho734851753e_bool)) (let ((_let_1 (tptp.hAPP_H1199573897l_bool tptp.member591555156_state X_2))) (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hAPP_f15397171l_bool tptp.ord_le1119700979e_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f355887345l_bool _let_1 B)))))) (forall ((A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (=> (= A B) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) A)))) (forall ((A tptp.fun_Ho734851753e_bool) (B tptp.fun_Ho734851753e_bool)) (=> (= A B) (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hAPP_f15397171l_bool tptp.ord_le1119700979e_bool B) A)))) (forall ((A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (=> (= A B) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) B)))) (forall ((A tptp.fun_Ho734851753e_bool) (B tptp.fun_Ho734851753e_bool)) (=> (= A B) (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hAPP_f15397171l_bool tptp.ord_le1119700979e_bool A) B)))) (forall ((A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (= (= A B) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) B)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) A))))) (forall ((A tptp.fun_Ho734851753e_bool) (B tptp.fun_Ho734851753e_bool)) (= (= A B) (and (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hAPP_f15397171l_bool tptp.ord_le1119700979e_bool A) B)) (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hAPP_f15397171l_bool tptp.ord_le1119700979e_bool B) A))))) (forall ((A tptp.fun_pname_bool)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) A))) (forall ((A tptp.fun_Ho734851753e_bool)) (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hAPP_f15397171l_bool tptp.ord_le1119700979e_bool A) A))) (forall ((B_1 tptp.hoare_1848483303_state) (F tptp.fun_pn447269700_state) (X_2 tptp.pname) (A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A)) (=> (= B_1 (tptp.hAPP_p675228438_state F X_2)) (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hAPP_H1199573897l_bool tptp.member591555156_state B_1) (tptp.image_1256224870_state F A)))))) (forall ((F tptp.fun_pn447269700_state) (X_2 tptp.pname) (A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A)) (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hAPP_H1199573897l_bool tptp.member591555156_state (tptp.hAPP_p675228438_state F X_2)) (tptp.image_1256224870_state F A))))) (forall ((Z tptp.hoare_1848483303_state) (F tptp.fun_pn447269700_state) (A tptp.fun_pname_bool)) (= (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hAPP_H1199573897l_bool tptp.member591555156_state Z) (tptp.image_1256224870_state F A))) (exists ((X_1 tptp.pname)) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A)) (= Z (tptp.hAPP_p675228438_state F X_1)))))) (forall ((P_1 tptp.fun_pname_bool) (Q_1 tptp.fun_pname_bool)) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.collect_pname (tptp.cOMBS_568398431l_bool (tptp.cOMBB_675860798_pname tptp.fdisj P_1) Q_1)))) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.collect_pname P_1))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.collect_pname Q_1)))))) (forall ((P_1 tptp.fun_Ho734851753e_bool) (Q_1 tptp.fun_Ho734851753e_bool)) (= (tptp.hBOOL (tptp.hAPP_f355887345l_bool tptp.finite1765195604_state (tptp.collec1708318610_state (tptp.cOMBS_1990964188l_bool (tptp.cOMBB_215065709_state tptp.fdisj P_1) Q_1)))) (and (tptp.hBOOL (tptp.hAPP_f355887345l_bool tptp.finite1765195604_state (tptp.collec1708318610_state P_1))) (tptp.hBOOL (tptp.hAPP_f355887345l_bool tptp.finite1765195604_state (tptp.collec1708318610_state Q_1)))))) (forall ((P_1 tptp.fun_fu1430349052l_bool) (Q_1 tptp.fun_fu1430349052l_bool)) (= (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.collec1974731493e_bool (tptp.cOMBS_350070575l_bool (tptp.cOMBB_2095475776e_bool tptp.fdisj P_1) Q_1)))) (and (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.collec1974731493e_bool P_1))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.collec1974731493e_bool Q_1)))))) (forall ((P_1 tptp.fun_fu1783763359l_bool) (Q_1 tptp.fun_fu1783763359l_bool)) (= (tptp.hBOOL (tptp.hAPP_f1526158591l_bool tptp.finite297877756e_bool (tptp.collec1657840446e_bool (tptp.cOMBS_1278217668l_bool (tptp.cOMBB_1418941603e_bool tptp.fdisj P_1) Q_1)))) (and (tptp.hBOOL (tptp.hAPP_f1526158591l_bool tptp.finite297877756e_bool (tptp.collec1657840446e_bool P_1))) (tptp.hBOOL (tptp.hAPP_f1526158591l_bool tptp.finite297877756e_bool (tptp.collec1657840446e_bool Q_1)))))) (forall ((X_1 tptp.pname) (Xa tptp.fun_pname_bool)) (= (tptp.insert_pname X_1 Xa) (tptp.collect_pname (tptp.cOMBS_568398431l_bool (tptp.cOMBB_675860798_pname tptp.fdisj (tptp.hAPP_p61793385e_bool (tptp.cOMBC_1149511130e_bool tptp.fequal_pname) X_1)) (tptp.hAPP_f759274231e_bool (tptp.cOMBC_1058051404l_bool tptp.member_pname) Xa))))) (forall ((X_1 tptp.hoare_1848483303_state) (Xa tptp.fun_Ho734851753e_bool)) (= (tptp.insert668001005_state X_1 Xa) (tptp.collec1708318610_state (tptp.cOMBS_1990964188l_bool (tptp.cOMBB_215065709_state tptp.fdisj (tptp.hAPP_H1618070847e_bool (tptp.cOMBC_1947058646e_bool tptp.fequal364418600_state) X_1)) (tptp.hAPP_f617245717e_bool (tptp.cOMBC_1803918242l_bool tptp.member591555156_state) Xa))))) (forall ((X_1 tptp.fun_pname_bool) (Xa tptp.fun_fu1430349052l_bool)) (= (tptp.insert1325755072e_bool X_1 Xa) (tptp.collec1974731493e_bool (tptp.cOMBS_350070575l_bool (tptp.cOMBB_2095475776e_bool tptp.fdisj (tptp.hAPP_f434788991l_bool (tptp.cOMBC_1284144636l_bool tptp.fequal533582459e_bool) X_1)) (tptp.hAPP_f559147733l_bool (tptp.cOMBC_1988546018l_bool tptp.member799430823e_bool) Xa))))) (forall ((X_1 tptp.fun_Ho734851753e_bool) (Xa tptp.fun_fu1783763359l_bool)) (= (tptp.insert1390540323e_bool X_1 Xa) (tptp.collec1657840446e_bool (tptp.cOMBS_1278217668l_bool (tptp.cOMBB_1418941603e_bool tptp.fdisj (tptp.hAPP_f15397171l_bool (tptp.cOMBC_80545690l_bool tptp.fequal1145749800e_bool) X_1)) (tptp.hAPP_f1360064833l_bool (tptp.cOMBC_1100692246l_bool tptp.member1948767740e_bool) Xa))))) (forall ((A_2 tptp.pname) (B_1 tptp.pname)) (=> (= (tptp.insert_pname A_2 tptp.bot_bo844097828e_bool) (tptp.insert_pname B_1 tptp.bot_bo844097828e_bool)) (= A_2 B_1))) (forall ((A_2 tptp.hoare_1848483303_state) (B_1 tptp.hoare_1848483303_state)) (=> (= (tptp.insert668001005_state A_2 tptp.bot_bo454148287e_bool) (tptp.insert668001005_state B_1 tptp.bot_bo454148287e_bool)) (= A_2 B_1))) (forall ((B_1 tptp.pname) (A_2 tptp.pname)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname B_1) (tptp.insert_pname A_2 tptp.bot_bo844097828e_bool))) (= B_1 A_2))) (forall ((B_1 tptp.hoare_1848483303_state) (A_2 tptp.hoare_1848483303_state)) (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hAPP_H1199573897l_bool tptp.member591555156_state B_1) (tptp.insert668001005_state A_2 tptp.bot_bo454148287e_bool))) (= B_1 A_2))) (forall ((A_2 tptp.pname) (B_1 tptp.pname) (C_1 tptp.pname) (D_1 tptp.pname)) (= (= (tptp.insert_pname A_2 (tptp.insert_pname B_1 tptp.bot_bo844097828e_bool)) (tptp.insert_pname C_1 (tptp.insert_pname D_1 tptp.bot_bo844097828e_bool))) (or (and (= A_2 C_1) (= B_1 D_1)) (and (= A_2 D_1) (= B_1 C_1))))) (forall ((A_2 tptp.hoare_1848483303_state) (B_1 tptp.hoare_1848483303_state) (C_1 tptp.hoare_1848483303_state) (D_1 tptp.hoare_1848483303_state)) (= (= (tptp.insert668001005_state A_2 (tptp.insert668001005_state B_1 tptp.bot_bo454148287e_bool)) (tptp.insert668001005_state C_1 (tptp.insert668001005_state D_1 tptp.bot_bo454148287e_bool))) (or (and (= A_2 C_1) (= B_1 D_1)) (and (= A_2 D_1) (= B_1 C_1))))) (forall ((B_1 tptp.pname) (A_2 tptp.pname)) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname B_1) (tptp.insert_pname A_2 tptp.bot_bo844097828e_bool))) (= B_1 A_2))) (forall ((B_1 tptp.hoare_1848483303_state) (A_2 tptp.hoare_1848483303_state)) (= (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hAPP_H1199573897l_bool tptp.member591555156_state B_1) (tptp.insert668001005_state A_2 tptp.bot_bo454148287e_bool))) (= B_1 A_2))) (forall ((A_2 tptp.pname) (A tptp.fun_pname_bool)) (not (= (tptp.insert_pname A_2 A) tptp.bot_bo844097828e_bool))) (forall ((A_2 tptp.hoare_1848483303_state) (A tptp.fun_Ho734851753e_bool)) (not (= (tptp.insert668001005_state A_2 A) tptp.bot_bo454148287e_bool))) (forall ((A_2 tptp.pname) (A tptp.fun_pname_bool)) (not (= tptp.bot_bo844097828e_bool (tptp.insert_pname A_2 A)))) (forall ((A_2 tptp.hoare_1848483303_state) (A tptp.fun_Ho734851753e_bool)) (not (= tptp.bot_bo454148287e_bool (tptp.insert668001005_state A_2 A)))) (forall ((A_2 tptp.pname) (A tptp.fun_pname_bool)) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.insert_pname A_2 A))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A)))) (forall ((A_2 tptp.hoare_1848483303_state) (A tptp.fun_Ho734851753e_bool)) (= (tptp.hBOOL (tptp.hAPP_f355887345l_bool tptp.finite1765195604_state (tptp.insert668001005_state A_2 A))) (tptp.hBOOL (tptp.hAPP_f355887345l_bool tptp.finite1765195604_state A)))) (forall ((A_2 tptp.fun_pname_bool) (A tptp.fun_fu1430349052l_bool)) (= (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.insert1325755072e_bool A_2 A))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A)))) (forall ((A_2 tptp.fun_Ho734851753e_bool) (A tptp.fun_fu1783763359l_bool)) (= (tptp.hBOOL (tptp.hAPP_f1526158591l_bool tptp.finite297877756e_bool (tptp.insert1390540323e_bool A_2 A))) (tptp.hBOOL (tptp.hAPP_f1526158591l_bool tptp.finite297877756e_bool A)))) (forall ((A tptp.fun_pname_bool)) (= (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 tptp.fun_Ho734851753e_bool)) (= (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hAPP_f15397171l_bool tptp.ord_le1119700979e_bool A) tptp.bot_bo454148287e_bool)) (= A tptp.bot_bo454148287e_bool))) (forall ((F tptp.fun_pn447269700_state) (A tptp.fun_pname_bool)) (= (= (tptp.image_1256224870_state F A) tptp.bot_bo454148287e_bool) (= A tptp.bot_bo844097828e_bool))) (forall ((F tptp.fun_pn447269700_state)) (= (tptp.image_1256224870_state F tptp.bot_bo844097828e_bool) tptp.bot_bo454148287e_bool)) (forall ((F tptp.fun_pn447269700_state) (A tptp.fun_pname_bool)) (= (= tptp.bot_bo454148287e_bool (tptp.image_1256224870_state F A)) (= A tptp.bot_bo844097828e_bool))) (forall ((A tptp.fun_fu1430349052l_bool) (B tptp.fun_fu1430349052l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool B)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A))))) (forall ((A tptp.fun_fu1783763359l_bool) (B tptp.fun_fu1783763359l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1526158591l_bool (tptp.hAPP_f511954751l_bool tptp.ord_le1819283413l_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f1526158591l_bool tptp.finite297877756e_bool B)) (tptp.hBOOL (tptp.hAPP_f1526158591l_bool tptp.finite297877756e_bool A))))) (forall ((A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A))))) (forall ((A tptp.fun_Ho734851753e_bool) (B tptp.fun_Ho734851753e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hAPP_f15397171l_bool tptp.ord_le1119700979e_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool tptp.finite1765195604_state B)) (tptp.hBOOL (tptp.hAPP_f355887345l_bool tptp.finite1765195604_state A))))) (forall ((A tptp.fun_fu1430349052l_bool) (B tptp.fun_fu1430349052l_bool)) (=> (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) B)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A))))) (forall ((A tptp.fun_fu1783763359l_bool) (B tptp.fun_fu1783763359l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1526158591l_bool tptp.finite297877756e_bool B)) (=> (tptp.hBOOL (tptp.hAPP_f1526158591l_bool (tptp.hAPP_f511954751l_bool tptp.ord_le1819283413l_bool A) B)) (tptp.hBOOL (tptp.hAPP_f1526158591l_bool tptp.finite297877756e_bool A))))) (forall ((A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (=> (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) B)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A))))) (forall ((A tptp.fun_Ho734851753e_bool) (B tptp.fun_Ho734851753e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool tptp.finite1765195604_state B)) (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hAPP_f15397171l_bool tptp.ord_le1119700979e_bool A) B)) (tptp.hBOOL (tptp.hAPP_f355887345l_bool tptp.finite1765195604_state A))))) (forall ((A_2 tptp.pname) (C_2 tptp.fun_pname_bool) (D tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool C_2) D)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.insert_pname A_2 C_2)) (tptp.insert_pname A_2 D))))) (forall ((A_2 tptp.hoare_1848483303_state) (C_2 tptp.fun_Ho734851753e_bool) (D tptp.fun_Ho734851753e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hAPP_f15397171l_bool tptp.ord_le1119700979e_bool C_2) D)) (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hAPP_f15397171l_bool tptp.ord_le1119700979e_bool (tptp.insert668001005_state A_2 C_2)) (tptp.insert668001005_state A_2 D))))) (forall ((X_2 tptp.pname) (A tptp.fun_pname_bool)) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A)) (tptp.hBOOL (tptp.hAPP_pname_bool A X_2)))) (forall ((X_2 tptp.hoare_1848483303_state) (A tptp.fun_Ho734851753e_bool)) (= (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hAPP_H1199573897l_bool tptp.member591555156_state X_2) A)) (tptp.hBOOL (tptp.hAPP_H2060173127e_bool A X_2)))) (forall ((P_1 tptp.fun_pname_bool)) (= (tptp.collect_pname P_1) P_1)) (forall ((P_1 tptp.fun_Ho734851753e_bool)) (= (tptp.collec1708318610_state P_1) P_1)) (forall ((P_1 tptp.fun_fu1430349052l_bool)) (= (tptp.collec1974731493e_bool P_1) P_1)) (forall ((P_1 tptp.fun_fu1783763359l_bool)) (= (tptp.collec1657840446e_bool P_1) P_1)) (forall ((B_1 tptp.pname) (A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.insert_pname B_1 B)))))) (forall ((B_1 tptp.hoare_1848483303_state) (A tptp.fun_Ho734851753e_bool) (B tptp.fun_Ho734851753e_bool)) (let ((_let_1 (tptp.hAPP_f15397171l_bool tptp.ord_le1119700979e_bool A))) (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool _let_1 B)) (tptp.hBOOL (tptp.hAPP_f355887345l_bool _let_1 (tptp.insert668001005_state B_1 B)))))) (forall ((B tptp.fun_pname_bool) (X_2 tptp.pname) (A tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A))) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A))) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.insert_pname X_2 B))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B)))))) (forall ((B tptp.fun_Ho734851753e_bool) (X_2 tptp.hoare_1848483303_state) (A tptp.fun_Ho734851753e_bool)) (let ((_let_1 (tptp.hAPP_f15397171l_bool tptp.ord_le1119700979e_bool A))) (=> (not (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hAPP_H1199573897l_bool tptp.member591555156_state X_2) A))) (= (tptp.hBOOL (tptp.hAPP_f355887345l_bool _let_1 (tptp.insert668001005_state X_2 B))) (tptp.hBOOL (tptp.hAPP_f355887345l_bool _let_1 B)))))) (forall ((X_2 tptp.pname) (A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.insert_pname X_2 A)) B)) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) B)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) B))))) (forall ((X_2 tptp.hoare_1848483303_state) (A tptp.fun_Ho734851753e_bool) (B tptp.fun_Ho734851753e_bool)) (= (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hAPP_f15397171l_bool tptp.ord_le1119700979e_bool (tptp.insert668001005_state X_2 A)) B)) (and (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hAPP_H1199573897l_bool tptp.member591555156_state X_2) B)) (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hAPP_f15397171l_bool tptp.ord_le1119700979e_bool A) B))))) (forall ((B tptp.fun_pname_bool) (A_2 tptp.pname)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B) (tptp.insert_pname A_2 B)))) (forall ((B tptp.fun_Ho734851753e_bool) (A_2 tptp.hoare_1848483303_state)) (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hAPP_f15397171l_bool tptp.ord_le1119700979e_bool B) (tptp.insert668001005_state A_2 B)))) (forall ((F tptp.fun_pn447269700_state) (X_2 tptp.pname) (A tptp.fun_pname_bool)) (let ((_let_1 (tptp.image_1256224870_state F A))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_2) A)) (= (tptp.insert668001005_state (tptp.hAPP_p675228438_state F X_2) _let_1) _let_1)))) (forall ((F tptp.fun_pn447269700_state) (A_2 tptp.pname) (B tptp.fun_pname_bool)) (= (tptp.image_1256224870_state F (tptp.insert_pname A_2 B)) (tptp.insert668001005_state (tptp.hAPP_p675228438_state F A_2) (tptp.image_1256224870_state F B)))) (forall ((F tptp.fun_pn447269700_state) (A tptp.fun_pname_bool) (B tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) B)) (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hAPP_f15397171l_bool tptp.ord_le1119700979e_bool (tptp.image_1256224870_state F A)) (tptp.image_1256224870_state F B))))) (forall ((B tptp.fun_Ho734851753e_bool) (F tptp.fun_pn447269700_state) (A tptp.fun_pname_bool)) (= (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hAPP_f15397171l_bool tptp.ord_le1119700979e_bool B) (tptp.image_1256224870_state F A))) (exists ((AA tptp.fun_pname_bool)) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool AA) A)) (= B (tptp.image_1256224870_state F AA)))))) (forall ((M tptp.fun_pname_option_com) (A_2 tptp.pname) (B_1 tptp.com)) (=> (= (tptp.hAPP_p799580910on_com M A_2) (tptp.some_com B_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A_2) (tptp.dom_pname_com M))))) (forall ((P_1 tptp.fun_pname_bool) (A_2 tptp.pname)) (let ((_let_1 (tptp.collect_pname (tptp.cOMBS_568398431l_bool (tptp.cOMBB_675860798_pname tptp.fconj (tptp.hAPP_p61793385e_bool (tptp.cOMBC_1149511130e_bool tptp.fequal_pname) A_2)) P_1)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_pname_bool P_1 A_2)))) (and (=> _let_2 (= _let_1 (tptp.insert_pname A_2 tptp.bot_bo844097828e_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bo844097828e_bool)))))) (forall ((P_1 tptp.fun_Ho734851753e_bool) (A_2 tptp.hoare_1848483303_state)) (let ((_let_1 (tptp.collec1708318610_state (tptp.cOMBS_1990964188l_bool (tptp.cOMBB_215065709_state tptp.fconj (tptp.hAPP_H1618070847e_bool (tptp.cOMBC_1947058646e_bool tptp.fequal364418600_state) A_2)) P_1)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_H2060173127e_bool P_1 A_2)))) (and (=> _let_2 (= _let_1 (tptp.insert668001005_state A_2 tptp.bot_bo454148287e_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bo454148287e_bool)))))) (forall ((P_1 tptp.fun_fu1430349052l_bool) (A_2 tptp.fun_pname_bool)) (let ((_let_1 (tptp.collec1974731493e_bool (tptp.cOMBS_350070575l_bool (tptp.cOMBB_2095475776e_bool tptp.fconj (tptp.hAPP_f434788991l_bool (tptp.cOMBC_1284144636l_bool tptp.fequal533582459e_bool) A_2)) P_1)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 A_2)))) (and (=> _let_2 (= _let_1 (tptp.insert1325755072e_bool A_2 tptp.bot_bo1649642514l_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bo1649642514l_bool)))))) (forall ((P_1 tptp.fun_fu1783763359l_bool) (A_2 tptp.fun_Ho734851753e_bool)) (let ((_let_1 (tptp.collec1657840446e_bool (tptp.cOMBS_1278217668l_bool (tptp.cOMBB_1418941603e_bool tptp.fconj (tptp.hAPP_f15397171l_bool (tptp.cOMBC_80545690l_bool tptp.fequal1145749800e_bool) A_2)) P_1)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_f355887345l_bool P_1 A_2)))) (and (=> _let_2 (= _let_1 (tptp.insert1390540323e_bool A_2 tptp.bot_bo2068035593l_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bo2068035593l_bool)))))) (forall ((P_1 tptp.fun_pname_bool) (A_2 tptp.pname)) (let ((_let_1 (tptp.collect_pname (tptp.cOMBS_568398431l_bool (tptp.cOMBB_675860798_pname tptp.fconj (tptp.hAPP_p61793385e_bool tptp.fequal_pname A_2)) P_1)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_pname_bool P_1 A_2)))) (and (=> _let_2 (= _let_1 (tptp.insert_pname A_2 tptp.bot_bo844097828e_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bo844097828e_bool)))))) (forall ((P_1 tptp.fun_Ho734851753e_bool) (A_2 tptp.hoare_1848483303_state)) (let ((_let_1 (tptp.collec1708318610_state (tptp.cOMBS_1990964188l_bool (tptp.cOMBB_215065709_state tptp.fconj (tptp.hAPP_H1618070847e_bool tptp.fequal364418600_state A_2)) P_1)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_H2060173127e_bool P_1 A_2)))) (and (=> _let_2 (= _let_1 (tptp.insert668001005_state A_2 tptp.bot_bo454148287e_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bo454148287e_bool)))))) (forall ((P_1 tptp.fun_fu1430349052l_bool) (A_2 tptp.fun_pname_bool)) (let ((_let_1 (tptp.collec1974731493e_bool (tptp.cOMBS_350070575l_bool (tptp.cOMBB_2095475776e_bool tptp.fconj (tptp.hAPP_f434788991l_bool tptp.fequal533582459e_bool A_2)) P_1)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 A_2)))) (and (=> _let_2 (= _let_1 (tptp.insert1325755072e_bool A_2 tptp.bot_bo1649642514l_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bo1649642514l_bool)))))) (forall ((P_1 tptp.fun_fu1783763359l_bool) (A_2 tptp.fun_Ho734851753e_bool)) (let ((_let_1 (tptp.collec1657840446e_bool (tptp.cOMBS_1278217668l_bool (tptp.cOMBB_1418941603e_bool tptp.fconj (tptp.hAPP_f15397171l_bool tptp.fequal1145749800e_bool A_2)) P_1)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_f355887345l_bool P_1 A_2)))) (and (=> _let_2 (= _let_1 (tptp.insert1390540323e_bool A_2 tptp.bot_bo2068035593l_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bo2068035593l_bool)))))) (forall ((A_2 tptp.pname)) (= (tptp.collect_pname (tptp.hAPP_p61793385e_bool (tptp.cOMBC_1149511130e_bool tptp.fequal_pname) A_2)) (tptp.insert_pname A_2 tptp.bot_bo844097828e_bool))) (forall ((A_2 tptp.hoare_1848483303_state)) (= (tptp.collec1708318610_state (tptp.hAPP_H1618070847e_bool (tptp.cOMBC_1947058646e_bool tptp.fequal364418600_state) A_2)) (tptp.insert668001005_state A_2 tptp.bot_bo454148287e_bool))) (forall ((A_2 tptp.fun_pname_bool)) (= (tptp.collec1974731493e_bool (tptp.hAPP_f434788991l_bool (tptp.cOMBC_1284144636l_bool tptp.fequal533582459e_bool) A_2)) (tptp.insert1325755072e_bool A_2 tptp.bot_bo1649642514l_bool))) (forall ((A_2 tptp.fun_Ho734851753e_bool)) (= (tptp.collec1657840446e_bool (tptp.hAPP_f15397171l_bool (tptp.cOMBC_80545690l_bool tptp.fequal1145749800e_bool) A_2)) (tptp.insert1390540323e_bool A_2 tptp.bot_bo2068035593l_bool))) (forall ((A_2 tptp.pname)) (= (tptp.collect_pname (tptp.hAPP_p61793385e_bool tptp.fequal_pname A_2)) (tptp.insert_pname A_2 tptp.bot_bo844097828e_bool))) (forall ((A_2 tptp.hoare_1848483303_state)) (= (tptp.collec1708318610_state (tptp.hAPP_H1618070847e_bool tptp.fequal364418600_state A_2)) (tptp.insert668001005_state A_2 tptp.bot_bo454148287e_bool))) (forall ((A_2 tptp.fun_pname_bool)) (= (tptp.collec1974731493e_bool (tptp.hAPP_f434788991l_bool tptp.fequal533582459e_bool A_2)) (tptp.insert1325755072e_bool A_2 tptp.bot_bo1649642514l_bool))) (forall ((A_2 tptp.fun_Ho734851753e_bool)) (= (tptp.collec1657840446e_bool (tptp.hAPP_f15397171l_bool tptp.fequal1145749800e_bool A_2)) (tptp.insert1390540323e_bool A_2 tptp.bot_bo2068035593l_bool))) (forall ((C_1 tptp.com) (G tptp.fun_Ho734851753e_bool)) (=> (tptp.hBOOL tptp.hoare_1310879719gleton) (=> (forall ((X_1 tptp.pname)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) (tptp.dom_pname_com tptp.body))) (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hoare_1193527299_state G) (tptp.insert668001005_state (tptp.hAPP_c379084956_state tptp.hoare_Mirabelle_MGT (tptp.hAPP_pname_com tptp.body_1 X_1)) tptp.bot_bo454148287e_bool))))) (=> (tptp.hBOOL (tptp.wt C_1)) (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hoare_1193527299_state G) (tptp.insert668001005_state (tptp.hAPP_c379084956_state tptp.hoare_Mirabelle_MGT C_1) tptp.bot_bo454148287e_bool))))))) _let_11 (forall ((B_1 tptp.hoare_1848483303_state) (F tptp.fun_pn447269700_state) (A tptp.fun_pname_bool)) (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hAPP_H1199573897l_bool tptp.member591555156_state B_1) (tptp.image_1256224870_state F A))) (not (forall ((X_1 tptp.pname)) (=> (= B_1 (tptp.hAPP_p675228438_state F X_1)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A)))))))) (forall ((P_1 tptp.fun_fu1430349052l_bool) (A tptp.fun_pname_bool) (Fa tptp.fun_pname_bool)) (=> (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)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 tptp.bot_bo844097828e_bool)) (=> (forall ((A_1 tptp.pname) (F_1 tptp.fun_pname_bool)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname A_1))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname F_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A)) (=> (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.insert_pname A_1 F_1))))))))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool P_1 Fa))))))) (forall ((P_1 tptp.fun_fu1783763359l_bool) (A tptp.fun_Ho734851753e_bool) (Fa tptp.fun_Ho734851753e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool tptp.finite1765195604_state Fa)) (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hAPP_f15397171l_bool tptp.ord_le1119700979e_bool Fa) A)) (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool P_1 tptp.bot_bo454148287e_bool)) (=> (forall ((A_1 tptp.hoare_1848483303_state) (F_1 tptp.fun_Ho734851753e_bool)) (let ((_let_1 (tptp.hAPP_H1199573897l_bool tptp.member591555156_state A_1))) (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool tptp.finite1765195604_state F_1)) (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool _let_1 A)) (=> (not (tptp.hBOOL (tptp.hAPP_f355887345l_bool _let_1 F_1))) (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool P_1 F_1)) (tptp.hBOOL (tptp.hAPP_f355887345l_bool P_1 (tptp.insert668001005_state A_1 F_1))))))))) (tptp.hBOOL (tptp.hAPP_f355887345l_bool P_1 Fa))))))) (forall ((P_1 tptp.fun_fu399576434l_bool) (A tptp.fun_fu1430349052l_bool) (Fa tptp.fun_fu1430349052l_bool)) (=> (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)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool P_1 tptp.bot_bo1649642514l_bool)) (=> (forall ((A_1 tptp.fun_pname_bool) (F_1 tptp.fun_fu1430349052l_bool)) (let ((_let_1 (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool A_1))) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool F_1)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool _let_1 A)) (=> (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.insert1325755072e_bool A_1 F_1))))))))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool P_1 Fa))))))) (forall ((P_1 tptp.fun_fu64031073l_bool) (A tptp.fun_fu1783763359l_bool) (Fa tptp.fun_fu1783763359l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1526158591l_bool tptp.finite297877756e_bool Fa)) (=> (tptp.hBOOL (tptp.hAPP_f1526158591l_bool (tptp.hAPP_f511954751l_bool tptp.ord_le1819283413l_bool Fa) A)) (=> (tptp.hBOOL (tptp.hAPP_f1526158591l_bool P_1 tptp.bot_bo2068035593l_bool)) (=> (forall ((A_1 tptp.fun_Ho734851753e_bool) (F_1 tptp.fun_fu1783763359l_bool)) (let ((_let_1 (tptp.hAPP_f1258983629l_bool tptp.member1948767740e_bool A_1))) (=> (tptp.hBOOL (tptp.hAPP_f1526158591l_bool tptp.finite297877756e_bool F_1)) (=> (tptp.hBOOL (tptp.hAPP_f1526158591l_bool _let_1 A)) (=> (not (tptp.hBOOL (tptp.hAPP_f1526158591l_bool _let_1 F_1))) (=> (tptp.hBOOL (tptp.hAPP_f1526158591l_bool P_1 F_1)) (tptp.hBOOL (tptp.hAPP_f1526158591l_bool P_1 (tptp.insert1390540323e_bool A_1 F_1))))))))) (tptp.hBOOL (tptp.hAPP_f1526158591l_bool P_1 Fa))))))) (forall ((P tptp.pname)) (=> (tptp.hBOOL (tptp.wt (tptp.hAPP_pname_com tptp.body_1 P))) (not (forall ((Y_1 tptp.com)) (not (= (tptp.hAPP_p799580910on_com tptp.body P) (tptp.some_com Y_1))))))) (forall ((B tptp.fun_pname_bool) (A tptp.fun_pname_bool)) (=> (forall ((X_1 tptp.pname)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname X_1))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B))))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A) B)))) (forall ((B tptp.fun_Ho734851753e_bool) (A tptp.fun_Ho734851753e_bool)) (=> (forall ((X_1 tptp.hoare_1848483303_state)) (let ((_let_1 (tptp.hAPP_H1199573897l_bool tptp.member591555156_state X_1))) (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f355887345l_bool _let_1 B))))) (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hAPP_f15397171l_bool tptp.ord_le1119700979e_bool A) B)))) (forall ((F tptp.fun_pn447269700_state) (A tptp.fun_pname_bool) (B tptp.fun_Ho734851753e_bool)) (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool tptp.finite1765195604_state B)) (=> (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hAPP_f15397171l_bool tptp.ord_le1119700979e_bool B) (tptp.image_1256224870_state F A))) (exists ((C tptp.fun_pname_bool)) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool C) A)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname C)) (= B (tptp.image_1256224870_state F C))))))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname _let_3)) (forall ((Pname_1 tptp.pname) (Pname tptp.pname)) (= (= (tptp.hAPP_pname_com tptp.body_1 Pname_1) (tptp.hAPP_pname_com tptp.body_1 Pname)) (= Pname_1 Pname))) (forall ((P tptp.bool)) (or (not (tptp.hBOOL (tptp.hAPP_bool_bool tptp.fNot P))) (not (tptp.hBOOL P)))) (forall ((P tptp.bool)) (or (tptp.hBOOL P) (tptp.hBOOL (tptp.hAPP_bool_bool tptp.fNot P)))) (forall ((Q tptp.bool) (P tptp.bool)) (or (not (tptp.hBOOL P)) (not (tptp.hBOOL Q)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fconj P) Q)))) (forall ((P tptp.bool) (Q tptp.bool)) (or (not (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fconj P) Q))) (tptp.hBOOL P))) (forall ((P tptp.bool) (Q tptp.bool)) (or (not (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fconj P) Q))) (tptp.hBOOL Q))) (forall ((Q tptp.bool) (P tptp.bool)) (or (not (tptp.hBOOL P)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fdisj P) Q)))) (forall ((P tptp.bool) (Q tptp.bool)) (or (not (tptp.hBOOL Q)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fdisj P) Q)))) (forall ((P tptp.bool) (Q tptp.bool)) (or (not (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fdisj P) Q))) (tptp.hBOOL P) (tptp.hBOOL Q))) (not (tptp.hBOOL tptp.fFalse)) (forall ((P tptp.bool)) (or (= P tptp.fTrue) (= P tptp.fFalse))) (forall ((Q tptp.bool) (P tptp.bool)) (or (tptp.hBOOL P) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fimplies P) Q)))) (forall ((P tptp.bool) (Q tptp.bool)) (or (not (tptp.hBOOL Q)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fimplies P) Q)))) (forall ((P tptp.bool) (Q tptp.bool)) (or (not (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fimplies P) Q))) (not (tptp.hBOOL P)) (tptp.hBOOL Q))) (forall ((X tptp.pname) (Y tptp.pname)) (or (not (tptp.hBOOL (tptp.hAPP_pname_bool (tptp.hAPP_p61793385e_bool tptp.fequal_pname X) Y))) (= X Y))) (forall ((X tptp.pname) (Y tptp.pname)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_pname_bool (tptp.hAPP_p61793385e_bool tptp.fequal_pname X) Y)))) (forall ((P tptp.bool) (Q tptp.pname)) (= (tptp.hAPP_pname_bool (tptp.cOMBK_bool_pname P) Q) P)) (forall ((P tptp.pname) (Q tptp.pname)) (= (tptp.hAPP_pname_pname (tptp.cOMBK_pname_pname P) Q) P)) (forall ((X tptp.fun_pname_bool) (Y tptp.fun_pname_bool)) (or (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.fequal533582459e_bool X) Y))) (= X Y))) (forall ((X tptp.fun_pname_bool) (Y tptp.fun_pname_bool)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.fequal533582459e_bool X) Y)))) (forall ((P tptp.fun_bool_bool) (Q tptp.fun_pname_bool) (R tptp.pname)) (= (tptp.hAPP_pname_bool (tptp.cOMBB_647938656_pname P Q) R) (tptp.hAPP_bool_bool P (tptp.hAPP_pname_bool Q R)))) (forall ((P tptp.fun_pn250273176l_bool) (Q tptp.fun_pname_bool) (R tptp.pname)) (= (tptp.hAPP_pname_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 tptp.fun_pn800050071e_bool) (Q tptp.pname) (R tptp.pname)) (= (tptp.hAPP_pname_bool (tptp.hAPP_p61793385e_bool (tptp.cOMBC_1149511130e_bool P) Q) R) (tptp.hAPP_pname_bool (tptp.hAPP_p61793385e_bool P R) Q))) (forall ((P tptp.bool) (Q tptp.fun_pname_bool)) (= (tptp.hAPP_f1664156314l_bool (tptp.cOMBK_1857069011e_bool P) Q) P)) (forall ((P tptp.pname) (Q tptp.fun_pname_bool)) (= (tptp.hAPP_f1297739591_pname (tptp.cOMBK_948730864e_bool P) Q) P)) (forall ((P tptp.fun_pname_bool) (Q tptp.pname)) (= (tptp.hAPP_p61793385e_bool (tptp.cOMBK_37193422_pname P) Q) P)) (forall ((X tptp.hoare_1848483303_state) (Y tptp.hoare_1848483303_state)) (or (not (tptp.hBOOL (tptp.hAPP_H2060173127e_bool (tptp.hAPP_H1618070847e_bool tptp.fequal364418600_state X) Y))) (= X Y))) (forall ((X tptp.hoare_1848483303_state) (Y tptp.hoare_1848483303_state)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_H2060173127e_bool (tptp.hAPP_H1618070847e_bool tptp.fequal364418600_state X) Y)))) (forall ((P tptp.fun_option_com_com) (Q tptp.fun_pname_option_com) (R tptp.pname)) (= (tptp.hAPP_pname_com (tptp.cOMBB_923936821_pname P Q) R) (tptp.hAPP_option_com_com P (tptp.hAPP_p799580910on_com Q R)))) (forall ((P tptp.fun_bool_bool) (Q tptp.fun_fu1430349052l_bool) (R tptp.fun_pname_bool)) (= (tptp.hAPP_f1664156314l_bool (tptp.cOMBB_307249310e_bool P Q) R) (tptp.hAPP_bool_bool P (tptp.hAPP_f1664156314l_bool Q R)))) (forall ((P tptp.fun_bo1549164019l_bool) (Q tptp.fun_pname_bool) (R tptp.pname)) (= (tptp.hAPP_p393069232l_bool (tptp.cOMBB_675860798_pname P Q) R) (tptp.hAPP_b589554111l_bool P (tptp.hAPP_pname_bool Q R)))) (forall ((P tptp.fun_fu31783638l_bool) (Q tptp.fun_fu1430349052l_bool) (R tptp.fun_pname_bool)) (= (tptp.hAPP_f1664156314l_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 tptp.fun_pn422929397l_bool) (Q tptp.fun_pname_bool) (R tptp.pname)) (= (tptp.hAPP_pname_bool (tptp.hAPP_f759274231e_bool (tptp.cOMBC_1058051404l_bool P) Q) R) (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool P R) Q))) (forall ((P tptp.bool) (Q tptp.hoare_1848483303_state)) (= (tptp.hAPP_H2060173127e_bool (tptp.cOMBK_2059960192_state P) Q) P)) (forall ((P tptp.pname) (Q tptp.hoare_1848483303_state)) (= (tptp.hAPP_H1494965722_pname (tptp.cOMBK_1568566301_state P) Q) P)) (forall ((P tptp.hoare_1848483303_state) (Q tptp.pname)) (= (tptp.hAPP_p675228438_state (tptp.cOMBK_240819937_pname P) Q) P)) (forall ((X tptp.fun_Ho734851753e_bool) (Y tptp.fun_Ho734851753e_bool)) (or (not (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hAPP_f15397171l_bool tptp.fequal1145749800e_bool X) Y))) (= X Y))) (forall ((X tptp.fun_Ho734851753e_bool) (Y tptp.fun_Ho734851753e_bool)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hAPP_f15397171l_bool tptp.fequal1145749800e_bool X) Y)))) (forall ((P tptp.fun_co1814942666_state) (Q tptp.fun_pname_com) (R tptp.pname)) (= (tptp.hAPP_p675228438_state (tptp.cOMBB_573322273_pname P Q) R) (tptp.hAPP_c379084956_state P (tptp.hAPP_pname_com Q R)))) (forall ((P tptp.fun_bool_bool) (Q tptp.fun_Ho734851753e_bool) (R tptp.hoare_1848483303_state)) (= (tptp.hAPP_H2060173127e_bool (tptp.cOMBB_1397003211_state P Q) R) (tptp.hAPP_bool_bool P (tptp.hAPP_H2060173127e_bool Q R)))) (forall ((P tptp.fun_Ho2109050089l_bool) (Q tptp.fun_Ho734851753e_bool) (R tptp.hoare_1848483303_state)) (= (tptp.hAPP_H2060173127e_bool (tptp.cOMBS_1990964188l_bool P Q) R) (tptp.hAPP_bool_bool (tptp.hAPP_H590162869l_bool P R) (tptp.hAPP_H2060173127e_bool Q R)))) (forall ((P tptp.fun_bo1549164019l_bool) (Q tptp.fun_fu1430349052l_bool) (R tptp.fun_pname_bool)) (= (tptp.hAPP_f1476298914l_bool (tptp.cOMBB_2095475776e_bool P Q) R) (tptp.hAPP_b589554111l_bool P (tptp.hAPP_f1664156314l_bool Q R)))) (forall ((P tptp.fun_fu1171508960l_bool) (Q tptp.fun_fu399576434l_bool) (R tptp.fun_fu1430349052l_bool)) (= (tptp.hAPP_f1935102916l_bool (tptp.cOMBS_811933079l_bool P Q) R) (tptp.hAPP_bool_bool (tptp.hAPP_f32027384l_bool P R) (tptp.hAPP_f1935102916l_bool Q R)))) (forall ((P tptp.fun_fu802393907l_bool) (Q tptp.fun_pname_bool) (R tptp.fun_pname_bool)) (= (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool (tptp.cOMBC_1284144636l_bool P) Q) R) (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool P R) Q))) (forall ((P tptp.bool) (Q tptp.fun_Ho734851753e_bool)) (= (tptp.hAPP_f355887345l_bool (tptp.cOMBK_2110745040e_bool P) Q) P)) (forall ((P tptp.pname) (Q tptp.fun_Ho734851753e_bool)) (= (tptp.hAPP_f50667184_pname (tptp.cOMBK_1423274227e_bool P) Q) P)) (forall ((P tptp.hoare_1848483303_state) (Q tptp.fun_pname_bool)) (= (tptp.hAPP_f141816996_state (tptp.cOMBK_354802397e_bool P) Q) P)) (forall ((P tptp.fun_pname_bool) (Q tptp.hoare_1848483303_state)) (= (tptp.hAPP_H1355725988e_bool (tptp.cOMBK_1288377053_state P) Q) P)) (forall ((P tptp.fun_Ho734851753e_bool) (Q tptp.pname)) (= (tptp.hAPP_p276714170e_bool (tptp.cOMBK_1197227241_pname P) Q) P)) (forall ((P tptp.fun_bool_bool) (Q tptp.fun_fu1783763359l_bool) (R tptp.fun_Ho734851753e_bool)) (= (tptp.hAPP_f355887345l_bool (tptp.cOMBB_1356070853e_bool P Q) R) (tptp.hAPP_bool_bool P (tptp.hAPP_f355887345l_bool Q R)))) (forall ((P tptp.fun_bo1549164019l_bool) (Q tptp.fun_Ho734851753e_bool) (R tptp.hoare_1848483303_state)) (= (tptp.hAPP_H590162869l_bool (tptp.cOMBB_215065709_state P Q) R) (tptp.hAPP_b589554111l_bool P (tptp.hAPP_H2060173127e_bool Q R)))) (forall ((P tptp.fun_fu947309171l_bool) (Q tptp.fun_fu1783763359l_bool) (R tptp.fun_Ho734851753e_bool)) (= (tptp.hAPP_f355887345l_bool (tptp.cOMBS_1278217668l_bool P Q) R) (tptp.hAPP_bool_bool (tptp.hAPP_f170941835l_bool P R) (tptp.hAPP_f355887345l_bool Q R)))) (forall ((P tptp.fun_bo1549164019l_bool) (Q tptp.fun_fu399576434l_bool) (R tptp.fun_fu1430349052l_bool)) (= (tptp.hAPP_f32027384l_bool (tptp.cOMBB_689948150l_bool P Q) R) (tptp.hAPP_b589554111l_bool P (tptp.hAPP_f1935102916l_bool Q R)))) (forall ((P tptp.fun_fu931343505l_bool) (Q tptp.fun_fu1430349052l_bool) (R tptp.fun_pname_bool)) (= (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f559147733l_bool (tptp.cOMBC_1988546018l_bool P) Q) R) (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool P R) Q))) (forall ((P tptp.bool) (Q tptp.fun_fu1783763359l_bool)) (= (tptp.hAPP_f1526158591l_bool (tptp.cOMBK_2014663096l_bool P) Q) P)) (forall ((P tptp.fun_Ho1480763635e_bool) (Q tptp.hoare_1848483303_state) (R tptp.hoare_1848483303_state)) (= (tptp.hAPP_H2060173127e_bool (tptp.hAPP_H1618070847e_bool (tptp.cOMBC_1947058646e_bool P) Q) R) (tptp.hAPP_H2060173127e_bool (tptp.hAPP_H1618070847e_bool P R) Q))) (forall ((P tptp.fun_bo1549164019l_bool) (Q tptp.fun_fu1783763359l_bool) (R tptp.fun_Ho734851753e_bool)) (= (tptp.hAPP_f170941835l_bool (tptp.cOMBB_1418941603e_bool P Q) R) (tptp.hAPP_b589554111l_bool P (tptp.hAPP_f355887345l_bool Q R)))) (forall ((P tptp.fun_fu296636465l_bool) (Q tptp.fun_fu64031073l_bool) (R tptp.fun_fu1783763359l_bool)) (= (tptp.hAPP_f1526158591l_bool (tptp.cOMBS_101732372l_bool P Q) R) (tptp.hAPP_bool_bool (tptp.hAPP_f2022158333l_bool P R) (tptp.hAPP_f1526158591l_bool Q R)))) (forall ((P tptp.hoare_1848483303_state) (Q tptp.fun_Ho734851753e_bool)) (= (tptp.hAPP_f2099317627_state (tptp.cOMBK_1270376774e_bool P) Q) P)) (forall ((P tptp.fun_Ho734851753e_bool) (Q tptp.hoare_1848483303_state)) (= (tptp.hAPP_H1618070847e_bool (tptp.cOMBK_1751623554_state P) Q) P)) (forall ((P tptp.fun_fu1911931399l_bool) (Q tptp.fun_fu1430349052l_bool) (R tptp.fun_fu1430349052l_bool)) (= (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool (tptp.cOMBC_7971162l_bool P) Q) R) (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool P R) Q))) (forall ((P tptp.fun_Ho1489168363l_bool) (Q tptp.fun_Ho734851753e_bool) (R tptp.hoare_1848483303_state)) (= (tptp.hAPP_H2060173127e_bool (tptp.hAPP_f617245717e_bool (tptp.cOMBC_1803918242l_bool P) Q) R) (tptp.hAPP_f355887345l_bool (tptp.hAPP_H1199573897l_bool P R) Q))) (forall ((P tptp.fun_bo1549164019l_bool) (Q tptp.fun_fu64031073l_bool) (R tptp.fun_fu1783763359l_bool)) (= (tptp.hAPP_f2022158333l_bool (tptp.cOMBB_1936369445l_bool P Q) R) (tptp.hAPP_b589554111l_bool P (tptp.hAPP_f1526158591l_bool Q R)))) (forall ((P tptp.fun_fu1478462177l_bool) (Q tptp.fun_Ho734851753e_bool) (R tptp.fun_Ho734851753e_bool)) (= (tptp.hAPP_f355887345l_bool (tptp.hAPP_f15397171l_bool (tptp.cOMBC_80545690l_bool P) Q) R) (tptp.hAPP_f355887345l_bool (tptp.hAPP_f15397171l_bool P R) Q))) (forall ((P tptp.fun_fu1086940979l_bool) (Q tptp.fun_fu399576434l_bool) (R tptp.fun_fu399576434l_bool)) (= (tptp.hAPP_f389811538l_bool (tptp.hAPP_f1759205631l_bool (tptp.cOMBC_336095980l_bool P) Q) R) (tptp.hAPP_f389811538l_bool (tptp.hAPP_f1759205631l_bool P R) Q))) (forall ((P tptp.fun_fu1259080373l_bool) (Q tptp.fun_fu1783763359l_bool) (R tptp.fun_Ho734851753e_bool)) (= (tptp.hAPP_f355887345l_bool (tptp.hAPP_f1360064833l_bool (tptp.cOMBC_1100692246l_bool P) Q) R) (tptp.hAPP_f1526158591l_bool (tptp.hAPP_f1258983629l_bool P R) Q))) (forall ((P tptp.fun_fu1483785331l_bool) (Q tptp.fun_fu1783763359l_bool) (R tptp.fun_fu1783763359l_bool)) (= (tptp.hAPP_f1526158591l_bool (tptp.hAPP_f511954751l_bool (tptp.cOMBC_1690116422l_bool P) Q) R) (tptp.hAPP_f1526158591l_bool (tptp.hAPP_f511954751l_bool P R) Q))) (forall ((P tptp.fun_fu325884881l_bool) (Q tptp.fun_fu64031073l_bool) (R tptp.fun_fu64031073l_bool)) (= (tptp.hAPP_f1359865257l_bool (tptp.hAPP_f1607907235l_bool (tptp.cOMBC_1420373658l_bool P) Q) R) (tptp.hAPP_f1359865257l_bool (tptp.hAPP_f1607907235l_bool P R) Q))) _let_10 _let_9 (tptp.hBOOL (tptp.hAPP_f355887345l_bool tptp.finite1765195604_state tptp.fa)) (not (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hAPP_H1199573897l_bool tptp.member591555156_state _let_1) tptp.fa))) (tptp.hBOOL (tptp.hAPP_f355887345l_bool (tptp.hAPP_f15397171l_bool tptp.ord_le1119700979e_bool tptp.fa) (tptp.image_1256224870_state (tptp.cOMBB_573322273_pname tptp.hoare_Mirabelle_MGT (tptp.cOMBB_923936821_pname tptp.the_com tptp.body)) _let_3))) _let_8 (tptp.hBOOL (tptp.hAPP_f355887345l_bool _let_5 tptp.fa)) _let_7 true)))))))))))))))))))))))))))))))))))))
% 0.76/0.95 )
% 0.76/0.95 % SZS output end Proof for SWW474_1
% 0.76/0.95 % cvc5---1.0.5 exiting
% 0.76/0.95 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------